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1. 4 5 6 7 8 910 11 12 13 14 15 16 1718 19 20 DC current signal mA This is not unlike the pneumatic instrument signal standard or 3 to 15 pounds per square inch PSI where a varying air pressure signal represents some process measurement in an analog proportional fashion DC current signals are also used in control systems to command the positioning of a final control element such as a control valve or a variable speed motor drive VSD In these cases the milliamp value does not directly represent a process measurement but rather how the degree to which the final control element influences the process Typically but not always 4 milliamps commands a closed shut control valve or a stopped motor while 20 milliamps commands a wide open valve or a motor running at full speed 8 1 4 TO 20 MA ANALOG CURRENT SIGNALS 189 Thus most industrial control systems use at least two different 4 20 mA signals one to represent the process variable PV and one to represent the command signal to the final control element the manipulated variable or MV Decides 4 20 mA PV signal 4 20 mA MV signal Senses Influences Reacts The relationship between these two signals depends entirely on the response of the controller There is no reason to ever ex
2. Flow measurement Operating Linearity Bi technology principle directional Differential pressure Fluid mass self acceleration potential kinetic energy exchange VAP some Laminar Viscous fluid friction linear yes Weirs amp flumes Fluid mass self acceleration potential kinetic energy exchange H no Turbine velocity Fluid velocity spinning a vaned wheel linear yes Vortex von K rm n effect linear no Magnetic Electromagnetic induction linear yes Ultrasonic Sound wave time of flight linear yes Coriolis Fluid inertia Coriolis effect linear yes Turbine mass Fluid inertia linear some Thermal Convective cooling specific heat of fluid linear no Positive displacement Movement of fixed volumes linear some A potentially important factor in choosing an appropriate flowmeter technology is energy loss caused by pressure drop Some flowmeter designs such as the common orifice plate are inexpensive to install but carry a high price in terms of the energy lost in permanent pressure drop Energy costs money and so industrial facilities would be wise to consider the long term cost of a flowmeter before settling on the one that is cheapest to install It could very well be for example that an expensive venturi tube will cost less after years of operation than a cheap orifice plate In this regard certain flowmeters stand above the rest those with obstructionless flowtubes Magnetic and ultrasonic flowmeters have no obst
3. Potential Potential ener ivati ener Activation ener gy pias ene Energy released gy with catalyst 7 Energy stored atalyst by reaction i by reaction Before After Before After reaction Time reaction reaction Time reaction 68 CHAPTER 2 CHEMISTRY 2 6 Ions in liquid solutions Many liquid substances undergo a process whereby their constituent molecules split into positively and negatively charged ion pairs Liquid tonic compounds split into ions completely or nearly completely while only a small percentage of the molecules in a liquid covalent compound split into ions The process of neutral molecules separating into ion pairs is called dissociation when it happens in ionic compounds and ionization when it happens to covalent compounds Molten salt NaCl is an example of the former while pure water H20 is an example of the latter The large presence of ions in molten salt explains why it is a good conductor of electricity while the comparative lack of ions in pure water explains why it is often considered an insulator In fact the electrical conductivity of a liquid substance is the definitive test of whether it is an ionic or a covalent molecular substance Pure water ionizes into positive hydrogen ions H and negative hydroxyl ions OH At room temperature the concentration of hydrogen and hydroxyl ions in a sample of pure water is quite small a molarity of 1077 M moles per liter each
4. ee 98 Of Resistors o a a a es AA ee ae A I eb ee 99 3 8 Bridge circuits econo ee eee dara ee ee ee ee a ee 100 3 8 1 Component measurement 2 0 a 101 3 8 2 Sensor signal conditioning 2 0 0 000000 0000008 103 39 Gapacibors 2 624s sn la ta Gog al be Boks e RAE Ak eee ANA A 108 3 10 Inductors p ikea ee ak ye ee ee pee Se HAs we Boe ae ada 110 AC electricity 113 4 1 RMS quantities s ae die a SO ee be ee ee Ae e 114 4 2 Resistance Reactance and Impedance 2 00000000 117 4 3 Series and parallel circuits ooa o 117 4 4 Phasor mathematics 2 0 0 a a e E EA E A E e a a a a a A 118 Introduction to Industrial Instrumentation 129 5 1 Example boiler water level control system sosoo o 132 5 2 Example wastewater disinfection a 137 5 3 Example chemical reactor temperature control osoa a 139 5 4 Other types of instruments 2 0 ee 141 CONTENTS 6 DIOSA a A hoe hye eared ghey a gee A oO aia es AA ead Instrumentation documents 6 1 Process Flow Diagrams 2 0 e e a ee ee 6 2 Process and Instrument Diagrams 0 2 2 0 0 e 6 3 Loopdiagiamisy enebro ad wee eee ee ah bo ee eee Es 6 4 SAMA diagrams ens be A eee ee eee eae DR aaa 6 5 Instrument and process equipment symbols o 6 5 1 Line types is ses ce ee eh a KO a ee ck BP a a 6 5 2 Process Instrument line connections o o
5. Weight measuring mechanism Vessel Liquid drained out of cage valve open Calculation of this buoyant force is a simple matter According to Archimedes Principle buoyant force is always equal to the weight of the fluid volume displaced In the case of a displacer based level instrument at full range this usually means the entire volume of the displacer element is submerged in the liquid Simply calculate the volume of the displacer if it is a cylinder V trl where r is the cylinder radius and 1 is the cylinder length and multiply that volume by the weight density y FPyuoyant ne yv 2 Fouoyant TT l For example if the weight density of the process fluid is 57 3 pounds per cubic foot and the displacer is a cylinder measuring 3 inches in diameter and 24 inches in length the necessary force to simulate a condition of buoyancy at full level may be calculated as follows 57 3 Ib 1 ft lb 0 0332 ft 5 in 386 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT V rr l 1 5 in 24 in 169 6 in Ib AY 0 0332 7 169 6 in 5 63 Ib in Note how important it is to maintain consistency of units The liquid density was given in units of pounds per cubic foot and the displacer dimensions in inches which would have caused serious problems without a conversion between feet and inches In my example work I opted to convert density into units of pounds per cubic inch but I could have just as easily con
6. 7 5 PRESSURE SWITCHES 179 7 5 Pressure switches A pressure switch is one detecting the presence of fluid pressure Pressure switches often use diaphragms or bellows as the pressure sensing element the motion of which actuates one or more switch contacts Recall that the normal status of a switch is the condition of minimum stimulus A pressure switch will be in its normal status when it senses minimum pressure e g no applied pressure or in some cases a vacuum condition Pressure switch symbols Normally open Normally closed NO NC The following photograph shows two pressure switches sensing the same fluid pressure as an electronic pressure transmitter the device on the far left lif the trip setting of a pressure switch is below atmospheric pressure then it will be actuated at atmospheric pressure and in its normal status only when the pressure falls below that trip point i e a vacuum 180 CHAPTER 7 DISCRETE PROCESS MEASUREMENT In this photograph we see a pressure switch actuated by differential pressure the difference in fluid pressure sensed between two ports The electrical switch element is located underneath the blue cover while the diaphragm pressure element is located within the grey metal housing The net force exerted on the diaphragm by the two fluid pressures varies in magnitude and direction with the magnitude of those pressures If the two fluid pressures are pr
7. Pinion gear Sector gear dots shown are pivot points Pointer Applied pressure A photograph of a C tube pressure gauge mechanism reveals the physical construction of such a pressure gauge 12 2 MECHANICAL PRESSURE ELEMENTS 297 It should be noted that bellows diaphragms and bourdon tubes alike may all be used to measure differential and or absolute pressure in addition to gauge pressure All that is needed for these other functionalities is to subject the other side of each pressure sensing element to either another applied pressure in the case of differential measurement or to a vacuum chamber in the case of absolute pressure measurement 298 CHAPTER 12 CONTINUOUS PRESSURE MEASUREMENT Differential pressure sensing mechanisms Applied pressure Applied pressure Applied pressure Bourdon tube Applied pressure Applied pressure Applied pressure The challenge in doing this of course is how to extract the mechanical motion of the pressure sensing element to an external mechanism such as a pointer while maintaining a good pressure seal In gauge pressure mechanisms this is no problem because one side of the pressure sensing element must be exposed to atmospheric pressure anyway and so that side is always available for mechanical connection 123 ELECTRICAL PRESSURE ELEMENTS 299 12 3 Electrical pressure elements Several different technologies exist for the conversion of fluid press
8. 14Liquids can and do compress the measurement of their compressibility being what is called the bulk modulus However this compressibility is too slight to be of any consequence in most flow measurement applications 15 1 PRESSURE BASED FLOWMETERS 483 15 1 6 Equation summary Q N CY Az a y Volumetric flow rate Q Mass flow rate W Where Q Volumetric flow rate e g gallons per minute flowing cubic feet per second W Mass flow rate e g kilograms per second slugs per minute N Unit conversion factor C Discharge coefficient accounts for energy losses Reynolds number corrections pressure tap locations etc Y Gas expansion factor Y 1 for liquids A Cross sectional area of mouth A gt Cross sectional area of throat pf Fluid density at flowing conditions actual temperature and pressure at the element The beta ratio 8 of a differential producing element is the ratio of throat diameter to mouth diameter 8 This is the primary factor determining acceleration as the fluid increases velocity entering the constricted throat of a flow element venturi tube orifice plate wedge etc The following expression is often called the velocity of approach factor commonly symbolized as Ey because it relates the velocity of the fluid through the constriction to the velocity of the fluid as it approaches the flow element 1 E Velocity of approach factor 1 pt This
9. Consider water flowing through a pipe with a magnetic field passing perpendicularly through the pipe The direction of liquid flow cuts perpendicularly through the lines of magnetic flux generating a voltage along an axis perpendicular to both Metal electrodes opposite each other in the pipe wall intercept this voltage making it readable to an electronic circuit A voltage induced by the linear motion of a conductor through a magnetic field is called motional EMF the magnitude of which is predicted by the following formula assuming perfect perpendicularity between the direction of velocity the orientation of the magnetic flux lines and the axis of voltage measurement 2Technically a gas must be super heated into a plasma state before it is able to conduct electricity 506 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT E Blw Where E Motional EMF volts B Magnetic flux density Tesla l Length of conductor passing through the magnetic field meters v Velocity of conductor meters per second Assuming a fixed magnetic field strength constant B and an electrode spacing equal to the fixed diameter of the pipe constant l d the only variable capable of influencing the magnitude of induced voltage is velocity v In our example v is not the velocity of a wire segment but rather the average velocity of the liquid flowstream v Since we see that this voltage will be proportional to average fluid velocity
10. 3 a oO gt Output LL signal Zero screw Diaphragm seal fulcrum a High pressure Low pressure input i _ input Flexure Force sensed Differential pressure is sensed by a liquid filled diaphragm capsule which transmits force to a force bar If the force bar moves out of position due to this applied force a highly sensitive baffle and nozzle mechanism senses it and causes a pneumatic amplifier called a relay to send a different amount of air pressure to a bellows unit The bellows presses against the range bar which pivots to counter act the initial motion of the force bar When the system returns to equilibrium the air pressure inside the bellows will be a direct linear representation of the process fluid pressure applied to the diaphragm capsule With minor modifications to the design of this pressure transmitter we may convert it from pneumatic to electronic force balancing 6Very loosely based on the design of Foxboro s popular E13 electronic DP cell differential pressure transmitter 314 CHAPTER 12 CONTINUOUS PRESSURE MEASUREMENT Amplifier Balance sensor Force Force sensed adjustable Range wheel fulcrum 3 a gt lt Force E adjustable Q g o 10 50 mA j output signal Diaphragm seal fulcrum bA High pressure input Low pressure lt _ input Force
11. 4 Force 4 Force P Bourdon tube Force Bellows Diaphragm Applied pressure Applied pressure Applied pressure Bellows resemble an accordion constructed from metal instead of fabric Increasing pressure inside a bellows unit causes it to elongate A diaphragm is nothing more than a thin disk of material which bows outward under the influence of a fluid pressure Many diaphragms are constructed from metal which gives them spring like qualities Some diaphragms are intentionally constructed out of materials with little strength such that there is negligible spring effect These are called slack diaphragms and they are used in conjunction with external mechanisms that produce the necessary restraining force to prevent damage from applied pressure Bourdon tubes are made of spring like metal alloys bent into a circular shape Under the influence of internal pressure a bourdon tube tries to straighten out into its original shape before being bent at the time of manufacture Most pressure gauges use a bourdon tube as their pressure sensing element Most pressure transmitters use a diaphragm as their pressure sensing element Bourdon tubes may be made in spiral or helical forms for greater motion and therefore greater gauge resolution A typical C tube bourdon tube pressure gauge mechanism is shown in the following illustration 296 Pressure gauge mechanism CHAPTER 12 CONTINUOUS PRESSURE MEASUREMENT Bourdon tube
12. Teacher I m sure viscosity has some effect but it must be minimal since it isn t in the equation Me Then why is honey so hard to suck through a straw Teacher Come again Me A straw is a narrow pipe similar to the throat of a venturi or the hole of an orifice right The difference in pressure between the suction in my mouth and the atmosphere is the AP across that orifice The result is flow through the straw If viscosity is of such little effect then why is liquid honey so much harder to suck through a straw than water The pressure is the same the density is about the same then why isn t the flow rate the same according to the equation you just gave us Teacher In industry we usually don t measure fluids as thick as honey and so it s safe to ignore viscosity in the flow equation My teacher s smokescreen that thick fluid flow streams were rare in industry did nothing to alleviate my confusion Despite my ignorance of the industrial world I could very easily imagine liquids that were more viscous than water honey or no honey Somewhere somehow someone had to be measuring the flow rate of such liquids and there the effects of viscosity on orifice AP must be apparent Surely my teacher knew this But then why did the flow equation not have a variable for viscosity in it How could this parameter be unimportant Like most students though I could see that arguing would get me nowhere and it was better f
13. This weir design is not used very often due to its inherently weak structure and tendency to clog with debris A variation on the theme of a weir is another open channel device called a flume If weirs may be thought of as open channel orifice plates then flumes may be thought of as open channel venturi tubes 492 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT Like weirs flumes generate upstream liquid level height changes indicative of flow rate One of the most common flume design is the Parshall flume named after its inventor R L Parshall when it was developed in the year 1920 The following formulae relate head upstream liquid height to flow rate for free flowing Parshall flumes Q 0 992H 4 3 inch wide throat Parshall flume Q 2 06H 8 6 inch wide throat Parshall flume Q 3 07H 9 inch wide throat Parshall flume Q 4LH 3 1 foot to 8 foot wide throat Parshall flume 3 2 foot to 50 foot wide throat Parshall flume Q 3 6875L 2 5 H 10 f 50 f ide throat Parshall fl Where Q Volumetric flow rate cubic feet per second CFS L Width of flume throat feet H Head feet Flumes are generally less accurate than weirs but they do enjoy the advantage of being inherently self cleaning If the liquid stream being measured is drainage or waste water a substantial amount of solid debris may be present in the flow that could cause repeated clogging problems for weirs In such applications flumes
14. 1 P P Agua V2A2 gt 2 A2 ye Now we have an equation solving for volumetric flow O 1 PE y1 3 Please note how many constants we have in this equation For any given venturi tube the mouth and throat areas A and A2 will be fixed This means the majority of this rather long equation are constant for any particular venturi tube and therefore do not change with pressure density or flow rate Knowing this we may re write the equation as a simple proportionality 15 1 PRESSURE BASED FLOWMETERS 453 P P gt p Q x To make this a more precise mathematical statement we may insert a constant of proportionality k and once more have a true equation to work with P P p Q k The value of k depends of course on the physical dimensions of the venturi mouth and throat A practical advantage to using a constant of proportionality is that we may adjust the value of k as necessary to account for factors other than just venturi tube geometry One very important factor to consider is units of measurement If the value of k is determined strictly by tube geometry then the units used to express volumetric flow rate must correspond to the units used to express pressures and fluid density For example Q will be in units of cubic feet per second only if we insert pressure values P and Po in units of pounds per square foot and mass density in units of slugs per cubic feet If we wish to use more conven
15. 4mA 8 mA 12 mA 16mA 20mA kl 0 25 50 75 100 194 CHAPTER 8 ANALOG ELECTRONIC INSTRUMENTATION If one were to ask the percentage corresponding to a 14 4 mA signal on a 4 20 mA range it would be as simple as determining the length of a line segment stretching from the 4 mA mark to the 14 4 mA mark 14 4 mA 4mA 8 mA 12 mA 16 mA 20 mA p j 0 25 50 75 100 10 4 mA length Y 16 mA span As a percentage this thick line is 10 4 mA long the distance between 14 4 mA and 4 mA over a total possible length of 16 mA the total span between 20 mA and 4 mA Thus 144 mA 4 mA 20 mA 4 mA Percentage 100 Percentage 65 This same number line approach may be used to visualize any conversion from one analog scale to another Consider the case of an electronic pressure transmitter calibrated to a pressure range of 5 to 25 PSI having an obsolete current signal output range of 10 to 50 mA The appropriate current signal value for an applied pressure of 12 PSI would be represented on the number line as such 12 PSI 5 PSI 25 PSI 10 PS 17 5 PSI 25 PSI AA gt 4 7 10 mA 20 mA 30 mA 40 mA 50 mA Proportion 17 PSI length 17 PSI g mA mA length 30 PSI 40 mA 30 PSI span 40 mA span Finding the length of this line segment in units of milliamps is as simple as setting up a proportion between the length of the line in units of PSI over the total span in PSI to the length
16. 566 CHAPTER 16 CONTINUOUS ANALYTICAL MEASUREMENT output signal e g 4 20 mA would only be able to transmit information about the concentration of any one component any one peak in the chromatogram This is perfectly adequate if only one component concentration is worth knowing about in the process 3 but some form of multi channel digital or multiple analog outputs transmission is necessary to make full use of a chromatograph s ability All modern chromatographs are smart instruments containing one or more digital computers which execute the calculations necessary to derive precise measurements from chromatogram data The computational power of modern chromatographs may be used to further analyze the process sample beyond simple determinations of concentration or quantity Examples of more abstract analyses include approximate octane value of gasoline based on the relative concentrations of several components or the heating value of natural gas based on the relative concentrations of methane ethane propane butane carbon dioxide helium etc in a sample of natural gas The following photograph shows a gas chromatograph GC fulfilling precisely this purpose the determination of heating value for natural gas 1814 is not uncommon to find chromatographs used in processes to measure the concentration of a single chemical component even though the device is capable of measuring the concentrations of multiple components
17. All density figures approximate for samples at standard temperature and pressure Liquids Gasoline y 41 lb ft to 43 lb ft Naphtha petroleum y 41 5 lb ft Acetone y 49 4 lb ft Ethanol ethyl alcohol y 49 4 lb ft Methanol methyl alcohol y 50 5 lb ft Kerosene y 51 2 lb ft Toluene y 54 1 lb ft Benzene y 56 1 lb ft Olive oil y 57 3 Ib ft3 Coconut oil y 57 7 lb ft Linseed oil boiled y 58 8 lb ft Castor oil y 60 5 lb ft Sea water y 63 99 lb ft Milk y 64 2 lb ft to 64 6 lb ft Ethylene glycol ethanediol y 69 22 lb ft Glycerin y 78 6 lb ft Mercury y 849 lb ft Solids Balsa wood y 7 lb ft to 9 lb ft Cork y 14 lb ft to 16 lb ft Maple wood y 39 Ib ft to 47 lb ft Ice y 57 2 lb ft Tar y 66 lb ft Rubber soft y 69 Ib ft Rubber hard y 74 lb ft 1 3 UNIT CONVERSIONS AND PHYSICAL CONSTANTS Calcium y 96 763 lb ft Sugar y 99 lb ft Magnesium y 108 50 lb ft Beryllium y 115 37 lb ft Rock salt y 136 lb ft Quartz y 165 lb ft Cement set y 170 lb ft to 190 Ib ft Carbon diamond y 196 65 lb ft to 220 37 lb ft Chromium y 448 86 lb ft Iron y 490 68 lb ft Brass y 524 4 lb ft Copper y 559 36 lb ft Molybdenum y 638 01 lb ft Lead y 708 56 lb ft Gold y 1178 6 lb ft 17 18 CHAPTER 1 PHYSICS 1 4 Dimensional analysis An interesting parallel to the
18. Given the fact that pure water has a mass of 1 kilogram 1000 grams per liter and one mole of pure water has a mass of 18 grams we must conclude that there are approximately 55 56 moles of water molecules in one liter 55 56 M If only 107 moles of those molecules ionize at room temperature that represents an extremely small percentage of the total 10 7 M 55 56 M It is not difficult to see why pure water is such a poor conductor of electricity With so few ions available to act as charge carriers the water is practically an insulator The vast majority of water molecules remain un ionized and therefore cannot transport electric charges from one point to another The molarity of both hydrogen and hydroxy ions in a pure water sample increases with increasing temperature For example at 60 C the molarity of hydrogen and hydroxyl ions increases to 3 1 x 1077 M which is still only 0 0056 parts per million but definitely larger than the concentration at room temperature 25 C 0 0000000018 0 00000018 0 0018 ppm parts per million 2 Actually the more common form of positive ion in water is hydronium H3O but we often simply refer to the positive half of an ionized water molecule as hydrogen H 2 7 PH 69 2 7 pH Hydrogen ion activity in aqueous water based solutions is a very important parameter for a wide variety of industrial processes Hydrogen ions are always measured on a logarithmic scale and referred
19. unity fraction unit conversion technique is something referred to in physics as dimensional analysis Performing dimensional analysis on a physics formula means to set it up with units of measurement in place of variables to see how units cancel and combine to form the appropriate unit s of measurement for the result For example let s take the familiar power formula used to calculate power in a simple DC electric circuit P IV Where P Power watts I Current amperes V Voltage volts Each of the units of measurement in the above formula watt ampere volt are actually comprised of more fundamental physical units One watt of power is one joule of energy transferred per second One ampere of current is one coulomb of electric charge moving by per second One volt of potential is one joule of energy per coulomb of electric charge When we write the equation showing these units in their proper orientations we see that the result power in watts or joules per second actually does agree with the units for amperes and volts because the unit of electric charge coulombs cancels out In dimensional analysis we customarily distinguish unit symbols from variables by using non italicized letters and surrounding each one with square brackets P IV Watts Amperes x Volts or W A V Joules _ Coulombs gt Joules oi J E C J Seconds Seconds Coulombs s s C Dimensional analysis gives us a way to check our wor
20. 12 6 PRESSURE SENSOR ACCESSORIES 337 12 6 5 Filled impulse lines An alternate method for isolating a pressure sensing instrument from direct contact with process fluid is to either fill or purge the impulse lines with a harmless fluid Filling impulse tubes with a static fluid works when gravity is able to keep the fill fluid in place such as in this example of a pressure transmitter connected to a water pipe by a glycerin filled impulse line Isolation block valve Impulse line filled with glycerin which is denser than water Pressure transmitter Air supply PV signal Fill valve A reason someone might do this is for freeze protection since glycerin freezes at a lower temperature than water If the impulse line were filled with process water it might freeze solid in cold weather conditions the water in the pipe cannot freeze so long as it is forced to flow The greater density of glycerin keeps it placed in the impulse line below the process water line A fill valve is provided near the transmitter so that a technician may re fill the impulse line with glycerin using a hand pump if ever needed As with a remote diaphragm a filled impulse line will generate its own pressure proportional to the height difference between the point of process connection and the pressure sensing element If the height difference is substantial the pressure offset resulting from this difference in elevation will require compensat
21. Helical bourdon tube 283 295 Henry 110 Herschel Clemens 469 Hertz 275 Hot tapping 533 Hot wire anemometer 524 HVAC 424 Hydration pH electrode 555 Hydraulic 31 Hydraulic lift 29 Hydraulic load cell 405 Hydrogen economy 65 Hydrogen ion 68 69 542 Hydronium ion 68 69 542 641 Hydrostatic pressure 36 Hydroxyl ion 68 69 542 Hysteresis 265 I P transducer 204 212 Ice point thermocouple 432 Ideal Gas Law 47 Ideal PID algorithm 617 Impedance 117 127 Impulse line 318 Impulse tube 318 325 Inches of mercury 36 Inches of water column 36 Inclined manometer 40 291 Indicator 141 Inductance 110 Inductor 110 Inferential measurement 284 289 374 574 Inferred variable 374 574 Instrument tube bundle 340 Integral control 611 Integral orifice plate 466 Integral windup 613 Integration applied to RMS waveform value 115 Interactive zero and span adjustments 260 283 Interface level measurement 347 Intrinsic safety 315 Intrinsic standard 271 Inverse function 573 Inviscid flow 51 Ion 61 lon selective membrane 592 Ionization 542 ISA PID algorithm 617 Isolating diaphragm 301 303 306 330 Isopotential point pH 560 Isotope 62 Joule 75 Joule s Law 99 KCL 96 Kelvin resistance measurement 424 545 Kinematic viscosity 49 642 Kinetic energy 22 Kirchhoff s Current Law 96 Kirchhoff s Voltage Law 94 Knockout drum 382
22. I also prefer the older label Cycles Per Second cps to Hertz as the unit of measurement for frequency You may have noticed by now that the instrumentation world does not yield to my opinions much to my chagrin 276 CHAPTER 11 INSTRUMENT CALIBRATION Dry block temperature calibrators also exist for creating accurate calibration temperatures in the instrument shop environment Instead of a fluid or fluidized powder bath as the thermal medium these devices use metal blocks with blind dead end holes drilled for the insertion of temperature sensing instruments An inexpensive dry block temperature calibrator intended for bench top service is shown in this photograph 11 8 PRACTICAL CALIBRATION STANDARDS 277 Optical temperature instruments require a different sort of calibration tool one that emits radiation equivalent to that of the process object at certain specified temperatures This type of calibration tool is called a blackbody calibrator having a target area where the optical instrument may be aimed Like oil and sand bath calibrators a blackbody calibrator relies on an internal temperature sensing element as a reference to control the optical emissions of the blackbody target at any specified temperature within a practical range 278 CHAPTER 11 INSTRUMENT CALIBRATION 11 8 3 Pressure standards In order to accurately calibrate a pressure instrument in a shop environment we must create fluid pressures of
23. Now a doubling of fluid flow rate still results in a quadrupling of needle motion but due to the nonlinear scale this translates into a simple doubling of indicated flow which is precisely what we need for this to function as an accurate flow indicator If the differential pressure instrument outputs a 4 20 mA analog electronic signal instead of a 3 15 PSI pneumatic signal we may apply the same nonlinear scale treatment to any current meter and achieve the same result 578 CHAPTER 17 SIGNAL CHARACTERIZATION D O FLOW FOXBORO E Another simple solution is to use a nonlinear manometer with a curved viewing tube Pressure input Curved manometer Pressure input The scale positioned alongside the curved viewing tube will be linear with equal spacings between division marks along its entire length The vertical height of the liquid column translates pressure into varying degrees of movement along the axis of the tube by the tube s curvature Literally any inverse function desired may be encoded into this manometer by fashioning the viewing tube into the desired custom shape without any need to print a nonlinear scale 1 This solution works best for measuring the flow rate of gases not liquids since the manometer obviously must use a liquid of its own to indicate pressure and mixing or other interference between the process liquid and the manometer liquid could be problematic 579 Shown here is a
24. Pivot It should be clear that the left hand bellows which experiences the same pressure Pout as the pressure gauge introduces negative feedback into the system If the output pressure happens to rise too high the baffle will be pushed away from the nozzle by the force of the feedback bellows causing backpressure to decrease and stabilize Likewise if the output pressure happens to go too low the baffle will move closer to the nozzle and cause the backpressure to rise again Once again we see the defining characteristic of negative feedback in action its self correcting nature works to counteract any change in output conditions As we have seen already the baffle nozzle is exceptionally sensitive to motion Only a few thousandths of an inch of motion is sufficient to saturate the nozzle backpressure at either extreme supply air pressure or zero depending on which direction the baffle moves This is analogous to the differential inputs of an operational amplifier which only need to see a few microvolts of potential difference to saturate the amplifier s output Introducing negative feedback to the opamp led to a condition where the differential input voltage was held to nearly zero In fact this potential is so small that we safely considered it zero for the purpose of more easily analyzing the output response of the system We may make the exact same simplifying assumption for the pneumatic mechanism we will assume the baffle
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26. m Controller output e Error difference between PV and SP Kp Proportional gain K Integral gain t Time b Bias The most confusing portion of this equation for those new to calculus is the part that says fe dt The integration symbol looks like an elongated letter S tells us the controller will accumulate sum multiple products of error e over tiny slices of time dt Quite literally the controller multiplies error by time for very short segments of time and continuously adds up all those products to contribute to the output signal which then drives the control valve or other final control element To see how this works in a practical sense let s imagine how a proportional integral controller would respond to the scenario of a heat exchanger whose inlet temperature suddenly dropped As we saw with proportional only control an inevitable offset occurs between PV and SP with changes in load because an error must develop if the controller is to generate the different output signal value necessary to halt further change in PV Once this error develops though integral action begins to work Over time a larger and larger quantity accumulates in the integral mechanism or register of the controller because an error persists over time That accumulated value adds to the controller s output driving the steam control valve further and further open This of course adds heat at a faster rate to the heat e
27. sensed Differential pressure is sensed by the same type of liquid filled diaphragm capsule which transmits force to the force bar If the force bar moves out of position due to this applied force a highly sensitive electromagnetic sensor detects it and causes an electronic amplifier to send a different amount of electric current to a force coil The force coil presses against the range bar which pivots to counter act the initial motion of the force bar When the system returns to equilibrium the milliampere current through the force coil will be a direct linear representation of the process fluid pressure applied to the diaphragm capsule A distinct advantage of force balance pressure instruments besides their inherent linearity is the constraining of sensing element motion Unlike a modern diaphragm based pressure transmitter which relies on the spring characteristics of the diaphragm to convert pressure into force and then into motion displacement which is sensed and converted into an electronic signal a force balance transmitter works best when the diaphragm is slack and has no spring characteristics at all Balance with the force of the process fluid pressure is achieved by the application of either an adjustable air pressure or an adjustable electric current not by the natural tensing of a spring element This makes a force balance instrument far less susceptible to errors due to metal fatigue or any other 12 4 FORCE BALANCE PRESSURE
28. 0 657 in this same venturi tube gives us the following flow rate 110 26 Q ce 0 657 Q 347 GPM If we wish to calculate mass flow instead of volumetric flow the equation does not change much The relationship between volume V and mass m for a sample of fluid is its mass density p pe m Pay Similarly the relationship between a volumetric flow rate Q and a mass flow rate W is also the fluid s mass density p e Solving for W in this equation leads us to a product of volumetric flow rate and mass density W pQ A quick dimensional analysis check using common metric units confirms this fact A mass flow rate in kilograms per second will be obtained by multiplying a mass density in kilograms per cubic meter by a volumetric flow rate in cubic meters per second Ee 5 Therefore all we have to do to turn our general volumetric flow equation into a mass flow equation is multiply both sides by fluid density p P Pa p P P pQ kp 2 p P P if p Q k 15 1 PRESSURE BASED FLOWMETERS 455 It is generally considered inelegant to show the same variable more than once in an equation if it is not necessary so let s try to consolidate the two densities p using algebra First we may write p as the product of two square roots P P W kvpyp at Next we will break up the last radical into a quotient of two separate square roots W kypyp i Now we see ho
29. A time honored standard for low temperature industrial calibrations is water specifically the freezing and boiling points of water Pure water at sea level full atmospheric pressure freezes at 32 degrees Fahrenheit 0 degrees Celsius and boils at 212 degrees Fahrenheit 100 degrees Celsius In fact the Celsius temperature scale is defined by these two points of phase change for water at sea level To use water as a temperature calibration standard simply prepare a vessel for one of two conditions thermal equilibrium at freezing or thermal equilibrium at boiling Thermal equilibrium in this context simply means equal temperature throughout the mixed phase sample In the case of freezing this means a well mixed sample of solid ice and liquid water In the case of boiling this means a pot of water at a steady boil vaporous steam and liquid water in direct contact What you are trying to achieve here is ample contact between the two phases either solid and liquid or liquid and vapor to eliminate hot or cold spots One major disadvantage of using phase changes to produce accurate temperatures in the shop is the limited availability of temperatures With water at sea level the only calibration standards you can create is O degrees Celsius and 100 degrees Celsius If you need to create some other temperature for calibration purposes you either need to find a suitable material with a phase change happening at that temperature good luck
30. All a controller does is turn the burner on when the metal s too cold and turn it off when it becomes too hot In its most basic form the mechanic s assessment of the control system was correct to turn the burner on when the process variable molten metal temperature drops below setpoint and turn it off when it rises above setpoint However the actual algorithm is much more complex than that finely adjusting the burner intensity according to the amount of error between PV and SP the amount of time the error has accumulated and the rate of change of the error over time In his limited observation of the furnace controllers though he had noticed nothing more than the full on full off action of the controller The technical term for a control algorithm that merely checks for the process variable exceeding or falling below setpoint is on off control In colloquial terms it is known as bang bang control since the manipulated variable output of the controller rapidly switches between fully on and fully off with no intermediate state Control systems this crude usually provide very imprecise control of the process variable Consider our example of the shell and tube heat exchanger if we were to implement simple on off control As you can see the degree of control is rather poor The process variable cycles between the upper and lower setpoints USP and LSP without ever stabilizing at the setpoint because that
31. KVL 94 Laminar flow 52 54 628 Laminar flowmeter 485 Law of Continuity fluids 53 449 495 Law of Intermediate Metals thermocouple circuits 430 Level gauge 348 Level switch 181 Limit switch 173 Linearity error 268 Linearization 580 Liquid 28 Liquid interface detection with radar 399 Live zero 259 Lo Loss flow tube 469 Load 80 608 Load cell 104 403 Load cell hydraulic 405 Load versus source 98 Loop powered transmitter 200 Lower range value 131 259 262 283 LRV 131 259 262 283 LVDT 311 Magnetic flowmeter 506 Magnetrol liquid level switch 181 Manifold pressure transmitter 322 323 Manipulated variable 598 Manometer 40 281 290 Manometer cistern 291 Manometer inclined 40 291 Manometer nonlinear 578 Manometer raised well 291 Manometer slack tube 283 Manometer U tube 291 Manometer well 291 Manual mode 131 Mass density 9 Mass flow 443 Maximum working pressure 320 Measurement electrode 550 INDEX Measurement junction thermocouple 428 MEMS 308 Meniscus 290 Mercury 345 Mercury barometer 294 Metal fatigue 300 Metrology 271 Micromanometer 41 Minutes per repeat 616 Mixture 61 Mobile phase 561 Molarity 63 285 Mole 63 Molecule 61 Moment balance system 234 Motion balance system 234 Motional EMF 505 Multi segment characterizer 587 Multi variable transmitter 253 399 481 522 566 Multidrop HART 252
32. Manometers sa e se 00000 0d dr dde do ee a ee 40 111 CONTENTS 1 8 5 Systems of pressure measurement 1 0 2 0 0 0000000000 43 1 8 6 BuOyaney se ish a tee dan we we a ee ae a A ad 45 LST GAS LAWS Ls een neh amp De a BS A died o ia tes 47 1 8 8 Fluid Viscosity lt 6 ia at Aas eM see 8 ok A ye atte ha 49 1 8 9 Reynolds UMD ic ya ee ee a ee a ae 51 1 8 10 Law of Continuity e 53 RUE no AA Gedo He es Whats nang ee ER EN Gye OR 54 1 8 12 Bernoulli s equation ee 55 1 8 13 Torricelli s equation ee 57 1 8 14 Flow through a venturi tube e 58 Chemistry 61 2 1 Terms and Definitions e ne ian ee We A A a ee ee A A 61 2 2 Periodic table a a a bee a E e LN a Pe i te See 62 2 3 Molecular quantities ys aia anan Ad gg SR Aaa de 63 24 Stoichiometry oeu te A als A A A a E E ee a ds Dl 64 2 5 Energy in chemical reactions 20 0 0 eee a 65 2 6 Tons in liquid Solutions ee ee ee ee A 68 Del SPE yeah a cece RR NN 69 DC electricity 73 301 Electrical voltage sars Ss ee A Sep ee ee oe ae bes 74 332 Hlectrical currenitco son Qe hoe sok Gee bE dak ORE A ti 79 3 2 1 Electron versus conventional flow 0 2 e 82 3 3 Electrical resistance and Ohm s Law e 87 3 4 Series versus parallel circuits o e e 90 30 Kirchhof Saws Toet oc la dr dt Gude rd a a bok ahd A Es 94 3 6 Electrical sources and loads
33. Multipath ultrasonic flowmeter 513 MWP 320 NBS 271 Needle valve 327 Nernst equation 550 556 592 Newton Isaac 21 NIST 271 Non bleeding pneumatic relay 227 Non contact radar 395 Non inertial reference frame 515 Non Newtonian fluid 50 Nonlinear manometer 578 NOx emissions 592 Nozzle 213 Nuclear versus chemical reaction 64 Ohm 87 Ohm s Law 99 Ohm Georg Simon 87 Oil bath temperature calibrator 275 Oleo degrees 39 On off control 602 Order of magnitude 230 Orifice plate 458 574 INDEX Orifice plate concentric 459 Orifice plate conical entrance 463 Orifice plate eccentric 460 Orifice plate integral 466 Orifice plate quadrant edge 463 Orifice plate segmental 461 Orifice plate square edged 459 Oxygen control burner 592 Parallel PID algorithm 616 Parshall flume 581 Particle 61 Parts per million 287 Pascal 29 Pascal s principle 33 Periodic table of the elements 62 Permanent pressure loss 58 Permittivity 108 Permittivity relative 397 pH 69 285 Phase change 275 Phasor 122 Pickup coil 497 Piecewise function 587 Piezometer 449 Pigtail siphon 342 Pilot valve 221 Pipe elbow flow element 472 Pipe hanger 404 Pipe taps orifice plate 466 Pitot tube 467 Pneumatic 31 Pneumatic resistor 486 Pneumatic control system 135 Pneumatic deadweight tester 280 Pneumatic relay 224 Poise 49 Polarity 77 Position PID algo
34. PSE or transmitter compares that signal to the desired value for that process variable called the setpoint and calculates an appropriate output signal value to be sent to a final control element FCE such as an electric motor or control valve Final Control Element or FCE A device that receives the signal from a controller to directly influence the process Examples variable speed electric motor control valve electric heater Automatic mode When the controller generates an output signal based on the relationship of process variable PV to the setpoint SP Manual mode When the controller s decision making ability is bypassed to let a human operator directly determine the output signal sent to the final control element Now I will show you some practical examples of measurement and control systems so you can get a better idea of these fundamental concepts 132 CHAPTER 5 INTRODUCTION TO INDUSTRIAL INSTRUMENTATION 5 1 Example boiler water level control system Steam boilers are very common in industry principally because steam power is so useful Common uses for steam in industry include doing mechanical work e g a steam engine moving some sort of machine heating producing vacuums through the use of steam eductors and augmenting chemical processes e g reforming of natural gas into hydrogen and carbon dioxide The process of converting water into steam is quite simple heat up the water until it boils Anyo
35. R 4 which means that tensile deformation stretching will increase electrical resistance by simultaneously increasing length and decreasing cross sectional area while compressive deformation squishing will decrease electrical resistance by simultaneously decreasing length and increasing cross sectional area Attaching a strain gauge to a diaphragm results in a device that changes resistance with applied pressure Pressure forces the diaphragm to deform which in turn causes the strain gauge to change resistance By measuring this change in resistance we can infer the amount of pressure applied to the diaphragm The classic strain gauge system represented in the previous illustration is made of metal both the test specimen and the strain gauge itself Within its elastic limits many metals exhibit good spring characteristics Metals however are subject to fatigue over repeated cycles of strain tension and compression and they will begin to flow if strained beyond their elastic limit This is a common source of error in metallic piezoresistive pressure instruments if overpressured they tend to lose accuracy due to damage of the spring and strain gauge elements Modern manufacturing techniques have made possible the construction of strain gauges made of silicon instead of metal Silicon exhibits very linear spring characteristics over its narrow range of motion and a high resistance to fatigue When a silicon strain gauge is over
36. Specific heat of water at 14 C 1 00002 calories g C 1 BTU lb F 4 1869 joules g C Specific heat of ice 0 5 calories g C Specific heat of steam 0 48 calories g C Absolute viscosity of water at 20 C 1 0019 centipoise cp 0 0010019 Pascal seconds Pa s Surface tension of water in contact with air at 18 C 73 05 dynes cm pH of pure water at 25 C 7 0 pH scale 0 to 14 1 3 14 Properties of dry air at sea level Density of dry air at 20 C and 760 torr 1 204 mg cm 1 204 kg m 0 075 lb ft 0 00235 slugs ft3 Absolute viscosity of dry air at 20 C and 760 torr 0 018 centipoise cp 1 8 x 1075 Pascal seconds Pa s 1 3 15 Miscellaneous physical constants Speed of light in a vacuum c 2 9979 x 10 meters per second m s 186 281 miles per second mi s Avogadro s number N4 6 0220 x 10 per mole mol Electronic charge e 1 6022 x 1071 Coulomb C Faraday constant F 9 6485 x 10 Coulombs per mole C mol Boltzmann s constant k 1 3807 x 107 joules per Kelvin J K Stefan Boltzmann constant 0 5 6703 x 107 Watts per square meter Kelvin W m K Molar gas constant R 8 3144 joules per mole Kelvin J mol K Note all physical constants listed here were derived rounded to the fifth significant digit from values given on page F 198 of the CRC Handbook of Chemistry and Physics 64th edition 16 CHAPTER 1 PHYSICS 1 3 16 Weight densities of common materials
37. The amount of pressure we apply will be in direct proportion to the density of the fluid and its rate of acceleration Conversely we may measure a fluid s rate of acceleration by measuring the pressure developed across a distance over which it accelerates We may easily force a fluid to accelerate by altering its natural flow path The difference of pressure generated by this acceleration will indirectly indicate the rate of acceleration Since the acceleration we see from a change in flow path is a direct function of how fast the fluid was originally moving the acceleration and therefore the pressure drop indirectly indicates fluid flow rate A very common way to cause linear acceleration in a moving fluid is to pass the fluid through a constriction in the pipe thereby increasing its velocity remember that the definition of acceleration is a change in velocity The following illustrations show several devices used to linearly accelerate moving fluids when placed in pipes with differential pressure transmitters connected to measure the pressure drop resulting from this acceleration 2What really matters in Newton s Second Law equation is the resultant force causing the acceleration This is the vector sum of all forces acting on the mass Likewise what really matters in this scenario is the resultant pressure acting on the fluid plug and this resultant pressure is the difference of pressure between one face of the plug and the other sinc
38. This makes the transmitter terminal voltage inversely proportional to loop current the transmitter sees approximately 25 volts at 4 mA loop current 0 signal and approximately 21 volts at 20 mA loop current 100 signal The use of the word approximate is very intentional here for loop power supplies are usually non regulated In other words the 26 volt rating is approximate and subject to change One of the advantages of the loop powered transmitter circuit is that the source voltage is largely irrelevant so long as it exceeds the minimum value necessary to ensure adequate power to the transmitter If the source voltage drifts for any reason it will have no impact on the measurement signal at all because the transmitter is built as a current regulator regulating current in the loop to whatever value represents the process measurement regardless of slight changes in loop source voltage wire resistance etc This rejection of power supply voltage changes means that the loop power supply need not be regulated and so in practice it rarely is This brings us to a common problem in loop powered 4 20 mA transmitter circuits maintaining sufficient operating voltage at the transmitter terminals Recall that a loop powered transmitter relies on the voltage dropped across its terminals combined with a current of less than 4 mA to power its internal workings This means the terminal voltage must not be allowed to dip below a certain minimu
39. and some are adept enough to switch between both without getting confused For what it s worth I personally prefer conventional flow notation The only objective arguments I have in favor of this preference are as follows e Conventional flow notation makes more intuitive sense to someone familiar with fluid systems as all instrument technicians need to be e Conventional flow notation matches all device arrows no need to go against the arrow when tracing current in a schematic diagram e Conventional flow notation is consistent with the right hand rule for vector cross products which are essential for understanding electromagnetics at advanced academic levels The so called left hand rule taught to students learning electron flow notation is mathematically wrong and must be un learned if the student ever progresses to the engineering level in his or her studies e Conventional flow notation is the standard for modern manufacturers documentation reference manuals troubleshooting guides datasheets etc 11 have yet to read a document of any kind written by an equipment manufacturer that uses electron flow notation and this is after scrutinizing literally hundreds of documents looking for this exact detail For the record though most technical documents do not bother to draw a direction for current at all leaving it to the imagination of the reader instead It is only when a direction must be drawn that
40. calculus 530 Differential pressure 43 294 Differential temperature sensing circuit 106 Differentiation applied to capacitive voltage and current 123 Digital multimeter 275 Dimensional analysis 18 23 37 Diode in current loop circuit 203 Dip tube 361 Direct acting controller 604 Direct acting pneumatic relay 225 Direct acting transmitter 154 Discharge coefficient 477 Discrete 169 266 Displacement 45 Displacer level instrument 382 Dissociation 542 DMM 275 Doppler effect 512 Doppler ultrasonic flowmeter 512 DP cell 239 Drift 270 Droop 610 Dry leg 368 Dry block temperature calibrator 276 Eccentric orifice plate 460 Einstein Albert 20 lectrical heat tracing 341 lectrodeless conductivity cell 546 lectrolysis 65 lectromagnetic induction 505 lectron flow 175 lectron shell configuration 63 lectronic manometer 283 lement 61 Emerson AMS software 254 590 Emerson DeltaV control system 254 590 Emissivity thermal 435 Emittance thermal 435 Endothermic 65 INDEX Endress Hauser magnetic flowmeter 509 Equivalent circuits series and parallel AC 117 Error controller 604 611 Euler s relation 122 Excitation source for bridge circuit 100 Exothermic 65 Farad 108 Feedback control system 600 Fieldbus 139 254 Fill fluid 301 303 306 325 328 419 Fillage 390 Filled bulb 32 419 Filled impulse line 337 Filtering 617 Final Control
41. continuously wet or if they are being stored on a shelf maintained in a wet state by a small quantity of potassium hydroxide held close to the glass probe by a liquid tight cap It is therefore impossible to extend the shelf life of a glass pH electrode indefinitely The voltage produced by the measurement electrode glass membrane is quite modest A calculation for voltage produced by a measurement electrode immersed in a 6 0 pH solution shows this First we must calculate hydrogen ion concentration activity for a 6 0 pH solution based on the definition of pH being the negative logarithm of hydrogen ion molarity pH log H 6 0 log H 6 0 log H 556 CHAPTER 16 CONTINUOUS ANALYTICAL MEASUREMENT 10760 oestH 1076 2 H H 1 x 10 M This tells us the concentration of hydrogen ions in the 6 0 pH solution which is practically the same as hydrogen ion activity for dilute solutions We know that the buffer solution inside the glass measurement bulb has a stable value of 7 0 pH hydrogen ion concentration of 1 x 1077 M or 0 0000001 moles per liter so all we need to do now is plug these values in to the Nernst equation to see how much voltage the glass electrode should generate Assuming a solution temperature of 25 C 298 15 K and knowing that n in the Nernst equation will be equal to 1 since each hydrogen ion has a single value electrical charge _ 2303RT C V AF log 2 AE 2 3
42. for the transmitter Safety concerns made the 10 50 mA standard unsuitable for some industrial installations and modern microelectronic circuitry with its reduced power consumption made the 4 20 mA standard practical for nearly all types of process transmitters 202 CHAPTER 8 ANALOG ELECTRONIC INSTRUMENTATION 8 6 Troubleshooting current loops Since the signal of interest is represented by an electric current in an instrumentation current loop circuit the obvious tool to use for troubleshooting is a multimeter capable of accurately measuring DC milliamperes Unfortunately though there is a major disadvantage to the use of a milliammeter the circuit must be broken at some point to connect the meter in series with the current and this means the current will fall to 0 mA until the meter is connected then fall to 0 mA when the meter is removed from the circuit Interrupting the current means interrupting the flow of information conveyed by that current be it a process measurement or a command signal to a final control element This will have adverse effects on a control system unless certain preparatory steps are taken Before breaking the loop to connect your meter one must first warn all appropriate personnel that the signal will be interrupted at least twice falling to a value of 25 each time If the signal to be interrupted is coming from a process transmitter to a controller the controller should be placed in Manual m
43. gt Here the setpoint SP appears as a perfectly straight red line the process variable as a slightly bumpy blue line and the controller output as a very bumpy purple line We can see from this trend that the controller is doing exactly what it should holding the process variable value close to setpoint manipulating the final control element as far as necessary to do so The erratic appearance of the output signal is not really a problem contrary to most peoples first impression The fact that the process variable never deviates significantly from the setpoint tells us the control system is operating quite well What accounts for the erratic controller output then Variations in process load As other variables in the process vary the controller is forced to compensate for these variations in order that the process variable does not drift from setpoint Now maybe this does indicate a problem somewhere else in the process but there is certainly no problem in this control system 5 4 OTHER TYPES OF INSTRUMENTS 143 Recorders become powerful diagnostic tools when coupled with the controller s manual control mode By placing a controller in manual mode and allowing direct human control over the final control element valve motor heater we can tell a lot about a process Here is an example of a trend recording for a process in manual mode where the process variable response is seen graphed in relation to the controller outpu
44. measurement Temperature is the measure of average molecular kinetic energy within a substance The concept is easiest to understand for gases under low pressure where gas molecules randomly shuffle about The average kinetic motional energy of these gas molecules defines temperature for that quantity of gas There is even a formula expressing the relationship between average kinetic energy Ej and temperature T for a monatomic single atom molecule gas 3kT Ej 5 Where Ep Average kinetic energy of the gas molecules joules k Boltzmann s constant 1 38 x 1072 joules Kelvin T Absolute temperature of gas Kelvin Thermal energy is a different concept the quantity of total kinetic energy for this random molecular motion If the average kinetic energy is defined as oa then the total kinetic energy for all the molecules in a monatomic gas must be this quantity times the total number of molecules N in the gas sample 3NkT Ethermal 2 This may be equivalently expressed in terms of the number of moles of gas rather than the number of molecules a staggeringly large number for any realistic sample 3nRT Ethermal 2 Where Ethermal Total thermal energy for a gas sample joules n Quantity of gas in the sample moles R Ideal gas constant 8 315 joules per mole Kelvin 415 416 CHAPTER 14 CONTINUOUS TEMPERATURE MEASUREMENT T Absolute temperature of gas Kelvin Heat is defined as the exchange of the
45. more than enough for practically any model of 4 20 mA loop powered transmitter to successfully operate Thus the problem of insufficient supply voltage only manifests itself when the process measurement nears 100 of range This could be a difficult problem to diagnose since it appears only during certain process conditions A technician looking only for wiring faults loose connections corroded terminals etc would never find the problem When a loop powered transmitter is starved of voltage its behavior becomes erratic This is especially true of smart transmitters with built in microprocessor circuitry If the terminal voltage dips below the required minimum the microprocessor circuit shuts down When the circuit shuts down the current draw decreases accordingly This causes the terminal voltage to rise again at which point the microprocessor has enough voltage to start up As the microprocessor boots back up again it increases loop current to reflect the near 100 process measurement This causes the terminal voltage to sag which subsequently causes the microprocessor to shut down again The result is a slow on off cycling of the transmitter s current which makes the process controller think the process variable is surging wildly The problem disappears though as soon as the process measurement decreases enough that the transmitter is allowed enough terminal voltage to operate normally 208 CHAPTER 8 ANALOG ELECTRONIC INS
46. rather than direct electrical contact to detect the conductivity of the liquid solution This cell design enjoys the distinct advantage of virtual immunity to fouling since there is no direct electrical contact between the measurement circuit and the liquid solution Instead of using two or four electrodes inserted into the solution for conductivity measurement this cell uses two toroidal inductors one to induce an AC voltage in the liquid solution and the other to measure the strength of the resulting current through the solution 6 Toroidal conductivity sensors may suffer calibration errors if the fouling is so bad that the hole becomes choked off with sludge but this is an extreme condition These sensors are far more tolerant to fouling than any form of contact type electrode conductivity cell 16 3 CONDUCTIVITY MEASUREMENT 547 AC voltage AC source voltmeter Since toroidal magnetic cores do an excellent job of containing their own magnetic fields there will be negligible mutual inductance between the two wire coils The only way a voltage will be induced in the secondary coil is if there is an AC current passing through the center of that coil through the liquid itself The primary coil is ideally situated to induce such a current in the solution The more conductive the liquid solution the more current will pass through the center of both coils through the liquid thus producing a greater induced voltage at the secondary c
47. s response and thereby reducing its ability to respond quickly to changing process conditions Pneumatic instruments cannot be made smart like electronic instruments either With all these disadvantages one might wonder why pneumatic instruments are still used at all in modern industry Part of the answer is legacy For an industrial facility built decades ago it makes little sense to replace instruments that still work just fine The cost of labor to remove old tubing install new conduit and wires and configure new expensive electronic instruments often is not worth the benefits However pneumatic instruments actually enjoy some definite technical advantages which secure their continued use in certain applications even in the 21 century One decided advantage is the intrinsic safety of pneumatic field instruments Instruments that do not run on electricity cannot generate electrical sparks This is of utmost importance in classified industrial environments where explosive gases liquids dusts and powders exist Pneumatic instruments are also self purging Their continual bleeding of compressed air from vent ports in pneumatic relays and nozzles acts as a natural clean air purge for the inside of the instrument preventing the intrusion of dust and vapor from the outside with a slight positive pressure inside the instrument case It is not uncommon to find a field mounted pneumatic instrument encrusted with corrosion and filth on th
48. strip Most chromatography techniques however allow the sample to completely wash through a packed column relying on a detector at the end of the column to indicate when each component has exited the column A simplified schematic of a process gas chromatograph GC shows how this type of analyzer functions 14This effect is particularly striking when paper strip chromatography is used to analyze the composition of ink It is really quite amazing to see how many different colors are contained in plain black ink 16 5 CHROMATOGRAPHY 563 Sample in Pressure regulator Sample valve Col mn Detector Vent Carrier gas supply for gas chromatographs only Sample out A Programmable controller 1 L i 1 L The sample valve periodically injects a very precise quantity of sample into the entrance of the column tube and then shuts off to allow the constant flow carrier gas to wash this sample through the length of the column tube Each component of the sample travels through the column at different rates exiting the column at different times All the detector needs to do is be able to tell the difference between pure carrier gas and carrier gas mixed with anything else components of the sample Several different detector designs exist for process gas chromatographs The two most common are the flame ionization detector FID and the thermal conductivity detector TCD All detectors exploit some
49. system and the high pressure alarm PAH or pressure alarm high activates to notify a human operator All three switches in this air compressor control system are directly actuated by the air pressure in the vessel In other words these are process sensing switches It is possible to build switch devices that interpret standardized instrumentation signals such as 3 to 15 PSI pneumatic or 4 to 20 milliamps analog electronic which allows us to build on off control systems and alarms for any type of process variable we can measure with a transmitter For example the chlorine wastewater disinfection system shown earlier may be equipped with a couple of alarm switches to alert an operator if the chlorine concentration ever exceeds pre determined high or low limits 146 CHAPTER 5 INTRODUCTION TO INDUSTRIAL INSTRUMENTATION Chlorine supply gat del aed Seriatn aE SP Contact chamber Effluent Influent Mixer The labels AAL and AAH refer to analytical alarm low and analytical alarm high respectively Since both alarms work off the 4 to 20 milliamp electronic signal output by the chlorine analytical transmitter AT rather than directly sensing the process their construction is greatly simplified If these were process sensing switches each one would have to be equipped with the capability of directly sensing chlorine concentration In other words each switch would have to be its own chlorine concentration analyzer with all
50. the number of moles of Ht ions per liter of solution The addition of hydrogen ions to the solution also decreases the molarity of hydroxyl ions the number of moles of OH ions per liter of solution because some of the water s OH ions combine with the acid s Ht ions to form deionized water molecules H20 If an alkaline substance otherwise known as a caustic or a base is added to water some of the alkaline molecules dissociate into negative hydroxyl ions OH and positive ions the type of positive ions depending on what type of alkaline it is This increases the molarity of OH ions in the solution as well as decreases the molarity of hydrogen ions again because some of the caustic s OH ions combine with the water s Ht ions to form deionized water molecules H20 The result of this complementary effect increasing one type of water ion decreasing the other keeps the overall ionization constant relatively constant at least for dilute solutions In other words the addition of an acid or a caustic may change H but it has little effect on Kw A simple way to envision this effect is to think of a laboratory balance scale balancing the number of hydrogen ions in a solution against the number of hydroxyl ions in the same solution When the solution is pure water this imaginary scale is balanced neutral with Ht OH7 Adding an acid to the solution tips the scale one way while adding a caustic to the solutio
51. transmitter s indication because its effect is canceled at the differential pressure instrument s sensing element If gas pressure inside the vessel were to increase while liquid level remained constant the pressure sensed at both ports of the differential pressure transmitter would increase by the exact same amount with the pressure difference between the high and low ports remaining absolutely constant with the constant liquid level This means the instrument s output signal is a representation of hydrostatic pressure only which represents liquid height assuming a known liquid density y Unfortunately it is common for enclosed vessels to hold condensible vapors which may over time fill a compensating leg full of liquid If the tube connecting the Low side of a differential pressure transmitter fills completely with a liquid this will add a hydrostatic pressure to that side of the transmitter causing another calibration shift This wet leg condition makes level measurement more complicated than a dry leg condition where the only pressure sensed by the transmitter s Low side is gas pressure Pyas 13 3 HYDROSTATIC PRESSURE 369 Gas pressure Peas Compensating leg wet Density Y hy Electronic Pressure P gas 7 h Pressure P as Yoh Pas T y h Pj s F y2h2 y h aha Gas pressure still cancels due to the differential nature of the pressure transmitter but now the tr
52. when the vessel is completely empty This of course will be the transmitter s calibrated lower range value LRV The upper range value URV will be the pressure seen with 11 feet of sea water in the vessel This much sea water will contribute an additional 4 89 PSI of hydrostatic pressure at the level of the remote seal diaphragm causing the transmitter to experience a pressure of 2 46 PSIP 5The sea water s positive pressure at the remote seal diaphragm adds to the negative pressure already generated by the downward length of the capillary tube s fill fluid 2 43 PSI which explains why the transmitter only sees 2 46 PSI of pressure at the 100 full mark 13 3 HYDROSTATIC PRESSURE 367 13 3 3 Compensated leg systems The simple and direct relationship between liquid height in a vessel and pressure at the bottom of that vessel is ruined if another source of pressure exists inside the vessel other than hydrostatic elevation head This is virtually guaranteed to be the case if the vessel in question is unvented Any gas or vapor pressure accumulation in an enclosed vessel will add to the hydrostatic pressure at the bottom causing any pressure sensing instrument to falsely register a high level Gas pressure Peas gt AS Electronic output signal vented Pressure Pag yh A pressure transmitter has no way of knowing how much of the sensed pressure is due to liquid elevation and how much of it is d
53. yh Having an accurate assessment of liquid density also implies that density must remain relatively constant despite other changes in the process If the liquid density is subject to random variation the accuracy of any hydrostatic pressure based level instrument will correspondingly vary It should be noted though that changes in liquid density will have absolutely no effect on hydrostatic measurement of liquid mass so long as the vessel has a constant cross sectional area throughout its entire height A simple thought experiment proves this imagine a vessel partially full of liquid with a pressure transmitter attached to the bottom to measure hydrostatic pressure 13 3 HYDROSTATIC PRESSURE 359 Now imagine the temperature of that liquid increasing so that its volume expands and has a lower density than before Assuming no addition or loss of liquid to or from the vessel any increase in liquid level will be strictly due to volume expansion density decrease Liquid level inside this vessel will rise but the transmitter will sense the exact same hydrostatic pressure as before since the rise in level is precisely countered by the decrease in density if h increases by the same factor that y decreases then P yh must remain the same In other words hydrostatic pressure is seen to be a direct indication of the liquid mass contained within the vessel regardless of changes in liquid density Differential pressure transmitters are the mo
54. yh Poas y h z x Prottom Fridde gas yh Poas yh yx Prottom Fmiddle YT Prottom 4 middle _ x 8 Assuming the liquid level is equal to or greater than x Otherwise the pressure difference between Pyottom and Pmiddle Will depend on liquid density and liquid height However this condition is easy to check the level computer simply checks to see if Pmiddie and Ptop are unequal If so then the computer knows the liquid level exceeds x and it is safe to calculate density If not and Pmiddie registers the same as Prop the computer knows those two transmitters are both registering gas pressure only and it knows to stop calculating density 374 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT Once the computer knows the value of y it may calculate the height of liquid in the tank with great accuracy based on the pressure measurements taken by the bottom and top transmitters Prottom Prop lt Pias yh a Poas Prottom Prop yh Pbottom a Prop Zp Y With all the computing power available in the LY it is possible to characterize the tank such that this height measurement converts to a precise volume measurement V which may then be converted into a total mass m measurement based on the mass density of the liquid p and the acceleration of gravity g First the computer calculates mass density based on the proportionality between mass and weight shown here starting with the equivalence between the tw
55. 103 Actinide Actinium Thorium Protactinium Uranium Neptunium Plutonium Americium Curium Berkelium Californium Einsteinium Fermium Mendelevium Nobelium Lawrencium series 227 232 0381 231 03588 238 0289 237 244 243 247 247 251 252 257 258 259 260 6d 7s 6d 7s 5f6d 7s 5f 6d 7s 5ff6d 7s 5ff6d 7s 5f 6d 7s 5f 6d 7s 5f 6d 7s 5f 6d 7s 5f 6d 7s 5 6d7s 5f ed 7s 6d 7s 6d 7s Attributes of each element may be interpreted in each table entry as such In this example we have the element Potassium K 19 Potassium 39 0983 4s The atomic number number of protons in the nucleus of each Potassium atom is 19 This number defines the element If we were to somehow to add or subtract protons from the nucleus of a Potassium atom it would cease being Potassium and transmutate into a different element The atomic mass or atomic weight combined number of protons and neutron in the nucleus of each Potassium atom is 39 Neutrons may be added to or taken away from an atom s nucleus without changing its elemental identity Atoms with the same number of protons but different numbers of neutrons in the nucleus are called isotopes Isotopes have the same chemical properties but may have different nuclear properties such as stability whether or not the atom is likely to spontaneously decay which we refer to as
56. 2 the power reflection ratio will only be 0 0294 2 94 or 15 3 dB with the vast majority of the wave s power successfully penetrating the air gasoline interface The longer version of the power reflection factor formula suggests liquid liquid interfaces should be detectable using radar and indeed they are All that is needed is a sufficiently large difference in relative permittivity between the two liquids to create a strong enough echo to reliably detect Liquid liquid interface level measurement with radar works best when the upper liquid has a substantially lesser permittivity value than the lower liquid A layer of hydrocarbon oil on top of water or any aqueous solution such as an acid or a caustic is a good candidate for guided wave radar level measurement An example of a liquid liquid interface that would be very difficult for a radar instrument to detect is water e 80 above glycerin e 42 If the radar instrument uses a digital network protocol to communicate information with a host system such as HART or any number of fieldbus standards it may perform as a multi variable transmitter transmitting both the interface level measurement and the total liquid level measurement simultaneously One reason why a lesser e fluid above a greater e fluid is easier to detect than the inverse is due to the necessity of the signal having to travel through a gas liquid interface above the liquid liquid interface With gases and vapors
57. 238 CHAPTER 9 PNEUMATIC INSTRUMENTATION Range wheel Range bar f a oO lt gt Output LL signal Erin Zero screw Diaphragm seal High pressure Low pressure input lt _ input Part of the reason for this instrument s popularity is the extreme utility of differential pressure transmitters in general A DP cell may be used to measure pressure vacuum pressure differential liquid level liquid or gas flow and even liquid density A reason for this particular differential 9 5 ANALYSIS OF A PRACTICAL PNEUMATIC INSTRUMENT 239 transmitter s popularity is excellent design the Foxboro model 13 transmitter is rugged easy to calibrate and quite accurate Like so many pneumatic instruments the model 13 transmitter uses the force balance more precisely the motion balance principle whereby any shift in position is sensed by a detector the baffle nozzle assembly and immediately corrected through negative feedback to restore equilibrium As a result the output air pressure signal becomes an analogue of the differential process fluid pressure sensed by the diaphragm capsule In the following photograph you can see my index finger pointing to the baffle nozzle mechanism at the top of the transmitter Let s analyze the behavior of this transmitter step by step as it senses an increasing pressure on the High pressure input port As the pressure here increases the large diaphragm capsule is
58. 3 Proportional only control Here is where math starts to enter the algorithm a proportional controller calculates the difference between the process variable signal and the setpoint signal and calls it the error This is a measure of how far off the process is deviating from its setpoint and may be calculated as SP PV or as PV SP depending on whether or not the controller has to produce an increasing output signal to cause an increase in the process variable or output a decreasing signal to do the same thing This choice in how we subtract determines whether the controller will be reverse acting or direct acting The direction of action required of the controller is determined by the nature of the process transmitter and final control element In this case we are assuming that an increasing output signal sent to the valve results in increased steam flow and consequently higher temperature so our algorithm will need to be reverse acting i e an increase in measured temperature results in a decrease in output signal error calculated as SP PV This error signal is then multiplied by a constant value called the gain which is programmed into the controller The resulting figure plus a bias quantity becomes the output signal sent to the valve to proportion it m Kpe b Where m Controller output e Error difference between PV and SP Kp Proportional gain b Bias If this equation appears to resemble the standard slope i
59. 4 0 85 53 0 0 0307 2 r ft in lb Fouoyant LRV 7 1 375 in 0 0307 30 in 5 47 Ib in Pre URV 7 1 375 in 0 0397 Z 30 in 7 08 lb Interface level inches Buoyant force pounds 0 5 47 7 5 5 87 15 6 27 22 5 6 68 30 7 08 13 5 ECHO 389 13 5 Echo A completely different way of measuring liquid level in vessels is to bounce a traveling wave off the surface of the liquid typically from a location at the top of the vessel using the time of flight for the waves as an indicator of distance and therefore an indicator of liquid height inside the vessel Echo based level instruments enjoy the distinct advantage of immunity to changes in liquid density a factor crucial to the accurate calibration of hydrostatic and displacement level instruments In this regard they are quite comparable with float based level measurement systems The single most important factor to the accuracy of an echo based level instrument is the speed at which the wave travels en route to the liquid surface and back This wave propagation speed is as fundamental to the accuracy of an echo instrument as liquid density is to the accuracy of a hydrostatic or displacer instrument So long as this velocity is known and stable good level measurement accuracy is generally easy to achieve From a historical perspective hydrostatic and displacement level instruments have a richer pedigree These
60. 4d 5s _ ads 4d 5s 5p 5p 5p 5p S s Cs 55 Ba 56 57 71 Hf 72 Ta 73 W 74 Re 75 0s 76 Ir 77 Pt 78 muW 79 g so i 81 Pb 82 Bi 83 Po 84 at 85 Rn 86 Cesium Barium Lanthanide Hafnium Tantalum Tungsten Rhenium Osmium tridium Platinum Gold Mercury Thallium Lead Bismuth Polonium Astatine Radon 132 90543 137 327 series 178 49 180 9479 183 85 186 207 190 2 19222 195 08 196 96654 200 59 204 3833 207 2 208 98037 209 210 222 6s 6s 5d 6s 5d 6s 5d6s 5d 6s 5d 6s 5d 6s 5d 6s 5d 6s __ 5d6s 6p 6p 6p 6p 6p 6p Fr 87 Ra_ 88 89 103 Unq 104 Unp 105 Unh 106fUns 107 108 109 Francium Radium Actinide Unniiquadium Unniipentium Unnithexium Unniiseptium 223 226 series 261 262 263 262 7s 78 6d 7s 6d 7s 6d 7s La 57 Ce 58 Pr 59 Nd 60 Pm 61 Sm 62 Eu 63 Gd 64 Th 65 Dy 66 Ho 67 Er 68 Tm 69 Ybo 70 lu 71 Lanthanide Lanthanum Cerium Praseodymium NeodymiumPromethium Samarium Europium Gadolinium Terbium Dysprosium Holmium Erbium Thulium Ytterbium Lutetium series 138 9055 140 115 140 90765 144 24 145 150 36 151 965 157 25 158 92534 162 50 164 93032 167 26 168 93421 173 04 174 967 5d 6s 4f sd 6s 4f6s aros a os a os a os 4f5d 6s 416s ares 41165 4f 6s 4165 4f6s 4f 5d 6s Ac 89 Th g0 Pa o1 U 92 Np 93 Pu 94 Am 95 Cm 96 Bk 97 Cf 98 Es 99 Fm 100 Md 101 No 102 tr
61. 6 941 9 012182 Name 39 0983 lt Atomic mass 10 81 12 011 14 0067 15 9994 18 9984 20 179 2s 2s As 2p 2p 2p 2p 2p 2p Electron Na 11 Mg 12 configuration A 13 si 14 P 15 S iweje i7 Ar 18 Sodium Magnesium Aluminum Silicon Phosphorus Sulfur Chlorine Argon 22 989768 24 3050 26 9815 28 0855 30 9738 32 06 35 453 39 948 i i Metals 4 2 3 A 6 3s 3s 3p 3p 3p ap 3p 3p K t9o ca 20 sc afti 22 w 23 Cr 24 Mm 25 Fe 26 Co 27 Ni 28 Cu 29 zn 30 Ga 31 Ge 32 As 33 Se 34 Br 35 Kr 36 Potassium Calcium Scandium Titanium Vanadium Chromium Manganese Iron Cobalt Nickel Copper Zinc Gallium Germanium Arsenic Selenium Bromine Krypton 39 0983 40 078 44 955910 47 88 50 9415 51 9961 54 93805 55 847 58 93320 58 69 63 546 65 39 69 723 72 61 74 92159 78 96 79 904 83 80 4s 4s 3d 4s 3d 4s 3d 4s 3d 4s 3d 4s 3d 4s 3d4s 3d 4s 3d 4s _ 3d 4s 4p 4p 4p 4p 4p 4p Ro 37 sr 38 Y 39 zr 40 Nb 41 Mo 42 Tc 43 Ru 44 Rh 45 Pd 46 Ag 47 cd 48 in a9 Sn sofsb 51 Te 521 53 Xe 54 Rubidium Strontium Yttrium Zirconium Niobium Molybdenum Technetium Ruthenium Rhodium Palladium Silver Cadmium Indium Tin Antimony Tellurium lodine Xenon 85 4678 87 62 88 90585 91 224 92 90638 95 94 98 101 07 102 90550 106 42 107 8682 112 411 114 82 118 710 121 75 127 60 126 905 131 30 5s 5s 4d 5s 40 58 4d 5s 4d 5s 4d 5s 4d 5s 4d 5s
62. 9 PNEUMATIC INSTRUMENTATION the baffle closer to the nozzle and tends to increase air pressure to the bellows as the system seeks equilibrium If a technician turns the range wheel the lever ratio of the range bar changes affecting the ratio of force bar force to bellows force The following photograph shows the range bar and range wheel of the instrument As in all instruments the zero adjustment works by adding or subtracting a quantity while the span adjustment works by multiplying or dividing a quantity In the Foxboro model 13 pneumatic transmitter the quantity in question is force The zero screw adds or subtracts force to the mechanical system by tensioning a spring while the range wheel multiplies or divides force in the 9 5 ANALYSIS OF A PRACTICAL PNEUMATIC INSTRUMENT system by changing the mechanical advantage force ratio of a lever 241 242 CHAPTER 9 PNEUMATIC INSTRUMENTATION 9 6 Proper care and feeding of pneumatic instruments Perhaps the most important rule to obey when using pneumatic instruments is to maintain clean and dry instrument air Compressed air containing dirt rust oil water or other contaminants will cause operational problems for pneumatic instruments First and foremost is the concern that tiny orifices and nozzles inside the pneumatic mechanisms will clog over time Clogged orifices tend to result in decreased output pressure while clogged nozzles tend to result in increased output pressure I
63. Distribute or Publicly Perform an Adaptation Licensor offers to the recipient a license to the original Work on the same terms and conditions as the license granted to You under this License 3 If any provision of this License is invalid or unenforceable under applicable law it shall not affect the validity or enforceability of the remainder of the terms of this License and without further action by the parties to this agreement such provision shall be reformed to the minimum extent necessary to make such provision valid and enforceable 4 No term or provision of this License shall be deemed waived and no breach consented to unless such waiver or consent shall be in writing and signed by the party to be charged with such waiver or consent 5 This License constitutes the entire agreement between the parties with respect to the Work licensed here There are no understandings agreements or representations with respect to the Work not specified here Licensor shall not be bound by any additional provisions that may appear in any communication from You This License may not be modified without the mutual written agreement of the Licensor and You 6 The rights granted under and the subject matter referenced in this License were drafted utilizing the terminology of the Berne Convention for the Protection of Literary and Artistic Works as amended on September 28 1979 the Rome Convention of 1961 the WIPO Copyright Treaty of 1996 the WIPO Perform
64. ELEMENTS 307 Just like the older model this instrument has two ports through which fluid pressure may be applied to the sensor The sensor in turn responds only to the difference in pressure between the ports The differential capacitance sensor construction is more complex in this particular pressure instrument with the plane of the sensing diaphragm lying perpendicular to the plane of the two isolating diaphragms This coplanar design is far more compact than the older style of sensor with general engineering advances providing much improved resolution and accuracy 308 CHAPTER 12 CONTINUOUS PRESSURE MEASUREMENT 12 3 3 Resonant element sensors As any guitarist violinist or other stringed instrument musician can tell you the natural frequency of a tensed string increases with tension This in fact is how stringed instruments are tuned the tension on each string is precisely adjusted to achieve the desired resonant frequency Mathematically the resonant frequency of a string may be described by the following formula Where f Fundamental resonant frequency of string Hertz L String length meters Fr String tension newtons u Unit mass of string kilograms per meter It stands to reason then that a string may serve as a force sensor All that is needed to complete the sensor is an oscillator circuit to keep the string vibrating at its resonant frequency and that frequency becomes an indication of tension
65. Ez final 1 mgh nos We can see from this equation that mass cancels out of both sides leaving us with this simpler form 1 It also leads to the paradoxical conclusion that the mass of a free falling object is irrelevant to its velocity That is both a heavy object and a light object in free fall will hit the ground with the same velocity and fall for the same amount of time if released from the same height under the influence of the same gravity Dimensional analysis confirms the common nature of energy whether in the form of potential kinetic or even mass as described by Einstein s equation First we will set these three energy equations next to each other for comparison of their variables E mgh Potential energy due to elevation l gt bi ate Ej gm Kinetic energy due to velocity E m Mass to energy equivalence Next we will dimensionally analyze them using standard SI metric units kilogram meter second Following the SI convention mass m is always expressed in kilograms kg distance h in meters m and time t in seconds s This means velocity v or c for the velocity of light in the SI system will be expressed in meters per second m s and acceleration a or g for gravitational acceleration in meters per second squared m s k 2 y kg 3 m Potential energy due to elevation k 2 2 e kg Kinetic energy due to velocity T n practice we usually see heavy objects
66. Fourth Edition CRC Press New York NY 2003 Miller Richard W Flow Measurement Engineering Handbook Second Edition McGraw Hill Publishing Company New York NY 1989 Price James F A Coriolis Tutorial version 3 3 Woods Hole Oceanographic Institution Woods Hole MA 2006 Spink L K Principles and Practice of Flow Meter Engineering Ninth Edition The Foxboro Company Foxboro MA 1967 Vennard John K Elementary Fluid Mechanics 3rd Edition John Wiley amp Sons Inc New York NY 1954 540 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT Chapter 16 Continuous analytical measurement 16 1 Density measurement 16 2 Turbidity measurement 541 542 CHAPTER 16 CONTINUOUS ANALYTICAL MEASUREMENT 16 3 Conductivity measurement Electrical conductivity in metals is the result of free electrons drifting within a lattice of atomic nuclei comprising the metal object When a voltage is applied across two points of a metal object these free electrons immediately drift toward the positive pole anode and away from the negative pole cathode Electrical conductivity in liquids is another matter entirely Here the charge carriers are ions electrically imbalanced atoms or molecules that are free to drift because they are not locked into a lattice structure as is the case with solid substances The degree of electrical conductivity of any liquid is therefore dependent on the ion density of the solution how many
67. HART are listed here e Diagnostic data may be transmitted by the field device self test results out of limit alarms preventative maintenance alerts etc e Field instruments may be re ranged remotely through the use of HART communicators e Technicians may use HART communicators to force field instruments into different manual modes for diagnostic purposes e g forcing a transmitter to output a fixed current so as to check calibration of other loop components manually stroking a valve equipped with a HART capable positioner e Field instruments may be programmed with identification data e g tag numbers corresponding to plant wide instrument loop documentation 252 CHAPTER 10 DIGITAL ELECTRONIC INSTRUMENTATION 10 1 1 HART multidrop mode The HART standard also supports a mode of operation that is totally digital and capable of supporting multiple HART instruments on the same pair of wires This is known as multidrop mode Every HART instrument has an address number which is typically set to a value of zero 0 A network address is a number used to distinguish one device from another on a broadcast network so messages broadcast across the network may be directed to specific destinations When a HART instrument operates in digital analog hybrid mode where it must have its own dedicated wire pair for communicating the 4 20 mA DC signal between it and an indicator or controller there is no need for a digital address An addre
68. It depends entirely on whether we consider the reference buffer solution s hydrogen ion activity to be C1 or C2 in the equation Which ever way we choose to calculate this voltage though the polarity will be opposite for acidic pH values as compared to alkaline pH values 16 4 PH MEASUREMENT 557 This numerical progression is reminiscent of the Richter scale used to measure earthquake magnitudes where each ten fold decade multiplication of power is represented by one more increment on the scale e g a 6 0 Richter earthquake is ten times more powerful than a 5 0 Richter earthquake The logarithmic nature of the Nernst equation means that pH probes and in fact all potentiometric sensors based on the same dynamic of voltage produced by ion exchange across a membrane have astounding rangeability they are capable of representing a wide range of conditions with a modest signal voltage span Of course the disadvantage of high rangeability is the potential for large pH measurement errors if the voltage detection within the pH instrument is even just a little bit inaccurate The problem is made even worse by the fact that the voltage measurement circuit has an extremely high impedance due to the presence of the glass membrane The pH instrument measuring the voltage produced by a pH probe assembly must have an input impedance that is orders of magnitude greater yet or else the probe s voltage signal will become loaded down by the v
69. P I or D setting adjustments though will correct for actual process or equipment failures The real solution is to diagnose the process to determine the root cause of the instability Tronically one of the best diagnostic tools available to the technician is the controller s manual mode By placing the controller in manual mode we disconnect the input from the output so the output no longer responds to changes in PV or SP This breaks the feedback loop of the system so that it has a definite beginning and end Input Output Controller manual mode Influences Senses Reacts By making carefully measured changes in the controller s output and examining the consequent changes in transmitter signal one may determine the existence of many different problems including transmitter and process noise improper transmitter ranges final control element hysteresis variations in process gain lag times dead times and other impediments to optimum control Only after examining the process and its response to changes in valve position should controller tuning be attempted 18 7 PID CONTROLLER TUNING 619 References Lavigne John R Instrumentation Applications for the Pulp and Paper Industry The Foxboro Company Foxboro MA 1979 Liptak B la G Instrument Engineers Handbook Process Control Volume IT Third Edition CRC Press Boca Raton FL 1999 Shinskey Francis G Energy Conservation through Contr
70. STANDARDS 281 Pneumatic deadweight tester Mass Gauge to be calibrated From gas source Restriction In fact the construction and operation of a pneumatic deadweight tester is quite similar to a self balancing force balance pneumatic instrument mechanism with a baffle nozzle assembly A moving element opens or closes a variable restriction downstream of a fixed restriction to generate a varying pressure In this case that pressure directly operates the bleed vent to self regulate gas pressure at whatever value is necessary to suspend the mass against gravity Deadweight testers both hydraulic and pneumatic lend themselves well to relatively high pressures owing to the practical limitations of mass and piston area You could use a deadweight tester to calibrate a 100 PSI pressure gauge used for measuring water mains pressure for example but you could not use a deadweight tester to calibrate a 0 to 1 W C zero to one inch water column pressure gauge used to measure draft pressure in a furnace flue For low pressure calibrations the simple manometer is a much more practical standard Manometers of course do not generate pressure on their own In order to use a manometer to calibrate a pressure instrument you must connect both devices to a source of variable fluid pressure typically instrument air through a precision pressure regulator 282 CHAPTER 11 INSTRUMENT CALIBRATION Gauge to be calibrated Precision press
71. Some practical examples of calculations between milliamp current values and process variable values follow 8 2 1 Example calculation controller output to valve An electronic loop controller outputs a signal of 8 55 mA to a direct responding control valve where 4 mA is shut and 20 mA is wide open How far open should the control valve be at this MV signal level We must convert the milliamp signal value into a percentage of valve travel This means determining the percentage value of the 8 55 mA signal on the 4 20 mA range First we need to manipulate the percentage milliamp formula to solve for percentage x x 16 mA 5007 4 mA current x 16 mA sax current 4 mA z current 4 mA 100 16 mA current 4 mA C 16 mA 200 Next we plug in the 8 55 mA signal value and solve for x 8 2 RELATING 4 TO 20 MA SIGNALS TO INSTRUMENT VARIABLES 191 mA 4 mA ae 16 mA tone x 28 4 Therefore the control valve should be 28 4 open when the MV signal is at a value of 8 55 mA 8 2 2 Example calculation flow transmitter A flow transmitter is ranged 0 to 350 gallons per minute 4 20 mA output direct responding Calculate the current signal value at a flow rate of 204 GPM First we convert the flow value of 204 GPM into a percentage of range This is a simple matter of division since the flow measurement range is zero based 204 GPM 350 GPM Next we take this perce
72. Where v Velocity of electromagnetic wave through a particular substance c Velocity of light in a perfect vacuum 3 x 10 meters per second er Relative permittivity dielectric constant of the substance In the case of a single liquid application where nothing but gas or vapor exists above the liquid the permittivity of that gas or vapor must be precisely known In the case of a two liquid interface with gas or vapor above the relative permittivities of both gas and upper liquids must be accurately known in order to accurately measure the liquid liquid interface Changes in dielectric constant value of the medium or media through which the microwaves must travel and echo will cause the microwave radiation to propagate at different velocities Since all radar measurement is based on time of flight through the media separating the radar transceiver from the echo interface changes in wave velocity through this media will affect the amount of time required for the wave to travel from the transceiver to the echo interface and reflect back to the transceiver Therefore changes in dielectric constant directly affect the accuracy of any radar level measurement Factors influencing the dielectric constant of gases include pressure and temperature which means the accuracy of a radar level instrument will vary as gas pressure and or gas temperature vary Whether or not this variation is substantial enough to consider for any application depends on the
73. a multipath ultrasonic flowmeter and to average the resulting velocity measurements Dual beam flowmeters have been in use for well over a decade and one manufacturer even has a five beam ultrasonic flowmeter model which they claim maintains an accuracy of 0 15 through the laminar to turbulent flow regime transition Some modern ultrasonic flowmeters have the ability to switch back and forth between Doppler and transit time counterpropagation modes automatically adapting to the fluid being sensed This capability enhances the suitability of ultrasonic flowmeters to a wider range of process applications Ultrasonic flowmeters are adversely affected by swirl and other large scale fluid disturbances and as such may require substantial lengths of straight pipe upstream and downstream of the measurement flowtube to stabilize the flow profile Advances in ultrasonic flow measurement technology have reached a point where it is now feasible to consider ultrasonic flowmeters for custody transfer measurement of natural gas The American Gas Association has released a report specifying the use of multipath ultrasonic flowmeters in this capacity Report 9 25See page 10 of Friedrich Hofmann s Fundamentals of Ultrasonic Flow Measurement for industrial applications paper 514 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT A unique advantage to ultrasonic flow measurement is the ability to measure flow through the use of temporary clamp on s
74. a pressure generating source is connected to both the instrument under test and a trusted calibration gauge test gauge and the two indications are compared at several points along the calibrated range Test equipment suitable for field pressure calibrations include slack tube manometers made from flexible plastic tubing hung from any available anchor point near eye level and test gauges typically of the helical bourdon tube variety Portable electronic test gauges are also available for field use many with built in hand pumps for generating precise air pressures A noteworthy example of a pneumatic pressure calibrator for field use was a device manufactured by the Wallace amp Tiernan corporation affectionately called a Wally box by at least one generation of instrument technicians A Wally box consisted of a large dial pressure gauge several inches in diameter with a multi turn needle and a very fine scale connected to a network of valves and regulators which were used to set different air pressures from any common compressed air source The entire mechanism was housed in an impact resistance case for ruggedness One of the many nice features of this calibration instrument was a selector valve allowing the technician to switch between two different pressures output by independent pressure regulators Once the two pressure regulator values were set to the instrument s lower and upper range values LRV and URV it was possible to sw
75. also cause hysteresis errors if cracked or bent In practice most calibration errors are some combination of zero span linearity and hysteresis problems 270 CHAPTER 11 INSTRUMENT CALIBRATION 11 5 1 As found and as left documentation An important principle in calibration practice is to document every instrument s calibration as it was found and as it was left after adjustments were made The purpose for documenting both conditions is so that data is available to calculate instrument drift over time If only one of these conditions is documented during each calibration event it will be difficult to determine how well an instrument is holding its calibration over long periods of time Excessive drift is often an indicator of impending failure which is vital for any program of predictive maintenance or quality control Typically the format for documenting both As Found and As Left data is a simple table showing the points of calibration the ideal instrument responses the actual instrument responses and the calculated error at each point The following table is an example for a pressure transmitter with a range of 0 to 200 PSI over a five point scale Percent Input Output current Output current Error of range pressure ideal measured percent of span 0 0 PSI 4 00 mA 25 50 PSI 8 00 mA 50 100 PSI 12 00 mA 75 150 PSI 16 00 mA 100 200 PSI 20 00 mA 11 5 2 Up tests and Down tests It
76. and then move the set point adjustment in the opposite direction as the intended direction of the stimulus in this case increasing the set point value until the switch changes states The basis for this technique is the realization that most comparison mechanisms cannot tell the difference between a rising process variable and a falling setpoint or visa versa Thus a falling pressure may be simulated by a rising set point adjustment You should still perform an actual changing stimulus test to ensure the instrument responds properly under realistic circumstances but this trick will help you achieve good calibration in less time 11 5 TYPICAL CALIBRATION ERRORS 267 11 5 Typical calibration errors Recall that the slope intercept form of a linear equation describes the response of a linear instrument y mzr b Where y Output m Span adjustment x Input b Zero adjustment A zero shift calibration error shifts the function vertically on the graph This error affects all calibration points equally creating the same percentage of error across the entire range 20 mA 12mA Output current 4mA OmA 0 PSI 50 PSI 100 PSI Input pressure A span shift calibration error shifts the slope of the function This error s effect is unequal at different points throughout the range 268 CHAPTER 11 INSTRUMENT CALIBRATION 20 mA 12 mA Output current ffect of a span shift y mx b 4mA OmA 0 PSI
77. any further than this This necessary error between PV and SP is called proportional only offset sometimes less formally known as droop The amount of droop depends on how severe the load change is and how aggressive the controller responds i e how much gain it has The term droop is very misleading as it is possible for the error to develop the other way i e the PV might rise above SP due to a load change Imagine the opposite load change scenario where the incoming feed temperature suddenly rises instead of falls If the controller was controlling exactly at setpoint before this upset the final 610 CHAPTER 18 CONTINUOUS FEEDBACK CONTROL result will be an outlet temperature that settles at some point above setpoint enough so that the controller is able to pinch the steam valve far enough closed to stop any further rise in temperature We can minimize proportional only offset by increasing controller gain This makes the controller more aggressive so that it moves the control valve further for any given change in PV or SP Thus not as much error needs to develop between PV and SP to move the valve to any new position it needs to go However too much gain and the control system will begin to oscillate just like a crude on off controller If we are limited in how much gain we can program in to the controller how do we minimize this offset One way is for a human operator to periodically place the controller in manual mode a
78. are often the more practical flow element for the task and more accurate over the long term as well since even the finest weir will not register accuracy once it becomes fouled by debris Once a weir or flume has been installed in an open channel to measure the flow of liquid some method must be employed to sense upstream liquid level and translate this level measurement into 181t is also possible to operate a Parshall flume in fully submerged mode where liquid level must be measured at both the upstream and throat sections of the flume Correction factors must be applied to these equations if the flume is submerged 15 3 VARIABLE AREA FLOWMETERS 493 a flow measurement Perhaps the most common technology for weir flume level sensing is ultrasonic see section 13 5 1 page number 390 for more information on how this technology works Ultrasonic level sensors are completely non contact which means they cannot become fouled by the process liquid or debris in the process liquid However they may be fooled by foam or debris floating on top of the liquid as well as waves on the liquid surface The following photograph shows a Parshall flume measuring effluent flow from a municipal sewage treatment plant with an ultrasonic transducer mounted above the middle of the flume to detect water level flowing through Once the liquid level is successfully measured a computing device is used to translate that level measurement into a s
79. be equal to the hydrostatic pressure of the process liquid at the bottom of the tube where the gas escapes In other words the purge gas acts to transmit the liquid s hydrostatic pressure to some remote point where a pressure sensing instrument is located A general rule of thumb is to limit purge gas flow to the point where you can easily count individual bubbles exiting the bubble tube or inside the sightfeed bubbler if one is provided on the system As with all purged systems certain criteria must be met for successful operation Listed here are a few pertinent questions to consider for a bubble tube system e How reliable is the supply of purge fluid If this stops for any reason the level measurement may be in error 362 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT Is the purge fluid supply pressure guaranteed to exceed the hydrostatic pressure at all times to ensure continuous purging bubbling What options exist for purge gases that will not adversely react with the process What options exist for purge gases that will not contaminate the process e How expensive will it be to maintain this constant flow of purge gas into the process One measurement artifact of a bubble tube system is a slight variation in pressure each time a new bubble breaks away from the end of the tube The amount of pressure variation is approximately equal to the hydrostatic pressure of process fluid at a height equal to the diameter of the bubble which
80. because our intent is to use pressure measurement P as an indirect inferred indication of flow rate Q If the two variables are not directly related to one 576 CHAPTER 17 SIGNAL CHARACTERIZATION another we will not be able to regard one as being directly representative of the other To make this problem more clear to see imagine a pressure gauge connected across the restriction with the face of the gauge labeled in percent Face of pressure gauge calibrated to read in percent of full flow rate Percent of full flow Consider a pressure gauge such as the one shown above registering 20 percent on a linear scale at some amount of flow through the pipe What will happen if the flow rate through that pipe suddenly doubles An operator or technician looking at the gauge ought to see a new reading of 40 percent if indeed the gauge is supposed to indicate flow rate However this will not happen Since the pressure dropped across the orifice in the pipe increases with the square of flow rate a doubling of flow rate will actually cause the pressure gauge reading to quadruple In other words it will go from reading 20 to reading 80 which is definitely not an accurate indication of the flow increase A couple of simple solutions exist for addressing this problem One is to re label the pressure gauge with a square root scale Examine this photograph of a 3 15 PSI receiver gauge having both linear and square root scales 577
81. cannot allow the fluid in question to become exposed to the atmosphere e g when the liquid or gas in question is toxic flammable under high pressure or any combination thereof One standard way to measure the flow rate of a fluid through a pipe is to intentionally place a restriction in the path of the fluid and measure the pressure drop across that restriction The most common form of intentional restriction used for this purpose is a thin plate of metal with a hole precisely machined in the center called an orifice plate A side view of the orifice plate assembly and pressure measuring instrument looks like this 575 Differential pressure instrument Direction of flow This approach should make intuitive sense the faster the flow rate of the fluid the greater the pressure difference developed across the orifice The actual physics of this process has to do with energy exchanging between potential and kinetic forms but that is incidental to this discussion The mathematically interesting characteristic of this flow measurement technique is its nonlinearity Pressure does not rise linearly with flow rate rather it increases with the square of the flow rate Diff pressure P Flow Q To write this as a proportionality we relate flow rate Q to pressure P as follows the constant k accounts for unit conversions and the geometries of the orifice plate and pipe P kQ This is a practical problem for us
82. case of a strain gauge for example mechanical strain is not the only variable affecting gauge resistance Temperature also affects gauge resistance Since we do not wish our strain gauge to also act as a thermometer which would make measurements very uncertain how would we differentiate the effects of changing temperature from the effects of changing strain we must find some way to nullify resistance changes due solely to temperature such that our bridge circuit will respond only to changes in strain The solution is to creatively use a dummy strain gauge as another arm of the bridge 106 CHAPTER 3 DC ELECTRICITY The dummy gauge is attached to the specimen in such a way that it maintains the same temperature as the active strain gauge yet experiences no strain Thus any difference in gauge resistances must be due solely to specimen strain The differential nature of the bridge circuit naturally translates the differential resistance of the two gauges into one voltage signal representing strain If thermistors are used instead of strain gauges this circuit becomes a differential temperature sensor Differential temperature sensing circuits are used in solar heating control systems to detect when the solar collector is hotter than the room or heat storage mass being heated Sensing bridge circuits may have more than one active arm as well The examples you have seen so far in this section have all been quarter activ
83. clothing you are doing work and storing potential energy in the tension between that sock and the rest of the clothing In a similar manner that stored energy could be released to do useful tasks if we placed the sock in some kind of machine that harnessed the return motion as the sock went back to its original place on the pile of laundry inside the dryer 3 1 ELECTRICAL VOLTAGE 75 If we make use of non mechanical means to move electric charge from one location to another the result is no different Moving attracting charges apart from one another means doing work a force exerted over a parallel distance and storing potential energy in that physical tension When we use chemical reactions to move electrons from one metal plate to another in a solution or when we spin a generator and electro magnetically motivate electrons to seek other locations we impart potential energy to those electrons We could express this potential energy in the same unit as we do for mechanical systems the Joule However it is actually more useful to express the potential energy in an electric system in terms of how many joules are available per a specific quantity of electric charge a certain number of electrons This measure of specific potential energy is simply called electric potential or voltage and we measure it in units of Volts in honor of the Italian physicist Alessandro Volta inventor of the first electrochemical battery 1 Joule of potential energ
84. coating such as alumina and the positions of the chemical drops after time distinguishes one component from another Other techniques are automated with machines called chromatographs performing the timed analysis of chemical travel through tightly packed tubular columns 562 CHAPTER 16 CONTINUOUS ANALYTICAL MEASUREMENT Thin layer chromatography Step 1 Step 2 Step 3 Solvent wicks up the plate N Component A Component A Sample As solvent wicks up the surface of the plate it carries along with it all components of the sample spot Each component travels at a different speed separating the components along the plate over time The simplest forms of chromatography reveal the chemical composition of the analyzed mixture as residue retained by the stationary phase In the case of thin layer chromatography the different liquid components of the mobile phase remain embedded in the stationary phase at distinct locations after sufficient developing time The same is true in paper strip chromatography where a simple strip of filter paper serves as the stationary phase through which the mobile phase liquid sample and solvent travels the different components of the sample remain in the paper as residue their relative positions along the paper s length indicating their extent of travel during the test period If the components have different colors the result will be a stratified pattern of colors on the paper
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86. comparison Another detail of phasor math that is both beautiful and practical is the famous expression of Euler s Relation the one all math teachers love because it directly relates several fundamental constants in one elegant equation e 1 If you understand that this equation is nothing more than the fuller version of Euler s Relation with O set to the value of 7 you may draw a few more practical insights from it e e7 cosO isinO e cosT isinr eT 1 10 126 CHAPTER 4 AC ELECTRICITY pr f After seeing this the natural question to ask is what happens when we set equal to other common angles such as 0 5 or 319 cos 0 isin 0 bisi 37 isin 2 0 il Ba ez i We may show all the equivalencies on the complex plane as unit vectors imaginary e 2 i A real imaginary 4 4 PHASOR MATHEMATICS 127 Going back to the result we got for the capacitor s opposition to current 5 we see that we can express the term or j term as it is more commonly written in electronics work as a complex exponential and gain a little more insight V 1 I 1 aC V jar 1 e TEES I wC What this means is that the capacitor s opposition to current takes the form of a phasor pointing down on the complex plane In other words it is a phasor with a fixed angle 35 or 5 radians rather than rotating around the origin like all the v
87. continuously calculate flow rate based on the AGA equation Such multi variable transmitters may provide an analog output for computed flow rate or a digital output where all three primary variables and the computed flow rate may be transmitted to a host system as shown in the previous illustration The Yokogawa EJX910A provides an interesting signal output option a digital pulse signal where each pulse represents a specific quantity either volume or mass of fluid The frequency of this pulse train represents flow rate while the total number of pulses counted over a period of time represents the total amount of fluid that has passed through the orifice plate over that amount of time Liquid flow measurement applications may also benefit from compensation because liquid density changes with temperature Static pressure is not a concern here because liquids are considered incompressible for all practical purposes Thus the formula for compensated liquid flow measurement does not include any terms for static pressure just differential pressure and temperature zV Pr Pall kr T Tres The constant kr shown in the above equation is the proportionality factor for liquid expansion with increasing temperature The difference in temperature between the measured condition T and the reference condition T ef multiplied by this factor determines how much less dense the liquid is compared to its density at the reference temperature
88. controllers and control valves are respective examples of each instrument type However other instruments exist to perform useful functions for us One common auxiliary instrument is the indicator the purpose of which is to provide a human readable indication of an instrument signal Quite often process transmitters are not equipped with readouts for whatever variable they measure they just transmit a standard instrument signal 3 to 15 PSI 4 to 20 mA etc to another device An indicator gives a human operator a convenient way of seeing what the output of the transmitter is without having to connect test equipment pressure gauge for 3 15 PSI ammeter for 4 20 mA and perform conversion calculations Moreover indicators may be located far from their respective transmitters providing readouts in locations more convenient than the location of the transmitter itself An example where remote indication would be practical is shown here in a nuclear reactor temperature measurement system Temperature Temperature indicator transmitter a 4 20 mA signal No human can survive inside the concrete walled containment vessel when the nuclear reactor is operating due to the strong radiation flux around the reactor The temperature transmitter is built to withstand the radiation though and it transmits a 4 to 20 milliamp electronic signal to an 142 CHAPTER 5 INTRODUCTION TO INDUSTRIAL INSTRUMENTATION indicating recorder located outside of
89. conversion technique shows its power by minimizing the number of conversion factors we must memorize We need not memorize how many cubic inches are in a cubic foot or how many square inches are in a square foot if we know how many linear inches are in a linear foot and we simply let the fractions tell us whether a power is needed for unit cancellation A major caveat to this method of converting units is that the units must be directly proportional to one another since this multiplicative conversion method is really nothing more than an exercise in mathematical proportions Here are some examples but not an exhaustive list of conversions that cannot be performed using the unity fraction method e Absolute Gauge pressures because one scale is offset from the other by 14 7 PSI atmospheric pressure e Celsius Fahrenheit because one scale is offset from the other by 32 degrees e Wire diameter gauge number because gauge numbers grow smaller as wire diameter grows larger inverse proportion rather than direct and because there is no proportion relating the two e Power decibels because the relationship is logarithmic rather than proportional The following subsections give sets of physically equal quantities which may be used to create unity fractions for unit conversion problems Note that only those quantities shown in the same line separated by symbols are truly equal to each other not quantities
90. desired measurement accuracy and the degree of permittivity change from one pressure temperature extreme to another In no case should a radar instrument be considered for any level measurement application unless the dielectric constant value s of the upper media are precisely known This is analogous to the dependence on liquid density that hydrostatic level instruments face It is futile to attempt level measurement based on hydrostatic pressure if liquid density is unknown and it is just as futile to attempt level measurement based on radar if the dielectric constants are unknown As with ultrasonic level instruments radar level instruments have the ability to measure the level of solid substances in vessels e g powders and granules The same caveat of repose angle applicable to ultrasonic level measurement see page 392 however is a factor for radar measurement as well When the particulate solid is not very dense i e much air between particles the dielectric constant may be rather low making the material surface more difficult to detect 19 For vented tank level measurement applications where air is the only substance above the point of interest the relative permittivity is so close to a value of 1 that there is little need for further consideration on this point Where the relative permittivity of fluids becomes a problem for radar is in high pressure non air gas applications and liquid liquid interface applications especially w
91. edie ty fn tect SETA a od cal Bes Capacitive ik tao eis ea Se A eo and AO AS E Radiation 2 3 4 44 Feces ee dk o Poe AS AA At ad A 13 10Level sensor accessories ooo ee 13 11Process instrument suitability 2 a 14 Continuous temperature measurement 14 1 14 2 14 3 14 4 14 5 14 6 14 7 Bi metal temperature sensors ee Filled bulb temperature sensors o oo a ee Thermistors and Resistance Temperature Detectors RTDs Mhermocouples merse 472 8 Bredesen eae Ae ee we EARP a PS ee RE ek Optical temperature sensing a a Temperature sensor accessories e a Process instrument suitability 2 o o vil 321 322 326 327 330 337 338 340 342 343 344 347 348 352 357 361 363 367 372 376 382 387 389 390 395 402 403 406 408 409 412 viii 15 16 17 CONTENTS Continuous fluid flow measurement 443 15 1 Pressure based flowmeters o ooa 444 15 1 1 Venturi tubes and basic principles o ooa 0 020 0004 449 15 112 Onficeplates sere ar 2 See a aes A e IE A Bok O A 458 15 1 3 Other differential producers ee 467 15 14 Propet installation 215 0520 Yee eb A Boe PRUE SR ee eo 473 15 1 5 High accuracy flow measurement e ATT 15 186 Equation summary 4 02 une ye be hak AR Pee eh le ee 483 15 2 Laminar flowmeters 0 00 0 ce 485 15 3 Variable area flowmeters oaoa ee 487 15 4 Velocity based flowmeters
92. ee 6 5 3 Instrument bubbles e 6 5 4 Process valve types e o u ae na a e e A a o e o A e aAa E 6 5 5 Valvetactuator types dr a A a a A Be OE aA 6 5 6 Valve failure Mode a a e 6 5 7 Flow measurement devices flowing left to right 6 5 8 Process equipment 0 ee ee ee 6 5 9 SAMA diagram symbols e Discrete process measurement 7 1 Normal status of aswitch ee 52 e Hand SWILCHES 0d a A GI ca Gedo te il a ts Bw Shed os a T TalMitswitGhes sh ed A AA AA A A a a e TA Proximity Switches gucci ot fd Bo Bo fn la ee AA ae ge Me tal at tad de ios Pressure switches d aaneen e AI 2 AAA Sek ad ee ee Rae E 7 6 Level switches ccd ka PE ee AA ee a 7 7 Temperature switches e LS TEIOWASWItCHES tai GPR did ar Gea A oe Ek og aoe A Analog electronic instrumentation 8 1 4 to 20 mA analog current signale e reret ora nakaa e ed e e 8 2 Relating 4 to 20 mA signals to instrument variables 8 2 1 Example calculation controller output to valve 8 2 2 Example calculation flow transmitter e 8 2 3 Example calculation temperature transmitter 8 2 4 Example calculation pH transmitter 0 8 2 5 Example calculation reverse acting I P transducer signal 8 2 6 Graphical interpretation of signal ranges
93. enough quantity to serve as a calibration standard for most industrial applications It is certainly an accessible standard 11 8 PRACTICAL CALIBRATION STANDARDS 287 other standard value An oxygen analyzer intended for the measurement of oxygen concentrations in excess of ambient air would require a different standard most likely a sample of 100 pure oxygen as a calibration reference An analyzer designed to measure the concentration of hydrogen sulfide H2S a toxic gas produced by anaerobic bacterial decomposition of organic matter will require a sample of gas with a precisely known concentration of hydrogen sulfide mixed in it as a calibration reference A typical reference gas concentration might be 25 or 50 parts per million ppm Gas mixtures with such precise concentration values as this may be purchased from chemical laboratories for the purpose of calibrating concentration analyzers and are often referred to as span gases because they are used to set the span of analyzer instruments Analytical instruments are generally subject to greater drifting over time than instruments that measure incidental quantities such as pressure level temperature or flow rate It is not uncommon for instrument technicians to be tasked with daily calibration checks of certain instruments responsible for monitoring atmospheric or water emissions at industrial facilities For this reason it is often practical to equip such critical analyzers with self
94. exchanger will act as a device that provides even consistent temperature oil out for any given temperature and flow rate of oil in One convenient way to throttle steam flow into the heat exchanger is to use a control valve labeled TV because it is a Temperature Valve In general terms a control valve is known as a final control element Other types of final control elements exist servo motors variable flow pumps and other mechanical devices used to vary some physical quantity at will but valves are the most 598 CHAPTER 18 CONTINUOUS FEEDBACK CONTROL common and probably the simplest to understand With a final control element in place the steam flow becomes known as the manipulated variable because it is the quantity we will manipulate in order to gain control over the process variable Steam in l Control signal J Steam out Valves come in a wide variety of sizes and styles Some valves are hand operated that is they have a wheel or other form of manual control that may be moved to pinch off or open up the flow passage through the pipe Other valves come equipped with signal receivers and positioner devices which move the valve mechanism to various positions at the command of a signal usually an electrical signal like the type output by transmitter instruments This feature allows for remote control so that a human operator or computer device may exert control over the manipulated variable f
95. fall faster than light objects due to the resistance of air Energy losses due to air friction nullify our assumption of constant total energy during free fall Energy lost due to air friction never translates to velocity and so the heavier object ends up hitting the ground faster and sooner because it had much more energy than the light object did to start 24 CHAPTER 1 PHYSICS k 2 2 a kg Mass to energy equivalence s s In all three cases the unit for energy is the same kilogram meter squared per second squared This is the fundamental definition of a joule of energy and it is the same result given by all three formulae 1 7 CLASSICAL MECHANICS 25 1 7 3 Mechanical springs Many instruments make use of springs to translate force into motion or visa versa The basic Ohm s Law equation for a mechanical spring relating applied force to spring motion displacement is called Hooke s Law F kzx Where F Force generated by the spring in newtons metric or pounds English k Constant of elasticity or spring constant in newtons per meter metric or pounds per foot English x Displacement of spring in meters metric or feet English Hooke s Law is a linear function just like Ohm s Law is a linear function doubling the displacement either tension or compression doubles the spring s force At least this is how springs behave when they are displaced a small percentage of their tot
96. fill fluid within the capillary tubing Just like the isolating diaphragms of the pressure sensing capsule these remote diaphragms need only transfer process fluid pressure to the fill fluid and ultimately to the taut sensing diaphragm inside the instrument Therefore these diaphragms perform their function best if they are designed 334 CHAPTER 12 CONTINUOUS PRESSURE MEASUREMENT to easily flex This allows the taut sensing diaphragm to provide the vast majority of the opposing force to the fluid pressure as though it were the only spring element in the fluid system The connection point between the capillary tube and the transmitter s sensor capsule is labeled with a warning never to disassemble since doing so would allow air to enter the filled system or fill fluid to escape from the system and thereby ruin its accuracy In order for a remote seal system to work the hydraulic connection between the sealing diaphragm and the pressure sensing element must be completely gas free so that there will be a solid transfer of motion from one end to the other A potential problem with using remote diaphragms is the hydrostatic pressure generated by the fill fluid if the pressure instrument is located far away vertically from the process connection point For example a pressure gauge located far below the vessel it connects to will register a greater pressure than what is actually inside the vessel because the vessel s pr
97. fluid meters per second p Mass density of fluid kilograms per cubic meter u Absolute viscosity of fluid Pascal seconds 3160 G Q Re Di Where Re Reynolds number unitless Gy Specific gravity of liquid unitless Q Flow rate gallons per minute D Diameter of pipe inches u Absolute viscosity of fluid centipoise The Reynolds number of a fluid stream may be used to qualitatively predict whether the flow regime will be laminar or turbulent Low Reynolds number values predict laminar flow where fluid molecules move in straight stream line paths and fluid velocity near the center of the pipe is substantially greater than near the pipe walls Laminar flow l A Velocity Fluid flow gt gt profile aM High Reynolds number values predict turbulent flow where individual molecule motion is chaotic on a microscopic scale and fluid velocities across the face of the flow profile are similar 52 CHAPTER 1 PHYSICS Turbulent flow Velocity profile Fluid flow gt me BPE VO A generally accepted rule of thumb is that Reynolds number values less than 10 000 will probably be laminar while values in excess of 10 000 will probably be turbulent There is no definite threshold value for all fluids and piping configurations though 1 8 FLUID MECHANICS 53 1 8 10 Law of Continuity Any fluid moving through a pipe obeys the Law of Continuity which states that th
98. force If the force stems from pressure applied to some sensing element such as a bellows or diaphragm the string s resonant frequency will indicate fluid pressure A proof of concept device based on this principle might look like this Diaphragm The Foxboro company pioneered this concept in an early resonant wire design of pressure transmitter Later the Yokogawa corporation of Japan applied the concept to a pair of micro machined silicon resonator structures which became the basis for their successful line of DPharp pressure transmitters A photograph of a Yokogawa model EJA110 pressure transmitter with this technology is seen here 4This is an example of a micro electro mechanical system or MEMS 12 3 ELECTRICAL PRESSURE ELEMENTS 309 Even when disassembled the transmitter does not look much different from the more common differential capacitance sensor design Process pressure enters through ports in two flanges presses against a pair of isolating diaphragms transferring motion to the sensing diaphragm where the resonant elements change frequency with diaphragm strain 310 CHAPTER 12 CONTINUOUS PRESSURE MEASUREMENT The important design differences are hidden from view inside the sensing capsule Functionally though this transmitter is much the same as its differential capacitance cousin An interesting advantage of the resonant element pressure sensor is that the sensor signal is very easy to digitize T
99. function of the orifice plate s 8 ratio and Reynolds number appropriate for flange taps Fs Slope factor another polynomial function of the orifice plate s ratio and Reynolds number appropriate for flange taps Fe Fs Ca Discharge coefficient appropriate for flange taps Y Gas expansion factor a function of 8 differential pressure static pressure and specific heats Fi Base pressure factor 14 73 PSI with pressure in PSIA absolute Fi Base temperature factor with temperature in degrees Rankine F Flowing temperature factor na with temperature in degrees Rankine Fyr Real gas relative density factor a Fy Supercompressibility factor Ze hw Differential pressure produced by orifice plate inches water column Py Flowing pressure of gas at the upstream tap PSI absolute 15 2 LAMINAR FLOWMETERS 485 15 2 Laminar flowmeters A unique form of differential pressure based flow measurement deserves its own section in this flow measurement chapter and that is the laminar flowmeter Laminar flow is a condition of fluid motion where viscous internal fluid friction forces greatly overshadow inertial kinetic forces A flowstream in a state of laminar flow exhibits no turbulence with each fluid molecule traveling in its own path with limited mixing and collisions with adjacent molecules The dominant mechanism for resistance to fluid motion in a laminar flow regime is fri
100. gas flow rate 15 4 VELOCITY BASED FLOWMETERS 501 15 4 2 Vortex flowmeters When a fluid moves with high Reynolds number past a stationary object a bluff body there is a tendency for the fluid to form vortices on either side of the object Each vortex will form then detach from the object and continue to move with the flowing gas or liquid one side at a time in alternating fashion This phenomenon is known as vortex shedding and the pattern of moving vortices carried downstream of the stationary object is known as a vortex street It is commonplace to see the effects of vortex shedding on a windy day by observing the motion of flagpoles light poles and tall smokestacks Each of these objects has a tendency to oscillate perpendicular to the direction of the wind owing to the pressure variations caused by the vortices as they alternately form and break away from the object Ae Flagpole looking down from above Win gt O _A et Side to side motion of the flagpole This alternating series of vortices was studied by Vincenc Strouhal in the late nineteenth century and later by Theodore von Karman in the early twentieth century It was determined that the distance between successive vortices downstream of the stationary object is relatively constant and directly proportional to the width of the object for a wide range of Reynolds number values If we view these vortices as crests of a continuous wave the distance between vortice
101. having such small e values the signal would have to pass through the gas liquid interface first in order to reach the liquid liquid interface This gas liquid interface having the greatest difference in e values of any interface within the vessel will be most reflective to radio energy in both directions Thus only a small portion of the incident wave will ever reach the liquid liquid interface and a similarly small portion of the wave reflected off the liquid liquid interface which itself is a fraction of the forward wave power that made it through the gas liquid interface on its way down will ever make it through the gas liquid interface on its way back up to the instrument The situation is much improved if the e values of the two liquid layers are inverted as shown in this hypothetical comparison all calculations assume no power dissipation along the way only reflection at the interfaces 17 Rosemount s Replacing Displacers with Guided Wave Radar technical note states that the difference in dielectric constant between the upper and lower liquids must be at least 10 18 R 0 5285 for the 1 40 interface R 0 02944 for the 40 80 interface and R 0 6382 for the 1 80 interface 400 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT Signal power strengths en route and reflected off of the liquid liquid interface El 100 0 655 100 0 585 As you can see in the illustration the difference in power received back at the instr
102. heat from the home to decrease temperature The job of this control system is to maintain air temperature at some comfortable level with the heater or air conditioner taking action to correct temperature if it strays too far from the desired value called the setpoint Industrial measurement and control systems have their own unique terms and standards which is the primary focus of this lesson Here are some common instrumentation terms and their definitions Process The physical system we are attempting to control or measure Examples water filtration system molten metal casting system steam boiler oil refinery unit power generation unit Process Variable or PV The specific quantity we are measuring in a process Examples pressure level temperature flow electrical conductivity pH position speed vibration Setpoint or SP The value at which we desire the process variable to be maintained at In other words the target value of the process variable 131 Primary Sensing Element or PSE A device that directly senses the process variable and translates that sensed quantity into an analog representation electrical voltage current resistance mechanical force motion etc Examples thermocouple thermistor bourdon tube microphone potentiometer electrochemical cell accelerometer Transducer A device that converts one standardized instrumentation signal into another standardized instrumentation signal and or pe
103. honor of Isaac Newton deal with forces and motions of objects in common circumstances The vast majority of instrumentation applications deals with this realm of physics Two other areas of physics relativistic and quantum will not be covered in this chapter because their domains lie outside the typical experience of industrial instrumentation 5Relativistic physics deals with phenomena arising as objects travel near the velocity of light Quantum physics deals with phenomena at the atomic level Neither is germane to the vast majority of industrial instrument applications 1 7 CLASSICAL MECHANICS 21 1 7 1 Newton s Laws of Motion These laws were formulated by the great mathematician and physicist Isaac Newton 1642 1727 Much of Newton s thought was inspired by the work of an individual who died the same year Newton was born Galileo Galilei 1564 1642 1 An object at rest tends to stay at rest an object in motion tends to stay in motion 2 The acceleration of an object is directly proportional to the net force acting upon it and inversely proportional to the object s mass 3 Forces between objects always exist in equal and opposite pairs Newton s first law may be thought of as the law of inertia because it describes the property of inertia that all objects having mass exhibit resistance to change in velocity Newton s second law is the verbal equivalent of the force mass acceleration formula F ma Newton s
104. illustrates the concept of a preamplifier 16 4 PH MEASUREMENT 559 V pH probe assembly R Cable pH instrument glass The preamplifier does not boost the probes voltage output at all Rather it serves to decrease the impedance the Th venin equivalent resistance of the probes by providing a low resistance relatively high current capacity voltage output to drive the cable and pH instrument By providing a voltage gain of 1 and a very large current gain the preamplifier practically eliminates RC time constant problems caused by cable capacitance and also helps reduce the effect of induced electrical noise As a consequence the practical cable length limit is extended by orders of magnitude Referring back to the Nernst equation we see that temperature plays a role in determining the amount of voltage generated by the glass electrode membrane The calculations we performed earlier predicting the amount of voltage produced by different solution pH values all assumed the same temperature 25 degrees Celsius 298 15 Kelvin If the solution is not at room temperature however the voltage output by the pH probe will not be 59 17 millivolts per pH unit For example if a glass measurement electrode is immersed in a solution having a pH value of 6 0 pH at 70 degrees Celsius 343 15 Kelvin the voltage generated by that glass membrane will be 68 11 mV rather than 59 17 mV as it would be at 25 degrees Celsius That is to say the slop
105. impart a vibratory force to the tubes whereas the sensor coils are both unpowered so they can detect tube motion by generating AC voltages to be sensed by the electronics module The force coil is shown in the left hand photograph while one of the two sensor coils appears in the right hand photograph Advances in sensor technology and signal processing have allowed the construction of Coriolis flowmeters employing straighter tubes than the U tube unit previously illustrated and photographed Straighter tubes are advantageous for reasons of reduced plugging potential and the ability to easily drain all liquids out of the flowmeter when needed 15 5 INERTIA BASED TRUE MASS FLOWMETERS 521 The tubes of a Coriolis flowmeter are not just conduits for fluid flow they are also precision spring elements As such it is important to precisely know the spring constant value of these tubes so that the Coriolis force may be inferred from tube displacement i e how far the tubes twist Every Coriolis flow element is factory tested to determine the flow tubes mechanical properties then the electronic transmitter is programmed with the various constant values describing those properties The following photograph shows a close up view of the nameplate on a Rosemount Micro Motion Coriolis mass flowmeter showing the physical constant values determined for that specific flowtube assembly at the time of manufacture Coriolis flowmeters are equipped w
106. in a fluid stream is neatly expressed in Bernoulli s Equation as a constant sum of elevation pressure and velocity heads see section 1 8 12 on page 55 for more details on this concept 2 2 U v apg E Pi 22g 2 Pa Where z Height of fluid from a common reference point usually ground level p Mass density of fluid g Acceleration of gravity v Velocity of fluid P Pressure of fluid We will use Bernoulli s equation to develop a precise mathematical relationship between pressure and flow rate in a venturi tube To simplify our task we will hold to the following assumptions for our venturi tube system e No energy lost or gained in the venturi tube all energy is conserved e No mass lost or gained in the venturi tube all mass is conserved e Fluid is incompressible 4To see a graphical relationship between fluid acceleration and fluid pressures in a venturi tube examine the illustration found on page 627 15 1 PRESSURE BASED FLOWMETERS 451 e Venturi tube centerline is level no height changes to consider Applying the last two assumptions to Bernoulli s equation we see that the elevation head term drops out of both sides since z p and g are equal at all points in the system 2 v2 pP Ar Pon An P ae ei Now we will algebraically re arrange this equation to show pressures at points 1 and 2 in terms of velocities at points 1 and 2 v3p vip 2 2 Factoring out of the velocity h
107. in that process stream In those cases chromatography is or was at the time of installation the most practical analytical technique to use for quantitative detection of that substance Why else use an inherently multi variable analyzer when you could have used a different single variable technology that was single variable By analogy it is possible to use a Coriolis flowmeter to measure nothing but fluid density even though such a device is fully capable of measuring fluid density and mass flow rate and temperature 19Since the heat of combustion is well known for various components of natural gas methane ethane propane etc all the chromatograph computer needs to do is multiply the different heat values by their respective concentrations in the gas flowstream then average the total heat value per unit volume or mass of natural gas 16 5 CHROMATOGRAPHY 567 This particular GC is used by a natural gas distribution company as part of its pricing system The heating value of the natural gas is used as data to calculate the selling price of the natural gas dollars per standard cubic foot so that the customers pay only for the actual benefit of the gas i e its ability to function as a fuel and not just volumetric or mass quantity Although the column cannot be seen in the photograph of the GC several high pressure steel bottles may be seen in the background holding carrier gas used to wash the natural gas sample through the c
108. in the generation of heat at the resistance according to Joule s Law P PR This dissipated power causes the thermistor or RTD to increase in temperature beyond its surrounding environment introducing a positive measurement error The effect may be minimized by limiting excitation current to a bare minimum but this results in less voltage dropped across the device The smaller the developed voltage the more sensitive the voltage measuring instrument must be to accurately sense the condition of the resistive element Furthermore a decreased signal voltage means we will have a decreased signal to noise ratio all other factors being equal One clever way to circumvent the self heating problem without diminishing excitation current to the point of uselessness is to pulse current through the resistive sensor and digitally sample the voltage only during those brief time periods while the thermistor or RTD is powered This technique works well when we are able to tolerate slow sample rates from our temperature instrument which 426 CHAPTER 14 CONTINUOUS TEMPERATURE MEASUREMENT is often the case because most temperature measurement applications are slow changing by nature The pulsed current technique enjoys the further advantage of reducing power consumption for the instrument an important factor in battery powered temperature measurement applications 14 4 THERMOCOUPLES 427 14 4 Thermocouples When two dissimilar metal wires are joined toge
109. in which the switch is used The answer to this question is that the manufacturer of the sensor has no idea whatsoever as to your intended use The manufacturer of the switch does not know and does not care whether you intend to use their flow switch as a low flow alarm or as a high flow alarm In other words the manufacturer cannot predict what the typical status of your process will be and so the definition of normal status for the switch must be founded on some common criterion unrelated to your particular application That common criterion is the status of minimum stimulus when the sensor is exposed to the least amount of stimulation from the process it senses Here is a listing of normal definitions for various discrete sensor types e Hand switch no one pressing the switch e Limit switch target not contacting the switch e Proximity switch target far away e Pressure switch low pressure or even a vacuum e Level switch low level empty e Temperature switch low temperature cold e Flow switch low flow rate fluid stopped These are the conditions represented by the switch statuses shown in a schematic diagram These may very well not be the statuses of the switches when they are exposed to typical operating conditions in the process 172 CHAPTER 7 DISCRETE PROCESS MEASUREMENT 7 2 Hand switches A hand switch is exactly what the name implies an electrical switch actuated by a person s hand motion These may t
110. industries the unit of degrees Balling was invented This scale was later revised to become the unit of degrees Brix which directly corresponds to the percent concentration of sugar in the liquid The density of tanning liquor may be measured in degrees Bark Milk density may be measured in degrees Sozhlet Vegetable oil density and in older times the density of oil extracted from sperm whales may be measured in degrees Oleo 40 CHAPTER 1 PHYSICS 1 8 4 Manometers Expressing fluid pressure in terms of a vertical liquid column makes perfect sense when we use a very simple kind of motion balance pressure instrument called a manometer A manometer is nothing more than a piece of clear glass or plastic tubing filled with a liquid of known density situated next to a scale for measuring distance The most basic form of manometer is the U tube manometer shown here U tube manometer vented vented gt vented Applied pressure Height difference p Pressure is read on the scale as the difference in height h between the two liquid columns One nice feature of a manometer is that it really cannot become uncalibrated so long as the fluid is pure and the assembly is maintained in an upright position If the fluid used is water the manometer may be filled and emptied at will and even rolled up for storage if the tubes are made of flexible plastic We may build even more sensitive manometers by purposely inclining o
111. industry because pH has a great effect on the outcome of many chemical processes Food processing water treatment pharmaceutical production steam generation thermal power plants and alcohol manufacturing are just some of the industries making extensive use of pH measurement and control pH is also a significant factor in the corrosion of metal pipes and vessels carrying aqueous water based solutions so pH measurement and control is important in the life extension of these capital investments In order to understand pH measurement you must first understand the chemistry of pH Please refer to section 2 7 beginning on page 69 for a theoretical introduction to pH 16 4 1 Colorimetric pH measurement One of the simplest ways to measure the pH of a solution is by color Certain specific chemicals dissolved in an aqueous solution will change color if the pH value of that solution falls within a certain range Litmus paper is a common laboratory application of this principle where a color changing chemical substance infused on a paper strip changes color when dipped in the solution Comparing the final color of the litmus paper to a reference chart yields an approximate pH value for the solution A natural example of this phenomenon is well know to flower gardeners who recognize that hydrangea blossoms change color with the pH value of the soil In essence these plants act as organic litmus indicators This hydrangea plant indicates acidic
112. instruments are simpler in nature than echo based instruments and were practical long before the advent of modern electronic technology Echo based instruments require precision timing and wave shaping circuitry plus sensitive and rugged transceiver elements demanding a much higher level of technology However modern electronic design and instrument manufacturing practices are making echo based level instruments more and more practical for industrial applications At the time of this writing 2008 it is common practice in some industries to replace old displacer level instruments with guided wave radar instruments even in demanding applications operating at high pressures Liquid liquid interfaces may also be measured with some types of echo based level instruments most commonly guided wave radar Echo based level instruments may be fooled by layers of foam resting on top of the liquid and the liquid to liquid interface detection models may have difficulty detecting non distinct interfaces such as emulsions Irregular structures residing within the vapor space of a vessel such as access portals mixer paddles and shafts ladders etc may wreak havoc with echo based level instruments by casting false echoes back to the instrument although this problem may be mitigated by installing guide tubes for the waves to travel in or using wave probes as in the cases of guided wave radar instruments Liquid streams pouring in to the vessel t
113. ions freely exist per unit volume of liquid When a voltage is applied across two points of a liquid solution negative ions will drift toward the positive pole anode and positive ions will drift toward the negative pole cathode In honor of this directional drifting negative ions are sometimes called anions attracted to the anode while positive ions are sometimes called cations attracted to the cathode Electrical conductivity in gases is much the same ions are the charge carriers However with gases at room temperature ionic activity is virtually nonexistent A gas must be superheated into a plasma state before substantial ions exist which can support an electric current 16 3 1 Dissociation and ionization in aqueous solutions Pure water is a very poor conductor of electricity Some water molecules will ionize into unbalanced halves instead of H20 you will find some negatively charged hydroxyl ions OH and some positively charged hydrogen ions H but the percentage is extremely small at room temperature Any substance that enhances electrical conductivity when dissolved in water is called an electrolyte This enhancement of conductivity occurs due to the molecules of the electrolyte separating into positive and negative ions which are then free to serve as electrical charge carriers If the electrolyte in question is an ionically bonded compound table salt is a common example the ions forming that compound naturally s
114. is an entry specifying input calibration and output calibration for each and every instrument in the system This is actually a very important concept to keep in mind when troubleshooting a complex instrumentation system every instrument has at least one input and at least one output with some sort of mathematical relationship between the two Diagnosing where a problem lies within a measurement or control system often reduces to testing various instruments to see if their output responses appropriately match their input conditions For example one way to test the flow transmitter in this system would be to subject it to a number of different pressures within its range specified in the diagram as 0 to 100 inches of water column differential and seeing whether or not the current signal output by the transmitter was consistently proportional to the applied pressure e g 4 mA at 0 inches pressure 20 mA at 100 inches pressure 12 mA at 50 inches pressure etc Given the fact that a calibration error or malfunction in any one of these instruments can cause a problem for the control system as a whole it is nice to know there is a way to determine which instrument is to blame and which instruments are not This general principle holds true regardless of the instrument s type or technology You can use the same input versus output test procedure to verify the proper operation of a pneumatic 3 to 15 PSI level transmitter or an analog electr
115. is completely unknown voltage measurements become useless for quantitative determination of loop current Voltage measurements would be useful only for qualitatively determining loop continuity i e whether there is a break in the wiring between the controller and I P Another example for consideration is this loop powered 4 20 mA transmitter and controller circuit where the controller supplies DC power for the loop Controller 2 wire transmitter A YN jl 2 wire cable ie MO Y 250 Q It is very common to find controllers with their own built in loop power supplies due to the popularity of loop powered 2 wire 4 20 mA transmitters If we know the transmitter requires a DC voltage source somewhere in the circuit to power it up it makes sense to include one in the controller right The only voltage measurement that directly and accurately correlates to loop current is the voltage directly across the 250 ohm precision resistor A loop current of 4 mA will yield a voltage drop of 1 volt 12 mA will drop 3 volts 20 mA will drop 5 volts etc A voltage measurement across the transmitter terminals will show us the difference in voltage between the 26 volt power supply and the voltage dropped across the 250 ohm resistor In other 206 CHAPTER 8 ANALOG ELECTRONIC INSTRUMENTATION words the transmitter s terminal voltage is simply what is left over from the source voltage of 26 volts after subtracting the resistor s voltage drop
116. is not uncommon for calibration tables to show multiple calibration points going up as well as going down for the purpose of documenting hysteresis and deadband errors Note the following example showing a transmitter with a maximum hysteresis of 0 313 the offending data points are shown in bold faced type Percent Input Output current Output current Error of range pressure ideal measured percent of span 0 0 PSI 4 00 mA 3 99 mA 0 0625 25 50 PSI 8 00 mA 7 98 mA 0 125 50 100 PSI 12 00 mA 11 99 mA 0 0625 75 150 PSI 16 00 mA 15 99 mA 0 0625 100 1 200 PSI 20 00 mA 20 00 mA 0 75 150 PSI 16 00 mA 16 01 mA 0 0625 50 100 PSI 12 00 mA 12 02 mA 0 125 25 50 PSI 8 00 mA 8 03 mA 0 188 0 0 PSI 4 00 mA 4 01 mA 0 0625 In the course of performing such a directional calibration test it is important not to overshoot any of the test points If you do happen to overshoot a test point in setting up one of the input conditions for the instrument simply back up the test stimulus and re approach the test point from the same direction as before Unless each test point s value is approached from the proper direction the data cannot be used to determine hysteresis deadband error 11 6 NIST TRACEABILITY 271 11 6 NIST traceability As defined previously calibration means the comparison and adjustment if necessary of an instrument s response to a stimulus o
117. it past the plummet without having to accelerate as much thereby developing less pressure drop across the plummet s body At some point the flowing area reaches a point where the pressure induced force on the plummet body exactly matches the weight of the plummet This is the point in the tube where the plummet stops moving indicating flow rate by it position relative to a scale mounted or etched on the outside of the tube The following rotameter uses a spherical plummet suspended in a flow tube machined from a solid block of clear plastic An adjustable valve at the bottom of the rotameter provides a means for adjusting gas flow 488 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT The same basic flow equation used for pressure based flow elements holds true for rotameters as well Q k P P However the difference in this application is that the value of the radicand is constant since the pressure difference will remain constant and the fluid density will likely remain constant as well Thus amp will change in proportion to Q The only variable within k relevant to plummet position is the flowing area between the plummet and the tube walls Most rotameters are indicating devices only They may be equipped to transmit flow information electronically by adding sensors to detect the plummet s position in the tube but this is not common practice 161f we know that the plummet s weight will remain constant its area will rem
118. itself An interesting alternative to a formal equation for linearizing the level measurement signal is to use something called a multi segment characterizer function also implemented in a digital computer This is an example of what mathematicians call a piecewise function a function made up of line segments Multi segment characterizer functions may be programmed to emulate virtually any continuous function with reasonable accuracy 588 CHAPTER 17 SIGNAL CHARACTERIZATION Continuous characterizing function Piecewise characterizing function Full Full V V Empty Empty 0 h D 0 h D The computer correlates the input signal height measurement h to a point on this piecewise function linearly interpolating between the nearest pair of programmed coordinate points The number of points available for multi point characterizers varies between ten and one hundred depending on the desired accuracy and the available computing power Although true fans of math might blanch at the idea of approximating an inverse function for level measurement using a piecewise approach rather than simply implementing the correct continuous function the multi point characterizer technique does have certain practical advantages For one it is readily adaptable to any shape of vessel no matter how strange Take for instance this vessel made of separate cylindrical sections welded together z a Empty V Full Here the vessel s very own height volume funct
119. least another half cycle of oscillation A similar problem called reset windup or integral windup happens when external conditions make it impossible for the controller to hold the process variable equal to setpoint Imagine what would happen in the heat exchanger system if the steam boiler suddenly stopped producing steam As outlet temperature dropped the controller s proportional action would open up the control valve 18 5 INTEGRAL RESET CONTROL 613 in a futile effort to raise temperature If and when steam service is restored proportional action would just move the valve back to its original position as the process variable returned to its original value before the boiler died This is how a proportional only controller would respond to a steam outage nice and predictably If the controller had integral action however a much worse condition would result All the time spent with the outlet temperature below setpoint causes the controller s integral term to wind up in a futile attempt to admit more steam to the heat exchanger This accumulated quantity can only be un done by the process variable rising above setpoint for an equal error time product which means when the steam supply resumes the temperature will rise well above setpoint until the integral action finally unwinds and brings the control valve back to a sane position again Various techniques exist to manage integral windup Controllers may be built with
120. length meters Fr String tension newtons u Unit mass of string kilograms per meter This means fluid density along with fluid temperature is another variable measured by a Coriolis flowmeter The ability to simultaneously measure these three variables mass flow rate temperature and density makes the Coriolis flowmeter a very versatile instrument indeed This is especially true when the flowmeter in question communicates digitally using a fieldbus standard rather than an analog 4 20 mA signal Fieldbus communication allows multiple variables to be transmitted by the device to the host system and or to other devices on the same fieldbus network allowing the Coriolis flowmeter to do the job of three instruments An example of a Coriolis mass flowmeter being used as a multi variable transmitter appears in the following photographs Note the instrument tag labels in the close up photograph FT TT and DT documenting its use as a flow transmitter temperature transmitter and density transmitter respectively Even though a Coriolis flowmeter inherently measures mass flow rate the continuous measurement of fluid density allows the meter to calculate volumetric flow rate if this is the preferred means of expressing fluid flow The relationship between mass flow W volumetric flow Q and mass density p is quite simple W pQ Q All the flowmeter s computer must do to output a volumetric flow measurement is take th
121. limits to restrict how far the integral term can accumulate under adverse conditions In some controllers integral action may be turned off completely if the error exceeds a certain value The surest fix for integral windup is human operator intervention by placing the controller in manual mode This typically resets the integral accumulator to a value of zero and loads a new value into the bias term of the equation to set the valve position wherever the operator decides Operators usually wait until the process variable has returned at or near setpoint before releasing the controller into automatic mode again While it might appear that operator intervention is again a problem to be avoided as it was in the case of having to correct for proportional only offset it is noteworthy to consider that the conditions leading to integral windup usually occur only during shut down conditions It is customary for human operators to run the process manually anyway during a shutdown and so the switch to manual mode is something they would do anyway and the potential problem of windup often never manifests itself 614 CHAPTER 18 CONTINUOUS FEEDBACK CONTROL 18 6 Derivative rate control The final facet of PID control is the D term which stands for derivative This is a calculus concept like integral except most people consider it easier to understand Simply put derivative is the expression of a variable s rate of change with respect to another
122. m Mass of sample component in micrograms W Instantaneous mass flow rate of sample component in micrograms per minute t Time in minutes t and tz are the interval times between which total mass is calculated This mathematical relationship may be seen in graphical form by shading the area underneath the peak of a chromatogram Area accumulated under the curve t represents the total mass of that 2 component passed through the e detector between times t and t D W 0 sea S t tz ug ug min 2 D m A A e er E aE S Time min Since process chromatographs have the ability to independently analyze the quantities of multiple components in a chemical sample these instruments are inherently multi variable A single analog in the carrier The inconsistent response of a chromatograph detector to different sampled components is not as troubling a problem as one might think though Since the chromatograph column does a good job separating each component from the other over time we may program the computer to re calibrate itself for each component at the specific time s each component is expected to exit the column So long as we know in advance the characteristic detector response for each expected compound separated by the chromatograph we may easily compensate for those variations in real time so that the chromatogram consistently and accurately represents component concentrations over the entire analysis cycle
123. measurement errors induced from severe disturbances as far as 60 to 100 pipe diameters upstream of the primary flow element ATA CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT illustration shows the effect of a pipe elbow on a flowstream and how the velocity profile returns to a normal symmetrical form after traveling through a sufficient length of straight pipe H Straight pipe length Velocity profile Velocity profile Velocity profile asymmetrical still somewhat asymmetrical symmetrical Recommendations for minimum upstream and downstream straight pipe lengths vary significantly with the nature of the turbulent disturbance piping geometry and flow element As a general rule elements having a smaller beta ratio ratio of throat diameter d to pipe diameter D are more tolerant of disturbances with profiled flow e g venturi tubes flow tubes having the greatest tolerance Ultimately you should consult the flow element manufacturer s documentation for a more detailed recommendation appropriate to any specific application In applications where sufficient straight run pipe lengths are impractical another option exists for taming turbulence generated by piping disturbances Devices called flow conditioners may be installed upstream of the flow element to help the flow profile achieve symmetry in a far shorter distance than simple straight pipe could do alone Flow conditioners take the form of a series of tubes or
124. metal with circular corrugations in it so that it looks like the bellows fabric on an accordion Pneumatic pressure applied to the interior of the bellows causes it to elongate If the metal of the bellows is flexible enough so it does not naturally restrain the motion of expansion the force generated by the expansion of the bellows will almost exactly equal that predicted by the force pressure area equation Force Bellows Applied pressure If the bellows expansion is externally restrained so it does not stretch appreciably and therefore the metal never gets the opportunity to act as a restraining spring the force exerted by the bellows on that restraining object will exactly equal the pneumatic pressure multiplied by the cross sectional area of the bellows end 218 CHAPTER 9 PNEUMATIC INSTRUMENTATION Applying this to the problem of the self balancing laboratory scale imagine fixing a bellows to the frame of the scale so that it presses downward on the pan where the brass weights normally go then connecting the bellows to the nozzle backpressure Tube Air supply A Orifice Now the scale will self balance When mass is added to the left hand pan the pointer baffle will move ever so slightly toward the nozzle until enough backpressure builds up behind the nozzle to make the bellows exert the proper amount of balancing force and bring the pointer back very close to its original balanced condition This b
125. much more accurate In the case of conductivity measurement it is not wire resistance that we care to ignore but rather the added resistance caused by plating of the electrodes By using four electrodes instead of two we are able to measure voltage dropped across a length of liquid solution only and completely ignore the resistive effects of electrode plating Current source 546 CHAPTER 16 CONTINUOUS ANALYTICAL MEASUREMENT In the 4 wire conductivity cell any electrode plating will merely burden the current source by causing it to output a greater voltage but it will not affect the amount of voltage detected by the two inner electrodes as that electric current passes through the liquid Some conductivity instruments employ a second voltmeter to measure the voltage dropped between the excitation electrodes to indicate electrode fouling Current source I Second voltmeter Any form of electrode fouling will cause this secondary voltage measurement to rise thus providing an indicator that instrument technicians may use for predictive maintenance telling them when the probes need cleaning or replacement Meanwhile the primary voltmeter will do its job of accurately measuring liquid conductivity so long as the current source is still able to output its normal amount of current 16 3 4 Electrodeless conductivity probes An entirely different design of conductivity cell called electrodeless uses electromagnetic induction
126. no permanent pressure loss 1 8 FLUID MECHANICS 59 Piezometer Piezometer Piezometer Ground level If we add three more piezometers to the venturi tube assembly each one equipped with its own Pitot tube facing upstream to catch the velocity of the fluid we see that total energy is indeed conserved at every point in the system Here each of the heads represented in Bernoulli s equation are shown in relation to the different piezometer heights z a constant 29 J v 2g v 2 Ye energy line p g UL P y v3 28 Py PAY 60 CHAPTER 1 PHYSICS A more realistic scenario would show the influence of energy lost in the system due to friction Here the total energy is seen to decrease as a result of friction energy line rae ace Ji sy Py v3 2g References Chow Ven Te Open Channel Hydraulics McGraw Hill Book Company Inc New York NY 1959 Giancoli Douglas C Physics for Scientists amp Engineers Third Edition Prentice Hall Upper Saddle River New Jersey 2000 Lipt k B la G Instrument Engineers Handbook Process Measurement and Analysis Volume I Fourth Edition CRC Press New York NY 2003 Miller Richard W Flow Measurement Engineering Handbook Second Edition McGraw Hill Publishing Company New York NY 1989 Rouse Hunter Characteristics of Laminar and Turbulent Flow video Iowa Institute of Hydraulic Research University of Iowa Shapiro Ascher H
127. nothing touching the switch actuator mechanism Limit switches find many uses in industry particular in robotic control and CNC Computer Numerical Control machine tool systems In many motion control systems the moving elements have home positions where the computer assigns a position value of zero For example the axis controls on a CNC machine tool such as a lathe or mill all return to their home positions upon start up so the computer can know with confidence the starting locations of each piece These home positions are detected by means of limit switches The computer commands each servo motor to travel fully in one direction until a limit switch on each axis trips The position counter for each axis resets to zero as soon as the respective limit switch detects that the home position has been reached A typical limit switch design uses a roller tipped lever to make contact with the moving part Screw terminals on the switch body provide connection points with the NC and NO contacts inside the switch Most limit switches of this design share a common terminal between the NC and NO contacts like this Push lever down to actuate Equivalent schematic Roller tip This switch contact arrangement is sometimes referred to as a form C contact set since it incorporates both a form A contact normally open as well as a form B contact normally closed 174 CHAPTER 7 DISCRETE PROCESS MEASUREMENT 7 4 PROXIMITY SW
128. numerator of the first fraction cancels with the PSI unit in the denominator of the second fraction leaving inches of water column W C as the only unit standing Multiplying the first fraction 35 PSI over 1 by the second fraction 27 68 W C over 1 PSI is legal to do since the second fraction has a physical value of unity 1 being that 27 68 inches of water column is the same physical pressure as 1 PSI the second fraction is really the number 1 in disguise As we know multiplying any quantity by unity does not change its value so the result of 968 8 W C we get has the exact same physical meaning as the original figure of 35 PSI If however we wished to express the car s tire pressure in terms of inches of water column absolute in reference to a perfect vacuum we would have to include the 14 7 PSI offset in our calculation and do the conversion in two steps 35 PSIG 14 7 PSI 49 7 PSIA 44 CHAPTER 1 PHYSICS 49 7PSIA 27 68 W C A 1 IPSA The proportion between inches of water column and pounds per square inch is still the same 27 68 in the absolute scale as it is in the gauge scale The only difference is that we included the 14 7 PSI offset in the very beginning to express the tire s pressure on the absolute scale rather than on the gauge scale From then on all conversions were in absolute units There are some pressure units that are always in absolute terms One is the unit of atmosph
129. o a 8 3 Controller output current loops ee 8 4 4 wire sel powered transmitter current loops o o o 8 5 2 wire loop powered transmitter current loops o o 8 6 Troubleshooting current loops e 146 147 149 151 153 156 160 160 160 161 162 163 164 165 166 167 169 170 172 173 175 179 181 183 185 187 vi CONTENTS 9 Pneumatic instrumentation 209 9 1 Pneumatic sensing elements 2 0 00 00 e 213 9 2 Self balancing pneumatic instrument principles 04 216 9 3 Pilot valves and pneumatic amplifying relays o o 220 9 4 Analogy to opamp Circuits 228 9 5 Analysis of a practical pneumatic instrument 2 2 200 237 9 6 Proper care and feeding of pneumatic instruments 242 9 7 Advantages and disadvantages of pneumatic instruments 243 10 Digital electronic instrumentation 245 10 1 The HART digital analog hybrid standard 2 0044 246 10 1 1 HART multidrop mode 0 000000 eee ee 252 10 1 2 HART multi variable transmitters o 253 10 2 Fieldbus standards m a cama a A ee ead 254 10 3 Wireless instrumentation 2 pp e a a a a e a ee 255 11 Instrument calibration 257 11 1 The meaning of calibration e 257 11 2 Zero and span adjustments analog transmitters o oo a 258 11 3 LRV and URV
130. of gravity Fweight mg and the constant g cancels out of both numerator and denominator Mary M ry9 Dry weight Specific Gravity gt i peci ravity Mary Mwet MaryJ Mweig Dry weight Wet weight 1 8 FLUID MECHANICS 47 1 8 7 Gas Laws The Ideal Gas Law relates pressure volume molecular quantity and temperature of an ideal gas together in one neat mathematical expression PV nRT Where P Absolute pressure atmospheres V Volume liters n Gas quantity moles R Universal gas constant 0 0821 L atm mol K T Absolute temperature K An alternative form of the Ideal Gas Law uses the number of actual gas molecules N instead of the number of moles of molecules n PV NkT Where P Absolute pressure atmospheres V Volume liters N Gas quantity moles k Boltzmann s constant 1 38 x 107 J K T Absolute temperature K Although no gas in real life is ideal the Ideal Gas Law is a close approximation for conditions of modest gas density and no phase changes gas turning into liquid or visa versa Since the molecular quantity of an enclosed gas is constant and the universal gas constant must be constant the Ideal Gas Law may be written as a proportionality instead of an equation PV xT Several gas laws are derived from this Ideal Gas Law They are as follows PV Constant Boyle s Law assuming constant temperature T VxT Charles s Law assuming constant
131. of the water displaced is equal to the total weight of the ship and all it holds cargo crew food fuel etc D Amount of water displaced by the ship If we could somehow measure the weight of that water displaced we would find it exactly equals the dry weight of the ship Archimedes Principle also explains why hot air balloons and helium aircraft float By filling a large enclosure with a gas that is less dense than the surrounding air that enclosure experiences an upward buoyant force equal to the difference between the weight of the air displaced and the weight of the gas enclosed If this buoyant force equals the weight of the craft and all it holds cargo crew food fuel etc it will exhibit an apparent weight of zero which means it will float If the buoyant force exceeds the weight of the craft the resultant force will cause an upward acceleration according to Newton s Second Law of motion F ma Submarines also make use of Archimedes Principle adjusting their buoyancy by adjusting the amount of water held by ballast tanks on the hull Positive buoyancy is achieved by blowing water out of the ballast tanks with high pressure compressed air so that the submarine weighs less but still occupies the same hull volume and therefore displaces the same amount of water Negative buoyancy is achieved by flooding the ballast tanks so that the submarine weighs more Neutral buoyancy is when the buoyant f
132. ohms between the DC power source and all other HART devices like this HART transmitter Power supply 250 lt R lt 1100 Oo Computer HART communicator Loop resistance must be at least 250 ohms to allow the 1 mA P P AC signal to develop enough voltage to be reliably detected by the HART modem in the listening device The upper limit 1100 250 CHAPTER 10 DIGITAL ELECTRONIC INSTRUMENTATION ohms is not a function of HART communication so much as it is a function of the DC voltage drop and the need to maintain a minimum DC terminal voltage at the transmitter for its own operation If there is too much loop resistance the transmitter will become starved of voltage and act erratically In fact 1100 ohms of loop resistance may even be excessive if the DC power supply voltage is too low Loop resistance is also necessary for the HART transmitter to receive data signals transmitted by the HART communicator If we analyze the circuit when the HART communicator s current source is active we get this result HART transmitter Power supply 250 lt R lt 1100 Computer HART communicator Without the loop resistance in place the DC power supply would short out the communicator s AC current signal just as effectively as it shorted out the transmitter s AC current signal The presence of a loop resistor in the circuit provides a place for an AC voltage to develop in response to the AC current injected
133. or d can affect the probe s capacitance Capacitive level probes come in two basic varieties one for conductive liquids and one for non conductive liquids If the liquid in the vessel is conductive it cannot be used as the dielectric insulating medium of a capacitor Consequently capacitive level probes designed for conductive liquids are coated with plastic or some other dielectric substance so that the metal probe forms one plate of the capacitor and the conductive liquid forms the other Probe Terminals NG Dielectric Metal vessel sheath Vapor Fa In this style of capacitive level probe the variable is distance d since the conductive liquid essentially acts to bring the vessel wall electrically closer to the probe This means total capacitance 13 8 CAPACITIVE 407 will be greatest when the vessel is full effective distance d is at a minimum and least when the vessel is empty If the liquid is non conductive it may be used as the dielectric itself with the metal wall of the storage vessel forming the second capacitor plate Probe Terminals NG Metal vessel Vapor In this style of capacitive level probe the variable is permittivity e provided the liquid has a substantially greater permittivity than the vapor space above the liquid This means total capacitance will be greatest when the vessel is full average permittivity e is at a maximum and least when the vessel is empty Permittivity of th
134. or lb ft p Mass density of liquid in kilograms per cubic meter metric or slugs per cubic foot British g Acceleration of gravity 9 8 meters per second squared or 32 feet per second squared y Weight density of liquid in newtons per cubic meter metric or pounds per cubic foot British h Vertical height of liquid column Dimensional analysis vindicates these formulae in their calculation of hydrostatic pressure Taking the second formula as an example P yh fel Le Ls As you can see the unit of feet in the height term cancels out one of the feet units in the denominator of the density term leaving an answer for pressure in units of pounds per square foot If one wished to set up the problem so that the answer presented in a more common pressure unit such as pounds per square inch both the liquid density and height would have to be expressed in appropriate units pounds per cubic inch and inches respectively 1 8 FLUID MECHANICS 37 Applying this to a realistic problem consider the case of a tank filled with 8 feet vertical of castor oil having a weight density of 60 5 pounds per cubic foot This is how we would set up the formula to calculate for hydrostatic pressure at the bottom of the tank P vyh 60 5 Ib 8 ft p ft ye 484 lb ft If we wished to convert this result into a more common unit such as PSI pounds per square inch we could do so using an appropriate fraction of conversion un
135. or undershoot With plain proportional control however this ideal goal is nearly impossible 608 CHAPTER 18 CONTINUOUS FEEDBACK CONTROL 18 4 Proportional only offset Another shortcoming of proportional control has to do with changes in process load A load in a controlled process is any variable subject to change which has an impact on the variable being controlled the process variable but is not subject to correction by the controller In other words a load is any variable in the process we cannot or do not control yet affects the process variable we are trying to control In our hypothetical heat exchanger system the temperature of the incoming process fluid is an example of a load Steam in l Changes in incoming feed temperature constitute a load on the process gt Steam out If the incoming fluid temperature were to suddenly decrease the immediate effect this would have on the process would be to decrease the outlet temperature which is the temperature we are trying to maintain at a steady value It should make intuitive sense that a colder incoming fluid will require more heat input to raise it to the same outlet temperature as before If the heat input remains the same at least in the immediate future this colder incoming flow must make the outlet flow colder than it was before Thus incoming feed temperature has an impact on the outlet temperature whether we like it or not and the control s
136. order to use the strapping table option the user would have to select Strapping Table from the list of Tank Types Otherwise the level transmitter s computer will attempt to calculate volume from an ideal tank shape 3The configuration software is Emerson s AMS running on an engineering workstation in a DeltaV control system network The radar level transmitter is a Rosemount model 3301 guided wave unit 17 3 RADIATIVE TEMPERATURE MEASUREMENT 591 17 3 Radiative temperature measurement Temperature measurement devices may be classified into two broad types contact and non contact Contact type temperature sensors detect temperature by directly touching the material to be measured and there are several varieties in this category Non contact temperature sensors work by detecting light emitted by hot objects Energy radiated in the form of electromagnetic waves photons or light relates to object temperature by an equation known as the Stefan Boltzmann equation which tells us the rate of heat lost by radiant emission from a hot object is proportional to the fourth power of its absolute temperature P ecAT Where P Radiated energy power watts e Emissivity factor unitless o Stefan Boltzmann constant 5 67 x 1078 W m K A Surface area square meters T Absolute temperature Kelvin Solving for temperature T involves the use of the fourth root to un do the fourth power function inherent to t
137. particular process chemistry to avoid reliability problems later References Beckerath Alexander von Eberlein Anselm Julien Hermann Kersten Peter and Kreutzer Jochem WIKA Handbook Pressure and Temperature Measurement WIKA Alexander Wiegand GmbH amp Co Klingenberg Germany 1995 Fribance Austin E Industrial Instrumentation Fundamentals McGraw Hill Book Company New York NY 1962 Irwin J David The Industrial Electronics Handbook CRC Press Boca Raton FL 1997 Kallen Howard P Handbook of Instrumentation and Controls McGraw Hill Book Company Inc New York NY 1961 Lipt k B la G Instrument Engineers Handbook Process Measurement and Analysis Volume I Fourth Edition CRC Press New York NY 2003 442 CHAPTER 14 CONTINUOUS TEMPERATURE MEASUREMENT Chapter 15 Continuous fluid flow measurement Fluid flow may be measured volumetrically or by mass Volumetric flow is expressed in volume units e g gallons liters cubic inches per unit time Mass flow is expressed in mass units slugs kilograms pounds mass per unit time Liquids are essentially incompressible that is they do not easily yield in volume to applied pressure Gases and vapors however easily change volume under the influence of changing pressure In other words a gas will yield to an increasing pressure by decreasing in volume as the gas molecules are forced closer together This makes volumetric flow measurement more comp
138. pascals newtons per square meter for pressure and newtons per cubic meter for weight density 1 8 FLUID MECHANICS 57 1 8 13 Torricelli s equation The velocity of a liquid stream exiting from a nozzle pressured solely by a vertical column of that same liquid is equal to the free fall velocity of a solid mass dropped from the same height as the top of the liquid column In both cases potential energy in the form of vertical height converts to kinetic energy motion This was discovered by Evangelista Torricelli almost 100 years prior to Bernoulli s more comprehensive formulation The velocity may be determined by solving for v after setting the potential and kinetic energy formulae equal to each other since all potential energy at the upper height must translate into kinetic energy at the bottom assuming no frictional losses 1 mgh gn 1 gh o 2gh v v y 2gh Note how mass m simply disappears from the equation neatly canceling on both sides This means the nozzle velocity depends only on height not the mass density of the liquid It also means the velocity of the falling object depends only on height not the mass of the object 58 CHAPTER 1 PHYSICS 1 8 14 Flow through a venturi tube If an incompressible fluid moves through a venturi tube a tube purposefully built to be narrow in the middle the continuity principle tells us the fluid velocity must increase through the narrow portion This increase in v
139. paths for liquid to move in and out simultaneously any flow rate calculated on change in quantity will be a net flow rate only It is impossible to use this flow measurement technique to measure one flow out of multiple flows common to one liquid storage vessel A simple thought experiment confirms this fact Imagine a water storage vessel receiving a flow rate in at 200 gallons per minute Next imagine that same vessel emptying water out of a second pipe at the exact same flow rate 200 gallons per minute With the exact same flow rate both entering and exiting the vessel the water level in the vessel will remain constant Any change of quantity flow measurement system would register zero change in mass or volume over time consequently calculating a flow rate of absolutely zero Truly the net flow rate for this vessel is zero but this tells us nothing about the flow in each pipe except that those flow rates are equal in magnitude and opposite in direction 33 To be precise the equation describing the function of this analog differentiator circuit is Vout RC Min The negative sign is an artifact of the circuit design being essentially an inverting amplifier with negative gain and not an essential element of the math 532 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT 15 10 Insertion flowmeters This section does not describe a particular type of flowmeter but rather a design that may be implemented for several differen
140. per centimeter may seem odd at first but it is necessary to account for all the units present in the variables of the equation A simple dimensional analysis proves this s 2 cm em For any particular conductivity cell the geometry may be expressed as a ratio of separation distance to plate area usually symbolized by the lower case Greek letter Theta 0 and always expressed in the unit of inverse centimeters cm 0 A Re writing the conductance equation using 0 instead of A and d we see that conductance is the quotient of conductivity k and the cell constant 0 C 7 Where G Conductance in Siemens S k Specific conductivity of liquid in Siemens per centimeter S cm 0 Cell constant in inverse centimeters cm7 Manipulating this equation to solve for conductivity k given electrical conductance G and cell constant 0 we have the following result k G0 Two electrode conductivity cells are not very practical in real applications because mineral and metal ions attracted to the electrodes tend to plate the electrodes over time forming solid insulating barriers on the electrodes While this electroplating action may be substantially reduced by using AC instead of DC to excite the sensing circuit it is usually not enough Over time the conductive barriers formed by ions bonded to the electrode surfaces will create calibration errors by making the instrument think the liquid i
141. photograph of an actual curved tube manometer This particular specimen does not have a scale reading in units of flow but it certainly could if it had the correct curve for a square root characterization A more sophisticated solution to the square root problem is to use a computer to manipulate the signal coming from the differential pressure instrument so that the characterized signal becomes a direct linear representation of flow In other words the computer square roots the pressure sensor s signal in order that the final signal becomes a direct representation of fluid flow rate 580 CHAPTER 17 SIGNAL CHARACTERIZATION Differential Indicati ressure l ndicatin instrument Characterizer gauge s i 1 Vena contracta Direction of flow Both solutions achieve their goal by mathematically un doing the nonlinear square function intrinsic to the physics of the orifice plate with a complementary inverse function This intentional compounding of inverse functions is sometimes called linearization because it has the overall effect of making the output of the instrument system a direct proportion of the input Output k Input Fluid flow rate measurement in pipes is not the only application where we find nonlinearities complicating the task of measurement Several other applications exhibit similar challenges e Liquid flow measurement in open channels over weirs e Liquid level measurement in non cylindrical vess
142. photograph shows a typical industrial combination pH electrode The red colored plastic cap on the right hand end of this combination electrode covers and protects a gold plated coaxial electrical connector to which the voltage sensitive pH indicator or transmitter attaches 504 CHAPTER 16 CONTINUOUS ANALYTICAL MEASUREMENT Another model of pH probe appears in the next photograph Here there is no protective plastic cap covering the probe connector allowing a view of the gold plated connector bars A close up photograph of the probe tip reveals the glass measurement bulb a weep hole for process liquid to enter the reference electrode assembly internal to the white plastic probe body and a metal solution ground electrode 16 4 PH MEASUREMENT 555 It is extremely important to always keep the glass electrode wet Its proper operation depends on complete hydration of the glass which allows hydrogen ions to penetrate the glass and develop the Nernst potential The probes shown in these photographs are shown in a dry state only because they have already exhausted their useful lives and cannot be damaged any further by dehydration The process of hydration so essential to the working of the glass electrode is also a mechanism of wear Layers of glass slough off over time if continuously hydrated which means that glass pH electrodes have a limited life whether they are being used to measure the pH of a process solution
143. predictably throughout the entire range of operation We may express this expectation in the form of a graph showing how the input and output of an instrument should relate URV 100 Output 50 LRV 0 0 50 100 LRV Input URV This graph shows how any given percentage of input should correspond to the same percentage of output all the way from 0 to 100 Things become more complicated when the input and output axes are represented by units of measurement other than percent Take for instance a pressure transmitter a device designed to sense a fluid pressure and output an electronic signal corresponding to that pressure Here is a graph for a pressure transmitter with an input range of 0 to 100 pounds per square inch PSI and an electronic output signal range of 4 to 20 milliamps mA electric current 11 2 ZERO AND SPAN ADJUSTMENTS ANALOG TRANSMITTERS 259 URV 20 mA Output 2 ma current LRV 4mA OmA 0 PSI 50 PSI 100 PSI LRV Input pressure URV Although the graph is still linear zero pressure does not equate to zero current This is called a live zero because the 0 point of measurement 0 PSI fluid pressure corresponds to a non zero live electronic signal 0 PSI pressure may be the LRV Lower Range Value of the transmitter s input but the LRV of the transmitter s output is 4 mA not 0 mA Any linear mathematical function may be expressed in slope intercept equation form y ma b Where y
144. pressure P PxT Gay Lussac s Law assuming constant volume V You will see these laws referenced in explanations where the specified quantity is constant or very nearly constant 48 CHAPTER 1 PHYSICS For non ideal conditions the Real Gas Law formula incorporates a corrected term for the compressibility of the gas PV ZnRT Where P Absolute pressure atmospheres V Volume liters Z Gas compressibility factor unitless n Gas quantity moles R Universal gas constant 0 0821 L atm mol K T Absolute temperature K The compressibility factor for an ideal gas is unity Z 1 making the Ideal Gas Law a limiting case of the Real Gas Law Real gases have compressibility factors less than unity lt 1 1 8 FLUID MECHANICS 49 1 8 8 Fluid viscosity Viscosity is a measure of a fluid s internal friction The more viscous a fluid is the thicker it is when stirred Clean water is an example of a low viscosity liquid while honey at room temperature is an example of a high viscosity liquid There are two different ways to quantify the viscosity of a fluid absolute viscosity and kinematic viscosity Absolute viscosity symbolized by the Greek symbol eta 7 or sometimes by the Greek symbol mu u also known as dynamic viscosity is a direct relation between stress placed on a fluid and its rate of deformation or shear The textbook definition of absolute viscosity is based on a mode
145. pressure fluctuations in the supply line Another killer of pneumatic instruments is mechanical vibration These are precision mechanical devices so they do not generally respond well to repeated shaking At the very least calibration adjustments may loosen and shift causing the instrument s accuracy to suffer At worst actual failure may result from component breakage Having said this pneumatic instruments can be remarkably rugged devices I once worked on a field mounted 9 7 ADVANTAGES AND DISADVANTAGES OF PNEUMATIC INSTRUMENTS 243 9 7 Advantages and disadvantages of pneumatic instruments The disadvantages of pneumatic instruments are painfully evident to anyone familiar with both pneumatic and electronic instruments Sensitivity to vibration changes in temperature mounting position and the like affect calibration accuracy to a far greater degree for pneumatic instruments than electronic instruments Compressed air is an expensive utility much more expensive per equivalent watt hour than electricity making the operational cost of pneumatic instruments far greater than electronic The installed cost of pneumatic instruments can be quite high as well given the need for special stainless steel copper or tough plastic tubes to carry supply air and pneumatic signals to distant locations The volume of air tubes used to convey pneumatic signals over distances acts as a low pass filter naturally damping the instrument
146. pressure in the compensating leg is constant y4h4 Constant since the fill fluid never changes density and the height never changes This means the transmitter s sensed pressure will differ from that of an uncompensated transmitter merely by a constant offset which may be calibrated out so as to have no impact on the measurement y h yah Constant At first it may seem as though determining the calibration points lower and upper range values LRV and URV for a hydrostatic interface level transmitter is impossibly daunting given all the different pressures involved A recommended problem solving technique to apply here is that of a thought experiment where we imagine what the process will look like at lower range value condition and at the upper range value condition drawing two separate illustrations For example suppose we must calibrate a differential pressure transmitter to measure the interface level between two liquids having specific gravities of 1 1 and 0 78 respectively over a 378 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT span of 3 feet The transmitter is equipped with remote seals each containing a halocarbon fill fluid with a specific gravity of 1 09 The physical layout of the system is as follows Fill fluid S G 1 09 S EE N Electronic output signal As the first step in our thought experiment we imagine what the process would look like with the interface at the LRV level calcul
147. primitive form of conductivity sensor sometimes referred to as a conductivity cell consists of two metal electrodes inserted in the solution connected to a circuit designed to measure conductance G the reciprocal of resistance Voltage source Ammeter Distance d The conductance measured by this instrument is a function of plate geometry surface area and distance of separation as well as the ionic activity of the solution A simple increase in separation distance between the probe electrodes will result in a decreased conductance measurement increased resistance R even if the liquid solution s ionic properties do not change Therefore conductance G is not particularly useful as an expression of liquid conductivity The mathematical relationship between conductance G plate area A plate distance d and the actual conductivity of the liquid k is expressed in the following equation A G k2 d 4This equation bears a striking similarity to the equation for resistance of metal wire R p where l is the length of a wire sample A is the cross sectional area of the wire and p is the specific resistance of the wire metal 544 CHAPTER 16 CONTINUOUS ANALYTICAL MEASUREMENT Where G Conductance in Siemens S k Specific conductivity of liquid in Siemens per centimeter S cm A Electrode area each in square centimeters cm d Electrode separation distance in centimeters cm The unit of Siemens
148. process changes 616 CHAPTER 18 CONTINUOUS FEEDBACK CONTROL 18 7 PID controller tuning So far we have seen three different controller actions which may be applied to stabilize an automated process proportional integral and derivative or PID The relative effect of each action in a controller may be set by the instrument technician by adjusting the values of Kp K and Kg The act of adjusting these three gain values to achieve optimum control stability is called tuning In a mechanical pneumatic PID controller these constants are typically adjusted by manually moving fulcrum positions and needle valve positions In analog electronic PID controllers potentiometers and switch selectable capacitors typically control the gain settings Digital electronic controllers of course are simply programmed with direct numerical values for Kp K and Ka A very unfortunate source of confusion in the world of PID controllers is different units for expressing P I and D constants Beginning with proportional we have two ways of expressing the aggressiveness of the controller gain and proportional band Gain is exactly what you might expect it to be if you have an electronics background a direct ratio of output change to input change For a proportional only controller a gain of 2 means that a 10 change in error results in a 20 change in output signal The other way of expressing proportional action called proportional band defines
149. pumping systems with automatic flow controls are further examples of how feedback may be used to maintain control over certain process variables Modern technology makes it possible to control nearly anything that may be measured in an industrial process This extends beyond the pale of simple pressure level temperature and flow variables to include even certain chemical properties In municipal water and wastewater treatment systems numerous chemical quantities must be measured and controlled automatically to ensure maximum health and minimum environmental impact Take for instance the chlorination of treated wastewater before it leaves the wastewater treatment facility into a large body of water such as a river bay or ocean Chlorine is added to the water to kill any residual bacteria so that they do not consume oxygen in the body of water they are released to Too little chlorine added and not enough bacteria are killed resulting in a high biological oxygen demand or BOD in the water which will asphyxiate the fish swimming in it Too much chlorine added and the chlorine itself poses a hazard to marine life Thus the chlorine content must be carefully controlled at a particular setpoint and the control system must take aggressive action if the dissolved chlorine concentration strays too low or too high A Analytical Chlorine supply indicating 4 20 mA controller control signal Motor operated p777 7 7 SP control val
150. radioactivity The periodic table entry shows an atomic mass of slightly more than 39 for Potassium because different isotopes of Potassium exist in nature The table s entries for atomic mass reflect the relative abundances of each element s isotopes as naturally found on the earth Individually though the atomic mass of a single atom will always be a whole number just like the atomic number The outer most electron shell configuration is shown here as 4s telling us that a neutral Potassium atom has 1 electron residing in the s subshell of the 4th shell The configuration of an 2 3 MOLECULAR QUANTITIES 63 atom s electrons in the outermost different shells and subshells determines its chemical properties i e its tendency to bond with other atoms to form molecules 2 3 Molecular quantities Sample sizes of chemical substances are often measured in moles One mole of a substance is defined as a sample having 6 022 x 10 Avogadro s number molecules An elemental sample s mass is equal to its molecular quantity in moles multiplied by the element s atomic mass in amu atomic mass units For example 2 00 moles of naturally occurring Potassium will have a mass of 78 2 grams When referring to liquid solutions the concentration of a solute is often expressed as a molarity defined as the number of moles of solute per liter of solution Molarity is usually symbolized by an italicized capital letter M It is important to
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152. require temperature compensation and even temperature control in some cases because flow measurement accuracy depends on fluid viscosity and fluid viscosity varies according to temperature The Hagen Poiseuille equation describing flow rate and differential pressure for laminar flow low Re is shown here for comparison G24 222 uL Where Q Flow rate gallons per minute k Unit conversion factor 7 86 x105 AP Pressure drop inches of water column D Pipe diameter inches u Liquid viscosity centipoise this is a temperature dependent variable L Length of pipe section inches Note that if the pipe dimensions and fluid viscosity are held constant the relationship between flow and differential pressure is a direct proportion Qx AP In engineering this goes by the romantic name of swamping We say that the overshadowing effect swamps out all others because of its vastly superior magnitude and so it is safe not to mention simpler to ignore the smaller effect s The most elegant cases of swamping are when an engineer intentionally designs a system so that the desired effect is many times greater than the undesired effect s thereby forcing the system to behave more like the ideal This application of swamping is prevalent in electrical engineering where resistors are often added to circuits for the purpose of overshadowing the effects of stray undesirable resistance in wiring and components
153. resistors lamps and electric motors In a working circuit electrical sources and loads may be easily distinguished by comparison of their current directions and voltage drop polarities An electrical source always manifests a voltage polarity in a direction that assists the direction of charge flow An electrical source always manifests a voltage polarity in a direction that opposes the direction of charge flow The convention used to designate direction of current charge flow becomes very important here Since there are two commonly accepted notations electron flow and conventional flow exactly opposite of each other it is easy to become confused First we see a diagram showing a source and a load using electron flow notation Electrons being negatively charged particles are repelled by the negative poles of both source and load and attracted to the positive poles of both source and load The difference between source and load is that the source device motivates the flow of electrons while the load device resists the flow of electrons Shown using electron flow notation Source 5 Load Generator 2 Resistor Electrons are repelled by the poles and attracted to the poles Next we see a diagram showing the same source and load this time using conventional flow notation to designate the direction of current Here we must imagine positively charged carriers moving through the wires instead of elec
154. same velocity approach factor may be expressed in terms of mouth and throat areas A and A respectively 1 E 7 Velocity of approach factor 2 When computing the volumetric flow of a gas in standard volume units e g SCFM the equation becomes much more complex than the simple flowing volumetric rate equation Any equation computing flow in standard units must predict the effective expansion of the gas if it were to transition from flowing conditions the actual pressure and temperature it experiences flowing through the pipe to standard conditions one atmosphere pressure at 60 degrees Fahrenheit The 484 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT compensated gas flow measurement equation published by the American Gas Association AGA Report 3 in 1992 for orifice plates with flange taps calculates this expansion to standard conditions with a series of factors accounting for flowing and standard base conditions in addition to the more common factors such as velocity of approach and gas expansion Most of these factors are represented in the AGA3 equation by different variables beginning with the letter F Q Fi Fe Fs Y Foo Fin Fis For Fv V hw Pp Where Q Volumetric flow rate standard cubic feet per hour SCFH F Numeric conversion factor accounts for certain numeric constants unit conversion coefficients and the velocity of approach factor E F Orifice calculation factor a polynomial
155. settings digital trim digital transmitters 261 11 4 Calibration procedures 265 11 4 1 Linear instrumentso sA e A A e Sk a i Pes 265 11 4 2 Nonlinear instruments 265 11 4 3 Discrete instruments ccoa e ea a et ee 266 11 5 Typical calibration errors ee 267 11 5 1 As found and as left documentation o soosoo a 270 11 5 2 Up tests and Down tests e 270 H 6 NIST traceability a A A IA A a ea ks 271 11 7 Instrument turndoWT s sor ea ede e a ed 271 11 8 Practical calibration standards 02 0000 ee ee 272 11 8 1 Electrical standards o 273 11 8 2 Temperature standards 0 0002 eee ee 275 11 8 3 Pressure standards es aua d oea E A E E e a a a 278 11 8 4 Flow standardse ia e A pb Rk ROG ER ee EE ek E a ae 284 11 8 5 Analytical standards ee ee 285 12 Continuous pressure measurement 289 12 1 Manometerssncsca bo he betes ee BO a RP eee ORE Pe PS ae 8 290 12 2 Mechanical pressure elements 0 0 ee ee 295 12 3 Electrical pressure elements ee 299 12 3 1 Piezoresistive strain gauge sensors 2 2 2 2000000000000 300 12 3 2 Differential capacitance sensors 303 12 3 3 Resonant element sensors 2 2 0 pee 308 12 3 4 Mechanical adaptations 0 00002 eee ee 311 12 4 Force balance pressure transmitters ee 312 12 5 Differential pressure transmitters ooo ee 31
156. signal sent to the control valve changes in response to the process variable PV and setpoint SP values Changes in the control valve position in turn naturally affect the process variable signal through the physical relationships of the process What we have here is a situation where causality is uncertain If we see the process variable changing erratically over time does this mean we have a faulty transmitter outputting an erratic signal or does it mean the controller output is erratic causing the control valve to shift position unnecessarily or does it mean the steam demand is fluctuating and causing the water level to vary as a result So long as the controller remains in automatic mode we can never be completely sure what is causing what to happen because the chain of causality is actually a loop with everything affecting everything else in the system 5 1 EXAMPLE BOILER WATER LEVEL CONTROL SYSTEM 135 A simple way to diagnose such a problem is to place the controller in manual mode Now the output signal to the control valve will be fixed at whatever level the human operator or technician sets it to If we see the process variable signal suddenly stabilize we know the problem has something to do with the controller output If we see the process variable signal suddenly become even more erratic once we place the controller in manual mode we know the controller was actually trying to do its job properly in automatic mode and the c
157. supplied clean compressed air at some nominal pressure 20 to 25 PSI usually and the instrument signals travel via tubing The following illustrations show what some of these applications look like 211 Biodiesel wash column temperature control Wash water in Foxboro model 12A temperature transmitter Instrument air supply 20 PSI Foxboro model 43 AP controller Condensate Supply out Element A Out Unwashed Spent wash feed in water out Control valve Steam Flow controller HE Flow control system AN E tubing Flow control valve AN Flow transmitter Orifice plate 212 CHAPTER 9 PNEUMATIC INSTRUMENTATION Two element boiler steam drum level control Square root extractor Vv bi bi p7 tubing p7 H FY 97 tubing H 7 Exhaust stack A S Flow transmitter A S FT Steam Level transmitter H LT Steam drum j AS 20 PSI supply O 7 YT Riser 3 tubes q Level controller Boiler SP gt Pv tubing Ca s e Downcomer tubes Feedwater P control valve po 3 E IBY tubing Feedwater Instruments functioning on compressed air and process measurement signals transmitted as air pressures through long runs of metal tubing was the norm for industrial instrumentation prior to the advent of reliable electronics In honor of this paradigm instrumen
158. switch The answer is not complex but it is often misunderstood The normal status for a switch is the status its electrical contacts are in under a condition of minimum physical stimulus For a momentary contact pushbutton switch this would be the status of the switch contact when it is not being pressed The normal status of any switch is the way it is drawn in an electrical schematic For instance the following diagram shows a normally open pushbutton switch controlling a lamp on a 120 volt AC circuit the hot and neutral poles of the AC power source labeled L1 and L2 respectively L L Switch al Normally open contacts We can tell this switch is a normally open NO switch because it is drawn in an open position The lamp will energize only if someone presses the switch holding its normally open contacts in the closed position Normally open switch contacts are sometimes referred to in the electrical industry as form A contacts If we had used a normally closed pushbutton switch instead the behavior would be exactly opposite The lamp would energize if the switch was left alone but it would turn off if anyone pressed the switch Normally closed switch contacts are sometimes referred to in the electrical industry as form B contacts L L Switch ali Normally closed contacts Lamp Y N This seems rather simple don t you think What could possibly be confusing about the normal st
159. than inside a building but the controller may be located a long distance away where human operators can adjust the setpoint from inside a safe and secure control room These elements comprise the essentials of a feedback control system the process the system to be controlled the process variable the specific quantity to be measured and controlled the transmitter the device used to measure the process variable and output a corresponding signal the controller the device that decides what to do to bring the process variable as close to setpoint as possible the final control element the device that directly exerts control over the process and the 600 CHAPTER 18 CONTINUOUS FEEDBACK CONTROL manipulated variable the quantity to be directly altered to effect control over the process variable Feedback control may be viewed as a sort of information loop from the transmitter measuring the process variable to the controller to the final control element and through the process itself back to the transmitter Ideally a process control loop not only holds the process variable at a steady level the setpoint but also maintains control over the process variable given changes in setpoint and even changes in other variables of the process Decides Senses Influences For example if we were to raise the temperature setpoint in the heat exchanger process the controller would automatically call for more steam flow by o
160. the containment building where it is safe for a human operator to be There is nothing preventing us from connecting multiple indicators at multiple locations to the same 4 to 20 milliamp signal wires coming from the temperature transmitter This allows us to display the reactor temperature in as many locations as we desire since there is no absolute limitation on how far we may conduct a DC milliamp signal along copper wires Another common auxiliary instrument is the recorder sometimes specifically referred to as a chart recorder or a trend recorder the purpose of which is to draw a graph of process variable s over time Recorders usually have indications built into them for showing the instantaneous value of the instrument signal s simultaneously with the historical values and for this reason are usually designated as indicating recorders A temperature indicating recorder for the nuclear reactor system shown previously would be designated as a TIR accordingly Recorders are extremely helpful for troubleshooting process control problems This is especially true when the recorder is configured to record not just the process variable but also the controller s setpoint and output variables as well Here is an example of a typical trend showing the relationship between process variable setpoint and controller output in automatic mode as graphed by a recorder 5 PV 45 SP 40 35 a Output 20 15 10 5 Time
161. the inherent complexity of such a device 5 5 Summary Instrument technicians maintain the safe and efficient operation of industrial measurement and control systems As this chapter shows this requires a broad command of technical skill Instrumentation is more than just physics or chemistry or mathematics or electronics or mechanics or control theory alone An instrument technician must understand all these subject areas to some degree and more importantly how these knowledge areas relate to each other The all inclusiveness of this profession makes it very challenging and interesting Adding to the challenge is the continual introduction of new technologies The advent of new technologies however does not necessarily relegate legacy technologies to the scrap heap It is quite common to find state of the art instruments in the very same facility as decades old instruments digital fieldbus networks running alongside 3 to 15 PSI pneumatic signal tubes microprocessor based sensors mounted right next to old mercury tilt switches Thus the competent instrument technician must be comfortable working with both old and new technologies understanding the relative merits and weaknesses of each This is why the most important skill for an instrument technician is the ability to teach oneself It is impossible to fully prepare for a career like this with any amount of preparatory schooling The profession is so broad and the responsibility so great and
162. the reference junction the voltmeter now only registers the voltage produced by the measurement junction J1 At first it may seem pointless to go through the trouble of building a reference junction compensation circuit After all why bother to do this just to be able to use a thermocouple to accurately measure temperature when we could simply use this other device thermistor RTD etc to directly measure the temperature of interest In other words isn t the usefulness of a thermocouple invalidated if we have to go through the trouble of integrating another type of electrical temperature sensor in the circuit just to compensate for an idiosyncrasy of thermocouples The answer to this very good question is that thermocouples enjoy certain advantages over these other sensor types Thermocouples are extremely rugged and have far greater temperature measurement ranges than thermistors RTDs and other primary sensing elements However if the application does not demand extreme ruggedness or large measurement ranges a thermistor or RTD would likely be the better choice Thermocouples exist in many different types each with its own color codes for the dissimilar metal wires Here is a table showing the more common thermocouple types Type Positive wire Negative wire Temperature range T copper blue constantan red 300 to 700 F J iron white constantan red 32 to 1400 F E chrome violet constantan
163. the vessel no matter how well or how often the vessel is cleaned Even automated Clean In Place and Steam In Place CIP and SIP respectively protocols where the vessel is chemically purged between batches cannot prevent this problem because the cleaning agents never purge the entire length of the tubing ultimately to the bourdon tube or other sensing element inside the gauge Here we see a valid application of an isolating diaphragm and fill fluid If we mount an isolating diaphragm to the vessel in such a way that the process fluid directly contacts the diaphragm sealed fill fluid will be the only material inside the tubing carrying that pressure to the instrument Furthermore the isolating diaphragm will be directly exposed to the vessel interior and therefore cleaned with every CIP cycle Thus the problem of microbial contamination is completely avoided 12 6 PRESSURE SENSOR ACCESSORIES 331 Wall Pressure gauge Isolating diaphragm Capillary tubing with fill fluid Such systems are often referred to as remote seals and they are available on a number of different pressure instruments including gauges transmitters and switches If the purpose of an isolating diaphragm and fill fluid is to protect the sensitive instrument from corrosive or otherwise harsh chemicals it is often referred to as a chemical seal The following photograph shows a pressure gauge equipped with a chemical seal diaphragm Note that the c
164. this Pneumatic DP Electronic DP transmitter transmitter Wires Force balance ios mechanism gt Airsigrial dut Electronics _ Air supply Diaphragm capsule Diaphragm capsule assembly assembly Two models of electronic differential pressure transmitter are shown here the Rosemount model 1151 left and model 3051 right Two more models of electronic differential pressure transmitter are shown in the next photograph the Yokogawa EJA110 left and the Foxboro IDP10 right 12 5 DIFFERENTIAL PRESSURE TRANSMITTERS 317 Regardless of make or model every differential pressure DP d p or AP transmitter has two pressure ports to sense different process fluid pressures One of these ports is labeled high and the other is labeled low This labeling does not necessarily mean that the high port must always be at a greater pressure than the low port What these labels represent is the effect that a pressure at that point will have on the output signal The concept of differential pressure instrument port labeling is very similar to the inverting and noninverting labels applied to operational amplifier input terminals Inverting Noninverting The and symbols do not imply polarity of the input voltage s It is not as though the input must be more positive than the input These symbols merely represent the different effects on the outp
165. two liquid interface the buoyant force is equal to the sum of the two liquid weights displaced each liquid weight term being equal to the weight density of that liquid multiplied by the displaced volume of that liquid Fruoyant Y1 Vi ra Va Assuming a displacer of constant cross sectional area throughout its length the volume for each liquid s displacement is simply equal to the same area rr multiplied by the length of the displacer submerged in that liquid Vessel 388 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT Pbuoyant y rr l yom ly Since the area rr is common to both buoyancy terms in this equation we may factor it out for simplicity s sake Fouoyant nr Guest ala Calculating the LRV buoyant force is as simple as setting l equal to zero and l2 equal to the displacer length L Frucyant LRV Sar b Calculating the URV buoyant force is as simple as setting l2 equal to zero and l equal to the displacer length L Pruoyant URV ar L The buoyancy for any measurement percentage between the LRV 0 and URV 100 may be calculated by interpolation Sample calculations are shown below for a displacer instrument measuring the interface level between two liquids having specific gravities of 0 850 and 1 10 with a displacer length of 30 inches and a displacer diameter of 2 75 inches radius 1 375 inches lb Ib Ib 62 4 1 10 68 6 0 0397 y r ft in lb lb lb 62
166. vessel each exploiting a different principle of physics This chapter explores the major level measurement technologies in current use 347 348 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT 13 1 Level gauges sightglasses The level gauge or sightglass is to liquid level measurement as manometers are to pressure measurement a very simple and effective technology for direct visual indication of process level In its simplest form a level gauge is nothing more than a clear tube through which process liquid may be seen The following photograph shows a simple example of a sightglass A functional diagram of a sightglass shows how it visually represents the level of liquid inside a vessel such as a storage tank 13 1 LEVEL GAUGES SIGHTGLASSES 349 gauge valve Level gauge glass tube Liquid column L gauge valve Level gauge valves exist to allow replacement of the glass tube without emptying or depressurizing the process vessel These valves are usually equipped with flow limiting devices in the event of a tube rupture so that too much process fluid does not escape even when the valves are fully open Some level gauges called reflex gauges are equipped with special optics to facilitate the viewing of clear liquids which is problematic for simple glass tube sightglasses As simple and apparently trouble free as level gauges may seem there are special circumstances where they will register incorrectly One
167. voltage Typically these tubes are connected to the transmitter and to the process by means of compression fittings which allow for relatively easy disconnection and reconnection of tubes The combination of two differential pressure ports makes the DP transmitter very versatile as a pressure measuring device We may use the DP transmitter to measure an actual difference of pressure across a fluid device such as a filter Here the amount of differential pressure across the filter represents how clogged the filter is 9 Also called impulse tubes gauge tubes or sensing tubes 12 5 DIFFERENTIAL PRESSURE TRANSMITTERS 319 Impulse line Impulse line Note how the high side of the DP transmitter connects to the upstream side of the filter and the low side of the transmitter to the downstream side of the filter This way increased filter clogging will result in an increased transmitter output Since the transmitter s internal pressure sensing diaphragm only responds to differences in pressure between the high and low ports the pressure in the filter and pipe relative to the atmosphere is completely irrelevant to the transmitter s output signal The filter could be operating at a pressure of 10 PSI or 10 000 PSI the only thing the DP transmitter measures is the pressure drop across the filter If the upstream side is at 10 PSI and the downstream side is at 9 PSI the differential pressure will be 1 PSI sometimes labeled as PSI
168. we arrive at the loop diagram sometimes called a loop sheet for the compressor surge control system loop number 42 Loop Diagram Compressor surge control IE O RN Date April 1 2003 Field process area Panel rear Panel front 0 2000PSID Jo fe SP 4 lt Compressor AS20PSI iff foot Ila be HOO sees Del 7 i a20mA BLAS O l ES 120VAC EA E cBier 60 Hz 0 1500 SCFM Tag number Description Input cal Output cal FE 42 Venturi tube 0 1500 SCFM 0 100 WC FT 42 Suction flow transmitter 0 100 WC 4 20 MA FY 42a Square root extractor 4 20 mA 4 20 mA FY 42b Current to pressure converter 4 20 mA 3 15 PSI FV 42 Anti surge control valve 3 15 PSI 100 0 Air to close PDT 42 Differential pressure transmitter 0 200 PSI 20 4 mA Reverse action FIC 42 Anti surge controller 4 20 mA 4 20 mA Here we see that the P amp ID didn t show us all the instruments in this control loop Not only do we have two transmitters a controller and a valve we also have two signal transducers Transducer 42a modifies the flow transmitter s signal before it goes into the controller and transducer 42b converts the electronic 4 to 20 mA signal into a pneumatic 3 to 15 PSI air pressure signal Each instrument bubble in a loop diagram represents an indi
169. were written in a shallow math phobic style that was well below the level I intended to teach to Some reference books I found contained great information but were often written for degreed engineers with lots of Laplace transforms and other mathematical techniques that were well above the level I intended to teach to Few on either side of the spectrum actually made an effort to explain certain concepts that students generally struggle to understand I needed a text that gave good practical information and theoretical coverage at the same time In a futile effort to provide my students with enough information to study outside of class I scoured the internet for free tutorials written by others While some manufacturer s tutorials were nearly perfect for my needs others were just as shallow as the textbooks I had found and or were little more than sales brochures I found myself starting to write my own tutorials on specific topics to plug the gaps but then another problem arose it became troublesome for students to navigate through dozens of tutorials in an effort to find the information they needed in their studies What 3 CONTENTS my students really needed was a book not a smorgasbord of tutorials So here I am again writing another textbook This time around I have the advantage of wisdom gained from the first textbook project For this project I will not attempt to maintain a parallel book in HTML markup for dire
170. which means it will blow down more often More frequent blow down events means a greater flow rate of steam into the tracing tube which adds more heat to the tubing bundle and raises its temperature Thus the system is naturally regulating with its own negative feedback loop to maintain bundle temperature at a relatively stable point 13In fact after you become accustomed to the regular popping and hissing sounds of steam traps blowing down you can interpret the blow down frequency as a crude ambient temperature thermometer Steam traps seldom 12 6 PRESSURE SENSOR ACCESSORIES 341 Steam traps are not infallible being susceptible to freezing in very cold weather and sticking open wasting steam by venting it directly to atmosphere However they are generally reliable devices capable of adding tremendous amounts of heat to impulse tubing for protection against freezing Electrically traced impulse lines are an alternative solution for cold weather problems The tracing used is a twin wire cable sometimes called heat tape that acts as a resistive heater When power is applied the cable heats up thus imparting thermal energy to the impulse tubing it is bundled with Heat tape may be self regulating or controlled with an external thermostat Self regulating heat tape exhibits an electrical resistance that varies with temperature automatically self regulating its own temperature without the need for externa
171. 000 pages at a cost of nearly 200 00 apiece These texts also lack some of the basic content my students do need and I don t have the heart to tell them to buy yet another textbook to fill the gaps CONTENTS 5 e Practically anything written by Francis Greg Shinskey Whether or not I achieve my goal of writing a better textbook is a judgment left for others to make One decided advantage my book will have over all the others is its openness If you don t like anything you see in these pages you have the right to modify it at will Delete content add content modify content it s all fair in this game we call open source My only condition is declared in the Creative Commons Attribution License that you give me credit for my original authorship What you do with it beyond that is wholly up to you This way perhaps I can spare someone else from having to write their own textbook from scratch CONTENTS Chapter 1 Physics 8 CHAPTER 1 PHYSICS 1 1 Terms and Definitions Mass m is the opposition that an object has to acceleration changes in velocity Weight is the force F imposed on a mass by a gravitational field Mass is an intrinsic property of an object regardless of the environment Weight on the other hand depends on the strength of the gravitational field in which the object resides A 20 kilogram slug of metal has the exact same mass whether it rests on Earth or in the zero gravity environment of outer sp
172. 02 Bark degrees 39 Barometer 294 Base 70 71 Base unit 19 Baum degrees 38 Bellows 217 295 Bernoulli s equation 55 450 Bernoulli Daniel 55 Beta ratio of flow element 483 Bethlehem flow tube 469 Bi metal strip 417 Biological oxygen demand 601 Blackbody 435 Blackbody calibrator 277 Bleed valve fitting 326 Bluff body 501 BOD 601 Boiling point of water 275 Bourdon tube 295 Boyle s Law 47 Bridge circuit 100 Brix degrees 39 Bubble tube 361 INDEX Buffer solution 285 550 560 Buoyancy 45 385 Buoyant test of density 46 Burnout thermocouple 433 Calibration 257 285 Calibration gas 287 Capacitance 108 Capacitor 108 Capillary tube 333 486 Cathode 542 Cation 542 Caustic 70 71 Celsius 275 Centigrade 275 Centrifugal force 515 Centripetal force 515 cgs 19 Charles s Law 47 Chart recorder 142 Chemical seal 331 Chemical versus nuclear reaction 64 Chromatogram 564 Chromatography 561 CIP 330 Cippoletti weir 489 582 Cistern manometer 291 Clamp on milliammeter 203 Class I filled system 419 Class II filled system 420 Class III filled system 419 Class V filled system 419 Clean In Place 330 Cold junction compensation 428 Cold junction thermocouple 429 Column chromatograph 561 Combination electrode 553 Combustion 65 Common mode rejection 320 Compensating leg 367 Complex number 121 Compound 61 Compressibility 48 Com
173. 03 8 315 298 15 1x 107 M 7 1 96485 x 10 7 ar V 59 17 mV log 10 59 17 mV If the measured solution had a value of 7 0 pH instead of 6 0 pH there would be no voltage generated across the glass membrane since the two solutions hydrogen ion activities would be equal Having a solution with one decade ten times more exactly one order of magnitude greater hydrogen ions activity than the internal buffer solution produces 59 17 millivolts at 25 degrees Celsius If the pH were to drop to 5 0 two units away from 7 0 instead of one unit the output voltage would be double 118 3 millivolts If the solution s pH value were more alkaline than the internal buffer for example 8 0 pH the voltage generated at the glass bulb would be the opposite polarity e g 8 0 pH 59 17 mV 9 0 pH 118 3 mV etc The following table shows the relationship between hydrogen ion activity pH value and probe voltage Hydrogen ion activity pH value Probe voltage at 25 C 1x 10 M 0 001 M 3 0 pH 236 7 mV 1 x 107 M 0 0001 M 4 0 pH 177 5 mV 1x 10 gt M 0 00001 M 5 0 pH 118 3 mV 1 x 107 M 0 000001 M 6 0 pH 59 17 mV 1 x 1077 M 0 0000001 M 7 0 pH 0 mV 1 x 1078 M 0 00000001 M 8 0 pH 59 17 mV 1 x 107 M 0 000000001 M 9 0 pH 118 3 mV 1 x 10710 M 0 0000000001 M 10 0 pH 177 5 mV 1 x 107 M 0 00000000001 M 11 0 pH 236 7 mV 10The mathematical sign of probe voltage is arbitrary
174. 15 5 INERTIA BASED TRUE MASS FLOWMETERS 519 Great care is taken by the manufacturer to ensure the two tubes are as close to identical as possible not only are their physical characteristics precisely matched but the fluid flow is split very evenly between the tubes so their respective Coriolis forces should be identical in magnitude A photograph of a Rosemount Micro Motion U tube Coriolis flowmeter demonstration unit shows the U shaped tubes one tube is directly above the other in this picture so you cannot tell there are actually two U tubes A closer inspection of this flowmeter shows that there are actually two U tubes one positioned directly above the other shaken in complementary directions by a common electromagnetic force coil 29 An alternative to splitting the flow is to plumb the tubes in series so they must share the exact same flow rate like series connected resistors sharing the exact same amount of electrical current 520 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT Two magnetic displacement sensors monitor the relative motions of the tubes and transmit signals to an electronics module for digital processing One of those sensor coils may be seen in the previous photograph Both the force coil and the sensor coil are nothing more than permanent magnets surrounded by movable copper wire coils The main difference between the force coil and the sensor coil is that the force coil is powered by an AC signal to
175. 1To be precise this form of on off control is known as differential gap because there are two setpoints with a gap in between While on off control is possible with a single setpoint FCE on when below setpoint and off when above it is usually not practical due to the frequent cycling of the final control element 18 2 ON OFF CONTROL 603 would require the steam valve to be position somewhere between fully closed and fully open This simple control algorithm may be adequate for temperature control in a house but not for a sensitive chemical process Can you imagine what it would be like if an automobile s cruise control system relied on this algorithm Not only is the lack of precision a problem but the frequent cycling of the final control element may contribute to premature failure due to mechanical wear In the heat exchanger scenario thermal cycling hot cold hot cold will cause metal fatigue in the tubes resulting in a shortened service life Furthermore every excursion of the process variable above setpoint is wasted energy because the process fluid is being heated to a greater temperature than what is necessary Clearly the only practical answer to this dilemma is a control algorithm able to proportion the final control element rather than just operate it at zero or full effect the control valve fully closed or fully open This in its simplest form is called proportional control 604 CHAPTER 18 CONTINUOUS FEEDBACK CONTROL 18
176. 2 0 e 495 15 4 1 Turbine flowmeters 2 0 0 0200 pe ee 496 15 4 2 Vortex flowmetets a2 2064 2 a dos be EAS Rae EL Oe ee AS 501 15 4 3 Magnetic flowmeters ee ee 505 15 4 4 Ultrasonic flowmeters 00 2 ee 512 15 5 Inertia based true mass flowmeters 2 0 0 000000 00000004 514 15 5 1 Coriolis flowmeters sama oe ee AA a 515 15 6 Thermal based mass flowmeters 2 0 0 ee ee 524 15 7 Positive displacement flowmeters o 527 15 8 Welghteeders io apu e at A a A es 528 15 9 Change of quantity flow measurement e 529 15 10Insertion fowmeters 02 0 ee 532 15 11Process instrument suitability 2 2 a 537 Continuous analytical measurement 541 16 1 Density measurement 541 16 2 Turbidity measurement 541 16 3 Conductivity measurement 2 2 2 ee 542 16 3 1 Dissociation and ionization in aqueous solutions 542 16 3 2 Two electrode conductivity probes o o e e 543 16 3 3 Four electrode conductivity probes o o e e 544 16 3 4 Electrodeless conductivity probes o o e e 546 16 4 pH Measurement ses ao Soe RO do A ee ee a Ds de 549 16 4 1 Colorimetric pH Measurememt 000000 e eee ee 549 16 4 2 Potentiometric pH measurement 000000000 550 16 5 Ghromatography 29s lt 4 Sol ve Wek Da Ba ela A E eae a SP a 561 Signal characterizatio
177. 2 4 Example calculation pH transmitter A pH transmitter has a calibrated range of 4 pH to 10 pH with a 4 20 mA output signal Calculate the pH sensed by the transmitter if its output signal is 11 3 mA First we must convert the milliamp value into a percentage Following the same technique we used for the control valve problem current 4 mA 16 mA 11 3 mA 4 mA 16 mA Next we take this percentage value and translate it into a pH value given the transmitter s measurement span of 6 pH 10 pH 4 pH and offset of 4 pH 100 percent of range 100 0 456 45 6 10 pH 507 4 pH pH value 45 6 10 pH ar 4 pH 8 56 pH Therefore the transmitter s 11 3 mA output signal reflects a measured pH value of 8 56 pH 8 2 5 Example calculation reverse acting I P transducer signal A current to pressure transducer is used to convert a 4 20 mA electronic signal into a 3 15 PSI pneumatic signal This particular transducer is configured for reverse action instead of direct meaning that its pressure output at 4 mA should be 15 PSI and its pressure output at 20 mA should be 3 PSI Calculate the necessary current signal value to produce an output pressure of 12 7 PSI Reverse acting instruments are still linear and therefore still follow the slope intercept line formula y mx b The only differences are a negative slope and a different intercept value 8 2 RELATING 4 TO 20 MA SIGNALS
178. 24 x 10 electrons moving past a point in a circuit for every second of time Like masses falling toward a source of gravity these electrons continually fall toward the positive pole of a voltage source After arriving at that source the energy imparted by that source lifts the electrons to a higher potential state where they once again fall down to the positive pole through the circuit Like rising and falling masses in a gravitational field these electrons act as carriers of energy within the electric field of the circuit This is very useful as we can use them to convey energy from one place to another using metal wires as conduits for this energy This is the basic idea behind electric power systems a source of power a generator is turned by some mechanical engine windmill water turbine steam engine etc creating an electric potential This potential is then used to motivate free electrons inside the metal wires to drift in a common direction The electron drift is conveyed in a circuit through long wires where they can do useful work at a load device such as an electric motor light bulb or heater Generator Turned by an engine a Turns a conveyor belt Motor or other mechanical load Current Wire Current f 3 2 ELECTRICAL CURRENT 81 Given the proper metal alloys the friction that electrons experience within the metal wires may be made very small allowing nearly all the energy to
179. 4 688 kilograms to 70 100 kilograms between 4 05 AM and 4 07 AM we could say that the average mass flow rate of water leaving the vessel is 2 294 kilograms per minute over that time span We Am 2 70100 kg 74688 kg _ see kg 929458 At 4 07 4 05 2 min min Note that this average flow measurement may be determined without any flowmeter of any kind installed in the pipe to intercept the water flow All the concerns of flowmeters studied thus far turbulence Reynolds number fluid properties etc are completely irrelevant We may measure practically any flow rate we desire simply by measuring stored weight or volume over time A computer may do this calculation automatically for us if we wish on practically any time scale desired Now suppose the practice of determining average flow rates every two minutes was considered too infrequent Imagine that operations personnel require flow data calculated and displayed more often than just 30 times an hour All we must do to achieve better time resolution is take weight mass measurements more often Of course each mass change interval will be expected to be less with more frequent measurements but the amount of time we divide by in each calculation will be proportionally smaller as well If the flow rate happens to be absolutely steady we may sample mass as frequently as we might like and we will still arrive at the same flow rate value as before sampling mass just once every two minutes If
180. 50 PSI 100 PSI Input pressure A linearity calibration error causes the function to deviate from a straight line This type of error does not directly relate to a shift in either zero b or span m because the slope intercept equation only describes straight lines If an instrument does not provide a linearity adjustment the best you can do for this type of error is split the error between high and low extremes so that the maximum absolute error at any point in the range is minimized 20 mA 12mA Output current effect of a linearity error 4mA 0mA 0 PSI 50 PSI 100 PSI Input pressure 11 5 TYPICAL CALIBRATION ERRORS 269 A hysteresis calibration error occurs when the instrument responds differently to an increasing input compared to a decreasing input The only way to detect this type of error is to do an up down calibration test checking for instrument response at the same calibration points going down as going up 20 mA 12mA Output current ffect of a hysteresis error te the arrows showing direction of motion 4mA 0mA 0 PSI 50 PSI 100 PSI Input pressure Hysteresis errors are almost always caused by mechanical friction on some moving element and or a loose coupling between mechanical elements such as bourdon tubes bellows diaphragms pivots levers or gear sets Flexible metal strips called flecures which are designed to serve as frictionless pivot points in mechanical instruments may
181. 6 CONTENTS 12 6 12 7 Pressure sensor accessories ee 12 6 Nalvesmanitolds tie po alar do eee 1236 2 Bleed fittings tri a e A amp Oe ee ad wie aS 12 6 3 Pressure pulsation dampening 0 00000 eee ee 12 6 4 Remote and chemical seals 0 o e e 12 6 5 Filled impulse lines e e 12 6 6 Purged impulse lines o a 12 6 7 Heat traced impulse lines 2 0 20 00 0 ee ee ee 12 6 8 Water traps and pigtail siphons e 12 6 9 Mounting brackets ee ee Process instrument suitability o o e 13 Continuous level measurement 13 1 13 2 13 3 13 4 13 5 13 6 13 7 13 8 13 9 Level gauges sightglasses 2 ee Flatir 24 e ii a ais a Sd A ete Hydrostatic pressure sos o a e e RE ad a ee ee 13 3 1 Bubblersyst ms so o mbasi Coni aasi a ee a a a Re AA 13 3 2 Transmitter suppression and elevation osoo 0 00000 eae 13 3 3 Compensated leg systems 2 0 13 3 4 Tank expert systems so sie me a e i an i op a e ad a a o a A 13 3 5 Hydrostatic interface level measurement ooo Displacement aro a it i e h a a eee be T 13 4 1 Displacement interface level measurement aooaa Echo isa Oy ara oe weal ae eee ee OE a Ae Ge OE ee e D e A aes 13 5 1 Ultrasonic level measurement 0 e 13 5 2 Radar level measurement eee ee Laser level measurement WECH rs otro
182. 629 In reality there is no such thing as a frictionless flow excepting superfluidic cases such as Helium II which are well outside the bounds of normal experience just as there is no such thing as a massless flow no inertia In normal applications there will always be both effects at work By not considering fluid friction for high Reynolds numbers and not considering fluid density for low Reynolds numbers engineers draw simplified models of reality which allow us to more easily measure fluid flow As in so many other areas of study we exchange accuracy for simplicity precision for convenience Problems arise when we forget that we ve made this Faustian exchange and wander into areas where our simplistic models are no longer accurate Perhaps the most practical upshot of all this for students of Instrumentation is to realize exactly why and how orifice plates work Bernoulli s equation does not include any considerations of friction To the contrary we must assume the fluid to be completely frictionless in order for the concept to make sense This explains several things e There is little permanent pressure drop across an orifice most of the pressure lost at the vena contracta is regained further on downstream as the fluid returns to its original slow speed Permanent pressure drop will occur only where there is energy lost through the constriction such as in cases where fluid friction is substantial Where the fluid is frictionless the
183. 99999 to 0 999999 Negative feedback clearly has a stabilizing effect on the closed loop gain of the opamp circuit which is the primary reason it finds such wide application in engineered systems It was this effect that led Harold Black in the late 1920 s to apply negative feedback to the design of very stable telephone amplifier circuits If we subject our negative feedback opamp circuit to a constant input voltage of exactly 5 volts we may expand the table to show the effect of changing open loop gain on the output voltage and also the differential voltage appearing between the opamp s two input terminals lAn order of magnitude is nothing more than a ten fold change Do you want to sound like yow re really smart and impress those around you Just start comparing ordinary differences in terms of orders of magnitude Hey dude that last snowboarder s jump was an order of magnitude higher than the one before Whoa that s some big air Just don t make the mistake of using decibels in the same way Whoa dude that last jump was at least 10 dB higher than the one before you don t want people to think you re a nerd 9 4 ANALOGY TO OPAMP CIRCUITS 231 Aoi Ay Vout Vin AE Internal gain Overall gain Output voltage Differential input voltage 100 000 0 99999 4 99995 0 00005 200 000 0 999995 4 999975 0 000025 300 000 0 999997 4 99998 0 00002 500 000 0 999998 4 99999 0 00001 1 000 000 0
184. 999999 4 999995 0 000005 With such extremely high open loop voltage gains it hardly requires any difference in voltage between the two input terminals to generate the necessary output voltage to balance the input Thus Vout Vin for all practical purposes One of the simplifying assumptions electronics technicians and engineers make when analyzing opamp circuits is that the differential input voltage in any negative feedback circuit is zero As we see in the above table this assumption is very nearly true Following this assumption to its logical consequence allows us to predict the output voltage of any negative feedback opamp circuit quite simply For example Voir 0 WV Vout 5 volts Vin 5 volts If we simply assume there will be no difference of voltage between the two input terminals of the opamp with negative feedback in effect we may conclude that the output voltage is exactly equal to the input voltage since that is what must happen in order for the two input terminals to see equal potentials Now let us apply similar techniques to the analysis of a pneumatic baffle nozzle mechanism Suppose we arrange a pair of identical bellows in opposition to one another on a force beam so that any difference in force output by the two bellows will push the baffle either closer to the nozzle or further away from it 232 CHAPTER 9 PNEUMATIC INSTRUMENTATION Air supply gt Feedback Input bellows bellows
185. D D for differential If the upstream pressure is 10 000 PSI and the downstream pressure is 9 999 PSI the DP transmitter will still see a differential pressure of just 1 PSID Likewise the technician calibrating the DP transmitter on the workbench could use a precise air pressure of just 1 PSI applied to the high port with the low port vented to atmosphere to simulate either of these real world conditions The DP transmitter simply cannot tell the difference between these three scenarios nor should it be able to tell the difference if its purpose is to exclusively measure differential pressure In the world of electronics we refer to the ability of a differential voltage sensor such as an 320 CHAPTER 12 CONTINUOUS PRESSURE MEASUREMENT operational amplifier to sense small differences in voltage while ignoring large potentials measured with reference to ground by the phrase common mode rejection An ideal operational amplifier completely ignores the amount of voltage common to both input terminals responding only to the difference in voltage between those terminals This is precisely what a well designed differential pressure instrument does except with fluid pressure instead of electrical voltage A differential pressure instrument all but ignores gauge pressure common to both ports while responding only to differences in pressure between those two ports A vivid example of this may be inferred from the nameplate of a Fox
186. E SENSOR ACCESSORIES 323 In normal operation the two block valves are left open so that process fluid pressure may reach the transmitter The equalizing valve is left tightly shut so that no fluid can pass between the high and low pressure sides To isolate the transmitter from the process for maintenance one must first close the block valves then open the equalizing valve to ensure the transmitter sees no differential pressure The bleed valve is opened at the very last step to relieve pent up fluid pressure within the manifold and transmitter chambers Normal operation Removed from service A variation on this theme is the five valve manifold shown in this illustration 324 CHAPTER 12 CONTINUOUS PRESSURE MEASUREMENT Equalizing valve Equalizing valve Block valve Block valve Bleed valve To process To process To atmosphere or safe location elsewhere Manifold valve positions for normal operation and maintenance are as follows Normal operation Removed from service It is critically important that the equalizing valve s never be open while both block valves are open Doing so will allow process fluid to flow through the equalizing valve s from the high pressure side of the process to the low pressure side of the process If the impulse tubes connecting the manifold to the process are intentionally filled with a fill fluid such as glycerin to displace process water from entering the impul
187. EASUREMENTS 593 cell ja Process gas gt inside furnace Reference gas air ambient atmosphere Platinum electrode Platinum electrode The electrical voltage generated by this sandwich of zirconium and platinum is sent to an electronic amplifier circuit and then to a microcomputer which applies an inverse function to the measured voltage in order to arrive at an inferred measurement for oxygen concentration This type of chemical analysis is called potentiometric since it measures metric based on an electrical voltage potential The Nernst equation is an interesting one to unravel to solve for ion activity in the sample a1 given voltage V RT ay Multiplying both sides by nF nFV RT In 2 a2 Dividing both sides by RT nFV 01 A RT ag Applying the rule that the difference of logs is equal to the log of the quotient nFV RT Ina lnag 594 CHAPTER 17 SIGNAL CHARACTERIZATION Adding In ag to both sides eV a RT nag nay Making both sides of the equation a power of e e Rr n a2 e ay Canceling the natural log and exponential functions on the right hand side nFV R e RT In as a In most cases the ionic activity of az will be relatively constant and so ln az will be relatively constant as well With this in mind we may simplify the equation further using k as our constant value Substituting k for ln az nFV e RT k 041 App
188. EUMATIC INSTRUMENTATION _ AOutput AlTnput For example if an input pressure change of A2 PSI results in an output pressure change of A12 PSI the gain of the pneumatic relay is 6 The Foxboro corporation used a very sensitive amplifying relay in many of their pneumatic instruments np Seu Pneumatic amplifying relay vent The motion of the diaphragm actuated a pair of valves one with a cone shaped plug and the other with a metal ball for a plug The ball plug allowed supply air to go to the output port while the cone shaped stem valve plug vented excess air pressure to the vent port The Fisher corporation used a different style of amplifying relay in some of their pneumatic instruments 9 3 PILOT VALVES AND PNEUMATIC AMPLIFYING RELAYS 227 Baffle Nozzle Input signal Relay Vent lt abel compressed supply The gain of this Fisher relay was much less than that of the Foxboro relay since output pressure in the Fisher relay was allowed to act against input pressure by exerting force on a sizable diaphragm The movable vent seat in the Fisher relay made this design a non bleeding type meaning it possessed the ability to close both supply and vent valves at the same time allowing it to hold an output air pressure between saturation limits without bleeding a substantial amount of compressed air to atmosphere through the vent The Foxboro relay design by contrast was a bleeding t
189. Edit View Tools Window Help alel Alem Elio 9 tal eal O I AMS Device Manager Ly Plant Database ABER Delta Network 1 E Controller CTLR 01 I O System Delta S BRL 110 HART card cua E e Af chos y 2 fie CTLR 01C04CH02 E chos S Bh vo Fieldbus Card coz 2 Fieldbus Port PO1 a g PT_501 10 3 Wireless instrumentation At the time of this writing several manufacturers have developed radio based process transmitters capable of establishing mesh networks with each other for the exchange and relaying of digital information These transmitters are battery powered which means they have no need for field wiring simply connect them to the process No clear winner has emerged as the technical standard for wireless data exchange in a process environment however Such technology has the potential to revolutionize the industry so long as the problems of data security and operational reliability may be adequately addressed 256 CHAPTER 10 DIGITAL ELECTRONIC INSTRUMENTATION References HART Communications Technical Information L452 EN SAMSON AG Chapter 11 Instrument calibration 11 1 The meaning of calibration Every instrument has at least one input and one output For a pressure sensor the input would be some fluid pressure and the output would most likely be an electronic signal For a loop indicator the input would be a 4 20 mA current signal and the output would be a hu
190. Element 131 First Law of Motion 21 Fisher LevelTrol displacer instrument 382 Five point calibration 265 Five valve manifold 323 Flame ionization detector GC 563 Flange taps orifice plate 465 Flapper 213 Flexure 269 Float level measurement 352 Flow conditioner 474 Flow prover 284 Flow switch 185 Flow tube 469 Flow straightening vanes 474 Fluid 27 28 Flume 491 581 Force balance system 234 312 Form A contact 170 Form B contact 170 Form C contact 173 Foxboro magnetic flowtube 510 Foxboro model 13 differential pressure transmitter 239 Foxboro model 557 pneumatic square root extractor 457 Foxboro model IDP10 differential pressure transmitter 302 316 Freezing point of water 275 Frequency shift keying 246 INDEX FSK 246 Full active bridge circuit 106 Full flow taps orifice plates 466 Function inverse 573 Function piecewise 587 Gain controller 604 616 Galilei Galileo 21 Gas 28 Gas expansion factor 477 Gas Laws 47 Gas calibration 287 Gas span 287 Gauge line 318 Gauge pressure 43 294 Gauge tube 318 Gay Lussac s Law 47 Generator 80 Gentile flow tube 469 Gerlach scale 38 Ground 96 Grounding magnetic flowmeters 509 Guided wave radar 395 Hagen Poiseuille equation 54 485 628 Hall Effect sensor 311 Hand switch 172 HART multidrop mode 252 Head fluid 55 Heat exchanger 596 Heat tape 341 Heat tracing 340
191. Flow Measurement Engineering Handbook states that venturi tubes may come within 1 to 3 percent of ideal while a square edged orifice plate may perform as poorly as only 60 percent of theoretical 478 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT True gas flow Theoretical gas flow True liquid flow Theoretical liquid flow Y Incorporating these factors into the ideal volumetric flow equation developed on page 452 we arrive at the following formulation Q v2 CY Az 2 3 A 1 4 If we wished we could even add another factor to account for any necessary unit conversions N getting rid of the constant 2 in the process 2 P A Sadly neither the discharge coefficient C nor the gas expansion factor Y will remain constant across the entire measurement range of any given flow element These variables are subject to some change with flow rate which further complicates the task of accurately inferring flow rate from differential pressure measurement However if we know the values of C and Y for typical flow conditions we may achieve good accuracy most of the time Likewise the fact that C and Y change with flow places limits on the accuracy obtainable with the proportionality constant formulae seen earlier Whether we are measuring volumetric or mass flow rate the k factor calculated at one particular flow condition will not hold constant for all flow conditions P P p W ky p Pi Pa
192. IC PRESSURE 381 Span 11 52 W C Looking at our two thought experiment illustrations we see that the only difference between the two scenarios is the type of liquid filling that 3 foot region between the LRV and URV marks Therefore the only difference between the transmitter s pressures in those two conditions will be the difference in height multiplied by the difference in density Not only is this an easy way for us to quickly calculate the necessary transmitter span but it also is a way for us to check our previous work we see that the difference between the LRV and URV pressures is indeed a difference of 11 52 inches water column just as this method predicts Interface level LRV Interface level URV Fill fluid Fill fluid 1 5 ft S G 1 09 1 5 ft S G 1 09 i f 7 9ft 3 ft 9 ft MN PE gt LRV 4 5 ft 4 5 ft 382 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT 13 4 Displacement Displacer level instruments exploit Archimedes Principle to detect liquid level by continuously measuring the weight of a rod immersed in the process liquid As liquid level increases the displacer rod experiences a greater buoyant force making it appear lighter to the sensing instrument which interprets the loss of weight as an increase in level and transmits a proportional output signal In practice a displacer level instrument usually takes the following form Cap Weight mea
193. ITCHES 175 7 4 Proximity switches A proximity switch is one detecting the proximity closeness of some object By definition these switches are non contact sensors using magnetic electric or optical means to sense the proximity of objects Recall that the normal status of a switch is the condition of minimum stimulus A proximity switch will be in its normal status when it is distant from any actuating object Being non contact in nature proximity switches are often used instead of direct contact limit switches for the same purpose of detecting the position of a machine part with the advantage of never wearing out over time due to repeated physical contact However the greater complexity and cost of a proximity switch over a mechanical limit switch relegates their use to applications where lack of physical contact yields tangible benefits Most proximity switches are active in design That is they incorporate a powered electronic circuit to sense the proximity of an object Inductive proximity switches sense the presence of metallic objects through the use of a high frequency magnetic field Capacitive proximity switches sense the presence of non metallic objects through the use of a high frequency electric field Optical switches detect the interruption of a light beam by an object The schematic diagram symbol for a proximity switch with mechanical contacts is the same as for a mechanical limit switch except the switch s
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195. Lessons In Industrial Instrumentation By Tony R Kuphaldt Version 0 2 Released September 29 2008 2008 Tony R Kuphaldt This book is licensed under the Creative Commons Attribution License version 3 0 To view a copy of this license turn to page 631 The terms and conditions of this license allow for free copying distribution and or modification of all licensed works by the general public Revision history e Version 0 1 July to September 2008 initial development e Version 0 2 released September 29 2008 for Fall quarter student use Version numbers ending in odd digits are developmental e g 0 7 1 23 4 5 with only the latest revision made accessible to the public Version numbers ending in even digits e g 0 6 1 0 2 14 are considered public release and will be archived Version numbers beginning with zero e g 0 1 0 2 etc represent incomplete editions lacking major chapters or topic coverage ii Contents Preface 3 1 Physics 7 1 1 Werms and Definitions db dt e leh ee oh AA dd 8 T2 Metric prefixes ras a A a E Se aa ag A RE 9 1 3 Unit conversions and physical constants o e e 10 1 3 1 Conversion formulae for temperature e 13 1 3 2 Conversion factors for distance e 13 1 3 3 Conversion factors for volume o 13 1 3 4 Conversion factors for velocity o o e e 0000004 13 1 3 5 Conversion factors f
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197. PHYSICAL CONSTANTS 11 Now we see how the unit of quarts cancels from the numerator of the first fraction and the denominator of the second unity fraction leaving only the unit of gallons left standing 35 qt 1 gal 8 l T te The reason this conversion technique is so powerful is that it allows one to do a large range of unit conversions while memorizing the smallest possible set of conversion factors Here is a set of six equal volumes each one expressed in a different unit of measurement 1 gallon gal 231 0 cubic inches in 4 quarts qt 8 pints pt 128 fluid ounces fl oz 3 7854 liters 1 Since all six of these quantities are physically equal it is possible to build a unity fraction out of any two to use in converting any of the represented volume units into any of the other represented volume units Shown here are a few different volume unit conversion problems using unity fractions built only from these factors 40 gallons converted into fluid ounces 40 gal 128 fl oz 5120 fl oz 1 1 gal 5 5 pints converted into cubic inches 5 pt 231 in dea oi 4883 in 1 8 pt 11701 4 at 12 i ron By contrast if we were to try to memorize a 6 x 6 table giving conversion factors between any two of six volume units we would have to commit 30 different conversion factors to memory Clearly the ability to set up unity fractions is a much more memory effi
198. Pressure Fields and Fluid Acceleration video Massachusetts Institute of Technology Educational Services Incorporated 1962 Vennard John K Elementary Fluid Mechanics 3rd Edition John Wiley amp Sons Inc New York NY 1954 Weast Robert C Astel Melvin J and Beyer Wiliam H CRC Handbook of Chemistry and Physics 64th Edition CRC Press Inc Boca Raton FL 1984 Chapter 2 Chemistry 2 1 Terms and Definitions e Atom the smallest unit of matter that may be isolated by chemical means e Element a substance composed of atoms all sharing the same number of protons in their nuclei e Particle a part of an atom separable from the other portions only by levels of energy far in excess of chemical reactions e Molecule the smallest unit of matter composed of two or more atoms joined by electron interaction in a fixed ratio The smallest unit of a compound e Jon an atom or molecule that is not electrically balanced e Compound a substance composed of identical molecules e Mixture a substance composed of different atoms or molecules 61 62 CHAPTER 2 CHEMISTRY 2 2 Periodic table fH 1 He 2 Hydrogen Periodic Table of the Elements Helium 1 00794 4 00260 A Metalloids Nonmetals A 1s 1s Li 3 Be 4 Symbol k 19 Atomic number B 5 C 6 N 7 Jo 8 F 9 Ne 10 Lithium Beryllium _ Potassium Boron Carbon Nitrogen Oxygen Fluorine Neon
199. RESSURE BASED FLOWMETERS 481 Note the special transmitter manifolds built to accept both the differential pressure and absolute pressure Rosemount model 3051 transmitters Also note the quick change fittings the ribbed cast iron housings holding the orifice plates which cannot be directly seen to facilitate convenient change out of the orifice plates which is periodically necessary due to wear It is not unheard of to replace orifice plates on a daily basis to ensure the sharp orifice edges necessary for accurate measurement An alternative strategy is to use a single multi variable transmitter capable of measuring gas temperature as well as both static and differential pressures This approach enjoys the advantage of simpler installation over the multi instrument approach 13 This is especially true in the gas exploration industry where natural gas coming out of the earth is laden with a substantial amount of sand rocks and grit 482 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT Digital bus o zz O O o Multivariable transmitter measures static pressure differential pressure and temperature in one unit Orifice plate The Rosemount model 3095MV and Yokogawa model EJX910 are examples of multi variable transmitters designed to perform compensated gas flow measurement equipped with multiple pressure sensors a connection port for an RTD temperature sensor and sufficient digital computing power to
200. TINUOUS FLUID FLOW MEASUREMENT 15 1 2 Orifice plates Of all the pressure based flow elements in existence the most common is the orifice plate This is simply a metal plate with a hole in the middle for fluid to flow through Orifice plates are typically sandwiched between two flanges of a pipe joint allowing for easy installation and removal Orifice plate Nut Nut gt point of maximum rm de Conos Y Nut Nut The point where the fluid flow profile constricts to a minimum cross sectional area after flowing through the orifice is called the vena contracta and it is the area of minimum fluid pressure The vena contracta corresponds to the narrow throat of a venturi tube The simplest design of orifice plate is the square edged concentric orifice This type of orifice plate is manufactured by machining a precise straight hole in the middle of a thin metal plate Looking at a side view of a square edged concentric orifice plate reveals sharp edges 90 corners at the hole 15 1 PRESSURE BASED FLOWMETERS 459 Square edged concentric orifice plate Paddle front view side view Sharp edge Square edged orifice plates may be installed in either direction since the orifice plate appears exactly the same from either direction of fluid approach In fact this allows square edged orifice plates to be used for measuring bidirectional flow rates where the fluid flow direction reverses itself from ti
201. TO INSTRUMENT VARIABLES 193 Instead of y 16x 4 as is the case for direct acting instruments this reverse acting instrument follows the linear equation y 16x 20 x 16 mA 5007 20 mA current First we need to to convert the pressure signal value of 12 7 PSI into a percentage of 3 15 PSI range We will manipulate the percentage pressure formula to solve for z T 12 PSI aa 3 PSI pressure 12 PSI pressure 3 PSI a 100 x pressure 3 PSI 100 12 PSI E pressure 3 PSI B 12 PSI ee Next we plug in the 12 7 PSI signal value and solve for x 2 PSI 3 PSI L 12 PSI ae x 80 8 This tells us that 12 7 PSI represents 80 8 of the 3 15 PSI signal range Plugging this percentage value into our modified negative slope percentage current formula will tell us how much current is necessary to generate this 12 7 PSI pneumatic output 16 mA 20 mA current es 100 80 8 16 mA 20 mA 7 07 mA Therefore a current signal of 7 07 mA is necessary to drive the output of this reverse acting I P transducer to a pressure of 12 7 PSI 8 2 6 Graphical interpretation of signal ranges A helpful illustration for students in understanding analog signal ranges is to consider the signal range to be expressed as a length on a number line For example the common 4 20 mA analog current signal range would appear as such
202. TRANSMITTERS 315 degradation of spring characteristics Unfortunately force balance instruments have significant disadvantages as well Force balance mechanisms tend to be bulky and they translate external vibration into inertial force which adds noise to the output signal Also the amount of electrical power necessary to provide adequate balancing force in an electronic force balance transmitter is such that it is nearly impossible to limit below the level necessary to ensure intrinsic safety protection against the accidental ignition of explosive atmospheres by limiting the amount of energy the instrument could possibly discharge into a spark 7One instrument technician I encountered referred to the Foxboro E13 differential pressure transmitter as pig iron after having to hoist it by hand to the top of a distillation tower 316 CHAPTER 12 CONTINUOUS PRESSURE MEASUREMENT 12 5 Differential pressure transmitters One of the most common and most useful pressure measuring instruments in industry is the differential pressure transmitter This device senses the difference in pressure between two ports and outputs a signal representing that pressure in relation to a calibrated range Differential pressure transmitters may be based on any of the previously discussed pressure sensing technologies so this section discusses practical application rather than internal workings Differential pressure transmitters look something like
203. TRUMENTATION Chapter 9 Pneumatic instrumentation While electricity is commonly used as a medium for transferring energy across long distances it is also used in instrumentation to transfer information A simple 4 20 mA current loop uses direct current to represent a process measurement in percentage of span such as in this example Indicator Pressure transmitter 24 VDC supply Applied pressure The transmitter senses an applied fluid pressure from the process being measured regulates electric current in the series circuit according to its calibration 4 mA no pressure 20 mA full pressure and the indicator ammeter registers this measurement on a scale calibrated to read in pressure units If the calibrated range of the pressure transmitter is 0 to 250 PSI then the indicator s scale will be labeled to read from 0 to 250 PSI as well No human operator reading that scale need worry about how the measurement gets from the process to the indicator the 4 20 mA signal medium is transparent to the end user as it should be Air pressure may be used as an alternative signaling medium to electricity Imagine a pressure transmitter designed to output a variable air pressure according to its calibration rather than a variable electric current Such a transmitter would have to be supplied with a source of constant pressure compressed air instead of an electric voltage and the resulting output signal would be conveyed to the
204. The HART transmitter may be modeled as two parallel current sources one DC and one AC The DC current source provides the 4 20 mA regulation necessary to represent the process measurement as an analog current value The AC current source turns on and off as necessary to inject the 1 mA P P audio tone HART signal along the two wires Inside the transmitter is also a HART modem for interpreting AC voltage tones as HART data packets Thus data transmission takes place through the AC current source and data reception takes place through a voltage sensitive modem all inside the transmitter all talking along the same two wires that carry the DC 4 20 mA signal For ease of connection in the field HART devices are designed to be connected in parallel with 10 1 THE HART DIGITAL ANALOG HYBRID STANDARD 247 each other This eliminates the need to break the loop and interrupt the DC current signal every time we wish to connect a HART communicator device to communicate with the transmitter A typical HART communicator may be modeled as another AC current source along with another HART voltage sensitive modem for receiving HART data Connected in parallel with the HART transmitter the complete circuit looks something like this HART transmitter Power supply Pa Computer HART communicator The actual hand held communicator may look like one of these devices 248 CHAPTER 10 DIGITAL ELECTRONIC INSTRUMENTATION With all thes
205. This concept will be immediately familiar to anyone who has ever had to bleed air bubbles out of an automobile brake system With air bubbles in the system the brake pedal has a spongy feel when depressed and much pedal motion is required to achieve adequate braking force After bleeding all air out of the brake fluid tubes the pedal motion feels much more solid than before with minimal motion required to achieve adequate braking force Imagine the brake pedal being the isolating diaphragm and the brake pads being the pressure sensing element inside the instrument If enough gas bubbles exist in the tubes the brake pedal might stop against the floor when fully pressed preventing full force from ever reaching the brake pads Likewise if the isolating diaphragm hits a hard motion limit due to gas bubbles in the fill fluid the sensing element will not experience full process pressure 330 CHAPTER 12 CONTINUOUS PRESSURE MEASUREMENT 12 6 4 Remote and chemical seals Isolating diaphragms have merit even in scenarios where pressure pulsations are not a problem Consider the case of a food processing system where we must remotely measure pressure inside a mixing vessel Wall Pressure gauge The presence of the tube connecting the vessel to the pressure gauge poses a hygiene problem Stagnant process fluid in this case some liquid food product inside the tube can support microbial growth which will eventually contaminate
206. This means after we have calculated a value for k based on a particular flow condition we can only trust the results of the equation for flow conditions not too different from the one we used to calculate k Q k As you can see in both flow equations the density of the fluid p is an important factor If fluid density is relatively stable we may treat p as a constant incorporating its value into the proportionality factor k to make the two formulae even simpler Q kovy Pi Pa W kwy Pi Po However if fluid density is subject to change over time we will need some means to continually calculate p so that our inferred flow measurement will remain accurate Variable fluid density is a 15 1 PRESSURE BASED FLOWMETERS 479 typical state of affairs in gas flow measurement since all gases are compressible by definition A simple change in static gas pressure within the pipe is all that is needed to make p change which in turn affects the relationship between flow rate and differential pressure drop The American Gas Association AGA provides a formula for calculating volumetric flow of any gas using orifice plates in their 3 Report compensating for changes in gas pressure and temperature A variation of that formula is shown here consistent with previous forms in this section Q N CY Az Z P Pi Po GpZ 1 T Where Q Volumetric flow rate e g gallons per minute standard cubic feet per second N Unit conversi
207. This particular controller has two digital displays one for process variable PV and one for setpoint SP with a bargraph for displaying the output value Out One pushbutton provides the operator with a way to switch between Automatic and Manual modes A M while two other pushbuttons provide means to decrement and increment either the setpoint value in Automatic mode or the Output value in Manual mode Inside the controller a dependent current source provides the 4 20 mA DC current signal to the I P transducer Like all current sources its purpose is to maintain current in the loop circuit regardless of circuit resistance or any external voltage sources Unlike a constant current source a dependent current source represented by a diamond shape instead of a circle shape varies its current value according to the dictates of some external stimulus In this case either the mathematical function of the controller Automatic mode or the arbitrary setting of the human operator Manual mode tells the current source how much DC current it should maintain in the circuit For example if the operator happened to switch the controller into Manual mode and set the output value at 50 the proper amount of DC current for this signal percentage would be 12 mA exactly half way between 4 mA and 20 mA If everything is working properly the current in the loop circuit to the I P transducer should remain exactly at 12 mA regardless of sl
208. U coaxial cable at 28 5 pF capacitance per foot the time constant will be T RC T 700 x 10 Q 28 5 x 107 F ft 30 ft T 700 x 10 0 8 55 x 107 F T 0 599 seconds Considering the simple approximation of 5 time constants being the time necessary for a first order system such as this to achieve within 1 of its final value after a step change this means a sudden change in voltage at the pH probe caused by a sudden change in pH will not be fully registered by the pH instrument until almost 3 seconds after the event has passed It may seem impossible for a cable with capacitance measured in picofarads to generate a time constant easily within the range of human perception but it is indeed reasonable when you consider the exceptionally large resistance value of a glass pH measurement electrode For this reason and also for the purpose of limiting the reception of external electrical noise it is best to keep the cable length between pH probe and instrument as short as possible When short cable lengths are simply not practical a preamplifier module may be connected between the pH probe assembly and the pH instrument Such a device is essentially a unity gain gain 1 amplifier designed to repeat the weak voltage output of the pH probe assembly in a much stronger i e lower impedance form so that the effects of cable capacitance will not be as severe A unity gain operational amplifier voltage buffer circuit
209. UMENT SUITABILITY 413 References Autolevel Application Note AN 01C22A01 01E Yokogawa Electric Corporation 2006 Boiler Drum Level Transmitter Calibration application data sheet 00800 0100 3055 Rosemount Inc Chanhassen MN 2001 Brumbi Detlef Fundamentals of Radar Technology for Level Gauging 4th Edition Krohne Messtechnik GmbH amp Co KG Duisburg Germany 2003 Bubble Tube Installations For Liquid Level Density and Interface Measurements document MI 020 328 The Foxboro Company Foxboro MA 1988 Fribance Austin E Industrial Instrumentation Fundamentals McGraw Hill Book Company New York NY 1962 Kallen Howard P Handbook of Instrumentation and Controls McGraw Hill Book Company Inc New York NY 1961 Level Measurement Technology Radar document 00816 0100 3209 revision AA Rosemount Inc Chanhassen MN 1999 Lipt k B la G Instrument Engineers Handbook Process Measurement and Analysis Volume I Fourth Edition CRC Press New York NY 2003 MacBeth Michael IAEA CANDU Instrumentation Es Control Course SNERDI Shanghai 1998 Model 1151 Alphaline Pressure Transmitters product manual 00809 0100 4360 revision AA Rosemount Inc Chanhassen MN 1997 Replacing Displacers with Guided Wave Radar technical note 3300_2 02_ CA Rosemount Inc Chanhassen MN 2003 414 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT Chapter 14 Continuous temperature
210. UOUS FLUID FLOW MEASUREMENT 15 4 4 Ultrasonic flowmeters Ultrasonic flowmeters measure fluid velocity by passing high frequency sound waves along the fluid flow path Fluid motion influences the propagation of these sound waves which may then be measured to infer fluid velocity Two major sub types of ultrasonic flowmeters exist Doppler and transit time Both types of ultrasonic flowmeter work by transmitting a high frequency sound wave into the fluid stream the incident pulse and analyzing the received pulse Doppler flowmeters exploit the Doppler effect which is the shifting of frequency resulting from waves emitted by or reflected by a moving object Doppler flowmeters bounce sound waves off of bubbles or particulate material in the flow stream measure the frequency shift and infer fluid velocity If the reflected wave returns from a bubble that is advancing toward the flowmeter sensor the reflected frequency will be greater than the incident frequency If the flow reverses direction and the reflected wave returns from a bubble that is traveling away from the sensor the reflected frequency will be less than the incident frequency Doppler effect ultrasonic flowmeters obviously require flowstream containing bubbles or particulate matter In many applications this is a normal state of affairs municipal wastewater for example However some process fluids are simply too clean and too homogeneous to reflect sound waves In such applic
211. URE MEASUREMENT 12 6 2 Bleed fittings Before removing a pressure transmitter from live service the technician must bleed stored fluid pressure to atmosphere in order to achieve a zero energy state prior to disconnecting the transmitter from the impulse lines Some valve manifolds provide a bleed valve for doing just this but many do not An inexpensive and common accessory for pressure sensing instruments especially transmitters is the bleed valve fitting installed on the instrument as a discrete device The most common bleed fitting is equipped with 1 4 inch male NPT pipe threads for installation into one of the 1 4 inch NPT threaded pipe holes typically provided on pressure transmitter flanges The bleed is operated with a small wrench loosening a ball tipped plug off its seat to allow process fluid to escape through a small vent hole in the side of the fitting The following photographs show close up views of a bleed fitting both assembled left and with the plug fully extracted from the fitting right The bleed hole may be clearly seen in both photographs When installed directly on the flanges of a pressure instrument these bleed valves may be used to bleed unwanted fluids from the pressure chambers for example bleeding air bubbles from an instrument intended to sense water pressure or bleeding condensed water out of an instrument intended to sense compressed air pressure The following photographs show bleed fittings insta
212. Vertical position on graph x Horizontal position on graph m Slope of line b Point of intersection between the line and the vertical y axis This instrument s calibration is no different If we let x represent the input pressure in units of PSI and y represent the output current in units of milliamps we may write an equation for this instrument as follows y 0 167 4 On the actual instrument the pressure transmitter there are two adjustments which let us match the instrument s behavior to the ideal equation One adjustment is called the zero while the other is called the span These two adjustments correspond exactly to the b and m terms of the linear function respectively the zero adjustment shifts the instrument s function vertically on the graph while the span adjustment changes the slope of the function on the graph By adjusting both zero and span we may set the instrument for any range of measurement within the manufacturer s limits 260 CHAPTER 11 INSTRUMENT CALIBRATION It should be noted that for most analog instruments these two adjustments are interactive That is adjusting one has an effect on the other Specifically changes made to the span adjustment almost always alter the instrument s zero point An instrument with interactive zero and span adjustments requires much more effort to accurately calibrate as one must switch back and forth between the lower and upper range points repeatedly to
213. We can have a voltage without having a current but we cannot have a current without first having a voltage to motivate it Current without voltage would be equivalent to motion without a motivating force When electric charges move through a material such as metal they will naturally encounter some friction just as fluid moving through a pipe will inevitably encounter friction We have a name for this friction to electrical charge motion resistance Like voltage and current resistance has its own special unit of measurement the ohm named in honor of the German physicist Georg Simon Ohm At this point it would be good to summarize and compare the symbols and units we use for voltage current and resistance Quantity Algebraic symbol Unit Unit abbreviation Voltage V or E Volt V Current I Ampere or Amp A Resistance R Ohm Q Ohm defined resistance as the mathematical ratio between applied voltage and resulting current v R I Verbally expressed resistance is how much voltage it takes to force a certain rate of current through a conductive material Many materials have relatively stable resistances while others do not Devices called resistors are sold which are manufactured to possess a very precise amount of resistance for the purpose of limiting current in circuits among other things Here is an example of Ohm s Law in action calculate the amount of current in a circuit with a voltage source
214. a Cippoletti weir Q 3 367LH Dividing both sides of the equation by 3 367 and L Q 3 33671 H 3 Taking the 5 root of both sides 3 2 Q 3 367L This in itself may be problematic as some calculators do not have an y function In cases such as this it is helpful to remember that a root is nothing more than an inverse power Therefore we could re write the final form of the equation using a 3 power instead of a 3 root Q Ne m mi 17 2 LIQUID VOLUME MEASUREMENT 583 17 2 Liquid volume measurement When businesses use large vessels to store liquids it is useful to know how much liquid is stored in each vessel A variety of technologies exist to measure stored liquid Hydrostatic pressure radar ultrasonic and tape and float are just a few of the more common technologies Hydrostatic Radar or Ultrasonic Tape and Float Pressure sensor infers Radio or sound waves Float riding on liquid liquid level by measuring bounced off the liquid surface surface moves a metal static pressure developed determine how far away the cable or tape which by the liquid head liquid is from the sensor directly registers level These liquid measuring technologies share a common trait they measure the quantity of liquid in the vessel by measuring liquid height If the vessel in question has a constant cross sectional area throughout its working height e g a vertical cylinder then liquid height will directly correspond
215. a diaphragm based pressure sensor must be designed in such a way that the diaphragm stretches very little over the normal range of operation Limiting the displacement of a diaphragm necessitates highly sensitive motion detection techniques such as strain gauge sensors differential capacitance cells and mechanical resonance sensors to convert that diaphragm s very slight motion into an electronic signal An alternative approach to electronic pressure measurement is to use mechanical pressure sensing elements with more linear pressure displacement characteristics such as bourdon tubes and spring loaded bellows and then detect the large scale motion of the pressure element using a less sophisticated electrical motion sensing device such as a potentiometer LVDT or Hall Effect sensor In other words we take the sort of mechanism commonly found in a direct reading pressure gauge and attach it to a potentiometer or similar device to derive an electrical signal from the pressure measurement This alternative approach is undeniably simpler and less expensive to manufacture than the more sophisticated approaches used with diaphragm based pressure instruments but is prone to greater inaccuracies Even bourdon tubes and bellows are not perfectly linear spring elements and the substantial motions involved with using such pressure elements introduces the possibility of hysteresis errors where the instrument does not respond accurately during reversals
216. a measurement of volume 404 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT so through flexible couplings and the weight of the pipes themselves is borne by outside structures through pipe hangers Support structure Pipe Flexible coupling Support structure Stress relief is very important because any forces acting upon the storage vessel will be interpreted by the load cells as more or less material stored in the vessel The only way to ensure that the load cell s measurement is a direct indication of material held inside the vessel is to ensure that no other forces act upon the vessel except the gravitational weight of the material An interesting problem associated with load cell measurement of vessel weight arises if there are ever electric currents traveling through the load cell s This is not a normal state of affairs but it can happen if maintenance workers incorrectly attach arc welding equipment to the support structure of the vessel or if certain electrical equipment mounted on the vessel such as lights or motors develop ground faults The electronic amplifier circuits interpreting a load cell s resistance will detect voltage drops created by such currents interpreting them as changes in load cell resistance and therefore as changes in material level Sufficiently large currents may even cause permanent damage to load cells as is often the case when the currents in question are generated by arc welding equipment A va
217. a more complex circuit we encounter the potential for mix ups 3500 Q Which resistance do we use to calculate current in this circuit Do we divide our 25 volts by 3500 ohms like we did last time or do we divide it by 1500 ohms or something entirely different The answer to this question lies in the identification of voltages and currents We know that the 25 volt potential will be impressed across the total of the two resistances R and Ra and since there is only one path for current they must share the same current Thus we actually have three voltages Vi Va and Viotat three resistances R1 Ra and Riotat and only one current 1 3 3 ELECTRICAL RESISTANCE AND OHM S LAW 89 Note arrows point in the direction of electron motion Manipulating the Ohm s Law equation originally given R X to solve for V we end up with three equations for this circuit Viotal I Riotal Ry F R V 1 Ri V2 IRo Thus the current in this circuit is 5 milliamps 5 mA the voltage across resistor Ry is 17 5 volts and the voltage across resistor R is 7 5 volts 90 CHAPTER 3 DC ELECTRICITY 3 4 Series versus parallel circuits In addition to Ohm s Law we have a whole set of rules describing how voltages currents and resistances relate in circuits comprised of multiple resistors These rules fall evenly into two categories series circuits and parallel circuits The two circuit types are shown here with squares repre
218. a shield to all the turbulence in the rest of the reservoir The displacer element will no longer be subject to a horizontal blast of oil entering the reservoir nor any wave action to make it bob up and down This section of pipe quiets or stills the oil surrounding the displacer making it easier to measure oil level 410 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT Stilling wells may be used in conjunction with many types of level instruments floats displacers ultrasonic radar and laser to name a few If the process application necessitates liquid liquid interface measurement however the stilling well must be properly installed to ensure the interface level inside the well match the interface levels in the rest of the vessel Consider this example of using a stilling well in conjunction with a tape and float system for interface measurement Yes No Tape a lape Stilling a well In the left hand installation where the stilling well is completely submerged the interface levels will always match In the right hand installation where the top of the stilling well extends above the total liquid level however the two levels may not always match 13 10 LEVEL SENSOR ACCESSORIES 411 The problem here is analogous to what we see with sightglass style level gauges interfaces may be reliably indicated if and only if both ends of the sightglass are submerged see page 350 for an illustrated description of the problem If it is n
219. acBeth in his CANDU Instrumentation amp Control course lesson 1 module 4 page 12 Foxboro s technical notes on bubble tube installations pages 4 through 7 and Rosemount s product manual for their 1151 Alphaline pressure transmitter page 3 7 Interestingly the Rosemount document defines zero range suppression as synonymous with suppression which disagrees with Lipt k s distinction My advice draw a picture if you want the other person to clearly understand what you mean 4As you are about to see the calibration of an elevated transmitter depends on us knowing how much hydrostatic pressure or vacuum in this case is generated within the tube connecting the transmitter to the process vessel If iquid were to ever escape from this tube the hydrostatic pressure would be unpredictable and so would be the accuracy of our transmitter as a level measuring instrument A remote seal diaphragm guarantees no fill fluid will be ost if and when the process vessel goes empty 366 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT 100 T Measurement span 11 ft Capillary tube with fill fluid y 58 3 1b ft 0 Remote seal In this example we see a remote seal system with a fill fluid having a density of 58 3 1b ft and a process level measurement range of 0 to 11 feet of sea water density 64 Ib ft The transmitter elevation is 6 feet which means it will see a vacuum of 2 43 PSI 67 2 inches of water column
220. accumulated area between r and h r is h r A 2y dx r Now writing y in terms of r and x y Vr x and moving the constant 2 outside the integrand h r A 2 Vr r de r Consulting a table of integrals we find this solution for the general form 2 veea a we sin 5 0 2 2 a 17 2 LIQUID VOLUME MEASUREMENT 585 Applying this solution to our particular integral _ 2 A Mr Shr 12 trsi OO 4 TE r Knowing that the stored liquid volume in the horizontal tank will be this area multiplied by the constant length L of the tank our formula for volume is as follows mO ry zz 2 V h rV T rsin EED EE F As you can see the result is far from simple Any instrumentation system tasked with the inference of stored liquid volume by measurement of liquid height in a horizontal cylinder must somehow apply this formula on a continuous basis This is a prime example of how digital computer technology is essential to certain continuous measurement applications Spherical vessels such as those used to store liquefied natural gas LNG and butane present a similar challenge The height volume function is nonlinear because the cross sectional area of the vessel changes with height Calculus provides a way for us to derive an equation solving for stored volume V with height A as the independent variable We begin in a similar manner to the last problem with the mathemati
221. accumulating inaccuracies over time However there is really nothing more definitive for measuring volumetric flow rate than an instrument built to measure individual volumes of fluid with each mechanical cycle As one might guess these instruments are completely immune to swirl and 528 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT other large scale fluid turbulence and may be installed nearly anywhere in a piping system no need for long sections of straight length pipe upstream or downstream Positive displacement flowmeters are also very linear since mechanism cycles are directly proportional to fluid volume 15 8 Weighfeeders A completely different kind of flowmeter is the weighfeeder used to measure the flow of solid material such as powders and grains One of the most common weighfeeder designs consists of a conveyor belt with a section supported by rollers coupled to one or more load cells such that a fixed length of the belt is continuously weighed Material from storage bin Feed chute Solid powder or granules Load cell M Belt motion To process Motor The load cell measures the weight of a fixed length belt section yielding a figure of material weight per linear distance on the belt A tachometer speed sensor measures the speed of the belt The product of these two variables is the mass flow rate of solid material through the weighfeeder FS pes d Where W Mass flow rate e g pounds per sec
222. ace However the weight of that mass depends on gravity zero weight in outer space where there is no gravity to act upon it some weight on Earth and a much greater amount of weight on the planet Jupiter due to the much stronger gravitational field Since mass is the opposition of an object to changes in velocity acceleration it stands to reason that force mass and acceleration for any particular object are directly related to one another F ma Where F Force in newtons metric or pounds British m Mass in kilograms metric or slugs British a Acceleration in meters per second squared metric or feet per second squared British If the force in question is the weight of the object then the acceleration a in question is the acceleration constant of the gravitational field where the object resides For Earth at sea level Ggravity 18 approximately 9 8 meters per second squared or 32 feet per second squared Earth s gravitational acceleration constant is usually represented in equations by the variable letter g instead of the more generic a Since acceleration is nothing more than the rate of velocity change with respect to time the force mass equation may be expressed using the calculus notation of the first derivative du F m Er Where F Force in newtons metric or pounds British m Mass in kilograms metric or slugs British v Velocity in meters per second metric or feet per second British t Ti
223. acting float will measure liquids and solids with equal ease The reason for this limitation is simple a float that always contacts the material surface is likely to become buried if the material in question is a solid powder or granules which must be fed into the vessel from above 354 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT The spring reel s angular position may be measured by a multi turn potentiometer or a rotary encoder located inside the head unit then converted to an electronic signal for transmission to a remote display control and or recording system Such systems are used extensively for measurement of water and fuel in storage tanks If the liquid inside the vessel is subject to turbulence guide wires may be necessary to keep the float cable in a vertical orientation 13 2 FLOAT 355 Guide wire The guide wires are anchored to the floor and roof of the vessel passing through ring lugs on the float to keep it from straying laterally One of the potential disadvantages of tape and float level measurement systems is fouling of the tape and guide wires if the substance is sticky or unclean A variation on the theme of float level measurement is to place a small float inside the tube of a sightglass style level gauge The float s position inside the tube may be readily detected by ultrasonic waves magnetic sensors or any other applicable means Locating the float inside a tube eliminates the need for gu
224. adjust for accuracy 11 3 LRV AND URV SETTINGS DIGITAL TRIM DIGITAL TRANSMITTERS 261 113 LRV and URV settings digital trim digital transmitters The advent of smart field instruments containing microprocessors has been a great advance for industrial instrumentation These devices have built in diagnostic ability greater accuracy due to digital compensation of sensor nonlinearities and the ability to communicate digitally with host devices for reporting of various parameters A simplified block diagram of a smart pressure transmitter looks something like this Smart pressure transmitter Range adjustments LRV URV A Trim adjustments Low High a Trim adjustments Low High Apply pressure here E gt i 4 20 mA ADC y DAC It is important to note all the adjustments within this device and how this compares to the relative simplicity of an all analog pressure transmitter 262 CHAPTER 11 INSTRUMENT CALIBRATION Analog pressure transmitter Calibration adjustments Zero Span Apply pressure here d Note how the only calibration adjustments available in the analog transmitter are the zero and span settings Not so with the smart transmitter Not only can we set lower and upper range values LRV and URV but it is also possible to calibrate the analog to digital and digital to analog converter circuits independently What this means for the calibration t
225. ain constant and that the force generated by the pressure drop will always be in equilibrium with the plummet s weight for any steady flow rate then the relationship F E dictates a constant pressure Thus we may classify the rotameter as a constant pressure variable area flowmeter This stands in contrast to devices such as orifice plates which are variable pressure constant area 15 3 VARIABLE AREA FLOWMETERS 489 Rotameters are very commonly used as purge flow indicators for pressure and level measurement systems requiring a constant flow of purge fluid see pages 338 and 361 for examples Such rotameters are usually equipped with hand adjustable needle valves for manual regulation of purge fluid flow rate A very different style of variable area flowmeter is used extensively to measure flow rate through open channels such as irrigation ditches If an obstruction is placed within a channel any liquid flowing through the channel must rise on the upstream side of the obstruction By measuring this liquid level rise it is possible to infer the rate of liquid flow past the obstruction The first form of open channel flowmeter is the weir which is nothing more than a dam obstructing passage of liquid through the channel Three styles of weir are shown in the following illustration the rectangular Cippoletti and V notch lA Rectangular Cippoletti V notch A rectangular weir has a notch of simple rectangular shape as the
226. ake the form of toggle pushbutton rotary pull chain etc A common form of industrial pushbutton switch looks something like this Button r4 Threaded neck lt Base NC terminal NC terminal NO terminal NO terminal The threaded neck inserts through a hole cut into a metal or plastic panel with a matching nut to hold it in place Thus the button faces the human operator s while the switch contacts reside on the other side of the panel When pressed the downward motion of the actuator breaks the electrical bridge between the two NC contacts forming a new bridge between the NO contacts y Switch in the actuated pressed state NC terminal NC terminal NO terminal NO terminal The schematic diagram symbol for this type of switch looks much like the real thing with the normally closed contact set on top and the normally open contact set below ali e e 7 3 LIMIT SWITCHES 173 7 3 Limit switches Limit switch symbols I A Normally open Normally closed NO NC A limit switch detects the physical motion of an object by direct contact with that object An example of a limit switch is the switch detecting the open position of an automobile door automatically energizing the cabin light when the door opens Recall that the normal status of a switch is the condition of minimum stimulus A limit switch will be in its normal status when it is not in contact with anything i e
227. al conditions of the vessel are too violent for any instrument to survive e g delayed coking vessels in the oil refining industry 21 Beta particles are not orbital electrons but rather than product of elementary particle decay in an atom s nucleus These electrons are spontaneously generated and subsequently ejected from the nucleus of the atom 13 10 LEVEL SENSOR ACCESSORIES 409 13 10 Level sensor accessories Disturbances in the liquid tend to complicate liquid level measurement These disturbances may result from liquid introduced into a vessel above the liquid level splashing into the liquid s surface the rotation of agitator paddles and or turbulent flows from mixing pumps Any source of turbulence for the liquid surface or liquid liquid interface is especially problematic for echo type level sensors which only sense interfaces between vapors and liquids or liquids and liquids If it is not possible to eliminate disturbances inside the process vessel a relatively simple accessory one may add to the process vessel is a vertical length of pipe called a stilling well To understand the principle of a stilling well first consider the application of a hydraulic oil reservoir where we wish to continuously measure oil level The oil flow in and out of this reservoir will cause problems for the displacer element choppy liquid surface A section of vertical pipe installed in the reservoir around the displacer will serve as
228. al length If you displace a spring more substantially the spring material will become strained beyond its elastic limit and either yield permanently deform or fail break The amount of potential energy stored in a tensed spring may be predicted using calculus We know that potential energy stored in a spring is the same as the amount of work done on the spring and work is equal to the product of force and displacement assuming parallel lines of action for both Ep Fx Thus the amount of work done on a spring is the force applied to the spring F ka multiplied by the displacement x The problem is the force applied to a spring varies with displacement and therefore is not constant as we compress or stretch the spring Thus in order to calculate the amount of potential energy stored in the spring E Fx we must calculate the amount of energy stored over infinitesimal amounts of displacement F dx or kx dx and then add those bits of energy up J to arrive at a total E fra dx We may evaluate this integral using the power rule x is raised to the power of 1 in the integrand 1 Ep 5 he Eo Where E Energy stored in the spring in joules metric or foot pounds English k Constant of elasticity or spring constant in newtons per meter metric or pounds per foot English 8Hooke s Law may be written as F kx without the negative sign in which case the force F is the force applied on the spri
229. alancing action is entirely automatic the nozzle backpressure adjusts to whatever it needs to be in order to keep the pointer at the balanced position applying or venting pressure to the bellows as needed to keep the system in a condition of equilibrium What we have created is a negative feedback system where the output of the system nozzle backpressure continuously adjusts to match and balance the input the applied mass This is all well and good but how does this help us determine the mass of the specimen in the left hand pan What good is this self balancing scale if we cannot read the balancing force All we have achieved so far is to make the scale sel balancing The next step is making the balancing force readable to a human operator Before we add the final piece to this automated scale it is worthwhile to reflect on what has been done so far By adding the baffle nozzle and bellows mechanisms to the scale we have abolished the need for brass weights and instead have substituted air pressure In effect the scale translates the specimen s mass into a proportional analogue air pressure What we really need is a way to now translate that air pressure into a human readable indication of mass The solution is simple add the pressure gauge back to the system The gauge will register air pressure but this time the air pressure will be proportionately equivalent to specimen mass In honor of this proportionality we may label the face of
230. ameter after being manufactured on an assembly line From compressed Orifice air supply gt ___ gt 20 PSI Pressure gauge Clearance If the shaft diameter is too small there will be excessive clearance between the shaft and the inside diameter of the test jig causing less air pressure to register on the gauge Conversely if the shaft diameter is too large the clearance will be less and the gauge will register a greater air pressure because the flow of air will be obstructed by the reduced clearance The exact pressure is of no particular consequence to the quality control operator reading the gauge What does matter is that the pressure falls within an acceptable range reflecting proper manufacturing tolerances for the shaft In fact just like the 3 15 PSI receiver gauges used as pneumatic instrument indicators the face of this pressure gauge might very well lack pressure units such as kPa or PSI but rather be labeled with a colored band showing acceptable limits of mechanical fit Test jig This is another example of the analogue nature of pneumatic pressure signals the pressure registered by this gauge represents a completely different variable in this case the mechanical fit of the shaft to the test jig 9 1 PNEUMATIC SENSING ELEMENTS 215 Although it is possible to construct a pneumatic instrument consisting only of a baffle nozzle mechanism this is rarely done Usually the baffle nozzle mechanism
231. amine the a transient pulse signal nanosecond by nanosecond and or when very high frequency AC signals exist over comparatively long conductor lengths Those exceptional cases mentioned earlier in the footnote are possible only because electric charge may be temporarily stored and released by a property called capacitance Even then the law of charge conservation is not violated because the stored charges re emerge as current at later times This is analogous to pouring water into a bucket just because water is poured into a bucket but no water leaves the bucket does not mean that water is magically disappearing It is merely being stored and can re emerge at a later time 3 4 SERIES VERSUS PARALLEL CIRCUITS 91 Series circuit resistors connected in line Voltages add up to equal the total Vota Vi V2 V IL Se Current is the same throughout I if PE total bb I gt pP Resistances add up to equal the total Rota Ry R m R The defining characteristic of a parallel circuit by contrast is that all components share the same two equipotential points Equipotential simply means at the same potential which points along an uninterrupted conductor must be This means there can be only one value of voltage anywhere in the circuit the exact same voltage for all components at any given time The principle of voltage being the same across all parallel connected com
232. ances and Phonograms Treaty of 1996 and the Universal Copyright Convention as revised on July 24 1971 These rights and subject matter take effect in the relevant jurisdiction in which the License terms are sought to be enforced according to the corresponding provisions of the implementation of those treaty provisions in the applicable national law If the standard suite of rights granted under applicable copyright law includes additional rights not granted under this License such additional rights are deemed to be included in the License this License is not intended to restrict the license of any rights under applicable law Creative Commons Notice Creative Commons is not a party to this License and makes no warranty whatsoever in connection with the Work Creative Commons will not be liable to You or any party on any legal theory for any damages whatsoever including without limitation any general special incidental or consequential damages arising in connection to this license Notwithstanding the foregoing two 2 sentences if Creative Commons has expressly identified itself as the Licensor hereunder it shall have all rights and obligations of Licensor Except for the limited purpose of indicating to the public that the Work is licensed under the CCPL Creative Commons does not authorize the use by either party of the trademark Creative Commons or any related trademark or logo of Creative Commons without the prior written consent of Cr
233. and on an RTD circuit Ryire 1 Q wire Ohmmeter Thermistor Re 30k Q R otal 50 002 Q R wire 1Q Ohmmeter RTD Rie 100 Q Rotat 102 Q Clearly wire resistance is more problematic for low resistance RTDs than for high resistance thermistors In the RTD circuit wire resistance counts for 1 96 of the total circuit resistance In the thermistor circuit the same 2 ohms of wire resistance counts for only 0 004 of the total circuit resistance The thermistor s huge reference resistance value swamps the wire resistance to the point that the latter becomes insignificant by comparison In HVAC Heating Ventilation and Air Conditioning systems where the temperature measurement range is relatively narrow the nonlinearity of thermistors is not a serious concern and their relative immunity to wire resistance is a decided advantage over RTDs In industrial temperature measurement applications where the temperature ranges are usually much wider the 1 Swamping is the term given to the overshadowing of one effect by another Here the normal resistance of the high value RTD greatly overshadows any wire resistance such that wire resistance becomes negligible 424 CHAPTER 14 CONTINUOUS TEMPERATURE MEASUREMENT nonlinearity of thermistors is a significant problem so we must find a way to deal with the lesser problem of wire resistance A very old electrical technique known as the Kelvin or four wire method is a pra
234. anged Heat cool traced direct Welded 6 5 INSTRUMENT AND PROCESS EQUIPMENT SYMBOLS 161 6 5 3 Instrument bubbles Main control panel Main control panel Auxiliary control panel Auxiliary control panel Field mounted front mounted rear mounted front mounted rear mounted Discrete instruments Shared Y OU S ho bh Nx fl instruments N N C Se 2 Computer function 2 2 a an a 7 162 CHAPTER 6 INSTRUMENTATION DOCUMENTS 6 5 4 Process valve types Valve generic Globe valve Butterfly valve Ball valve Characterized Gate valve Saunders valve Plug valve ball valve SI HE Ur Pneumatic pinch valve Diaphragm valve Angle valve Three way valve Pressure regulator Pressure relief Check valve or safety valve generic Ball check valve NH o 6 5 INSTRUMENT AND PROCESS EQUIPMENT SYMBOLS 163 6 5 5 Valve actuator types Diaphragm Electric motor Solenoid Piston a 2 3 Electric motor Diaphragm w hand jack w hand jack Electro hydraulic Hand manual Eha pk lt 164 CHAPTER 6 INSTRUMENTATION DOCUMENTS 6 5 6 Valve failure mode Fail open Fail closed or or FO Fail locked Fail indeterminate or FL Fail last drift open Fail last drift closed or or FL DO 6 5 INSTRUMENT AND PROCESS EQUIPMENT SYMBOLS 165 6 5 7 Flow measurement devices flowing left to right Orifice plate Pitot tub
235. anges A solution to this problem is to fill the pressure sensor mechanism with a clean liquid called a fill fluid then transfer pressure from the process fluid to the fill fluid and then to the pressure sensing element using a slack diaphragm or some other membrane Pressure gauge Needle valve partially open Isolating diaphragm In order for the fill fluid and isolating diaphragm to work effectively there cannot be any gas bubbles in the fill fluid it must be a solid hydraulic system from the diaphragm to the sensing element The presence of gas bubbles means that the fill fluid is compressible which means the 12 6 PRESSURE SENSOR ACCESSORIES 329 isolating diaphragm may have to move more than necessary to transfer pressure to the instrument s sensing element This will introduce pressure measurement errors if the isolating diaphragm begins to tense from excessive motion and thereby oppose some process fluid pressure from fully transferring to the fill fluid or hit a stop point where it cannot move any further thereby preventing any further transfer of pressure from process fluid to fill fluid For this reason isolating diaphragm systems for pressure instruments are usually packed with fill fluid at the point and time of manufacture then sealed in such a way that they cannot be opened for any form of maintenance Consequently any fill fluid leak in such a system immediately ruins it 11
236. ansferring simple process data but they can also convey device status information such as self diagnostic test results In other words the 140 CHAPTER 5 INTRODUCTION TO INDUSTRIAL INSTRUMENTATION digital signal coming from this transmitter not only tells the controller how hot the reactor is but it can also tell the controller how well the transmitter is functioning The dashed line exiting the controller shows it to be analog electronic most likely 4 to 20 milliamps DC This electronic signal does not go directly to the control valve however It passes through a device labeled TY which is a transducer to convert the 4 to 20 mA electronic signal into a 3 to 15 PSI pneumatic signal which then actuates the valve In essence this signal transducer acts as an electrically controlled air pressure regulator taking the supply air pressure usually 20 to 25 PSI and regulating it down to a level commanded by the controller s electronic output signal At the temperature control valve TV the 3 to 15 PSI pneumatic pressure signal applies a force on a diaphragm to move the valve mechanism against the restraining force of a large spring The construction and operation of this valve is the same as for the feedwater valve in the pneumatic boiler water control system 5 4 OTHER TYPES OF INSTRUMENTS 141 5 4 Other types of instruments So far we have just looked at instruments that sense control and influence process variables Transmitters
237. ansmitter s output indicates a difference of hydrostatic pressures between the vessel and the wet leg rather than just the hydrostatic pressure of the vessel s liquid level Fortunately the hydrostatic pressure generated by the wet leg will be constant so long as the density of the condensed vapors filling that leg y2 is constant If the wet leg s hydrostatic pressure is constant we can compensate for it by calibrating the transmitter with an intentional zero shift so that it indicates as though it were measuring hydrostatic pressure on a vented vessel Differential pressure y h Constant We may ensure a constant density of wet leg liquid by intentionally filling that leg with a liquid known to be denser than the densest condensed vapor inside the vessel We could also use a differential pressure transmitter with remote seals and capillary tubes filled with liquid of known density 370 Gas pressure with condensible vapors Fill valve CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT Gas pressure with condensible vapors N Remote seal Capillary tube Remote seal Capillary tube The following example shows the calibration table for a compensated leg wet hydrostatic level measurement system for a gasoline storage vessel and water as the wet leg fill fluid Here I am assuming a density of 41 0 lb ft for gasoline and 62 4 lb ft for water with a 0 to 10 foot measurement range and an 11 foot w
238. appearing in different lines 1 3 UNIT CONVERSIONS AND PHYSICAL CONSTANTS 13 1 3 1 Conversion formulae for temperature e F C 9 5 32 e C F 32 5 9 e R F 459 67 e K C 273 15 1 3 2 Conversion factors for distance 1 inch in 2 540000 centimeter cm 1 foot ft 12 inches in 1 yard yd 3 feet ft 1 mile mi 5280 feet ft 1 3 3 Conversion factors for volume 1 gallon gal 231 0 cubic inches in 4 quarts qt 8 pints pt 128 fluid ounces fl oz 3 7854 liters 1 1 milliliter ml 1 cubic centimeter cm 1 3 4 Conversion factors for velocity 1 mile per hour mi h 88 feet per minute ft m 1 46667 feet per second ft s 1 60934 kilometer per hour km h 0 44704 meter per second m s 0 868976 knot knot international 1 3 5 Conversion factors for mass 1 pound Ibm 0 45359 kilogram kg 0 031081 slugs 1 3 6 Conversion factors for force 1 pound force lbf 4 44822 newton N 1 3 7 Conversion factors for area 1 acre 43560 square feet ft 4840 square yards yd 4046 86 square meters m 1 3 8 Conversion factors for pressure either all gauge or all absolute 1 pound per square inch PSI 2 03603 inches of mercury in Hg 27 6807 inches of water in W C 6 894757 kilo pascals kPa 14 CHAPTER 1 PHYSICS 1 3 9 Conversion factors for pressure absolute pressure units only 1 atmosphere Atm 14 7 pounds per squ
239. appears in the next photograph mounted to a yellow wooden base 11 8 PRACTICAL CALIBRATION STANDARDS 279 When sufficient pressure has been accumulated inside the tester to overcome the weight on the piston the piston rises off its rest and floats on the pressurized oil as shown in this close up photograph 280 CHAPTER 11 INSTRUMENT CALIBRATION A common operating practice for any deadweight tester is to gently spin the mass during testing so that the primary piston continually rotates within its cylinder Any motion will prevent static friction from taking hold helping to ensure the only force on the primary piston is the force of the fluid within the deadweight tester Most modern deadweight testers include extra features such as hand pumps and bleed valves in addition to secondary pistons to facilitate both rapid and precise operation The next photograph shows a newer deadweight tester with these extra features There is also such a thing as a pneumatic deadweight tester In these devices a constant flow of gas such as compressed air or bottled nitrogen vents through a bleed port operated by the primary piston The piston moves as necessary to maintain just enough gas pressure inside the unit to suspend the mass es against gravity This gas pressure passes on to the instrument under test just as liquid pressure in a hydraulic deadweight tester passes to the test instrument for comparison 11 8 PRACTICAL CALIBRATION
240. application of physical stimuli to the device a full re calibration Here and here alone we see where calibration is not necessary for a smart instrument If overall measurement accuracy must be verified however there is no substitute for an actual physical calibration and this entails both ADC and DAC trim procedures for a smart instrument 11 4 CALIBRATION PROCEDURES 265 11 4 Calibration procedures 11 4 1 Linear instruments The simplest calibration procedure for a linear instrument is the so called zero and span method The method is as follows 1 Apply the lower range value stimulus to the instrument wait for it to stabilize Move the zero adjustment until the instrument registers accurately at this point Apply the upper range value stimulus to the instrument wait for it to stabilize Move the span adjustment until the instrument registers accurately at this point SS EOE DS Repeat steps 1 through 4 as necessary to achieve good accuracy at both ends of the range An improvement over this crude procedure is to check the instrument s response at several points between the lower and upper range values A common example of this is the so called five point calibration where the instrument is checked at 0 LRV 25 50 75 and 100 URV of range A variation on this theme is to check at the five points of 10 25 50 75 and 90 while still making zero and span adjustments at 0 and 100 Regardless of the
241. are inch absolute PSIA 760 millimeters of mercury absolute mmHgA 760 torr torr 1 01325 bar bar 1 3 10 Conversion factors for energy or work 1 British thermal unit Btu International Table 251 996 calories cal International Table 1055 06 joules J 1055 06 watt seconds W s 0 293071 watt hour W hr 1 05506 x 101 ergs erg 778 169 foot pound force ft lbf 1 3 11 Conversion factors for power 1 horsepower hp 550 ft Ibf s 745 7 watts W 2544 43 British thermal units per hour Btu hr 0 0760181 boiler horsepower hp boiler 1 3 12 Terrestrial constants Acceleration of gravity at sea level 9 806650 meters per second per second m s 32 1740 feet per second per second ft s Atmospheric pressure 14 7 pounds per square inch absolute PSIA 760 millimeters of mercury absolute mmHgA 760 torr torr 1 01325 bar bar Atmospheric gas concentrations e Nitrogen 78 084 e Oxygen 20 946 e Argon 0 934 e Carbon Dioxide CO2 0 033 e Neon 18 18 ppm Helium 5 24 ppm Methane CH4 2 ppm Krypton 1 14 ppm Hydrogen 0 5 ppm Nitrous Oxide N20 0 5 ppm Xenon 0 087 ppm 1 3 UNIT CONVERSIONS AND PHYSICAL CONSTANTS 15 1 3 13 Properties of water Freezing point at sea level 32 F 0 C Boiling point at sea level 212 F 100 C Density of water at 4 C 1000 kg m 1 g cm 1 kg liter 62 428 lb ft 1 951 slugs ft
242. art liquid interface level indication in a sightglass is to keep both ports nozzles submerged 13 1 LEVEL GAUGES SIGHTGLASSES 351 Nozzle is submerged Oil Water Nozzle is submerged Another troublesome scenario for level gauges is when the liquid inside the vessel is substantially hotter than the liquid in the gauge causing the densities to be different This is commonly seen on boiler level gauges where the water inside the sightglass cools off substantially from its former temperature inside the boiler drum Water cold Looking at the sightglass as a U tube manometer again we see that unequal height liquid columns may indeed balance each other s hydrostatic pressures if the two columns are comprised of liquids with different densities The weight density of water is 62 4 lb ft at standard temperature but may be as low as only 36 lb ft at temperatures common for power generation boilers 352 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT 13 2 Float Perhaps the simplest form of solid or liquid level measurement is with a float a device that rides on the surface of the fluid or solid within the storage vessel The float itself must be of substantially lesser density than the substance of interest and it must not corrode or otherwise react with the substance Floats may be used for manual gauging of level as illustrated here Person A person lowers a float down into a storage vessel using a
243. as a scalar quantity In other words we use the sine and cosine functions to represent what this wave is doing just like we used the crank diagram to represent the voltage as a rotating vector By doing this we can represent the waveforms as static amplitudes vector lengths rather than as instantaneous quantities that alternately peak and dip over time The problem with this approach is that the math gets a lot tougher V coswt j sin wt d CG coswt j sinwt I C wsin wt jw cos wt 4 4 PHASOR MATHEMATICS 125 I wC sinwt j coswt V coswt j sin wt I wC sinwt j coswt The final result is so ugly no one would want to use it We may have succeeded in obtaining a ratio of V to I that doesn t blow up at certain values of t but it provides no practical insight into what the capacitor will really do when placed in the circuit Phasors to the rescue Instead of representing the source voltage as a sum of trig functions V coswt jsinwt we will use Euler s Relation to represent it as a complex exponential and differentiate from there I N jwt C F V e Dos I xA ek jwt Cae I juCet V ejut I jwCesvt V 1 I jw V e ad I JOC Note how the exponential term completely drops out of the equation leaving us with a clean ratio strictly in terms of capacitance C angular velocity w and of course j This is the power of phasors it transforms an ugly math problem into something trivial by
244. ascend or descend in a vehicle where the pressure inside our bodies does not have time to equalize with the pressure outside and we feel the force of that differential pressure on our eardrums If we wish to speak of a fluid pressure in terms of how it compares to a perfect vacuum absolute zero pressure we specify it in terms of absolute units For example when I said earlier that the atmospheric pressure at sea level was 14 7 PSI what I really meant is that it is 14 7 PSIA pounds per square inch absolute meaning 14 7 pounds per square inch greater than a perfect vacuum When I said earlier that the air pressure inside an inflated car tire was 35 PSI what I really meant is that it was 35 PSIG pounds per square inch gauge meaning 35 pounds per square inch greater than ambient air pressure When units of pressure measurement are specified without a G or A suffix it is usually but not always assumed that gauge pressure relative to ambient pressure is meant This offset of 14 7 PSI between absolute and gauge pressures can be confusing if we must convert between different pressure units Suppose we wished to express the tire pressure of 35 PSIG in units of inches of water column W C If we stay in the gauge pressure scale all we have to do is multiply by 27 68 35 PSI g 27 68 W C 1 1 PSI 968 8 W C Note how the fractions have been arranged to facilitate cancellation of units The PSI unit in the
245. asurement and Analysis Volume I Fourth Edition CRC Press New York NY 2003 Novak Joe What Is Conductivity And How Is It Measured Hach Company 2003 Sadar Michael J Turbidity Science Technical Information Series Booklet No 11 Hach Company 1998 Scott Raymond P W Gas Chromatography Library4Science LLC 2003 Scott Raymond P W Gas Chromatography Detectors Library4Science LLC 2003 Scott Raymond P W Liquid Chromatography Library4Science LLC 2003 Scott Raymond P W Liquid Chromatography Detectors Library4Science LLC 2003 Scott Raymond P W Principles and Practice of Chromatography Library4Science LLC 2003 Sherman R E Rhodes L J Analytical Instrumentation practical guides for measurement and control ISA Research Triangle Park NC 1996 Shinskey Francis G pH and pION Control in Process and Waste Streams John Wiley amp Sons New York NY 1973 Theory and Practice of pH Measurement PN 44 6033 Rosemount Analytical 1999 Chapter 17 Signal characterization Mathematics is full of complementary principles and symmetry Perhaps nowhere is this more evident than with inverse functions functions that un do one another when put together A few examples of inverse functions are shown in the following table Fe FTE Addition Subtraction Multiplication Division Power Root Exponential Logarithm Derivative Integral Inverse functions are vi
246. ate of energy to a low state of energy releasing the difference in energy in some form heat light etc Conversely an input of energy is required to break that chemical and force the atoms to separate An example of this is the strong bond between two atoms of hydrogen H and one atom of oxygen O to form water H20 When hydrogen and oxygen atoms bond together to form water they release energy This by definition is an exothermic reaction but we know it better as combustion hydrogen is flammable in the presence of oxygen A reversal of this reaction occurs when water is subjected to an electrical current breaking water molecules up into hydrogen and oxygen gas molecules This process of forced separation requires a substantial input of energy to accomplish which by definition makes it an endothermic reaction Specifically the use of electricity to cause a chemical reaction is called electrolysis Energy storage and release is the purpose of the so called hydrogen economy where hydrogen is a medium of energy distribution The reasoning behind a hydrogen economy is that different sources of energy will be used to separate hydrogen from oxygen in water then that hydrogen will be transported to points of use and consumed as a fuel releasing energy All the energy released by the hydrogen at the point of use comes from the energy sources tapped to separate the hydrogen from oxygen in water Thus the purpose of hydrogen in a hydroge
247. ating hydrostatic pressures seen at each side of the transmitter Interface level LRV Fill fluid SG 1 09 ey E Electronic output signal We know from our previous exploration of this setup that any hydrostatic pressure resulting from liquid level above the top remote seal location is irrelevant to the transmitter since it is seen on both sides of the transmitter and thus cancels out All we must do then is calculate hydrostatic pressures as though the total liquid level stopped at that upper diaphragm connection point First calculating the hydrostatic pressure seen at the high port of the transmitter 10Here I will calculate all hydrostatic pressures in units of inches water column This is relatively easy because we have been given the specific gravities of each liquid which make it easy to translate actual liquid column height into column heights of pure water 13 3 HYDROSTATIC PRESSURE 379 Phigh 4 5 feet of heavy liquid 4 5 feet of light liquid Phigh 54 inches of heavy liquid 54 inches of light liquid Phigh W C 54 inches of heavy liquid 1 1 54 inches of light liquid 0 78 Phnign W C 59 4 W C 42 12 W C Phign 101 52 W C Next calculating the hydrostatic pressure seen at the low port of the transmitter Prow 9 feet of fill fluid Prow 108 inches of fill fluid Prow W C 108 inches of fill fluid 1 09 Piow 117 72 W C The differen
248. ations a different sort of ultrasonic velocity detection technique must be applied Transit time flowmeters sometimes called counterpropagation flowmeters use a pair of opposed sensors to measure the time difference between a sound pulse traveling with the fluid flow versus a sound pulse traveling against the fluid flow Since the motion of fluid tends to carry a sound wave along the sound pulse transmitted downstream will make the journey faster than a sound pulse transmitted upstream 15 4 VELOCITY BASED FLOWMETERS 513 In this flowmeter design a clean fluid with no solid impurities is essential for good signal transmission One potential problem with the transit time flowmeter is being able to measure the true average fluid velocity when the flow profile changes with Reynolds number If just one ultrasonic beam is used to probe the fluid velocity the path this beam takes will likely see a different velocity profile as the flow rate changes and the Reynolds number changes along with it Recall the difference in fluid velocity profiles between low Reynolds number flows left and high Reynolds number flows right Laminar flow Turbulent flow Velocity e Velocity profile OLAS Fluid flow gt OO 55 profile OF 0S CO gt Fluid flow gt gt AAA A popular way to mitigate this problem is to use multiple sensor pairs sending acoustic signals along multiple paths through the fluid i e
249. atus of a switch The confusion becomes evident though when you consider the case of a different kind of discrete sensor such as a flow switch A flow switch is built to detect fluid flow through a pipe In a schematic diagram the switch symbol appears to be a toggle switch with a flag hanging below The schematic diagram of course only shows the circuitry and not the pipe where the switch is physically mounted 7 1 NORMAL STATUS OF A SWITCH 171 A low coolant flow alarm circuit L L Flow switch This particular flow switch is used to trigger an alarm light if coolant flow through the pipe ever falls to a dangerously low level and the contacts are normally closed as evidenced by the closed status in the diagram Here is where things get confusing even though this switch is designated as normally closed it will spend most of its lifetime being held in the open status by the presence of adequate coolant flow through the pipe Only when the flow through the pipe slows down enough will this switch return to its normal status remember the condition of minimum stimulus and conduct electrical power to the lamp In other words the normal status of this switch closed is actually an abnormal status for the process it is sensing low flow Students often wonder why process switch contacts are labeled according to this convention of minimum stimulus instead of according to the typical status of the process
250. ause of the problem lies within the process itself As was mentioned before this is an example of a pneumatic compressed air control system where all the instruments operate on compressed air and use compressed air as the signaling medium Pneumatic instrumentation is an old technology dating back many decades While most modern instruments are electronic in nature pneumatic instruments still find application within industry The most common industry standard for pneumatic pressure signals is 3 to 15 PSI with 3 PSI representing low end of scale and 15 PSI representing high end of scale The following table shows the meaning of different signal pressures are they relate to the level transmitter s output Transmitter air signal pressure Steam drum water level 3 PSI 0 Empty 6 PSI 25 9 PSI 50 12 PSI 75 15 PSI 100 Full Likewise the controller s pneumatic output signal to the control valve uses the same 3 to 15 PSI standard to command different valve positions Controller output signal pressure Control valve position 3 PSI 0 open Fully shut 6 PSI 25 open 9 PSI 50 open 12 PSI 75 open 15 PSI 100 Fully open It should be noted the previously shown transmitter calibration table assumes the transmitter measures the full range of water level possible in the drum Usually this is not the case Instead the transmitter will be calibrated so that it only senses a narr
251. ay 15 4 VELOCITY BASED FLOWMETERS 495 15 4 Velocity based flowmeters The Law of Continuity for fluids states that the product of mass density p cross sectional pipe area A and average velocity U must remain constant through any continuous length of pipe ee S mp ap PA pA P3A3V3 If the density of the fluid is not subject to change as it travels through the pipe a very good assumption for liquids we may simplify the Law of Continuity by eliminating the density terms from the equation AyD A207 The product of cross sectional pipe area and average fluid velocity is the volumetric flow rate of the fluid through the pipe Q Av This tells us that fluid velocity will be directly proportional to volumetric flow rate given a known cross sectional area and a constant density for the fluid flowstream Any device able to directly measure fluid velocity is therefore capable of inferring volumetric flow rate of fluid in a pipe This is the basis for velocity based flowmeter designs 496 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT 15 4 1 Turbine flowmeters Turbine flowmeters use a free spinning turbine wheel to measure fluid velocity much like a miniature windmill installed in the flow stream The fundamental design goal of a turbine flowmeter is to make the turbine element as free spinning as possible so that no torque is required to sustain the turbine s rotation If this goal is achieved the turbine blades
252. ay up the column as it is at the bottom 1 8 FLUID MECHANICS 35 Water column weight 62 4 Ibs Pressure gauge Half way up 31 2 PSI Cross sectional Pressure gauge tube area 1 in 62 4 PSI The reason for this apparent discrepancy is that the source of pressure in this fluid system comes from the weight of the water column itself Half way up the column the water only experiences half the total weight 31 2 pounds and so the pressure is half of what it is at the very bottom We never dealt with this effect before because we assumed the force exerted by the piston in the hydraulic lift was so large that it swamped the weight of the fluid itself Here with our very tall column of water 144 feet tall the effect of gravity upon the water s mass is quite substantial Indeed without a piston to exert an external force on the water weight is the only source of force we have to consider when calculating pressure An interesting fact about pressure generated by a column of fluid is that the width or shape of the containing vessel is irrelevant the height of the fluid column is the only dimension we need to consider Examine the following tube shapes all connected at the bottom 36 CHAPTER 1 PHYSICS Since the force of fluid weight is generated only along the axis of gravitational attraction straight down that is the only axis of measurement important in determining hydrostatic fluid pressure The fix
253. be expended at the load motor with very little wasted along the path wires This makes electricity the most efficient means of energy transport known The electric currents common in electric power lines may range from hundreds to thousands of amperes The currents conveyed through power receptacles in your home typically are no more than 15 or 20 amperes The currents in the small battery powered circuits you will build are even less fractions of an ampere For this reason we commonly use the metric prefix milli one one thousandth to express these small currents For instance 10 milliamperes is 0 010 amperes and 500 milliamperes is one half of an ampere 82 CHAPTER 3 DC ELECTRICITY 3 2 1 Electron versus conventional flow When Benjamin Franklin advanced his single fluid theory of electricity he defined positive and negative as the surplus and deficiency of electric charge respectively These labels were largely arbitrary as Mr Franklin had no means of identifying the actual nature of electric charge carriers with the primitive test equipment and laboratory techniques of his day As luck would have it his hypothesis was precisely opposite of the truth for metallic conductors where electrons are the dominant charge carrier This means that in an electric circuit consisting of a battery and a light bulb electrons slowly move from the negative side of the battery through the metal wires through the light bulb and on t
254. bear in mind that the volume used to calculate molarity is that of the total solution solute plus solvent and not the solvent alone Suppose we had a solution of salt water comprised of 33 1 grams of table salt thoroughly mixed with pure water to make a total volume of 1 39 liters In order to calculate the molarity of this solution we first need to determine the equivalence between moles of salt and grams of salt Since table salt is sodium chloride NaCl and we know the atomic masses of both sodium 23 0 amu and chlorine 35 5 amu we may easily calculate the mass of one mole of salt 1 mole of NaCl 23 0 g 35 5 g 58 5 g We may use this equivalence as a unity fraction to help us convert the number of grams of salt per unit volume of solution into a molarity moles of salt molecules per liter 33 1 g 1 mol mol 0 407 0 407 M 5 E z l 1 Truth be told a mole is 6 022 x 102 of literally any discrete entities There is nothing wrong with measuring the amount of eggs in the world using the unit of the mole Think of mole as a really big dozen 64 CHAPTER 2 CHEMISTRY 2 4 Stoichiometry Stoichiometry is the balancing of atoms in a chemical equation It is an expression of the Law of Mass Conservation in that elements are neither created nor destroyed in a chemical reaction Thus the numbers and types of atoms in a reaction product sample must be the same as the numbers and types of atoms in th
255. between computers along copper wire Here fluid pressure represents some other quantity and the principle of force being distributed equally throughout the fluid is exploited to transmit that representation to some distant location through piping or tubing Pressure gauge Closed bulb filled with fluid 32 CHAPTER 1 PHYSICS This illustration shows a simple temperature measuring system called a filled bulb where an enclosed bulb filled with fluid is exposed to a temperature that we wish to measure Heat causes the fluid pressure to increase which is sent to the gauge far away through the pipe and registered at the gauge The purpose of the fluid here is two fold first to sense temperature and second to relay this temperature measurement a long distance away to the gauge The principle of even pressure distribution allows the fluid to act as a signal medium to convey the information bulb temperature to a distant location 1 8 FLUID MECHANICS 33 1 8 2 Pascal s Principle and hydrostatic pressure We learned earlier that fluids tend to evenly distribute the force applied to them This tendency is known as Pascal s principle and it is the fundamental principle upon which fluid power and fluid signaling systems function In the example of a hydraulic lift given earlier we assume that the pressure throughout the fluid pathway is equal Resulting force App ag 1350 Ibs 150 lbs Hydraulic lift y Small Large p
256. bject in kilograms metric or slugs British g Acceleration of gravity in meters per second squared metric or feet per second squared British h Height of lift in meters metric or feet British Kinetic energy is energy in motion The kinetic energy of a moving mass is equal to 1 Ex gn Where Ep Potential energy in joules metric or foot pounds British m Mass of object in kilograms metric or slugs British v Velocity of mass in meters per second metric or feet per second British The Law of Energy Conservation is extremely useful in projectile mechanics problems where we typically assume a projectile loses no energy and gains no energy in its flight The velocity of 6 Technically the best way to express work resulting from force and displacement is in the form of a vector dot product W F z The result of a dot product is always a scalar quantity neither work nor energy possesses a direction so it cannot be a vector and the result is the same magnitude as a scalar product only if the two vectors are pointed in the same direction 1 7 CLASSICAL MECHANICS 23 a projectile therefore depends on its height above the ground because the sum of potential and kinetic energies must remain constant E Ex constant In free fall problems where the only source of energy for a projectile is its initial height the initial potential energy must be equal to the final kinetic energy E initial
257. ble pure water will be 6 51 pH at 60 C and 7 47 pH at freezing If we add an electrolyte to a sample of pure water at least some of the molecules of that electrolyte will separate into positive and negative ions If the positive ion of the electrolyte happens to be a hydrogen ion Ht we call that electrolyte an acid If the negative ion of the electrolyte happens to be a hydroxyl ion OH7 we call that electrolyte a caustic or alkaline or base Some common acidic and alkaline substances are listed here showing their respective positive and negative ions in solution Sulfuric acid is an acid produces H in solution H2504 2H SO Nitric acid is an acid produces H in solution HNO gt Ht NO37 Hydrocyanic acid is an acid produces H7 HCN gt H CN in solution Hydrofluoric acid is an acid produces H HF gt Ht F7 in solution Lithium hydroxide is a caustic produces OH in solution LiOH Lit OH Potassium hydroxide is a caustic produces OH in solution KOH Kt OH 2 7 PH 71 Sodium hydroxide is a caustic produces OH in solution NaOH gt Na OH Calcium hydroxide is a caustic produces OH in solution Ca OH 2 Ca t 20H When an acid substance is added to water some of the acid molecules dissociate into positive hydrogen ions Ht and negative ions the type of negative ions depending on what type of acid it is This increases the molarity of hydrogen ions
258. boro model 13A differential pressure transmitter shown in this photograph Es FO X BORO gt 15 PSI This nameplate tells us that the transmitter has a calibrated differential pressure range of 50 H20 50 inches water column which is only about 1 8 PSI However the nameplate also tells us that the transmitter has a maximum working pressure MWP of 1500 PSI Working pressure refers to the amount of gauge pressure common to each port not the differential pressure between ports Taking these figures at face value means this transmitter will register zero no differential pressure even if the gauge pressure applied equally to both ports is a full 1500 PSI In other words this differential pressure transmitter will reject up to 1500 PSI of gauge pressure and respond only to small differences in pressure between the ports 1 8 PSI differential being enough to stimulate the transmitter to full scale output 12 6 PRESSURE SENSOR ACCESSORIES 321 12 6 Pressure sensor accessories Multiple accessories exist for pressure sensing devices to function optimally in challenging process environments Sometimes we must use special accessories to protect the pressure instrument against hazards of certain process fluids One such hazard is pressure pulsation for example at the discharge of a piston type positive displacement high pressure pump Pulsating pressure can quickly damage mechanical sensors such as bourdon tubes either by wear of th
259. by the communicator This AC voltage across the loop resistor is seen in the diagram as being directly in parallel with the transmitter where its internal HART modem receives the audio tones and processes the data packets Generally manufacturer instructions recommend that HART communicator devices be connected in parallel with the HART field instrument as shown in the above schematic diagrams However it is also perfectly valid to connect the communicator device directly in parallel with the loop resistor like this 10 1 THE HART DIGITAL ANALOG HYBRID STANDARD 251 HART transmitter a Power T supply 250 lt R lt 1100 Computer HART communicator Connected directly in parallel with the loop resistor the communicator is able to receive transmissions from the HART transmitter just fine as the DC power source acts as a dead short to the AC current HART signal and passes it through to the transmitter This is nice to know as it is often easier to achieve an alligator clip connection across the leads of a resistor than it is to clip in parallel with the loop wires when at a terminal strip or at the controller end of the loop circuit HART technology has given a new lease on the venerable 4 20 mA analog instrumentation signal standard It has allowed new features and capabilities to be added on to existing analog signal loops without having to upgrade wiring or change all instruments in the loop Some of the features of
260. by the orifice plate However experiments have also shown that decreased Reynolds number in a venturi type flow element causes an increase in differential pressure due to the effects of friction against the entrance cone walls By manufacturing an orifice plate in such a way that the hole exhibits venturi like properties i e a dull edge where the fast moving fluid stream has more contact with the plate these two effects tend to cancel each other 6To read more about the concept of Reynolds number refer to section 1 8 9 beginning on page 51 15 1 PRESSURE BASED FLOWMETERS 463 resulting in an orifice plate that maintains consistent accuracy at lower flow rates and or higher viscosities than the simple square edged orifice Two common non square edge orifice plate designs are the quadrant edge and conic entrance orifices The quadrant edge is shown first Quadrant edge orifice plate Paddle front view side view The conical entrance orifice plate looks like a beveled square edge orifice plate installed backwards with flow entering the conical side and exiting the square edged side 464 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT Conical entrance orifice plate Paddle front view side view Here is it vitally important to pay attention to the paddle s text label This is the only sure indication of which direction an orifice plate needs to be installed One can easily imagine an inst
261. cal definition of a circle except now we consider the filling of a sphere with a series of thin circular disks 586 CHAPTER 17 SIGNAL CHARACTERIZATION If y r the mathematical definition of a circle then the volume of each circular disk comprising the accumulated volume between r and h r is equal to my dx In other words the total accumulated area between r and h r is h r v ay dx Now writing y in terms of r and x y Vr x and moving the constant m outside the integrand h r 2 V rf r2 22 dx r Immediately we see how the square and the square root cancel one another leaving us with a fairly simple integrand h r per r r dx P We may write this as the difference of two integrals h r h r V rf r da a f 2 dx Since r is a constant the left hand integral is simply rr x The right hand integral is solvable by the power rule 17 2 LIQUID VOLUME MEASUREMENT 587 V mhr 5 n 3h r 4 3hr h3 V thr gt th r thr 3 a 0 sit 3 h3 V ahr E Thr 3 h V rh r nh r 3 This function will un do the inherent height volume nonlinearity of a spherical vessel allowing a height measurement to translate directly into a volume measurement A characterizing function such as this is typically executed in a digital computer connected to the level sensor or sometimes in a computer chip within the sensor device
262. calibration systems A self calibration system is a system of solenoid electrically controlled on off valves and reference gas bottles set up in such a way that a computer is able to switch the analyzer off line and subject it to standard reference gases on a regular schedule to check calibration Many analyzers are programmed to automatically calibrate themselves against these reference gases thus eliminating tedious work for the instrument technician A typical self calibration system for a gas analyzer might look like this 288 CHAPTER 11 INSTRUMENT CALIBRATION 9 O O 2 Span 5 gas D Sample block valve Shutoff valve DE Filter Zero Y gas ES gt lt Sample bypass valve gt Output signal ba See gt Alarm signal Vents The gas analyzer is equipped with its own auto calibration controls and programming allowing it to periodically shut off the process sample and switch to known reference gases for zero and span calibration checks If these checks indicate excessive drift or any other questionable results the analyzer has the ability to flag a maintenance alarm to alert an instrument technician to a potential problem that may require servicing This sort of self calibration and self diagnostic capability saves the instrument technician from having to spend substantial time running manual calibration checks yet alerts the technician if anything is in need of actual repair Barring any component failures wit
263. ce This meant that the data communication rate for the digital data had to be very slow even by 1980 s standards Digital data is encoded in HART using the Bell 202 modem standard two audio frequency tones 1200 Hz and 2200 Hz are used to represent the binary states of 1 and 0 respectively transmitted at a rate of 1200 bits per second This is known as frequency shift keying or FSK The physical representation of these two frequencies is an AC current of 1 mA peak to peak superimposed on the 4 20 mA DC signal Thus when a HART compatible device talks digitally on a two wire loop circuit it produces tone bursts of AC current at 1 2 kHz and 2 2kHz The receiving HART device listens for these AC current frequencies and interprets them as binary bits An important consideration in HART current loops is that the total loop resistance precision resistor values plus wire resistance must fall within a certain range 250 ohms to 1100 ohms Most 4 20 mA loops containing a single 250 ohm resistor for converting 4 20 mA to 1 5 V measure in at just over 250 ohms total resistance and work quite well with HART Even loops containing two 250 ohm precision resistors meet this requirement Where technicians often encounter problems is when they set up a loop powered HART transmitter on the test bench with a lab style power supply and no 250 ohm resistor anywhere in the circuit HART transmitter Y 2 Power Y supply
264. ce system instead of a force balance system because we see two motions canceling each other out to maintain a constant nozzle gap instead of two forces canceling each other out to maintain a constant nozzle gap The gain of a motion balance pneumatic instrument may be changed by altering the bellows to nozzle distance so that one of the two bellows has more effect than the other For instance this system has a gain of 2 since the feedback bellows must move twice as far as the input bellows in order to maintain a constant nozzle gap Pa 2 Pig Air supply Force balance and moment balance instruments are generally considered more accurate than motion balance instruments because motion balance instruments rely on the pressure elements bellows diaphragms or bourdon tubes possessing predictable spring characteristics Since pressure must accurately translate to motion in a motion balance system there must be a predictable relationship between pressure and motion in order for the instrument to maintain accuracy If anything happens to affect this pressure motion relationship such as metal fatigue or temperature change the instrument s calibration will drift Since there is negligible motion in a force balance system pressure element spring characteristics are irrelevant to the operation of these devices and their calibrations remain more stable over time Both force and motion balance pneumatic instruments are usually equipped with an a
265. cess which in turn is necessary for the analyzer to obtain analyses of current conditions If it were not for the continuous flow of sample to waste it would take a very long time for a sample of process 16 5 CHROMATOGRAPHY 971 gas to make its way through the long impulse tube to the analyzer to be sampled Block valve Impulse line length Sample conditioning cooling heating filtering Waste to vent flare or other safe location ease gt Signal output s Even with continuous flow in the impulse line process chromatographs exhibit substantial dead time in their analyses for the simple reason of having to wait for the next sample to progress through the entire length of the column It is the basic nature of a chromatograph to separate components of a chemical stream over time and so a certain amount of dead time will be inevitable However dead time in any measuring instrument is an undesirable quality Dead time in a feedback control loop is especially bad as it greatly increases the chances of instability One way to reduce the dead time of a chromatograph is to alter some of its operating parameters during the analysis cycle in such a way that it speeds up the progress of the mobile phase during periods of time where slowness of elution is not as important for fine separation of components The flow rate of the mobile phase may be altered the temperature of the column may be rampe
266. cient and practical approach But what if we wished to convert to a unit of volume measurement other than the six shown in the long equality For instance what if we wished to convert 5 5 pints into cubic feet instead of cubic inches Since cubic feet is not a unit represented in the long string of quantities what do we do We do know of another equality between inches and feet though Everyone should know that there are 12 inches in 1 foot All we need to do is set up another unity fraction in the original problem to convert cubic inches into cubic feet 1170 liters converted into quarts 5 5 pints converted into cubic feet our first attempt 3 5 5 pt 231 in 1 ft _ 299 1 8 pt 12 in 12 CHAPTER 1 PHYSICS Unfortunately this will not give us the result we seek Even though T ft is a valid unity fraction it does not completely cancel out the unit of inches What we need is a unity fraction relating cubic 1 ft 12 in feet to cubic inches We can get this though simply by cubing the unity fraction 5 5 pints converted into cubic feet our second attempt 5 5 pt 231 in 1 ft 1 8 pt 12 in Distributing the third power to the interior terms of the last unity fraction 5 5 pt 231 in 18 ft 1 8 pt 123 in Calculating the values of 1 and 123 inside the last unity fraction then canceling units and solving 231 in 1 ft BE 3 0 0919 ft 1 8 pt 1728 in Once again this unit
267. cohesion Since this cohesive force is overcome with increasing temperature most liquids tend to become thinner less viscous as they heat up The mechanism of viscosity in gases however is inter molecular collisions Since these collisions increase in frequency and intensity with increasing temperature gases tend to become thicker more viscous as they heat up As a ratio of stress to strain applied force to yielding velocity viscosity is often constant for a given fluid at a given temperature Interesting exceptions exist though Fluids whose viscosities change with applied stress and or over time with all other factors constant are referred to as non Newtonian fluids A simple example of a non Newtonian fluid is cornstarch mixed with water which solidifies under increasing stress then returns to a liquid state when the stress is removed 1 8 FLUID MECHANICS 51 1 8 9 Reynolds number Viscous flow is when friction forces dominate the behavior of a moving fluid typically in cases where viscosity internal fluid friction is great Inviscid flow by contrast is where friction within a moving fluid is negligible The Reynolds number of a fluid is a dimensionless quantity expressing the ratio between a moving fluid s momentum and its viscosity A couple of formulae for calculating Reynolds number of a flow are shown here Where Re Reynolds number unitless D Diameter of pipe meters V Average velocity of
268. conomically If we compare the true flow rate through a pressure generating primary sensing element against the theoretical flow rate predicted by an idealized equation we may notice a substantial discrepancy Causes of this discrepancy include but are not limited to e Energy losses due to turbulence and viscosity Energy losses due to friction against the pipe and element surfaces e Uneven flow profile especially at low Reynolds numbers Fluid compressibility e Thermal expansion or contraction of the element e Non ideal pressure tap location s The ratio between true flow rate and theoretical flow rate for any measured amount of differential pressure is known as the discharge coefficient of the flow sensing element symbolized by the variable C Since a value of 1 represents a theoretical ideal the actual value of C for any real pressure generating flow element will be less than 1 7 True flow Theoretical flow For gas and vapor flows true flow rate deviates even more from the theoretical ideal flow value than liquids do for reasons that have to do with the compressible nature of gases and vapors A gas expansion factor Y may be calculated for any flow element by comparing its discharge coefficient for gases against its discharge coefficient for liquids As with the discharge coefficient values of Y for any real pressure generating element will be less than 1 Y Cgas Cliquid 11Richard W Miller in his book
269. constant value and so we may move it out of the integrand 2 T En n sin t dt R R Jo Multiplying both sides of the equation by R eliminates it completely This should make intuitive sense as our RMS equivalent value for a voltage is defined strictly by the ability to produce the same amount of power as the same value of DC voltage for any resistance value Therefore the actual value of resistance R should not matter and it should come as no surprise that it falls out T Vr f sin t dt 0 Now we may simplify the integrand by substituting the half angle equivalence for the sin t function T 1 vn cos 2t de 0 2 Factoring one half out of the integrand and moving it outside because it s a constant 1 T vn 5 1 cos 2t dt 2 Jo We may write this as the difference between two integrals treating each term in the integrand as its own integration problem 9 1 T T Vir l dt cos 2t dt 2 Jo 0 116 CHAPTER 4 AC ELECTRICITY The second integral may be solved simply by using substitution with u 2t du 2 dt and dt amp 5 1 E T cosu Vir 1 dt du 2 Moving the one half outside the second integrand 1 is 1 7 von 3 1a f cosu du 2 Jo 2 Jo Finally now we can integrate the silly thing Vn 5 ia E sin 24 ven 5 tn 0 a sin2r sind 2 1 1 Vir 0 n 3 tr 0 310 0 1 Ver z0 0 1 Vn 37 We can see that m cancels out of both sides 1 La E ls 2 Taking
270. control valve uses a large diaphragm to convert the air pressure signal into a mechanical force to move the valve open and closed A large spring inside the valve mechanism provides the force necessary to return the valve to its normal position while the force generated by the air pressure on the diaphragm works against the spring to move the valve the other direction When the controller is placed in the automatic mode it will move the control valve to whatever position it needs to be in order to maintain a constant steam drum water level The phrase whatever position it needs to be suggests that the relationship between the controller output signal the process variable signal PV and the setpoint SP can be quite complex If the controller senses a water level above setpoint it will take whatever action is necessary to bring that level back down to setpoint Conversely if the controller senses a water level below setpoint it will take whatever action is necessary to bring that level up to setpoint What this means in a practical sense is that the controller s output signal equating to valve position is just as much a function of process load i e how much steam is being used from the boiler as it is a function of setpoint Consider a situation where the steam demand from the boiler is very low If there isn t much steam being drawn off the boiler this means there will be little water boiled into steam and therefore little nee
271. corporation may be thought of as a venturi tube in reverse instead of narrowing the tube s diameter to cause fluid acceleration fluid must flow around a cone shaped obstruction placed in the middle of the tube The tube s effective area will be reduced by the presence of this cone causing fluid to accelerate through the restriction just as it would through the throat of a classic venturi tube _3 This cone is hollow with a pressure sensing port on the downstream side allowing for easy detection of fluid pressure near the vena contracta Upstream pressure is sensed by another port in 15 1 PRESSURE BASED FLOWMETERS 471 the pipe wall upstream of the cone The following photograph shows a V cone flow tube cut away for demonstration purposes Segmental wedge elements are special pipe sections with wedge shaped restrictions built in These devices albeit crude are useful for measuring the flow rates of slurries especially when pressure is sensed by the transmitter through remote seal diaphragms to eliminate the possibility of impulse tube plugging Segmental wedge Flow gt 472 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT Finally the lowly pipe elbow may be pressed into service as a flow measuring element since fluid turning a corner in the elbow experiences radial acceleration and therefore generates a differential pressure along the axis of acceleration Pipe elbow Pipe elbows should be considered for
272. ct s temperature without having to touch it Not all hope is lost for optical techniques though All we have to do is obtain an emittance value for that object one time and then we may calibrate an optical temperature sensor for that object s particular emittance so as to measure its temperature in the future without contact Beyond the issue of emittance other idiosyncrasies plague optical techniques as well Objects also have the ability to reflect and transmit radiation from other bodies which taints the accuracy of any optical device sensing the radiation from that body An example of the former is trying to 436 CHAPTER 14 CONTINUOUS TEMPERATURE MEASUREMENT measure the temperature of a silver mirror using an optical pyrometer the radiation received by the pyrometer is mostly from other objects merely reflected by the mirror An example of the latter is trying to measure the temperature of a gas or a clear liquid and instead primarily measuring the temperature of a solid object in the background through the gas or liquid Nevertheless optical techniques for measuring temperature have been and will continue to be useful in specific applications where other contact based techniques are impractical 14 6 TEMPERATURE SENSOR ACCESSORIES 437 14 6 Temperature sensor accessories One of the most important accessories for any temperature sensing element is a pressure tight sheath known as a thermowell This may be thought of as a thermal
273. ct viewing on the internet I had to go to the trouble of inventing my own markup language last time in an effort to have multiple format versions of the book from the same source code Instead this time I will use stock TfXas the source code format and regular Adobe PDF format for the final output which anyone may read thanks to its ubiquity use a GNU GPL style copyleft license Instead I will use the Creative Commons Attribution only license which makes things a lot easier for anyone wishing to incorporate my work into derivative works My interest is maximum flexibility for those who may adapt my material to their own needs not the imposition of certain philosophical ideals start from a conceptual state of ground zero I will assume the reader has certain familiarity with electronics and mathematics which I will build on If a reader finds they need to learn more about electronics they should go read Lessons In Electric Circuits avoid using calculus to help explain certain concepts Not all my readers will understand these parts and so I will be sure to explain what I can without using calculus However I want to give my more mathematically adept students an opportunity to see the power of calculus applied to instrumentation where appropriate By occasionally applying calculus and explaining my steps I also hope this text will serve as a practical guide for students who might wish to learn calculus so they can see its util
274. ctical solution for this problem Commonly employed to make precise resistance measurements for scientific experiments in laboratory conditions the four wire technique uses four wires to connect the resistance under test in this case the RTD to the measuring instrument Voltmeter RTD Rye 100 Q Current source Current is supplied to the RTD from a current source whose job it is to precisely regulate current regardless of circuit resistance A voltmeter measures the voltage dropped across the RTD and Ohm s Law is used to calculate the resistance of the RTD R 4 None of the wire resistances are consequential in this circuit The two wires carrying current to the RTD will drop some voltage along their length but this is of no concern because the voltmeter only sees the voltage dropped across the RTD The two wires connecting the voltmeter to the RTD have resistance but drop negligible voltage because the voltmeter draws so little current through them remember an ideal voltmeters has infinite input impedance and modern semiconductor amplified voltmeters have impedances of several mega ohms or more The only disadvantage of the four wire method is the sheer number of wires necessary Four wires per RTD can add up to a sizeable wire count when many different RTDs are involved on the same process Wires cost money and occupy expensive conduit so there are situations where the four wire method is a burden A compro
275. ction Iron J ice water bath Junction J a Copper In fact this is how thermocouple temperature voltage tables are referenced describing the amount of voltage produced for given temperatures at the measurement junction with the reference junction held at the freezing point of water 0 C 32 F However this is not a very practical solution for dealing with the reference junction s voltage Instead we could apply an additional electrical circuit to counter act the voltage produced by the reference junction This is called a reference junction compensation or cold junction compensation circuit Compensating for the effects of J using a reference junction compensation circuit to generate a counter voltage Junction Iron 42 Junction J Please note that cold junction is just a synonymous label for reference junction In fact the cold reference junction may very well be at a warmer temperature than the so called 14 4 THERMOCOUPLES 429 hot measurement junction Nothing prevents anyone from using a thermocouple to measure temperatures below freezing This compensating voltage source V j in the above schematic uses some other temperature sensing device such as a thermistor or RTD to sense the local temperature at the terminal block where junction J2 is formed and produce a counter voltage that is precisely equal and opposite to J2 s voltage Having canceled the effect of
276. ction with the pipe or tube walls Laminar flow is qualitatively predicted by low values of Reynolds number This pressure drop created by fluid friction in a laminar flowstream is quantifiable and is expressed in the Hagen Poiseuille equation APD a uL Where Q Flow rate AP Pressure dropped across a length of pipe D Pipe diameter H Fluid viscosity L Pipe length k Coefficient accounting for units of measurement Laminar flowmeter elements generally consist of one or more tubes whose length greatly exceeds the inside diameter arranged in such a way as to produce a slow moving flow velocity An example is shown here Laminar flowmeter p gt Tubes The expanded diameter of the flow element ensures a lower fluid velocity than in the pipes entering and exiting the element This decreases the Reynolds number to the point where the flow 486 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT regime exhibits laminar behavior The large number of small diameter tubes packed in the wide area of the element provide adequate wall surface area for the fluid s viscosity to act upon creating an overall pressure drop from inlet to outlet which is measured by the differential pressure transmitter This pressure drop is permanent no recovery of pressure downstream because the mechanism of pressure drop is friction total dissipation loss of energy in the form of heat Another common form of laminar flow element is simpl
277. cycle Many positive displacement flowmeters are rotary in nature meaning each shaft revolution represents a certain volume of fluid has passed through the meter Positive displacement flowmeters have been the traditional choice for residential and commercial natural gas flow and water flow measurement in the United States a simple application of custody transfer flow measurement where the fluid being measured is a commodity bought and sold The cyclic nature of a positive displacement meter lends itself well to total gas quantity measurement and not just flow rate as the mechanism may be coupled to a mechanical counter which is read by utility personnel on a monthly basis A rotary gas flowmeter is shown in the following photograph Note the odometer style numerical display on the left hand end of the meter totalizing gas usage over time ES 5 Positive displacement flowmeters rely on moving parts to shuttle quantities of fluid through them and these moving parts must effectively seal against each other to prevent leakage past the mechanism which will result in the instrument indicating less fluid passing through than there actually is The finely machined construction of a positive displacement flowmeter will suffer damage from grit or other abrasive materials present in the fluid which means these flowmeters are applicable only to clean fluid flowstreams Even with clean fluid flowing through the mechanisms are subject to wear and
278. d arrangement of their contents constitute intellectual creations in which the Work is included in its entirety in unmodified form along with one or more other contributions each constituting separate and independent works in themselves which together are assembled into a collective whole A work that constitutes a Collection will not be considered an Adaptation as defined above for the purposes of this License 3 Distribute means to make available to the public the original and copies of the Work or Adaptation as appropriate through sale or other transfer of ownership 4 Licensor means the individual individuals entity or entities that offer s the Work under the terms of this License 5 Original Author means in the case of a literary or artistic work the individual individuals entity or entities who created the Work or if no individual or entity can be identified the publisher and in addition i in the case of a performance the actors singers musicians dancers and other persons who act sing deliver declaim play in interpret or otherwise perform literary or artistic works or expressions of folklore ii in the case of a phonogram the producer being the person or legal entity who first fixes the sounds of a performance or other sounds and iii in the case of broadcasts the organization that transmits the broadcast 6 Work means the literary and or artistic work offered under the terms of this Licen
279. d buffer with a different pH value After another stabilization period the pH instrument is standardized to this second pH value It only takes two points to define a line so these two buffer measurements are all that is required by a pH instrument to define the linear transfer function relating probe voltage to solution pH 2 3 4 02 pH buffer 4 ss pH 7 Isopotential point 10 06 pH buffer 49 11 12 1 t 1 i 300 240 180 120 60 0 60 120 180 240 300 f Probe voltage mV i 165 mV 172 mV Most modern pH instruments will display the calculated slope value after calibration This value should ideally be 59 17 millivolts per pH unit at 25 degrees Celsius but it will likely be a bit less than this The voltage generating ability of a glass electrode decays with age so a low slope value may indicate a probe in need of replacement Another informative feature of the voltage pH transfer function graph is the location of the isopotential point that point on the graph corresponding to 0 voltage In theory this point should correspond to a pH value of 7 0 pH However if there exist stray potentials in the pH measurement circuit for example voltage differences caused by ion mobility problems in the porous junction of the reference electrode this point will be shifted A quick way to check the isopotential point of any calibrated pH instrument is to short
280. d by a slow moving viscous fluid through a pipe is described by the Hagen Poiseuille equation This equation applies only for conditions of low Reynolds number i e when viscous forces are the dominant restraint to fluid motion through the pipe and turbulence is nonexistent APD o uL Where Q Flow rate gallons per minute k Unit conversion factor 7 86 x105 AP Pressure drop inches of water column D Pipe diameter inches u Liquid viscosity centipoise this is a temperature dependent variable L Length of pipe section inches 1 8 FLUID MECHANICS 55 1 8 12 Bernoulli s equation Bernoulli s equation is an expression of the Law of Energy Conservation for an inviscid fluid stream named after Daniel Bernoulli It states that the sum total energy at any point in a passive fluid stream i e no pumps or other energy imparting machines in the flow path must be constant Two versions of the equation are shown here 2 2 UV VU apg TL P zopg 2 Pa 2 2 v P v P zn o a ot 29 7 29 7 Where z Height of fluid from a common reference point usually ground level p Mass density of fluid y Weight density of fluid y pg g Acceleration of gravity v Velocity of fluid P Pressure of fluid Each of the three terms in Bernoulli s equation is an expression of a different kind of energy commonly referred to as head zpg Elevation head 2 gt Velocity head P Pressure head El
281. d for additional feedwater to be pumped into the boiler Therefore in this situation one would expect the control valve to hover near the fully closed position allowing just enough water into the boiler to keep the steam drum water level at setpoint If however there is great demand for steam from this boiler the rate of evaporation will be much higher This means the control system will have to add feedwater to the boiler at a much greater flow rate in order to maintain the steam drum water level at setpoint In this situation we would expect to see the control valve much closer to being fully open as the control system works harder to maintain a constant water level in the steam drum A human operator running this boiler has the option of placing the controller into manual mode In this mode the control valve position is under direct control of the human operator with the controller essentially ignoring the signal sent from the water level transmitter Being an indicating controller the controller faceplate will still show how much water is in the steam drum but it is now the human operator s sole responsibility to move the control valve to the appropriate position to hold water level at setpoint Manual mode is useful to the human operator s during start up and shut down conditions It is also useful to the instrument technician for troubleshooting a mis behaving control system When a controller is in automatic mode the output
282. d up and down both variable restrictions change in complementary fashion As one restriction opens up the other pinches shut The combination of two restrictions changing in opposite direction results in a much more aggressive change in output pressure as registered by the gauge A similar design of pilot valve reverses the directions of the two plugs and seats The only operational difference between this pilot valve and the previous design is an inverse relationship between control rod motion and pressure 9 3 PILOT VALVES AND PNEUMATIC AMPLIFYING RELAYS 223 Pneumatic pilot valve Equivalent electrical circuit Compressed air supply V Output pressure Control __ knob ll an vent vent moves up Control rod and down At this point all we ve managed to accomplish is build a better baffle nozzle mechanism We still do not yet have a pneumatic equivalent of an electronic transistor To accomplish that we must have some way of allowing an air pressure signal to control the motion of a pilot valve s control rod This is possible with the addition of a diaphragm as shown in this illustration 224 CHAPTER 9 PNEUMATIC INSTRUMENTATION Compressed air Supply Output pressure gt vent diaphragm Input pressure The diaphragm is nothing more than a thin disk of sheet metal upon which an incoming air pressure signal presses Force on the diaphragm is a simple function of signal pressure P and diaphra
283. d up or down and even different columns may be switched into the mobile phase stream In chromatography we refer to this on line alteration of parameters as programming Temperature programming is an especially popular feature of process gas chromatographs due to the direct effect temperature has on the viscosity of a flowing gas Carefully altering the operating temperature of a GC column while a sample washes through it is an excellent way to optimize the separation and time delay properties of a column effectively realizing the high separation properties of a long column with the reduced dead time of a much shorter column 20Whereas most liquids decrease in viscosity as temperature rises gases increase in viscosity as they get hotter Since the flow regime through a chromatograph column is most definitely laminar and not turbulent viscosity has a great effect on flow rate 572 CHAPTER 16 CONTINUOUS ANALYTICAL MEASUREMENT References Boylestad Robert L Introductory Circuit Analysis 9th Edition Prentice Hall Upper Saddle River New Jersey 2000 Fribance Austin E Industrial Instrumentation Fundamentals McGraw Hill Book Company New York NY 1962 Kohlmann Frederick J What Is pH And How Is It Measured Hach Company 2003 Lavigne John R Instrumentation Applications for the Pulp and Paper Industry Miller Freeman Publications Foxboro MA 1979 Lipt k B la G Instrument Engineers Handbook Process Me
284. e 8 mA 25 12 mA 50 16 mA 75 20 mA 100 Full concentration 138 CHAPTER 5 INTRODUCTION TO INDUSTRIAL INSTRUMENTATION The controller is labeled AIC because it is an Analytical Indicating Controller Controllers are always designated by the process variable they are charged with controlling in this case the chlorine analysis of the effluent Indicating means there is some form of display that a human operator or technician can read showing the chlorine concentration SP refers to the setpoint value entered by the operator which the controller tries to maintain by adjusting the position of the chlorine injection valve A dashed line going from the controller to the valve indicates another electronic signal most likely 4 to 20 mA DC again Just as with the 3 to 15 PSI pneumatic signal standard in the pneumatic boiler control system the amount of electric current in this signal path directly relates to a certain valve position Controller output signal current Control valve position 4mA 0 open Fully shut 8mA 25 open 12 mA 50 open 16 mA 75 open 20 mA 100 Fully open Note it is possible and in some cases even preferable to have either a transmitter or a control valve that responds in reverse fashion to an instrument signal such as 3 to 15 PSI or 4 to 20 milliamps For example this valve could have been set up to be wide open at 4 mA and fully shut at 20 mA The main poi
285. e When the prongs of the fork contact anything with substantial mass the resonant frequency of the structure dramatically decreases The circuit detects this change and indicates the presence of material contacting the fork 7 7 TEMPERATURE SWITCHES 183 7 7 Temperature switches A temperature switch is one detecting the temperature of an object Temperature switches often use bimetallic strips as the pressure sensing element the motion of which actuates one or more switch contacts Recall that the normal status of a switch is the condition of minimum stimulus A temperature switch will be in its normal status when it senses minimum temperature i e cold in some cases a condition colder than ambient Temperature switch symbols Normally open Normally closed NO NC The following photograph shows a temperature actuated switch 21f the trip setting of a temperature switch is below ambient temperature then it will be actuated at ambient temperature and in its normal status only when the temperature falls below that trip point i e colder than ambient 184 CHAPTER 7 DISCRETE PROCESS MEASUREMENT 7 8 FLOW SWITCHES 185 7 8 Flow switches A flow switch is one detecting the flow of some fluid through a pipe paddles as the flow sensing element the motion of which actuates one or more switch contacts Recall that the normal status of a switch is the condition of minimum stimulus A
286. e mass flow measurement value and divide that by the fluid s measured density A simple exercise in 15 5 INERTIA BASED TRUE MASS FLOWMETERS 523 dimensional analysis performed with metric units of measurement validates this concept for both forms of the equation shown above 5 FI Coriolis mass flowmeters are very accurate and dependable They are also completely immune to swirl and other fluid disturbances which means they may be located nearly anywhere in a piping system with no need at all for straight run pipe lengths upstream or downstream of the meter Their natural ability to measure true mass flow along with their characteristic linearity and accuracy makes them ideally suited for custody transfer applications where the flow of fluid represents product being bought and sold Perhaps the greatest disadvantage of Coriolis flowmeters is their high initial cost especially for large pipe sizes 524 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT 15 6 Thermal based mass flowmeters Wind chill is a phenomenon common to nearly everyone who has ever lived in a cold environment When the ambient air temperature is substantially colder than the temperature of your body heat will transfer from your body to the surrounding air If there is no breeze to move air past your body the air molecules immediately surrounding your body will begin to warm up as they absorb heat from your body which will then decrease the rate of hea
287. e 0 7 volt drop appears to turn on the diode and all loop current flows through the diode again At no time is the loop current ever interrupted which means a technician may take current measurements this way and never have to worry about generating false process variable indications setting off alarms or upsetting the process 204 CHAPTER 8 ANALOG ELECTRONIC INSTRUMENTATION Such a diode may be installed at the nearest junction box between terminals on a terminal strip or even incorporated into the transmitter itself Some process transmitters have an extra pair of terminals labeled Test for this exact purpose A diode is already installed in the transmitter and these test terminals serve as points to connect the milliammeter across A similar method for non invasively measuring current in a 4 20 mA instrumentation circuit is to install a precision resistor in series If the resistance value is precisely known the technician merely needs to measure voltage across it with a voltmeter and use Ohm s Law to calculate current Power Transmitter supply If neither component diode nor resistor is pre installed in the circuit and if a Hall effect clamp on precision milliammeter is unavailable a technician may still perform useful troubleshooting measurements using nothing but a DC voltmeter Here however one must be careful of how to interpret these voltage measurements for they may not directly correspond to the loop cu
288. e Averging pitot tubes or Flume Weir Turbine Target LEO HOF GO POI BO Positive displacement Vortex Coriolis Rotameter HO a HO ho Ultrasonic Magnetic Wedge V cone NN BHO BO ES BO Flow nozzle Venturi Generic yO O o 166 CHAPTER 6 INSTRUMENTATION DOCUMENTS 6 5 8 Process equipment Pressure vessels Centrifugal Positive displacement i pump pump Dual stage Rotary Single stage reciprocating Screw Motor driven fan reciprocating compressor compressor compressor OS oF EA Motor driven axial compressor Shell and tube Jacketed vessel Conveyor belt heat exchanger ASS O os NY Turbogenerator Turbocompressor 6 5 INSTRUMENT AND PROCESS EQUIPMENT SYMBOLS 167 6 5 9 SAMA diagram symbols PID controllers Pl controller D Pl controller PD I controller P 1 p ea Characterized Manual adjust Manual transfer Control valve control valve So lt gt rcv Automatic Manual Control valve function function w positioner Indicator I Bey Transmitter Time delay Summer Square root Characterizer O References Instrumentation Systems and Automation Society Standards 5 1 1984 R1992 Instrumentation Symbols and Identification Research Triangle Park NC 1984 Lipt k B la G Instrument Engineers Handbook Process Measurement and Analysis Volume I Fourth Edition CRC Press New York NY 2003 Lipt k B la G Instrument Engineers Handbook Process Softwar
289. e Tref ohms a Temperature coefficient of resistance ohms per ohm degree Due to nonlinearities in the RTD s behavior the above formula is only an approximation A better approximation is the Callendar van Dusen formula which introduces second third and fourth degree terms for a better fit Ry Rres 1 AT BT 100CT CT for temperatures ranging 200 C lt T lt 0 Cand Rr Rref 1 AT BT for temperatures ranging 0 C lt T lt 661 C both assuming Tref 0 C Water s melting freezing point is the standard reference temperature for most RTDs Here are some typical values of a for common metals e Nickel 0 00672 Q Q C e Tungsten 0 0045 2 0 C e Silver 0 0041 2 0 C 14 3 THERMISTORS AND RESISTANCE TEMPERATURE DETECTORS RTDS 423 e Gold 0 0040 2 2 C e Platinum 0 00392 0 0 C e Copper 0 0038 2 0 C 100 Q is a very common reference resistance Rref for industrial RTDs 1000 Q is another common reference resistance Compared to thermistors with their tens or even hundreds of thousands of ohms nominal resistance an RTD s resistance is comparatively small This can cause problems with measurement since the wires connecting an RTD to its ohmmeter possess their own resistance which will be a more substantial percentage of the total circuit resistance than for a thermistor The following schematic diagrams show the relative effects of 2 ohms total wire resistance on a thermistor circuit
290. e an extremely stiff spring The strain gauges bonded to this structure measure the strain translating applied force into electrical resistance changes You can see what a load cell looks like in the following photograph 3 8 BRIDGE CIRCUITS 105 Strain gauges are not the only dynamic element applicable to bridge circuits In fact any resistance based sensor may be used in a bridge circuit to translate a physical measurement into an electrical voltage signal Thermistors changing resistance with temperature and photocells changing resistance with light exposure are just two alternatives to strain gauges It should be noted that the amount of voltage output by this bridge circuit depends both on the amount of resistance change of the sensor and the value of the excitation source This dependency on source voltage value is a major difference between a sensing bridge circuit and a Wheatstone balanced bridge circuit In a perfectly balanced bridge the excitation voltage is irrelevant the output voltage is zero no matter what source voltage value you use In an unbalanced bridge circuit however source voltage value matters For this reason these bridge circuits are often rated in terms of how many millivolts of output they produce per volt of excitation per unit of physical measurement microns of strain newtons of stress etc An interesting feature of a sensing bridge circuit is its ability to cancel out unwanted variables In the
291. e and Digital Networks Third Edition CRC Press New York NY 2002 168 CHAPTER 6 INSTRUMENTATION DOCUMENTS Chapter 7 Discrete process measurement The word discrete means individual or distinct In engineering a discrete variable or measurement refers to a true or false condition Thus a discrete sensor is one that is only able to indicate whether the measured variable is above or below a specified setpoint Discrete sensors typically take the form of switches built to trip when the measured quantity either exceeds or falls below a specified value These devices are less sophisticated than so called continuous sensors capable of reporting an analog value but they are quite useful in industry Many different types of discrete sensors exist detecting variables such as position fluid pressure material level temperature and fluid flow rate The output of a discrete sensor is typically electrical in nature whether it be an active voltage signal or just resistive continuity between two terminals on the device 169 170 CHAPTER 7 DISCRETE PROCESS MEASUREMENT 7 1 Normal status of a switch Perhaps the most confusing aspect of discrete sensors is the definition of a sensor s normal status Electrical switch contacts are typically classified as either normally open or normally closed referring to the open or closed status of the contacts under normal conditions But what exactly defines normal for a
292. e bridge circuits It is possible however to incorporate more than one sensor into the same bridge circuit So long as the sensors resistance changes are coordinated their combined effect will be to increase the sensitivity and often the linearity as well of the measurement For example full active bridge circuits are sometimes built out of four strain gauges where each strain gauge comprises one arm of the bridge Two of the strain gauges must compress and the other two must stretch under the application of the same mechanical force in order that the bridge will become unbalanced with strain 3 8 BRIDGE CIRCUITS 107 FORCE Gauge 1 Tension Gauge 3 Compression Gauges Not only does a full active bridge circuit provide greater sensitivity and linearity than a quarter active bridge but it also naturally provides temperature compensation without the need for dummy strain gauges since the resistances of all four strain gauges will change by the same proportion if the specimen temperature changes 108 CHAPTER 3 DC ELECTRICITY 3 9 Capacitors Any two electrical conductors separated by an insulating medium possess the characteristic called capacitance the ability to store energy in the form of an electric field Capacitance is symbolized by the capital letter C and is measured in the unit of the Farad F The relationship between capacitance stored electric charge Q and voltage V is as follows Q CV For e
293. e fill fluid commonly a silicone based or fluorocarbon based liquid A metal isolating diaphragm transfers process fluid pressure to the fill fluid Another simplified illustration shows how this works Silicon diaphragm strain gauge Metal isolating diaphragm Be Rigid housing Applied pressure The isolating diaphragm is designed to be much more flexible less rigid than the silicon diaphragm because its purpose is to seamlessly transfer fluid pressure from the process fluid to 302 CHAPTER 12 CONTINUOUS PRESSURE MEASUREMENT the fill fluid not to act as a spring element In this way the silicon sensor experiences the same pressure that it would if it were directly exposed to the process fluid without having to contact the process fluid An example of a pressure instrument utilizing a silicon strain gauge element is the Foxboro model IDP10 differential pressure transmitter shown in the following photograph 123 ELECTRICAL PRESSURE ELEMENTS 303 12 3 2 Differential capacitance sensors Another common electrical pressure sensor design works on the principle of differential capacitance In this design the sensing element is a taut metal diaphragm located equidistant between two stationary metal surfaces forming a complementary pair of capacitances An electrically insulating fill fluid usually a liquid silicone compound transfers motion from the isolating diaphragms to the sensing diaphragm and also doubles as an e
294. e mechanism transferring pressure element motion to an indicating needle and or fatigue of the metal element itself 322 CHAPTER 12 CONTINUOUS PRESSURE MEASUREMENT 12 6 1 Valve manifolds An important accessory to the differential pressure transmitter is the three valve manifold This device incorporates three manual valves to isolate and equalize pressure from the process to the transmitter for maintenance and calibration purposes The following illustration shows the three valves comprising a three valve manifold within the dotted line box as well as a fourth valve called a bleed valve used to vent trapped fluid pressure to atmosphere Bleed valve Equalizing valve Block valve Block valve Impulse lines to process While this illustration shows the three valves as separate devices connected together and to the transmitter by tubing three valve manifolds are more commonly manufactured as monolithic devices the three valves cast together into one block of metal attaching to the pressure transmitter by way of a flanged face with O ring seals Bleed valves are most commonly found as separate devices threaded into one or more of the ports on the transmitter s diaphragm chambers The following photograph shows a three valve manifold bolted to a Honeywell model ST3000 differential pressure transmitter A bleed valve fitting may be seen inserted into the upper port on the nearest diaphragm capsule flange 12 6 PRESSUR
295. e of the pH to voltage function will be 68 11 millivolts per pH unit rather than 59 17 millivolts per pH unit as it was at room temperature In order for a pH instrument to accurately infer a solution s pH value from the voltage generated by a glass electrode it must know the expected slope of the Nernst equation Since the only variable in the Nernst equation beside the two ion concentration values C and C2 is temperature T a simple temperature measurement will provide the pH instrument the information it needs to function accurately For this reason many pH instruments are constructed to accept an RTD input for solution temperature sensing and many pH probe assemblies have built in RTD temperature sensors ready to sense solution temperature The slope of a pH instrument is generally set by performing a two point calibration using buffer solutions as the pH calibration standard A buffer solution is a specially formulated solution that maintains a stable pH value even under conditions of slight contamination For more information on pH buffer solutions see section 11 8 5 on page 285 The pH probe assembly is inserted into a cup containing a buffer solution of known pH value then the pH instrument is standardized to 560 CHAPTER 16 CONTINUOUS ANALYTICAL MEASUREMENT that pH value After standardizing at the first calibration point the pH probe is removed from the buffer rinsed then placed into another cup containing a secon
296. e on the merry go round it appears to be deflected by an invisible force which we call the Coriolis force In order to generate a Coriolis force we must have a mass moving at a velocity perpendicular to an axis of rotation Axis of rotation 4 Apparent trajectory of the ball as viewed from the rotating platform A O Ball 516 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT The magnitude of this force is predicted by the following vector equation Where F Coriolis force vector Q Angular velocity rotation vector v Velocity vector as viewed from the rotating reference frame m Mass of the object If we replace the ball with a fluid moving through a tube and we introduce a rotation vector by tilting that tube around a stationary axis a fulcrum a Coriolis force develops on the tube in such a way as to oppose the direction of rotation just like the Coriolis force opposed the direction of rotation of the rotating platform in the previous illustration _ gt 3 Fluid motion a Coriolis force C vector Axis of rotation To phrase this in anthropomorphic terms the fluid fights against this rotation because it wants to keep traveling in a straight line For any given rotational velocity the amount of fight will be directly proportional to the product of fluid velocity and fluid mass In other words the magnitude of the Coriolis force will be in direct proportion to the fluid s mass flo
297. e outside but factory clean on the inside due to this continual purge of clean air Pneumatic instruments mounted inside larger enclosures with other devices tend to protect them all by providing a positive pressure air purge for the entire enclosure Some pneumatic instruments can also function in high temperature and high radiation environments that would damage electronic instruments Although it is often possible to harden electronic field instruments to such harsh conditions pneumatic instruments are practically immune by nature An interesting feature of pneumatic instruments is that they may operate on compressed gases other than air This is an advantage in remote natural gas installations where the natural gas itself is sometimes used as a source of pneumatic power for instruments So long as there is compressed natural gas in the pipeline to measure and to control the instruments will operate No air compressor or electrical power source is needed in these installations What is needed however is good filtering equipment to prevent contaminants in the natural gas dirt debris liquids from pneumatic controller attached to the same support as a badly cavitating control valve The vibrations of the control valve transferred to the controller through the support causing the baffle to hammer repeatedly against the nozzle until the nozzle s tip had been worn down to a flattened shape Remarkably the only indication of this p
298. e pipe had an area 5 times as great as the area of the throat then we would expect the fluid velocity in the throat to be 5 times as great as the velocity at the mouth Simply put the narrow throat causes the fluid to accelerate from a lower velocity to a higher velocity We know from our study of energy in physics that kinetic energy is proportional to the square of a mass s velocity Ex mu If we know the fluid molecules increase velocity as they travel through the venturi tube s throat we may safely conclude that those molecules kinetic energies must increase as well However we also know that the total energy at any point in the fluid stream must remain constant because no energy is added to or taken away from the stream in this simple fluid system Therefore if kinetic energy increases at the throat potential energy must correspondingly decrease to keep the total amount of energy constant at any point in the fluid Potential energy may be manifest as height above ground or as pressure in a fluid system Since this venturi tube is level with the ground there cannot be a height change to account for a change in potential energy Therefore there must be a change of pressure P as the fluid travels through the venturi throat The Laws of Mass and Energy Conservation invariably lead us to this conclusion fluid pressure must decrease as it travels through the narrow throat of the venturi tube Conservation of energy at different points
299. e power goes up by a factor of nine If we are to figure out the RMS equivalent value of a sine wave we must take this nonlinearity into consideration First let us begin with a mathematical equivalence between the DC and AC cases On one hand the amount of work done by the DC voltage source will be equal to the power of that circuit multiplied by time The unit of measurement for power is the Watt which is defined as 1 Joule 4 1 RMS QUANTITIES 115 of work per second So multiplying the steady power rate in a DC circuit by the time we keep it powered will result in an answer of joules total energy dissipated by the resistor y Work Jt n On the other hand the amount of work done by a sine wave shaped AC voltage is equal to the square of the sine function divided by resistance integrated over a specified time period In other words we will use the calculus process of integration to calculate the area underneath the function sin t rather than under the function sin t Since the interval from 0 to 7 will encompass the essence of the sine wave s shape this will be our integration interval Tos 2 Wore J Sa t gt R Setting these two equations equal to each other since we want the amount of work in each case to be equal and making sure the DC side of the equation has 7 for the amount of time being the same interval as the AC side we get this y2 e sin t y R jh R First we know that R is a
300. e process substance is a critical variable in the non conductive style of capacitance level probe and so good accuracy may be obtained with this kind of instrument only if the process permittivity is accurately known A clever way to ensure good level measurement accuracy when the process permittivity is not stable over time is to equip the instrument with a special compensating probe sometimes called a composition probe below the LRV point in the vessel that will always be submerged in liquid Since this compensating probe is always immersed and always experiences the same A and d dimensions its capacitance is purely a function of the liquid s permittivity e This gives the instrument a way to continuously measure process permittivity which it then uses to calculate level based on the capacitance of the main probe The inclusion of a compensating probe to measure and compensate for changes in liquid permittivity is analogous to the inclusion of a third pressure transmitter in a hydrostatic tank expert system to continuously measure and compensate for liquid density It is a way to correct for changes in the one remaining system variable that is not related to changes in liquid level Capacitive level instruments may be used to measure the level of solids powders and granules in addition to liquids In these applications and solid substance is almost always non conductive and therefore the permittivity of the substance becomes a factor in measur
301. e product of average velocity V pipe cross sectional area 4 and fluid density p for a given flow stream must remain constant A A lis gt E P3A3V3 Fluid continuity is an expression of a more fundamental law of physics the Conservation of Mass If we assign appropriate units of measurement to the variables in the continuity equation we see that the units cancel in such a way that only units of mass per unit time remain A kg m pm kg e 5 651 This means that in order for the product pAv to differ between any two points in a pipe mass would have to mysteriously appear and disappear So long as the pipe does not leak this is impossible without violating the Law of Mass Conservation The continuity principle for fluid through a pipe is analogous to the principle of current being the same everywhere in a series circuit and for equivalently the same reason We refer to a fluid as incompressible if its density does not substantially change For this limiting case the continuity equation simplifies to the following form Av A202 The practical implication of this principle is that fluid velocity is inversely proportional to the cross sectional area of a pipe That is fluid slows down when the pipe s diameter expands and visa versa We see this principle easily in nature deep rivers run slow while rapids are relatively shallow and or narrow 54 CHAPTER 1 PHYSICS 1 8 11 Viscous flow The pressure droppe
302. e reactants which reacted to produce it For example CH 202 CO 2H20 Reactants Reaction products Carbon 1 x 1 Carbon 1 x 1 Hydrogen 1 x 4 Hydrogen 2 x 2 Oxygen 2 x 2 Oxygen 1 x 2 2 x 1 As you can see in this example every single atom entering the reaction is accounted for in the reaction products The only exception to this rule is in nuclear reactions where elements transmutate No such transmutation occurs in any mere chemical reaction and so we may safely assume equal numbers and types of atoms before and after any chemical reaction Chemical reactions strictly involve re organization of molecular bonds with electrons as the constituent particles comprising those bonds Nuclear reactions involve the re organization of atomic nuclei protons neutrons etc with far greater energy levels associated 2 5 ENERGY IN CHEMICAL REACTIONS 65 2 5 Energy in chemical reactions A chemical reaction that results in the net release of energy is called exothermic Conversely a chemical reaction that requires a net input of energy to occur is called endothermic The relationship between chemical reactions and energy exchange is correlated with the breaking or making of chemical bonds Atoms bonded together represent a lower state of total energy than those same atoms existing separately all other factors being equal Thus when separate atoms join together to form a molecule they go from a high st
303. e resulting pressure drop AP across that restriction to infer flow rate You may have already seen a diagram such as the following illustrating how an orifice plate works 621 622APPENDIX A DOCTOR STRANGEFLOW OR HOW I LEARNED TO RELAX AND LOVE REYNOLDS NUMBERS Differential pressure instrument Pipe oe N 1 i i i Vena contracta gt Direction of flow Now the really weird thing about measuring flow this way is that the resulting AP signal does not linearly correspond to flow rate Double the flow rate and the AP quadruples Triple the flow rate and the AP increases by a factor of nine To express this relationship mathematically Q x AP In other words differential pressure across an orifice plate AP is proportional to the square of the flow rate Q To be more precise we may include a coefficient k with a precise value that turns the proportionality into an equality Q k AP Expressed in graphical form the function looks like one half of a parabola 623 Diff pressure AP Flow Q To obtain a linear flow measurement signal from the differential pressure instrument s output signal we must square root that signal either with a computer inside the transmitter with a computer inside the receiving instrument or a separate computing instrument a square root extractor We may see mathematically how this yields a value for flow rate Q following from our original equat
304. e source always wanting to maintain voltage across its terminals at the same value The amount of potential energy Ep in units of joules stored by a capacitor is proportional to the square of the voltage 1 2 Ep 30V In an AC circuit the amount of capacitive reactance Xc offered by a capacitor is inversely proportional to both capacitance and frequency 1 Xo O 110 CHAPTER 3 DC ELECTRICITY 3 10 Inductors Any conductor possesses a characteristic called inductance the ability to store energy in the form of a magnetic field Inductance is symbolized by the capital letter L and is measured in the unit of the Henry H Inductance is a non dissipative quantity Unlike resistance a pure inductance does not dissipate energy in the form of heat rather it stores and releases energy from and to the rest of the circuit Inductors are devices expressly designed and manufactured to possess inductance They are typically constructed of a wire coil wound around a ferromagnetic core material Inductors have current ratings as well as inductance ratings Due to the effect of magnetic saturation inductance tends to decrease as current approaches the rated maximum value in an iron core inductor Here are some schematic symbols for inductors 5 OI An inductor s inductance is related to the magnetic permeability of the core material j the number of turns in the wire coil N the cross sectional area of the coil A and the len
305. e sources in the same circuit it is advisable to use the Superposition Theorem for analysis This involves turning off all but one source at a time to see what the effect is for each source then superimposing the results to see what all the sources do when all are working simultaneously We really only need to consider the effects of either AC current source to see what the problem is in this circuit with no loop resistance Consider the situation where the transmitter is sending HART data to the communicator The AC current source inside the transmitter will be active injecting its 1 mA P P audio tone signal onto the two wires of the circuit To apply the Superposition Theorem we replace all the other sources with their own equivalent internal resistances voltage sources become shorts and current sources become opens 10 1 THE HART DIGITAL ANALOG HYBRID STANDARD 249 HART transmitter Power supply Lo Computer HART communicator The HART communicator is listening for those audio tone signals sent by the transmitter s AC source but it hears nothing because the DC power supply s equivalent short circuit prevents any significant AC voltage from developing across the two wires This is what happens when there is no loop resistance no HART device is able to receive data sent by any other HART device The solution to this dilemma is to install a resistance of at least 250 ohms but not greater than 1100
306. e those two pressures will be acting in direct opposition to each other 446 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT Venturi tube Flow nozzle Orifice plate Segmental wedge Flow gt Nut Nut Another way we may accelerate a fluid is to force it to turn a corner through a pipe fitting called 15 1 PRESSURE BASED FLOWMETERS 447 an elbow This will generate radial acceleration causing a pressure difference between the outside and inside of the elbow which may be measured by a differential pressure transmitter Pipe elbow The pressure tap located on the outside of the elbow s turn registers a greater pressure than the tap located on the inside of the elbow s turn due to the inertial force of the fluid s mass being flung to the outside of the turn as it rounds the corner Yet another way to cause fluid acceleration is to force it to decelerate by bringing a portion of it to a full stop The pressure generated by this deceleration called the stagnation pressure tells us how fast it was originally flowing A few devices working on this principle are shown here 448 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT Pitot tube Target Averaging pitot
307. e vessel wall will certainly register less than at the center but the level detected mid way between the vessel wall and vessel center may not be an accurate average of those two heights Moreover this angle may decrease over time if mechanical vibrations cause the material to flow and tumble from center to edge In fact the angle will probably reverse itself if the vessel empties from a center located chute Outlet For this reason solids storage measurement applications demanding high accuracy generally use other techniques such as weight based measurement see section 13 7 for more information 394 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT Since the speed of sound is so important to accurate distance calculations for ultrasonic instruments some ultrasonic level instruments are equipped with temperature sensors to measure the temperature of the fluid through which the sound waves travel A formula programmed into the transmitter calculates the speed of sound based on temperature so that the instrument may continuously compensate for changes in sound velocity rooted in temperature changes and therefore maintain superior accuracy over a wide range of ambient conditions In the vast majority of ultrasonic level transmitter installations where the instrument is mounted above the liquid level such that the sound waves travel through air bounce off liquid and travel back through air it is the speed of sound through air that matter
308. e work will be required to accelerate it through a constriction resulting in greater AP all other conditions being equal AP Q k E Our old friend the orifice plate equation This equation is only accurate however when fluid friction is negligible when the viscosity of the fluid is so low and or its speed is so high that the effects of potential and kinetic energy exchange completely overshadow the effects of friction against the pipe walls and against the orifice plate This is indeed the case for most industrial flow applications and so this is what students first study as they learn how flow is measured Unfortunately this is often the only equation two year Instrumentation students study with regard to flow measurement In situations where Reynolds number is low fluid friction becomes the dominant factor and the standard orifice plate equation no longer applies Here the AP generated by a viscous fluid moving through a pipe really does depend primarily on how thick the fluid is And just like electrons moving through a resistor in an electric circuit the pressure drop across the area of friction is directly proportional to the rate of flow AP Q for fluids V I for electrons This is why laminar flowmeters which work only when Reynolds number is low yield a nice linear relationship between AP and flow rate and therefore do not require square root extraction of the AP signal These flowmeters do however
309. each other the pressure in the system will be precisely equal to the saturated vapor pressure at the vapor liquid interface This makes the Class II system sensitive to temperature only at the bulb and nowhere else along the system s volume Because of this phenomenon a Class II filled bulb system requires no compensation for temperature changes at the indicator Class II systems do have one notable idiosyncrasy though they have a tendency to switch from Class IIA to Class IIB when the temperature of the sensing bulb crosses the ambient temperature at the indicator Simply put the liquid tends to seek the colder portion of a Class II system while the vapor tends to seek the warmer portion This causes problems when the indicator and sensing bulb exchange identities as warmer colder The rush of liquid up or down the capillary tubing as the system tries to reach a new equilibrium causes intermittent measurement errors Class I filled bulb systems designed to operate in either IIA or IIB mode are classified as IC One calibration problem common to all systems with liquid filled capillary tubes is an offset in temperature measurement due to hydrostatic pressure or suction resulting from a different in height between the measurement bulb and the indicator This represents a zero shift in calibration which may be permanently offset by a zero adjustment at the time of installation Class III gas filled and Class IIB vapor filled system
310. ead terms P P z2 01 P P The Continuity equation shows us the relationship between velocities v and v2 and the areas at those points in the venturi tube assuming constant density p Av Agve Specifically we need to re arrange this equation to define v in terms of va so we may substitute into Bernoulli s equation Apo v v 1 Ai 2 Performing the algebraic substitution Distributing the square power p A2y 2 5 02 2 va P Pa Factoring v3 out of the outer parentheses set 2 2 pu Ag 1 P P 2 2 a 2 Solving for v2 step by step 2 Pv2 452 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT The result shows us how to solve for fluid velocity at the venturi throat v2 based on a difference of pressure measured between the mouth and the throat P P2 We are only one step away from a volumetric flow equation here and that is to convert velocity v into flow rate Q Velocity is expressed in units of length per time feet or meters per second or minute while volumetric flow is expressed in units of volume per time cubic feet or cubic meters per second or minute Simply multiplying throat velocity v2 by throat area 42 will give us the result we seek General flow area velocity relationship Q Av Equation for throat velocity 1 P P ve V2 gt 1 2 ay Ar Multiplying both sides of the equation by throat area
311. easuring the weight of the vessel If the vessel s empty weight tare weight is known process weight becomes a simple calculation of total weight minus tare weight Obviously weight based level sensors can measure both liquid and solid materials and they have the benefit of providing inherently linear mass storage measurement Load cells strain gauges bonded to a steel element of precisely known modulus are typically the primary sensing element of choice for detecting vessel weight As the vessel s weight changes the load cells compress or relax on a microscopic scale causing the strain gauges inside to change resistance These small changes in electrical resistance become a direct indication of vessel weight The following photograph shows three bins each one supported by pillars equipped with load cells near their bases One very important caveat for weight based level instruments is to isolate the vessel from any external mechanical stresses generated by pipes or machinery The following illustration shows a typical installation for a weight based measurement system where all pipes attaching to the vessel do 20Regardless of the vessel s shape or internal structure the measurement provided by a weight sensing system is based on the true mass of the stored material Unlike height based level measurement technologies float ultrasonic radar etc no characterization will ever be necessary to convert a measurement of height into
312. eative Commons Any permitted use will be in compliance with Creative Commons then current trademark usage guidelines as may be published on its website or otherwise made available upon request from time to time For the avoidance of doubt this trademark restriction does not form part of this License Creative Commons may be contacted at http creativecommons org Index j operator 121 10 to 50 mA 201 3 to 15 PSI 210 3 valve manifold 322 4 to 20 mA 187 209 4 wire resistance measurement circuit 424 545 4 wire transmitter 198 5 point calibration 265 5 valve manifold 323 Absolute pressure 43 294 Absolute viscosity 49 AC excitation magnetic flowmeter 510 Acid 70 71 Activation energy 65 Address 252 AGA Report 3 479 484 AGA Report 7 499 AGA Report 9 513 Algorithm 601 Algorithm control 156 Alkaline 70 71 American Gas Association 479 484 499 513 Amp re Andr 80 Ampere 80 Analyzer 285 Angle of repose 392 Anion 542 Annubar 467 532 Anode 542 API degrees 38 Archimedes Principle 45 385 As found calibration 270 As left calibration 270 Atmospheres 44 Atom 61 638 Atomic clock 271 Atomic mass 62 Atomic number 62 Atomic weight 62 Automatic mode 131 Averaging Pitot tube 467 Avogadro s number 63 B I F Universal Venturi tube 469 Backpressure nozzle 213 Baffle 213 Balance beam scale 216 Balling degrees 39 Bang bang control 6
313. echnician is that a full calibration procedure on a smart transmitter will potentially require more work and a greater number of adjustments than an all analog transmitter A common mistake made among students and experienced technicians alike is to confuse the range settings LRV and URV for actual calibration adjustments Just because you digitally set the LRV of a pressure transmitter to 0 00 PSI and the URV to 100 00 PSI does not necessarily mean it will register accurately at points within that range The following example will illustrate this fallacy Suppose we have a smart pressure transmitter ranged for 0 to 100 PSI with an analog output range of 4 to 20 mA but this transmitter s pressure sensor is fatigued from years of use such that an actual applied pressure of 100 PSI generates a signal that the analog to digital converter interprets as only 96 PSI Assuming everything else in the transmitter is in perfect condition with perfect calibration the output signal will still be in error 11 3 LRV AND URV SETTINGS DIGITAL TRIM DIGITAL TRANSMITTERS 263 Smart pressure transmitter Range adjustments LRV URV E Trim adjustments 0 PSI 100 PSI Trim adjustments 7 96 PSI Low High Low High equivalent analog signal 100 PSI applied pressure E ADC 96 00 PSI 19 36 ma DAC digital value digital value As the saying goes a chain is only as strong as its weakest link Here we see how the calibration of a so
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315. ecisely equal the diaphragm experiences no net force zero differential pressure 7 6 LEVEL SWITCHES 181 7 6 Level switches A level switch is one detecting the level of liquid or solid granules or powder in a vessel Level switches often use floats as the level sensing element the motion of which actuates one or more switch contacts Recall that the normal status of a switch is the condition of minimum stimulus A level switch will be in its normal status when it senses minimum level e g an empty vessel Level switch symbols om Oo Normally open Normally closed NO NC Two water level switches appear in this photograph of an old boiler The switches sense water level in the steam drum of the boiler Both water level switches are manufactured by the Magnetrol corporation ZS The switch mechanism is a mercury tilt bulb tilted by a magnet s attraction to a steel rod lifted into position by a float The float directly senses liquid level which positions the steel rod either 182 CHAPTER 7 DISCRETE PROCESS MEASUREMENT closer to or further away from the magnet If the rod comes close enough to the magnet the mercury bottle will tilt and change the switch s electrical status This level switch uses a metal tuning fork structure to detect the presence of a liquid or solid powder or granules in a vessel An electronic circuit continuously excites the tuning fork causing it to mechanically vibrat
316. ed and the device will not receive enough voltage Here we must pay special attention to how we use our voltmeter since polarity matters All 78 CHAPTER 3 DC ELECTRICITY voltmeters are standardized with two colors for the test leads red and black To make sense of the voltmeter s indication especially the positive or negative sign of the indication we must understand what the red and black test lead colors mean A positive reading indicates a gain in potential from black to red A negative reading indicates a loss in potential from black to red pe 3 To From Connecting these test leads to different points in a circuit will tell you whether there is potential gain or potential loss from one point black to the other point red 3 2 ELECTRICAL CURRENT 79 3 2 Electrical current Current is the name we give to the motion of electric charges from a point of high potential to a point of low potential All we need to form an electric current is a source of potential voltage and some electric charges that are free to move between the poles of that potential For instance if we connected a battery to two metal plates we would create an electric field between those plates analogous to a gravitational field except that it only acts on electrically charged objects while gravity acts on anything with mass A free charge placed between those plates would fall toward one of the plates just as a mass would fall toward a lar
317. ed in instrumentation including the poise and the stokes both used to express fluid viscosity Then of course we have the British engineering system which uses such wonderful units as feet pounds and thankfully seconds Despite the fact that the majority of the world uses the metric SI system for weights and measures the British system is sometimes referred to as the Customary system 2The only exception to this rule being units of measurement for angles over which there has not yet been full agreement whether the unit of the radian and its solid counterpart the steradian is a base unit or a derived unit 3The older name for the SI system was MKS representing meters kilograms and seconds Pm noting my sarcasm here just in case you are immune to my odd sense of humor 20 CHAPTER 1 PHYSICS 1 6 Conservation Laws The Law of Mass Conservation states that matter can neither be created nor destroyed The Law of Energy Conservation states that energy can neither be created nor destroyed However both mass and energy may change forms and even change into one another in the case of nuclear phenomena Conversion of mass into energy or of energy into mass is quantitatively described by Albert Einstein s famous equation E me Where E Energy joules m Mass kilograms c Speed of light approximately 3 x 10 meters per second 1 7 Classical mechanics Classical mechanics often called Newtonian mechanics in
318. ed relationship between the vertical height of a water column and pressure is such that sometimes water column height is used as a unit of measurement for pressure That is instead of saying 30 PSI we could just as correctly quantify that same pressure as 830 4 inches of water W C or H20 the conversion factor being approximately 27 68 inches of vertical water column per PSI As one might guess the density of the fluid in a vertical column has a significant impact on the hydrostatic pressure that column generates A liquid twice as dense as water for example will produce twice the pressure for a given column height For example a column of this liquid twice as dense as water 14 inches high will produce a pressure at the bottom equal to 28 inches of water 28 W C or just over 1 PSI An extreme example is liquid mercury which is over 13 5 times as dense as water Due to its exceptional density and ready availability the height of a mercury column is also used as a standard unit of pressure measurement For instance 25 PSI could be expressed as 50 9 inches of mercury Hg the conversion factor being approximately 2 036 inches of vertical mercury column per PSI The mathematical relationship between vertical liquid height and hydrostatic pressure is quite simple and may be expressed by either of the following formulae P pgh P yh Where P Hydrostatic pressure in units of weight per square area unit Pascals N m
319. eem like a very informal definition of differential it is actually rooted in a field of mathematics called nonstandard analysis and closely compares with the conceptual notions envisioned by calculus founders 15 9 CHANGE OF QUANTITY FLOW MEASUREMENT 531 exploits the natural properties of resistors and capacitors to essentially do this very thing in real time Differentiator circuit e R Voltage signal i in from mass transmitter m Voltage signal out representing mass flow rate dm dt In the vast majority of applications you will see digital computers used to calculate average flow rates rather than analog electronic circuits calculating instantaneous flow rates The broad capabilities of digital computers virtually ensures they will be used somewhere in the measurement control system so the rationale is to use the existing digital computer to calculate flow rates albeit imperfectly rather than complicate the system design with additional analog circuitry As fast as modern digital computers are able to process simple calculations such as these anyway there is little practical reason to prefer analog signal differentiation except in specialized applications where high speed performance is paramount Perhaps the single greatest disadvantage to inferring flow rate by differentiating mass or volume measurements over time is the requirement that the storage vessel have but one flow path in and out If the vessel has multiple
320. eflected signal However it is possible for foam and floating solids to also cause echos when the transducer is above mounted which may or may not be desirable depending on the application Ultrasonic level instruments enjoy the advantage of being able to measure the height of solid materials such as powders and grains stored in vessels not just liquids Certain challenges unique to these level measurement applications include low material density not causing strong reflections and uneven profiles causing reflections to be scattered laterally instead of straight back to the ultrasonic instrument A classic problem encountered when measuring the level of a powdered or granular material in a vessel is the angle of repose formed by the material as a result of being fed into the vessel at one point 131f the goal is to only detect the liquid then reflections from foam or solids would be bad However if the goal of measuring level is to prevent a vessel from overflowing it is good to measure anything floating on the liquid surface 13 5 ECHO 393 Feed chute Angle of repose This angled surface is difficult for an ultrasonic device to detect because it tends to scatter the sound waves laterally instead of reflecting them strongly back toward the instrument However even if the scattering problem is not significant there still remains the problem of interpretation what is the instrument actually measuring The detected level near th
321. eived notions aside for something new A leap of faith however is not the same as a leap in understanding I believed what I was told but I really didn t understand why it was true The problem intensified when my teacher showed a more detailed flow equation This new equation contained a term for fluid density p What this equation showed us is that orifice plate flow measurement depended on density If the fluid density changed our instrument calibration would have to change in order to maintain good accuracy of measurement Something disturbed me about this equation though so I raised my hand The subsequent exchange between me and my teacher went something like this Me What about viscosity Teacher What Me Doesn t fluid viscosity have an effect on flow measurement just like density Teacher You don t see a variable for viscosity in the equation do you Me Well no but it s got to have some effect on flow measurement Teacher How come Me Imagine clean water flowing through a venturi or through the hole of an orifice plate At a certain flow rate a certain amount of AP will develop across the orifice Now imagine 625 that same orifice flowing an equal rate of liquid honey approximately the same density as water but much thicker Wouldn t the increased thickness or viscosity of the honey result in more friction through the orifice and thus more of a pressure drop than what the water would create
322. eled For those familiar with electricity what you see here in either the lever system or the hydraulic lift is analogous to a transformer we can step AC voltage up but only by reducing AC current Being a passive device a transformer cannot boost power Therefore power out can never be greater than power in and given a perfectly efficient transformer power out will always be precisely equal to power in Power Voltage in Current in Voltage out Current out Work Force in Distance in Force out Distance out 1 8 FLUID MECHANICS 31 Fluid may be used to transfer power just as electricity is used to transfer power Such systems are called hydraulic if the fluid is a liquid usually oil and pneumatic if the fluid is a gas usually air In either case a machine pump or compressor is used to generate a continuous fluid pressure pipes are used to transfer the pressurized fluid to the point of use and then the fluid is allowed to exert a force against a piston or a set of pistons to do mechanical work Hydraulic power system Pipe Pump Cylinder Reservoir Piston Pneumatic power system Pipe Cylinder Compressor Ml Piston An interesting use of fluid we see in the field of instrumentation is as a signaling medium to transfer information between places rather than to transfer power between places This is analogous to using electricity to transmit voice signals in telephone systems or digital data
323. elocity causes kinetic energy to increase at that point If the tube is level with the earth there is negligible difference in elevation z between different points of the tube s centerline which means elevation head remains constant According to the Law of Energy Conservation some other form of energy must decrease to account for the increase in kinetic energy This other form is the pressure head which decreases at the throat of the venturi Pressure Pressure Pressure greatest least less than upstream Ideally the pressure downstream of the narrow throat should be the same as the pressure upstream assuming equal pipe diameters upstream and down However in practice the downstream pressure gauge will show slightly less pressure than the upstream gauge due to some inevitable energy loss as the fluid passed through the venturi Some of this loss is due to fluid friction against the walls of the tube and some is due to viscous losses within the fluid driven by turbulent fluid motion at the high velocity throat passage The difference between upstream and downstream pressure is called permanent pressure loss while the difference in pressure between the narrow throat and downstream is called pressure recovery If we install vertical sight tubes called piezometers along a horizontal venturi tube the differences in pressure will be shown by the heights of liquid columns within the tubes Here we assume an ideal inviscid liquid with
324. els e Temperature measurement by radiated energy e Chemical composition measurement The following sections will describe the mathematics behind each of these measurement applications 17 1 FLOW MEASUREMENT IN OPEN CHANNELS 581 17 1 Flow measurement in open channels Measuring the flow rate of liquid through an open channel is not unlike measuring the flow rate of a liquid through a closed pipe one of the more common methods for doing so is to place a restriction in the path of the liquid flow and then measure the pressure dropped across that restriction The easiest way to do this is to install a low dam in the middle of the channel then measure the height of the liquid upstream of the dam as a way to infer flow rate This dam is technically referred to as a weir and three styles of weir are commonly used Different styles of weirs for measuring open channel liquid flow Rectangular Cippoletti V notch Another type of open channel restriction used to measure liquid flow is called a flume An illustration of a Parshall flume is shown here Weirs and flumes may be thought of being somewhat like orifice plates and venturi tubes respectively for open channel liquid flow Like an orifice plate a weir or a flume generates a differential pressure that varies with the flow rate through it However this is where the similarities end Exposing the fluid stream to atmospheric pressure means the differential pres
325. ement accuracy This 408 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT can be problematic as moisture content variations in the solid may greatly affect permittivity as can variations in granule size They are not known for great accuracy though primarily due to sensitivity to changes in process permittivity and errors caused by stray capacitance in probe cables 13 9 Radiation Certain types of nuclear radiation easily penetrates the walls of industrial vessels but is attenuated by traveling through the bulk of material stored within those vessels By placing a radioactive source on one side of the vessel and measuring the radiation making it through to the other side of the vessel an approximate indication of level within that vessel may be obtained The three most common forms of nuclear radiation are alpha particles a beta particles 3 and gamma rays y Alpha particles are helium nuclei 2 protons bound together with 2 neutrons ejected at high velocity from the nuclei of certain decaying atoms They are easy to detect but have very little penetrating power and so are not used for industrial level measurement Beta particles are electrons ejected at high velocity from the nuclei of certain decaying atoms Like alpha particles though they have little penetrating power and so are not used for industrial level measurement Gamma rays on the other hand are electromagnetic in nature like X rays and light waves and have great penetrat
326. ends electrons out to another device where they travel up to a point of more positive potential 86 CHAPTER 3 DC ELECTRICITY In fact the association between conventional flow notation and sourcing sinking descriptions is so firm that I have yet to see a professionally published textbook on digital circuits that uses electron flow This is true even for textbooks written for technicians and not engineers Once again though it should be understood that either convention of current notation is adequate for circuit analysis I dearly wish this horrible state of affairs would come to an end but the plain fact is that it will not Electron flow notation may have the advantage of greater correspondence to the actual state of affairs in the vast majority of circuits but conventional flow has the weight of over a hundred years of precedent cultural inertia and convenience No matter which way you choose to think at some point you will be faced with the opposing view Pick the notation you like best and may you live long and prosper 21f by chance I have missed anyone s digital textbook that does use electron flow please accept my apologies I can only speak of what I have seen myself 3 3 ELECTRICAL RESISTANCE AND OHM S LAW 87 3 3 Electrical resistance and Ohm s Law To review voltage is the measure of potential energy available to electric charges Current is the uniform drifting of electric charges in response to a voltage
327. ensors rather than a specialized flowtube with built in ultrasonic transducers While clamp on sensors are not without their share of problems they constitute an excellent solution for certain flow measurement applications 15 5 Inertia based true mass flowmeters Flowmeters based on true mass measurement ignore fluid density outputting a signal directly and linearly proportional to mass flow rate These are quite useful in the chemical industries where stoichiometric ratios must be accurately maintained 26Most notably the problem of achieving good acoustic coupling with the pipe wall so that signal transmission to the fluid and signal reception back to the sensor may be optimized 15 5 INERTIA BASED TRUE MASS FLOWMETERS 515 15 5 1 Coriolis flowmeters In physics certain types of forces are classified as fictitious or pseudoforces because they only appear to exist when viewed from an accelerating perspective called a non inertial reference frame The feeling you get in your stomach when you accelerate either up or down in an elevator or when riding a roller coaster at an amusement park feels like a force acting against your body when it is really nothing more than the reaction of your body s inertia to being accelerated by the vehicle you are in The real force is the force of the vehicle against your body causing it to accelerate What you perceive is merely a reaction to that force and not the primary cause of your discom
328. ent of time forming the basis of the so called atomic clock So far as anyone knows this frequency is fixed in nature and cannot vary Intrinsic standards therefore serve as absolute references which we may calibrate certain instruments against The machinery necessary to replicate intrinsic standards for practical use are quite expensive and usually delicate This means the average metrologist let alone the average industrial instrument technician simply will never have access to one In order for these intrinsic standards to be useful within the industrial world we use them to calibrate other instruments which are used to calibrate other instruments and so on until we arrive at the instrument we intend to calibrate for field service in a process So long as this chain of instruments is calibrated against each other regularly enough to ensure good accuracy at the end point we may calibrate our field instruments with confidence The documented confidence is known as NIST traceability that the accuracy of the field instrument we calibrate is ultimately ensured by a trail of documentation leading to intrinsic standards maintained by the NIST 11 7 Instrument turndown An important performance parameter for transmitter instruments is something often referred to as turndown or rangedown Turndown is defined as the ratio of maximum allowable span to the minimum allowable span for a particular instrument Suppose a pressure transmitter ha
329. ent present in the original sample may be determined by applying the calculus technique of integration to each chromatogram peak calculating the area underneath each curve The vertical axis represents detector signal which is proportional to component concentration 17Detector response also varies substantially with the type of substance being detected and not just its concentration A flame ionization detector FID for instance yields different responses for a given mass flow rate of butane C4H10 than it does for the same mass flow rate of methane CH4 due to the differing carbon count per mass ratios of the two compounds This means the same raw signal from an FID sensor generated by a concentration of butane versus a concentration of methane actually represents different concentrations of butane versus methane 16 5 CHROMATOGRAPHY 565 which is proportional to flow rate given a fixed carrier flow rate This means the height of each peak represents mass flow rate of each component W in units of micrograms per minute or some similar units The horizontal axis represents time so therefore the integral sum of infinitesimal products of the detector signal over the time interval for any specific peak time t to t2 represents a mass quantity that has passed through the column In simplified terms a mass flow rate micrograms per minute multiplied by a time interval minutes equals mass in micrograms ta m W dt ti Where
330. eparate in solution and this separation is called dissociation If the electrolyte in question is a covalently bonded compound hydrogen chloride is an example the separation of those molecules into positive and negative ions is called ionization Both dissociation and ionization refer to the separation of formerly joined atoms upon entering a solution The difference between these terms is the type of substance that splits dissociation refers to the division of ionic compounds such as table salt while ionization refers to covalent bonded molecular compounds such as HCl which are not ionic in their pure state Ionic impurities added to water such as salts and metals immediately dissociate and become available to act as charge carriers Thus the measure of a water sample s electrical conductivity is 1Truth be told free hydrogen ions are extremely rare in an aqueous solution You are far more likely to find them bound to normal water molecules to form positive hydronium ions H30 For simplicity s sake though professional literature often refers to these positive ions as hydrogen ions and even represent them symbolically as H 2Tonic compounds are formed when oppositely charged atomic ions bind together by mutual attraction The distinguishing characteristic of an ionic compound is that it is a conductor of electricity in its pure liquid state That is it readily separates into anions and cations all by itself E
331. er shown in assembled form in the following photograph 12 3 ELECTRICAL PRESSURE ELEMENTS 305 By removing four bolts from the transmitter we are able to remove two flanges from the pressure capsule exposing the isolating diaphragms to plain view A close up photograph shows the construction of one of the isolating diaphragms which unlike 306 CHAPTER 12 CONTINUOUS PRESSURE MEASUREMENT the sensing diaphragm is designed to be very flexible The concentric corrugations in the metal of the diaphragm allow it to easily flex with applied pressure transmitting process fluid pressure through the silicone fill fluid to the taut sensing diaphragm inside the differential capacitance cell The differential capacitance sensor inherently measures differences in pressure applied between its two sides In keeping with this functionality this pressure instrument has two threaded ports into which fluid pressure may be applied A later section in this chapter will elaborate on the utility of differential pressure transmitters section 12 5 beginning on page 316 All the electronic circuitry necessary for converting the sensor s differential capacitance into an electronic signal representing pressure is housed in the blue colored structure above the capsule and flanges A more modern realization of the differential capacitance pressure sensing principle is the Rosemount model 3051 differential pressure transmitter 12 3 ELECTRICAL PRESSURE
332. er instruments taking some 18 1 BASIC FEEDBACK CONTROL PRINCIPLES 597 form of control action In instrumentation terms the measuring device is known as a transmitter because it transmits the process measurement in the form of a signal Transmitters are represented in process diagrams by small circles with identifying letters inside in this case TT which stands for Temperature Transmitter Steam in l Process Variable PV signal Steam out The signal coming from the transmitter shown in the illustration by the dashed line representing the heated fluid s exiting temperature is called the process variable Like a variable in a mathematical equation that represents some story problem quantity this signal represents the measured quantity we wish to control in the process In order to exert control over the process variable we must have some way of altering fluid flow through the heat exchanger either of the process fluid the steam or both Generally it makes more sense to alter the flow of the heating medium the steam and let the process fluid flow rate be dictated by the demands of the larger process If this heat exchanger were part of an oil refinery unit for example it would be far better to throttle steam flow to control oil temperature rather than to throttle the oil flow itself since altering the oil s flow will undoubtedly affect other processes upstream and downstream of the exchanger Ideally the
333. er of these two equations and so an equation form better suited for mechanical design became popular Known as the series PID algorithm its equation looks like this d m Kp e Ki edt 1 Ka b Even though pneumatic and analog electronic PID controllers are mostly obsolete we still see the old series algorithm implemented in some modern digital controllers for the sake of direct interchangeability This way someone can upgrade their old control system and use the exact same P I and D tuning constants in the new controller to control the process just as well Just in case you thought things still weren t complicated enough we have even more variations on PID control algorithms to consider Some controllers calculate the derivative term on error while others calculate it on process variable alone The difference in response between these two controller types is revealed when a human operator makes a setpoint change the PV based derivative controller does nothing while the error based derivative controller makes a sudden jump in its output value Furthermore many digital electronic controllers calculate the PID equation based on changes in PV rather than the absolute value of PV This is known as the velocity algorithm as opposed to the position algorithm The difference between these two variations of PID control becomes evident when one changes the gain setting the velocity algorithm controller does nothing while the po
334. er second We know that the capacitor s relationship between voltage and current is as follows dV I C Ji Therefore we may substitute the expression for voltage in this circuit into the equation and use calculus to differentiate it with respect to time rag ai sin wt I wC cos wt 124 CHAPTER 4 AC ELECTRICITY The ratio of Y the opposition to electric current analogous to resistance R will then be V _ sin wt I wC cos wt 1 tan wi nu I wC This might look simple enough until you realize that the ratio Y will become undefined for certain values of t notably 5 and at If we look at a time domain plot of voltage and current for a capacitor it becomes clear why this is There are points in time where voltage is maximum and current is zero Max voltage zero current Max voltage zero current Max voltage Max voltage zero current zero current At these instantaneous points in time it truly does appear as if the resistance of the capacitor is undefined infinite with multiple incidents of maximum voltage and zero current However this does not capture the essence of what we are trying to do relate the peak amplitude of the voltage with the peak amplitude of the current to see what the ratio of these two peaks are The ratio calculated here utterly fails because those peaks never happen at the same time One way around this problem is to express the voltage as a complex quantity rather than
335. er second or Hz Pulses _ Pulses gal s gal s Using algebra to solve for flow Q we see that it is the quotient of frequency and K factor that yields a volumetric flow rate for a turbine flowmeter Ly e If pickup signal frequency directly represents volumetric flow rate then the total number of pulses accumulated in any given time span will represent the amount of fluid volume passed through the turbine meter over that same time span We may express this algebraically as the product of average flow rate Q average frequency f K factor and time un ft V Q k A more sophisticated way of calculating total volume passed through a turbine meter requires calculus representing total volume as the time integral of instantaneous signal frequency and K factor over a period of time from t 0 to t T T T Ff ve Q dt or v dt 0 o k We may achieve approximately the same result simply by using a digital counter circuit to totalize pulses output by the pickup coil and a microprocessor to calculate volume in whatever unit of measurement we deem appropriate As with the orifice plate flow element standards have been drafted for the use of turbine flowmeters as precision measuring instruments in gas flow applications particularly the custody transfer of natural gas The American Gas Association has published a standard called the Report 7 specifying the installation of turbine flowmeters for high accuracy gas flo
336. er what happens to the process Obviously then we must set the gain somewhere between infinity and zero in order for this algorithm to function any better than on off control Just how much gain a controller needs to have depends on the process and all the other instruments in the control loop If the gain is set too high there will be oscillations as the PV converges on a new setpoint value 606 CHAPTER 18 CONTINUOUS FEEDBACK CONTROL 85 PV 15 SP 70 65 60 55 50 45 40 35 30 25 20 15 10 3 0 Time gt If the gain is set too low the process response will be stable under steady state conditions but sluggish to changes in setpoint because the controller does not take aggressive enough action to cause quick changes in the process 75 SP 60 PV P 59 Time gt With proportional only control the only way to obtain fast acting response to setpoint changes or upsets in the process is to set the gain constant high enough that some overshoot results 18 3 PROPORTIONAL ONLY CONTROL 607 100 a sp PV 50 Time gt As with on off control instances of overshoot the process variable rising above setpoint and undershoot drifting below setpoint are generally undesirable and for the same reasons Ideally the controller will be able to respond in such a way that the process variable is made equal to setpoint as quickly as the process dynamics will allow yet with no substantial overshoot
337. eres 1 atmosphere being 14 7 PSIA There is no such thing as atmospheres gauge pressure For example if we were given a pressure as being 4 5 atmospheres and we wanted to convert that into pounds per square inch gauge PSIG the conversion would be a two step process 1375 7 W C A 45atm 14 7 PSIA x 66 15 PSIA 1 l atm 66 15 PSIA 14 7 PSI 51 45 PSIG Another unit of pressure measurement that is always absolute is the torr equal to 1 millimeter of mercury column absolute mmHgA 0 torr is absolute zero equal to 0 atmospheres 0 PSIA or 14 7 PSIG Atmospheric pressure at sea level is 760 torr equal to 1 atmosphere 14 7 PSIA or 0 PSIG If we wished to convert the car tire s pressure of 35 PSIG into torr we would once again have to offset the initial value to get everything into absolute terms 35 PSIG 14 7 PSI 49 7 PSIA 49 7 PSIA 760 torr i x iL7 PSIA 2569 5 torr 1 8 FLUID MECHANICS 45 1 8 6 Buoyancy When a solid body is immersed in a fluid it displaces an equal volume of that fluid This displacement of fluid generates an upward force on the object called the buoyant force The magnitude of this force is equal to the weight of the fluid displaced by the solid body and it is always directed exactly opposite the line of gravitational attraction This is known as Archimedes Principle Buoyant force is what makes ships float A ship sinks into the water just enough so that the weight
338. erred by a nail from a hammer to a piece of wood Hammer Force exerted on nail Nail The impact of the hammer s blow is directed straight through the solid nail into the wood below Nothing surprising here But now consider what a fluid would do when subjected to the same hammer blow 1 8 FLUID MECHANICS 29 Hammer Force exerted on piston y N Fluid Cylinder Given the freedom of a fluid s molecules to move about the impact of the hammer blow becomes directed everywhere against the inside surface of the container the cylinder This is true for all fluids liquids and gases alike The only difference between the behavior of a liquid and a gas in the same scenario is that the gas will compress i e the piston will move down as the hammer struck it whereas the liquid will not compress i e the piston will remain in its resting position Gases yield under pressure liquids do not It is very useful to quantify force applied to a fluid in terms of force per unit area since the force applied to a fluid becomes evenly dispersed in all directions to the surface containing it This is the definition of pressure P how much force F is distributed across how much area A In the metric system the standard unit of pressure is the Pascal Pa defined as one Newton N of force per square meter m of area In the English system of measurement the standard unit of pressure is the PSI po
339. erview of the process to see how the major components interact Then once you have identified which instrument loop you need to investigate you go to the appropriate loop diagram to see the interconnection details of that instrument system so you know where to connect your test equipment and what signals you expect to find when you do Another analogy for this progression of documents is a map or more precisely a globe an atlas and a city street map The globe gives you the big picture of the Earth countries and major cities An atlas allows you to zoom in to see details of particular provinces states and principalities and the routes of travel connecting them all A city map shows you major and minor roads canals alleyways and perhaps even some addresses in order for you to find your way to a particular destination It would be impractical to have a globe large enough to show you all the details of every city Furthermore a globe comprehensive enough to show you all these details would have to be updated very frequently to keep up with all cities road changes There is a certain economy inherent to the omission of fine details both in ease of use and in ease of maintenance 6 1 PROCESS FLOW DIAGRAMS 149 6 1 Process Flow Diagrams To show a practical process example let s examine three diagrams for a compressor control system In this fictitious process water is being evaporated from a process solution under pa
340. es directly oppose one another in the same line of action to constrain the motion of a beam are known as force balance systems Instruments built such that bellows forces oppose one another through different lever lengths such as in the last system are technically known as moment balance systems referencing the moment arm lengths through which the bellows forces act to balance each other However one will often find that moment balance instruments are commonly referred to as force balance because the two principles are so similar An entirely different classification of pneumatic instrument is known as motion balance The same simplifying assumption of zero baffle nozzle gap motion holds true for the analysis of these mechanisms as well Po S3 Pos Air supply In this mechanism there is no fixed pivot for the beam Instead the beam hangs between the ends of two bellows units affixed by pivoting links As input pressure increases the input bellows 9 4 ANALOGY TO OPAMP CIRCUITS 235 expands outward attempting to push the beam closer to the nozzle However if we follow our assumption that negative feedback holds the nozzle gap constant we see that the feedback bellows must expand the same amount and thus if it has the same area and spring characteristics as the input bellows the output pressure must equal the input pressure Fis 2 A Pin Air supply gt We call this a motion balan
341. ess conditions that none of the wave s energy is converted to heat while traveling through the dielectric For many situations this is true enough to assume 398 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT ref Relative permittivity of the same gas at standard pressure P f and temperature Tres P Absolute pressure of gas bars P e Absolute pressure of gas under standard conditions 1 bar T Absolute temperature of gas Kelvin Tref Absolute temperature of gas under standard conditions 273 K If a radio wave encounters a sudden change in dielectric permittivity some of that wave s energy will be reflected in the form of another wave traveling the opposite direction In other words the wave will echo when it reaches a discontinuity This is the basis of all radar devices Radar transceiver Air E 1 F r P incident reflected This same principle explains reflected signals in copper transmission lines as well If anything happens along the length of a transmission line to cause a discontinuity a sudden change in characteristic impedance a portion of the signal s power will be reflected back to the source In a transmission line continuities may be formed by pinches breaks or short circuits In a radar level measurement system any sudden change in permittivity is a discontinuity that will reflect some of the radio energy back to the source The ratio of reflected power to incident tran
342. essure adds to the hydrostatic pressure caused by the liquid in the tubing 12 6 PRESSURE SENSOR ACCESSORIES 335 Isolating diaphragm P levoton E pgh gt yh Tube Elevation 4 86 PSI with fill fluid h Pressure Process YP arevaton Pressure gauge 4 86 to 54 86 PSI calibrated range This pressure may be calculated by the formula pgh or yh where p is the mass density of the fill liquid or y is the weight density of the fill liquid For example a 12 foot capillary tube height filled with a fill liquid having a weight density of 58 3 Ib ft will generate an elevation pressure of almost 700 Ib ft or 4 86 PSI If the pressure instrument is located below the process connection point this 4 86 PSI offset must be incorporated into the instrument s calibration range If we desire this pressure instrument to accurately measure a process pressure range of 0 to 50 PSI we would have to calibrate it for an actual range of 4 86 to 54 86 PSI The reverse problem exists where the pressure instrument is located higher than the process connection here the instrument will register a lower pressure than what is actually inside the vessel offset by the amount predicted by the hydrostatic pressure formulae pgh or yh In all fairness this problem is not limited to remote seal systems even non isolated systems where the tubing is filled with process liquid will exhibit this offset error However in filled capillary sy
343. et flow sensor consisting of 15 1 PRESSURE BASED FLOWMETERS 469 a blunt paddle or drag disk inserted into the flowstream The force exerted on this paddle by the moving fluid is sensed by a special transmitter mechanism which then outputs a signal corresponding to flow rate proportional to the square of fluid velocity just like an orifice plate The classic venturi tube pioneered by Clemens Herschel in 1887 has been adapted in a variety of forms broadly classified as flow tubes All flow tubes work on the same principle developing a differential pressure by channeling fluid flow from a wide tube to a narrow tube The differ from the classic venturi only in construction details Examples of flow tube designs include the Dall tube Lo Loss flow tube Gentile or Bethlehem flow tube and the B I F Universal Venturi Another variation on the venturi theme is called a flow nozzle designed to be clamped between the faces of two pipe flanges in a manner similar to an orifice plate The goal here is to achieve simplicity of installation approximating that of an orifice plate while improving performance less permanent pressure loss over orifice plates 470 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT Flow nozzle T Nut Two more variations on the venturi theme are the V cone and Segmental wedge flow elements The V cone or venturi cone a trade name of the McCrometer division of the Danaher
344. et leg height Gasoline level Percent of range Pressure at transmitter Transmitter output O ft 0 4 77 PSI 4 mA 2 5 ft 25 4 05 PSI 8 mA 5 ft 50 3 34 PSI 12 mA 7 5 ft 75 2 63 PSI 16 mA 10 ft 100 1 92 PSI 20 mA Note that due to the superior density and height of the wet water leg the transmitter always sees a negative pressure pressure on the Low side exceeds pressure on the High side With some older differential pressure transmitter designs this was a problem Consequently it is common to see wet leg hydrostatic transmitters installed with the Low port connected to the bottom of the vessel and the High port connected to the compensating leg In fact it is still common to see modern differential pressure transmitters installed in this manner although modern transmitters may be calibrated for negative pressures just as easily as for positive pressures It is vitally important to recognize that any differential pressure transmitter connected as such for any reason will respond in reverse fashion to increases in liquid level That is to say as the liquid level in the vessel rises the transmitter s output signal will decrease instead of increase 6Sometimes this is done out of habit other times because instrument technicians do not know the capabilities of new technology 13 3 HYDROSTATIC PRESSURE 371 High side of DP transmitter connected to the co
345. etric system would go a long way toward alleviating this problem but until then it is important for students of instrumentation to master the art of unit conversions It is possible to convert from one unit of measurement to another by use of tables designed expressly for this purpose Such tables usually have a column of units on the left hand side and an identical row of units along the top whereby one can look up the conversion factor to multiply by to convert from any listed unit to any other listed unit While such tables are undeniably simple to use they are practically impossible to memorize The goal of this section is to provide you with a more powerful technique for unit conversion which lends itself much better to memorization of conversion factors This way you will be able to convert between many common units of measurement while memorizing only a handful of essential conversion factors I like to call this the unity fraction technique It involves setting up the original quantity as a fraction then multiplying by a series of fractions having physical values of unity 1 so that by multiplication the original value does not change but the units do Let s take for example the conversion of quarts into gallons an example of a fluid volume conversion 35 qt gal Now most people know there are four quarts in one gallon and so it is tempting to simply divide the number 35 by four to arrive at the proper number of gallons Howe
346. evation and Pressure heads are potential forms of energy while Velocity head is a kinetic form of energy Note how the elevation and velocity head terms so closely resemble the formulae for potential and kinetic energy of solid objects Ep mgh Potential energy formula 2 E mu Kinetic energy formula 2 It is very important to maintain consistent units of measurement when using Bernoulli s equation Each of the three energy terms elevation velocity and pressure must possess the exact same units if they are to add appropriately Here is an example of dimensional analysis applied to the first version of Bernoulli s equation using British units 11 According to Ven Te Chow in Open Channel Hydraulics who quotes from Hunter Rouse and Simon Ince s work History of Hydraulics Bernoulli s equation was first formulated by the great mathematician Leonhard Euler and made popular by Julius Weisbach not by Daniel Bernoulli himself 12Surely you ve heard the expression Apples and Oranges don t add up Well pounds per square inch and pounds per square foot don t add up either 56 CHAPTER 1 PHYSICS 2 v se e ET Es 2 Ss As you can see both the first and second terms of the equation elevation and velocity heads bear the same unit of slugs per foot second squared after all the feet are canceled The third term pressure head does not appear as though its units agree with the other two terms until you rea
347. f precisely known quantity to ensure operational accuracy In order to perform a calibration one must be reasonably sure that the physical quantity used to stimulate the instrument is accurate in itself For example if I try calibrating a pressure gauge to read accurately at an applied pressure of 200 PSI I must be reasonably sure that the pressure I am using to stimulate the gauge is actually 200 PSI If it is not 200 PSI then all I am doing is adjusting the pressure gauge to register 200 PSI when in fact it is sensing something different Ultimately this is a philosophical question of epistemology how do we know what is true There are no easy answers here but teams of scientists and engineers known as metrologists devote their professional lives to the study of calibration standards to ensure we have access to the best approximation of truth for our calibration purposes Metrology is the science of measurement and the central repository of expertise on this science within the United States of America is the National Institute of Standards and Technology or the NIST formerly known as the National Bureau of Standards or NBS Experts at the NIST work to ensure we have means of tracing measurement accuracy back to intrinsic standards which are quantities inherently fixed as far as anyone knows The vibrational frequency of an isolated cesium atom when stimulated by radio energy for example is an intrinsic standard used for the measurem
348. face 15 1 PRESSURE BASED FLOWMETERS 461 Square edged eccentric orifice plate Paddle front view side view For gas flows the hole should be offset downward so that any liquid droplets or solid particles may easily pass through For liquid flows the hole should be offset upward to allow gas bubbles to pass through and offset downward to allow heavy solids to pass through The second off center orifice plate type is called the segmental orifice plate where the hole is not circular but rather just a segment of a concentric circle 462 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT Square edged segmental orifice plate Paddle front view side view As with the eccentric orifice plate design the segmental hole should be offset downward in gas flow applications and either upward or downward in liquid flow applications depending on the type of undesired material s in the flowstream Some orifice plates employ non square edged holes for the purpose of improving performance at low Reynolds number values where the effects of fluid viscosity are more apparent These orifice plate types employ rounded or conical entrance holes in an effort to minimize the effects of fluid viscosity Experiments have shown that decreased Reynolds number causes the flowstream to not contract as much when traveling through an orifice thus limiting fluid acceleration and decreasing the amount of differential pressure produced
349. ffective dielectric for the two capacitors Output terminals Solid insulation SN Wi SS ua ros Isolating T diaphragm Silicone fill fluid Pressure gt A Isolating diaphragm SS LL Sensing diaphragm Any difference of pressure across the cell will cause the diaphragm to flex in the direction of least pressure Since capacitance between conductors is inversely proportional to the distance separating them this causes capacitance on the low pressure side to increase and capacitance on the high pressure side to decrease 304 CHAPTER 12 CONTINUOUS PRESSURE MEASUREMENT Output terminals l Solid insulation Low dea Pressure Isolating diaphragm High Pressure gt Isolating diaphragm LD A capacitance detector circuit connected to this cell uses a high frequency AC excitation signal to measure the different in capacitance between the two halves translating that into a DC signal which ultimately becomes the signal output by the instrument representing pressure These pressure sensors are highly accurate stable and rugged The solid frame bounds the motion of the two isolating diaphragms such that the sensing diaphragm cannot move past its elastic limit This gives the differential capacitance excellent resistance to overpressure damage A classic example of a pressure instrument based on the differential capacitance sensor is the Rosemount model 1151 differential pressure transmitt
350. fle 20 18 16 14 12 Backpressure at 10 nozzle PSI O N A O 0123 45 67 8 9 10 Clearance mils thousandths of an inch The physical distance between the baffle and the nozzle alters the resistance of air flow through the nozzle This in turn affects the air pressure built up inside the nozzle called the nozzle backpressure Like a voltage divider circuit formed by one fixed resistor and one variable resistor the baffle nozzle mechanism divides the pneumatic source pressure to a lower value based on the ratio of restrictiveness between the nozzle and the fixed orifice This crude assemblage is surprisingly sensitive as shown by the graph With a small enough orifice just a few thousandths of an inch of motion is enough to drive the pneumatic output between its saturation limits Pneumatic transmitters typically employ a small sheet metal lever as the baffle The slightest motion imparted to this baffle by changes in the process variable pressure temperature flow level etc detected by some sensing element will cause the air pressure to 214 CHAPTER 9 PNEUMATIC INSTRUMENTATION change in response The principle behind the operation of a baffle nozzle mechanism is often used directly in quality control work checking for proper dimensioning of machined metal parts Take for instance this shaft diameter checker using air to determine whether or not a machined shaft inserted by a human operator is of the proper di
351. flexible measuring tape until the tape goes slack due to the float coming to rest on the material surface At that point the person notes the length indicated on the tape reading off the lip of the vessel access hole Obviously this method of level measurement is tedious and may pose risk to the person conducting the measurement If the vessel is pressurized this method is simply not applicable If we automate the person s function using a small winch controlled by a computer having the computer automatically lower the float down to the material surface and measure the amount of cable played out at each measurement cycle we may achieve better results without human intervention Such a level gauge may be enclosed in such a way to allow pressurization of the vessel too 13 2 FLOAT 353 A simpler version of this technique uses a spring reel to constantly tension the cable holding the float so that the float continuously rides on the surface of the liquid in the vessel Spring loaded Pulley Pulley cable reel Cable Spring loaded cable reel The following photograph shows the measurement head of a spring reel tape and float liquid level transmitter with the vertical pipe housing the tape on its way to the top of the storage tank where it will turn 180 degrees via two pulleys and attach to the float inside the tank 1A spring loaded cable float only works with liquid level measurement while a retr
352. flow measurement only as a last resort Their inaccuracies tend to be extreme owing to the non precise construction of most pipe elbows and the relatively weak differential pressures generated 8 The fact that a pipe elbow generates small differential pressure is an accuracy concern because other sources of pressure become larger by comparison Noise generated by fluid turbulence in the elbow for example becomes a significant portion of the pressure sensed by the transmitter when the differential pressure is so low i e the signal to noise ratio becomes smaller Errors caused by differences in elbow tap elevation and different impulse line fill fluids for example become more significant as well 15 1 PRESSURE BASED FLOWMETERS 473 15 1 4 Proper installation Perhaps the most common way in which the flow measurement accuracy of any flowmeter becomes compromised is incorrect installation and pressure based flowmeters are no exception to this rule The following list shows some of the details one must consider in installing a pressure based flowmeter element e Necessary upstream and downstream straight pipe lengths Beta ratio Impulse tube tap locations Tap finish Transmitter location in relation to the pipe Sharp turns in piping networks introduce large scale turbulence into the flowstream Elbows tees valves fans and pumps are some of the most common causes of large scale turbulence in piping systems When the natural f
353. flow switch will be in its normal status when it senses minimum flow i e no fluid moving through the pipe Flow switches often use Flow switch symbols S Normally open Normally closed NO NC A simple paddle placed in the midst of a fluid stream generates a mechanical force which may be used to actuate a switch mechanism as shown in the following photograph 186 CHAPTER 7 DISCRETE PROCESS MEASUREMENT Chapter 8 Analog electronic instrumentation 8 1 4 to 20 mA analog current signals The most popular form of signal transmission used in modern industrial instrumentation systems as of this writing is the 4 to 20 milliamp DC standard This is an analog signal standard meaning that the electric current is used to proportionately represent measurements or command signals Typically a 4 milliamp current value represents 0 of scale a 20 milliamp current value represents 100 of scale and any current value in between 4 and 20 milliamps represents a commensurate percentage in between 0 and 100 For example if we were to calibrate a 4 20 mA temperature transmitter for a measurement range of 50 to 250 degrees C we could relate the current and measured temperature values on a graph like this 187 188 CHAPTER 8 ANALOG ELECTRONIC INSTRUMENTATION 250 240 230 220 210 200 190 180 170 Measured 160 temperature 150 C 140 130 120 110 100 90 80 70 60 50
354. for more details on this subject 13 3 HYDROSTATIC PRESSURE 375 this are known as custody transfer because they represent the transfer of custody ownership of a substance exchanged in a business agreement It is common for both buyer and seller to operate and maintain their own custody transfer instrumentation and to compare the instruments readings for concurrence within a mutually agreed margin of error 376 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT 13 3 5 Hydrostatic interface level measurement Hydrostatic pressure sensors may be used to detect the level of a liquid liquid interface if and only if the total height of liquid sensed by the instrument is fixed A single hydrostatic based level instrument cannot discern between a changing interface level and a changing total level so the latter must be fixed in order to measure the former One way of fixing total liquid height is to equip the vessel with an overflow pipe and ensure that drain flow is always less than incoming flow so that some flow must always go through the overflow pipe This strategy naturally lends itself to separation processes where a mixture of light and heavy liquids are separated by their differing densities Inlet pipe Overflow pipe light liquid out ee Interface A Electronic M output signal l vented Pressure Y h Sh Yoho Drain pipe heavy liquid out Here we see a practical application for liquid liquid interface leve
355. forced to the right The same effect would occur if the pressure on the Low pressure input port were to decrease This is a differential pressure transmitter so what it responds to is changes in pressure difference between the two input ports This resultant motion of the capsule tugs on the thin flexure connecting it to the force bar The force bar pivots at the fulcrum where the small diaphragm seal is located in a counter clockwise rotation tugging the flexure at the top of the force bar This motion causes the range bar to also pivot at its fulcrum the sharp edged range wheel moving the baffle closer to the nozzle As the baffle approaches the nozzle air flow through the nozzle becomes more restricted accumulating backpressure in the nozzle This backpressure increase is greatly amplified in the relay which sends an increasing air pressure signal both to the output line and to the bellows at the bottom of the range bar Increasing pneumatic pressure in the bellows causes it to push harder on the bottom of the range bar counterbalancing the initial motion and returning the range bar and force bar to their near original positions Calibration of this instrument is accomplished through two adjustments the zero screw and the range wheel The zero screw simply adds tension to the bottom of the range bar pulling it in such a direction as to collapse the bellows as the zero screw is turned clockwise This action pushes 240 CHAPTER
356. fort as it might appear to be Centrifugal force is another example of a pseudoforce because although it may appear to be a real force acting on any rotating object it is in fact nothing more than an inertial reaction Centrifugal force is a common experience to any child who has ever played on a merry go round that perception of a force drawing you away from the center of rotation toward the rim The real force acting on any rotating object is toward the center of rotation a centripetal force which is necessary to make the object radially accelerate toward a center point rather than travel in a straight line as it normally would without any forces acting upon it When viewed from the perspective of the spinning object however it would seem there is a force drawing the object away from the center a centrifugal force Yet another example of a pseudoforce is the Coriolis force more complicated than centrifugal force arising from motion perpendicular to the axis of rotation in a non inertial reference frame The example of a merry go round works to illustrate Coriolis force as well imagine sitting at the center of a spinning merry go round holding a ball If you gently toss the ball away from you and watch the trajectory of the ball you will notice it curve rather than travel away in a straight line In reality the ball is traveling in a straight line as viewed from an observer standing on the ground but from your perspectiv
357. from the vessel interior by means of a dielectric window made of some substance that is relatively transparent to radio waves yet acts as an effective vapor barrier 13 5 ECHO 397 Non contact radar liquid level measurement Dielectric window Radio waves travel at the velocity of light 2 9979 x108 meters per second in a perfect vacuum The velocity of a radio wave through space depends on the dielectric permittivity symbolized by the Greek letter epsilon e of that space A formula relating wave velocity to relative permittivity the ratio of a substance s permittivity to that of a perfect vacuum symbolized as e and sometimes called the dielectric constant of the substance and the velocity of light in a perfect vacuum c is shown here The relative permittivity of air at standard pressure and temperature is very nearly unity 1 The permittivity of any gas is a function of both pressure and temperature as shown by the following formula PT ret Pret T Er 14 ref 1 Where er Relative permittivity of a gas at a given pressure P and temperature T 15In actuality both radio waves and light waves are electromagnetic in nature The only difference between the two is frequency while the radio waves used in radar systems are classified as microwaves with frequencies in the gigahertz GHz region visible light waves range in the hundred of terahertz THz 16This formula assumes lossl
358. g wheel a little bit extra after reversing steering direction Anyone who has ever driven an old farm tractor knows what this phenomenon is like and how it detrimentally affects one s ability to steer the tractor in a straight line Another type of instrument commonly seen in measurement and control systems is the process switch The purpose of a switch is to turn on and off with varying process conditions Usually switches are used to activate alarms to alert human operators to take special action In other situations switches are directly used as control devices The following P amp ID of a compressed air control system shows both uses of process switches 5 4 OTHER TYPES OF INSTRUMENTS 145 Filter Blowdown The PSH pressure switch high activates when the air pressure inside the vessel reaches its high control point The PSL pressure switch low activates when the air pressure inside the vessel drops down to its low control point Both switches feed discrete on off electrical signals to a logic control device signified by the diamond which then controls the starting and stopping of the electric motor driven air compressor Another switch in this system labeled PSHH pressure switch high high activates only if the air pressure inside the vessel exceeds a level beyond the high shut off point of the high pressure control switch PSH If this switch activates something has gone wrong with the compressor control
359. ge present as a result of stray electric currents in the piping and or liquid To combat this problem magnetic flowmeters are usually equipped to shunt stray electric currents around the flowtube so that the only voltage intercepted by the electrodes will be the motional EMF produced by liquid flow The following photograph shows a Rosemount model 8700 magnetic flowtube with braided wire grounding straps clearly visible Note how both grounding straps attach to a common junction point on the flowtube housing This common junction point should also be bonded to a functional earth ground when the flowtube is installed in the process line On this particular flowtube you can see a stainless steel grounding ring on the face of the near flange connected to one of the braided grounding straps An identical grounding ring lays on the other flange but it is not clearly visible in this photograph These rings provide points of electrical contact with the liquid in installations where the pipe is made of plastic 15 4 VELOCITY BASED FLOWMETERS 509 or where the pipe is metal but lined with a plastic material for corrosion resistance Magnetic flowmeters are fairly tolerant of swirl and other large scale turbulent fluid behavior They do not require the long straight runs of pipe upstream and downstream that orifice plates do which is a great advantage in many piping systems Some magnetic flowmeters have their signal conditioning electronics located inte
360. ger mass Gravitational field Metal plate Earth Metal plate An electric charge will fall in an electric field just as a mass will fall in a gravitational field Some substances most notably metals have very mobile electrons That is the outer valence electrons are very easily dislodged from the parent atoms to drift to and fro throughout the material In fact the electrons of metals are so free that physicists sometimes refer to the structure of a metal as atoms floating in a sea of electrons The electrons are almost fluid in their mobility throughout a solid metal object and this property of metals may be exploited to form definite pathways for electric currents If the poles of a voltage source are joined by a continuous path of metal the free electrons within that metal will drift toward the positive pole electrons having a negative charge opposite charges attracting one another 80 CHAPTER 3 DC ELECTRICITY Direction of electron motion inside metal If the source of this voltage is continually replenished by chemical energy mechanical energy or some other form of energy the free electrons will continually loop around this circular path We call this unbroken path an electric circuit We typically measure the amount of current in a circuit by the unit of amperes or amps for short named in honor of the French physicist Andr Amp re One ampere of current is equal to one coulomb of electric charge 6
361. ght will always be the sum of fillage and ullage though If the ultrasonic level transmitter is programmed with the vessel s total height it may calculate fillage via simple subtraction Fillage Total height Ullage The instrument itself consists of an electronics module containing all the power computation and signal processing circuits plus an ultrasonic transducer to send and receive the sound waves This transducer is typically piezoelectric in nature being the equivalent of a very high frequency audio speaker A typical example is shown in the following photograph 13 5 ECHO 391 If the ultrasonic transducer is rugged enough and the process vessel sufficiently free of sludge and other sound dampening materials accumulating at the vessel bottom the transducer may be mounted at the bottom of the vessel bouncing sound waves off the liquid surface through the liquid itself rather than through the vapor space 392 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT Ullage Fillage This arrangement makes fillage the natural measurement and ullage a derived measurement calculated by subtraction from total vessel height Ullage Total height Fillage Whether the ultrasonic transducer is mounted above or below the liquid level the principle of detection is any significant difference in material density If the detection interface is between a gas and a liquid the abrupt change in density is enough to create a strong r
362. gisters the desired value The measurement shown by the instrument under test is then compared against the reference meter and adjusted until matching to within the required tolerance The following illustration shows how a high accuracy voltmeter could be used to calibrate a handheld voltmeter in this fashion Handheld multimeter High accuracy benchtop multimeter DOdDooO OOOOOO Variable voltage source Terminal block 274 CHAPTER 11 INSTRUMENT CALIBRATION It should be noted that the variable voltage source shown in this test arrangement need not be sophisticated It simply needs to be variable to allow precise adjustment until the high accuracy voltmeter registers the desired voltage value and stable so that the adjustment does not drift appreciably over time 11 8 PRACTICAL CALIBRATION STANDARDS 275 11 8 2 Temperature standards The most common technologies for industrial temperature measurement are electronic in nature RTDs and thermocouples As such the standards used to calibrate such devices are the same standards used to calibrate electrical instruments such as digital multimeters DMMs However there are some temperature measuring instruments that are not electrical in nature This category includes bimetallic thermometers filled bulb temperature systems and optical pyrometers In order to calibrate these types of instruments we must accurately create the calibration temperatures in the instrument shop
363. gm area A as described by the standard force pressure area equation If the diaphragm is taut the elasticity of the metal allows it to also function as a spring This allows the force to translate into displacement motion forming a definite relationship between applied air pressure and control rod position Thus the applied air pressure input will exert control over the output pressure The addition of an actuating mechanism to the pilot valve turns it into a pneumatic relay which is the pneumatic equivalent of the electronic transistor we were looking for It is easy to see how the input air signal exerts control over the output air signal in these two illustrations 9 3 PILOT VALVES AND PNEUMATIC AMPLIFYING RELAYS 225 Compressed Compressed air supply air supply High output pressure Low output pressure gt vent gt vent diaphragm High input pressure Low input pressure Since there is a direct relationship between input pressure and output pressure in this pneumatic relay we classify it as a direct acting relay If we were to add an actuating diaphragm to the first pilot valve design we would have a reverse acting relay as shown here Compressed air Supply Output pressure gt vent diaphragm Input pressure The gain A of any pneumatic relay is defined just the same as the gain of any electronic amplifier circuit the ratio of output change to input change 226 CHAPTER 9 PN
364. gn the transmitter to be loop powered A loop powered transmitter connects to a process controller in the following manner Controller Power source 2 wire transmitter DA ji 2 wire cable z YA Here the transmitter is not really a current source in the sense that a 4 wire transmitter is Instead a 2 wire transmitter s circuitry is designed to act as a current regulator limiting current in the series loop to a value representing the process measurement while relying on a remote source of power to motivate current to flow Please note the direction of the arrow in the transmitter s dependent current source symbol and how it relates to the voltage polarity marks Refer back to the illustration of a 4 wire transmitter circuit for comparison The current source in this loop powered transmitter actually behaves as an electrical load while the current source in the 4 wire transmitter functions as a true electrical source A loop powered transmitter gets its operating power from the minimum terminal voltage and current available at its two terminals With the typical source voltage being 24 volts DC and the maximum voltage dropped across the controller s 250 ohm resistor being 5 volts DC the transmitter should always have at least 19 volts available at its terminals Given the lower end of the 4 20 mA signal range the transmitter should always have at least 4 mA of current to run on Thus the transmitter will always have a ce
365. gnal is pneumatic a variable air pressure sent through metal or plastic tubes The greater the water level in the drum the more air pressure output by the level transmitter Since the transmitter is pneumatic it must be supplied with a source of clean compressed air on which to run This is the meaning of the A S tube Air Supply entering the top of the transmitter This pneumatic signal is sent to the next instrument in the control system the level indicating controller or LIC The purpose of this instrument is to compare the level transmitter s signal with a setpoint value entered by a human operator the desired water level in the steam drum The controller then generates an output signal telling the control valve to either introduce more or less water into the boiler to maintain the steam drum water level at setpoint As with the transmitter the controller in this system is pneumatic operating entirely on compressed air This means the output of the controller is also a variable air pressure signal just like the signal output by the level transmitter Naturally the controller requires a constant supply of clean compressed air on which 134 CHAPTER 5 INTRODUCTION TO INDUSTRIAL INSTRUMENTATION to run which explains the A S Air Supply tube connecting to it The last instrument in this control system is the control valve being operated directly by the air pressure signal generated by the controller This particular
366. gral to the flowtube assembly A couple of examples are shown here a pair of small Endress Hauser flowmeters on the left and a large Toshiba flowmeter on the right Other magnetic flowmeters have separate electronics and flowtube assemblies connected together by shielded cable In these installations the electronics assembly is referred to as the flow transmitter FT and the flowtube as the flow element FE 510 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT While in theory a permanent magnet should be able to provide the necessary magnetic flux for a magnetic flowmeter to function this is almost never done in practice The reason for this has to do with a phenomenon called polarization which occurs when a DC voltage is impressed across a liquid containing ions electrically charged molecules Ionic polarization would soon interfere with detection of the motional EMF if a magnetic flowmeter were to use a constant magnetic flux such as that produced by a permanent magnet A simple solution to this problem is to alternate the polarity of the magnetic field so that the motional EMF polarity also alternates and never gives the fluid ions enough time to polarize This is why magnetic flowmeter tubes almost always use electromagnet coils to generate the magnetic flux necessary for induction to occur A photograph of a Foxboro magnetic flowtube with one of the protective covers removed shows these wire coils clearly in blue Perhaps the
367. gth of the coil l uN A iy Inductance adds when inductors are connected in series It diminishes when inductors are connected in parallel L 1 Lseries Ly La SS Ln Lparallel Tg ee a Li La In The relationship between voltage and current for an inductor is as follows dl L e dt As such inductors oppose changes in current over time by dropping a voltage This behavior makes inductors useful for stabilizing current in DC circuits One way to think of an inductor in a DC circuit is as a temporary current source always wanting to maintain current through its coil at the same value The amount of potential energy Ep in units of joules stored by an inductor is proportional to the square of the current 1 Ep 5L P 2 In an AC circuit the amount of inductive reactance Xz offered by an inductor is directly proportional to both inductance and frequency Xr 2nfL 3 10 INDUCTORS 111 References Boylestad Robert L Introductory Circuit Analysis 9th Edition Prentice Hall Upper Saddle River New Jersey 2000 112 CHAPTER 3 DC ELECTRICITY Chapter 4 AC electricity 113 114 CHAPTER 4 AC ELECTRICITY 4 1 RMS quantities It is often useful to be able to express the amplitude of an AC quantity such as voltage or current in terms that are equivalent to direct current DC Doing so provides an apples to apples comparison between AC and DC quantities that makes comparat
368. happen to these three groups of runners over time supposing they all begin the race at the same location and at the exact same time As you can probably imagine the runners within each speed group will stay with each other throughout the race with the three groups becoming further spread apart over time The first of these three groups to cross the finish line will be the 8 MPH runners followed by the 6 MPH runners a bit later and then followed by the 5 MPH runners after that To an observer at the very start of the race it would be difficult to tell exactly how many 6 MPH runners there were in the crowd but to an observer at the finish line with a stop watch it would be very easy to tell how many 6 MPH runners competed in the race by counting how many runners crossed the finish line at the exact time corresponding to a speed of 6 MPH Now imagine a mixture of chemicals in a fluid state traveling through a very small diameter capillary tube filled with an inert porous material such as sand Some of those fluid molecules will find it easier to progress down the length of the tube than others with similar molecules sharing similar propagation speeds Thus a small sample of that chemical mixture injected into such a capillary tube and carried along the tube by a continuous flow of solvent gas or liquid will tend to separate into its constituent components over time just like the crowd of marathon runners separate over time according to ru
369. he Instrument Engineers Handbook series this wonderful work was to be our primary text as we 626APPENDIX A DOCTOR STRANGEFLOW OR HOW I LEARNED TO RELAX AND LOVE REYNOLDS NUMBERS explored the world of process measurement during the 2002 2003 academic year It was in reading this book that I had an epiphany Section 2 8 of the text discussed a type of flowmeter I had never seen or heard of before the laminar flowmeter As I read this section of the book my jaw hit the floor Here was a differential pressure based flowmeter that was linear That is there was no square root extraction required at all to convert the AP measurement into a flow measurement Furthermore its operation was based on some weird equation called the Hagen Poiseuille Law rather than Bernoulli s Law Early in the section s discussion of this flowmeter a couple of paragraphs explained the meaning of something called Reynolds number of a flow stream and how this was critically important to laminar flowmeters Now I had heard of Reynolds number before when I worked in industry but I never knew what it meant All I knew is that it had something to do with the selection of flowmeter types one must know the Reynolds number of a fluid before one could properly select which type of flow measuring instrument to use in a particular application Since this determination typically fell within the domain of instrument engineers and not instrument technicians as I was I gave myse
370. he ability to report multiple process variables A good example of this is Coriolis effect flowmeters which by their very nature simultaneously measure the density flow rate and temperature of the fluid passing through them A single pair of wires can only convey one 4 20 mA analog signal but that same pair of wires may convey multiple digital signals encoded in the HART protocol Digital signal transmission is required to realize the full capability of such multi variable transmitters If the host system receiving the transmitter s signal s is HART ready it may digitally poll the transmitters for all variables If however the host system does not talk using the HART protocol some other means must be found to decode the wealth of digital data coming from the multi variable transmitter One such device is Rosemount s model 333 HART Tri Loop demultiplexer shown in the following photograph This device polls the multi variable transmitter and converts up to three HART variables into independent 4 20 mA analog output signals which any suitable analog indicator or controller device may receive It should be noted that the same caveat applicable to multidrop HART systems i e slow speed applies to HART polling of multi variable transmitters HART is a relatively slow digital bus standard and as such it should never be considered for applications demanding quick response In applications where speed is not a concern howe
371. he original function Ea eo A Any optical temperature sensor measuring the emitted power P must characterize the power measurement using the above equation to arrive at an inferred temperature This characterization is typically performed inside the temperature sensor by a microcomputer T 592 CHAPTER 17 SIGNAL CHARACTERIZATION 17 4 Analytical measurements A great many chemical composition measurements may be made indirectly by means of electricity if those measurements are related to the concentration of ions electrically charged molecules Such measurements include e pH of an aqueous solution e Oxygen concentration in air e Ammonia concentration in air e Lead concentration in water The basic principle works like this two different chemical samples are placed in close proximity to each other separated only by an ion selective membrane able to pass the ion of interest As the ion activity attempts to reach equilibrium through the membrane an electrical voltage is produced across that membrane If we measure the voltage produced we can infer the relative activity of the ions on either side of the membrane Not surprisingly the function relating ion activity to the voltage generated is nonlinear The standard equation describing the relationship between ionic activity on both sides of the membrane and the voltage produced is called the Nernst equation RT ay V m nF i a2 Where V Electrical voltage
372. he vibration of each resonant element is sensed by the electronics package as an AC frequency Any frequency signal may be easily counted over a given span of time and converted to a binary digital representation Quartz crystal electronic oscillators are extremely precise providing the stable frequency reference necessary for comparison in any frequency based instrument In the Yokogawa DPharp design the two resonant elements oscillate at a nominal frequency of 90 kHz As the sensing diaphragm deforms with applied differential pressure one resonator experiences tension while the other experiences compression causing the frequency of the former to shift up and the latter to shift down as much as 20 kHz The signal conditioning electronics inside the transmitter measures this difference in resonator frequency to infer applied pressure 123 ELECTRICAL PRESSURE ELEMENTS 311 12 3 4 Mechanical adaptations Most modern electronic pressure sensors convert very small diaphragm motions into electrical signals through the use of sensitive motion sensing techniques strain gauge sensors differential capacitance cells etc Diaphragms made from elastic materials behave as springs but circular diaphragms exhibit very nonlinear behavior when significantly stretched unlike classic spring designs such as coil and leaf springs which exhibit linear behavior over a wide range of motion Therefore in order to yield a linear response to pressure
373. hemical seal on this particular gauge is close coupled to the gauge since the only goal here is protection of the gauge from harsh process fluids not the ability to remotely mount the gauge 332 CHAPTER 12 CONTINUOUS PRESSURE MEASUREMENT A view facing the bottom of the flange reveals the thin metal isolating diaphragm which keeps process fluid from entering the gauge mechanism Only inert fill fluid occupies the space between this diaphragm and the gauge s bourdon tube 12 6 PRESSURE SENSOR ACCESSORIES 333 The only difference between this chemical seal gauge and a remote seal gauge is that a remote seal gauge uses a length of very small diameter tubing called capillary tubing to transfer fill fluid pressure from the sealing diaphragm to the gauge mechanism Direct reading gauges are not the only type of pressure instrument that may benefit from having remote seals Electronic pressure transmitters are also manufactured with remote seals for the same reasons protection of the transmitter sensor from harsh process fluid or prevention of dead end tube lengths where organic process fluid would stagnate and harbor microbial growths The following photograph shows a pressure transmitter equipped with a remote sealing diaphragm The capillary tube is protected by a coiled metal armor sheath A close up view of the sealing diaphragm shows its corrugated design allowing the metal to easily flex and transfer pressure to the
374. here the upper substance composition is subject to change 402 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT 13 6 Laser level measurement The least common form of echo based level measurement is laser which uses pulses of laser light reflected off the surface of a liquid to detect the liquid level Perhaps the most limiting factor with laser measurement is the necessity of having a sufficiently reflective surface for the laser light to echo off of Many liquids are not reflective enough for this to be a practical measurement technique and the presence of dust or thick vapors in the space between the laser and the liquid will disperse the light weakening the light signal and making the level more difficult to detect However lasers have been applied with great success in measuring distances between objects Applications of this technology include motion control on large machines where a laser points at a moving reflector the laser s electronics calculating distance to the reflector based on the amount of time it takes for the laser echo to return The advent of mass produced precision electronics has made this technology practical and affordable for many applications At the time of this writing 2008 it is even possible for the average American consumer to purchase laser tape measures for use in building construction 13 7 WEIGHT 403 13 7 Weight Weight based level instruments sense process level in a vessel by directly m
375. hin this system the only maintenance this system will need is periodic replacement of the calibration gas bottles References Calibration Philosophy In Practice Second Edition Fluke Corporation Everett WA 1994 Lipt k B la G Instrument Engineers Handbook Process Measurement and Analysis Volume I Fourth Edition CRC Press New York NY 2003 Chapter 12 Continuous pressure measurement In many ways pressure is the primary variable for a wide range of process measurements Many types of industrial measurements are actually inferred from pressure such as e Flow measuring the pressure dropped across a restriction e Liquid level measuring the pressure created by a vertical liquid column e Liquid density measuring the pressure difference across a fixed height liquid column e Weight hydraulic load cell Even temperature may be inferred from pressure measurement as in the case of a fluid filled chamber where fluid pressure and fluid temperature are directly related As such pressure is a very important quantity to measure and measure accurately This section describes different technologies for the measurement of pressure 289 290 CHAPTER 12 CONTINUOUS PRESSURE MEASUREMENT 12 1 Manometers A very simple device used to measure pressure is the manometer a fluid filled tube where an applied gas pressure causes the fluid height to shift proportionately This is why pressure is often measured in units of li
376. hird pressure transmitter to this system located a known distance x above the bottom transmitter we have all the pieces necessary for what is called a tank expert system These systems are used on large storage tanks operating at or near atmospheric pressure and have the ability to measure infer liquid height liquid density total liquid volume and total liquid mass stored in the tank This is due to limited transmitter resolution Imagine an application where the elevation head was 10 PSI maximum yet the vapor space pressure was 200 PSI The majority of each transmitter s working range would be consumed measuring gas pressure with hydrostatic head being a mere 5 of the measurement range This would make precise measurement of liquid level very difficult akin to trying to measure the sound intensity of a whisper in a noisy room 13 3 HYDROSTATIC PRESSURE 373 A tank expert system Pop Gas pressure vented Peas Pressure Pos eres aekeas gt Height P oldie h Poa vented vented Pressure Pas Uh x f Pressure Pay Yh The pressure difference between the bottom and middle transmitters will change only if the liquid density changes since the two transmitters are separated by a known and fixed height difference This allows the level computer LY to continuously calculate liquid density 7 Prottom Emiddle Ejas yh a Pias y h x Prottom E middle Pias
377. his means we must know the specific heat value of whatever fluid we plan to measure with a thermal mass flowmeter and we must be assured its specific heat value will remain constant For this reason thermal mass flowmeters are not suitable for measuring the flow rates of fluid streams whose chemical composition is likely to change over time This limitation is analogous to that of a pressure sensor used to hydrostatically measure the level of liquid in a vessel in order for this level measurement technique to be accurate we must know the density of the liquid and also be assured that density will be constant over time 31For example the specific heat of water is 1 00 kcal kg C meaning that the addition of 1000 calories of heat energy is required to raise the temperature of 1 kilogram of water by 1 degree Celsius or that we must remove 1000 calories of heat energy to cool that same quantity of water by 1 degree Celsius Ethyl alcohol by contrast has a specific heat value of only 0 58 kcal kg C meaning it is almost twice as easy to warm up or cool down as water little more than half the energy required to heat or cool water needs to be transferred to heat or cool the same mass quantity of ethyl alcohol by the same amount of temperature 15 7 POSITIVE DISPLACEMENT FLOWMETERS 527 15 7 Positive displacement flowmeters A positive displacement flowmeter is a cyclic mechanism built to pass a fixed volume of fluid through with every
378. however the flow rate is not steady sampling more often will allow us to better see the immediate ups and downs of flow behavior Imagine now that we had our hypothetical flow computer take weight mass measurements at an infinitely fast pace an infinite number of samples per second Now we are no longer averaging flow rates over finite periods of time instead we would be calculating instantaneous flow rate at any given point in time Calculus has a special form of symbology to represent such hypothetical scenarios we replace the Greek letter delta A meaning change with the roman letter d meaning differential A simple way of picturing the meaning of d is to think of it as meaning an infinitesimal interval of whatever variable follows the d in the equation When we set up two differentials in a quotient we call the g fraction a derivative Re writing our average flow rate equations in derivative calculus form _ dm de _ dv ee Where W Instantaneous mass flow rate Q Instantaneous volumetric flow rate dm Infinitesimal infinitely small change in mass dV Infinitesimal infinitely small change in volume dt Infinitesimal infinitely small change in time We need not dream of hypothetical computers capable of infinite calculations per second in order to derive a flow measurement from a mass or volume measurement Analog electronic circuitry 32While this may s
379. hrough the vapor space may similarly cause problems for an echo instrument Additionally all echo based instruments have dead zones where liquid level is too close to the transceiver to be accurately measured or even detected the echo time of flight being too short for the receiving electronics to distinguish from the incident pulse 12My own experience with this trend is within the oil refining industry where legacy displacer instruments typically Fisher brand LevelTrol units are being replaced with new guided wave radar transmitters both for single liquid and liquid liquid interface applications 390 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT 13 5 1 Ultrasonic level measurement Ultrasonic level instruments measure the distance from the transmitter located at some high point to the surface of a process material located further below The time of flight for a sound pulse indicates this distance and is interpreted by the transmitter electronics as process level These transmitters may output a signal corresponding either to the fullness of the vessel fillage or the amount of empty space remaining at the top of a vessel ullage Transmitted Received sound sound Ullage Fillage Ullage is the natural mode of measurement for this sort of level instrument because the sound wave s time of flight is a direct function of how much empty space exists between the liquid surface and the top of the vessel Total tank hei
380. ht One half times 4 feet times 240 pounds is 480 foot pounds 1 8 FLUID MECHANICS 27 1 8 Fluid mechanics A fluid is any substance having the ability to flow to freely change shape and move under the influence of a motivating force Fluid motion may be analyzed on a microscopic level treating each fluid molecule as an individual projectile body This approach can be extraordinarily tedious on a practical level but still useful as a simple model of fluid motion Some fluid properties are accurately predicted by this model especially predictions dealing with potential and kinetic energies However the ability of a fluid s molecules to independently move give it unique properties that solids do not possess One of these properties is the ability to effortlessly transfer pressure defined as force applied over area 28 CHAPTER 1 PHYSICS 1 8 1 Pressure The common phases of matter are solid liquid and gas Liquids and gases are fundamentally distinct from solids in their intrinsic inability to maintain a fixed shape In other words liquids and gases tend to fill whatever solid containers they are held in Similarly both liquids and gases both have the ability to flow which is why they are collectively called fluids Due to their lack of definite shape fluids tend to disperse any force applied to them This stands in marked contrast to solids which tend to transfer force with the direction unchanged Take for example the force transf
381. id pressure rushes into the empty chamber of the ball valve and hot tapping drill as soon as the pipe wall is breached 15 10 INSERTION FLOWMETERS High pressure seals Hot tapping drill motor gt Ball valve open Drill bit 535 Once the hole has been completely drilled the bit is extracted and the ball valve shut to allow removal of the hot tapping drill 536 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT Hot tapping drill motor gt Ball valve Now there is a flanged and isolated connection into the hot pipe through which an insertion flowmeter or other instrument device may be installed Hot tapping is a technical skill with many safety concerns specific to different process fluids pipe types and process applications This brief introduction to the technique is not intended to be instructional but merely informational 15 11 PROCESS INSTRUMENT SUITABILITY 537 15 11 Process instrument suitability Every flow measuring instrument exploits a physical principle to measure the flow rate of fluid stream Understanding each of these principles as they apply to different flow measurement technologies is the first and most important step in properly applying a suitable technology to the measurement of a particular process stream flow rate The following table lists the specific operating principles exploited by different flow measurement technologies
382. ide wires or a sophisticated tape retraction or tensioning system If no visual indication is necessary the level gauge tube may be constructed out of metal instead of glass greatly reducing the risk of 356 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT tube breakage All the problems inherent to sightglasses however still apply to this form of float instrument 13 3 HYDROSTATIC PRESSURE 357 13 3 Hydrostatic pressure A vertical column of fluid exerts a pressure due to the column s weight The relationship between column height and fluid pressure at the bottom of the column is constant for any particular fluid density regardless of vessel width or shape This principle makes it possible to infer the height of liquid in a vessel by measuring the pressure generated at the bottom Same pressure The mathematical relationship between liquid column height and pressure is as follows P pgh P yh Where P Hydrostatic pressure p Mass density of fluid in kilograms per cubic meter metric or slugs per cubic foot British g Acceleration of gravity y Weight density of fluid in newtons per cubic meter metric or pounds per cubic foot British h Height of vertical fluid column above point of pressure measurement For example the pressure generated by a column of oil 12 feet high having a weight density 7 of 40 pounds per cubic foot is 358 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT Note the cancellation of units
383. ient units of measurement such as inches of water column for pressure and specific gravity unitless for density the volumetric flow value produced by the raw equation will not be in any useful unit However if we know the differential pressure produced by any particular venturi tube with any particular fluid density at a specified flow rate we may calculate the k value necessary to characterize that venturi tube for any other condition using those units For example if we know a particular venturi tube develops 45 inches of water column differential pressure at a flow rate of 180 gallons per minute of water specific gravity 1 we may plug these values into the equation and solve for k P P Q k p 45 180 ky 80 i 1 pa Pe 58 45 1 Now that we know a value of 26 83 for k will yield gallons per minute of liquid flow through this venturi tube given pressure in inches of water column and density as a specific gravity we may readily predict the flow rate through this tube for any other pressure drop we might happen to measure gal 26 83 e ACA m Specific gravity 60 inches of water column differential pressure generated by a flow of water specific gravity 1 in this particular venturi tube gives us the following flow rate 454 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT 60 Q 26 834 7 Q 207 8 GPM 110 inches of water column differential pressure generated by a flow of gasoline specific gravity
384. ight changes in wire resistance I P coil resistance or anything else the current source inside the controller will fight as hard as it has to in order to maintain this set amount of current This current as it flows 8 3 CONTROLLER OUTPUT CURRENT LOOPS 197 through the wire coil of the I P transducer mechanism creates a magnetic field inside the I P to actuate the pneumatic mechanism and produce a 9 PSI pressure signal output to the control valve 9 PSI being exactly half way between 3 PSI and 15 PSI in the 3 15 PSI signal standard range This should move the control valve to the half way position The details of the controller s internal current source are not terribly important Usually it takes the form of an operational amplifier circuit driven by the voltage output of a DAC Digital to Analog Converter The DAC converts a binary number either from the controller s automatic calculations or from the human operator s manual setting into a small DC voltage which then commands the op amp circuit to regulate output current at a proportional value The scenario is much the same if we replace the I P and control valve with a variable speed motor drive From the controller s perspective the only difference it sees is a resistive load instead of an inductive load The input resistance of the motor drive circuit converts the 4 20 mA signal into an analog voltage signal typically 1 5 V but not always This voltage signal then cons
385. illing it with measured quantities of liquid one sample at a time and taking level readings Introduced liquid volume Measured liquid level 150 gallons 2 46 feet 300 gallons 4 72 feet 450 gallons 5 8 feet 600 gallons etc etc 750 gallons etc etc Each of these paired numbers would constitute the coordinates to be programmed into the characterizer function computer by the instrument technician or engineer 600 1 500 400 300 200 100 0 gallons 0123 4 5 6 h feet 590 CHAPTER 17 SIGNAL CHARACTERIZATION Many smart level transmitter instruments have enough computational power to perform the level to volume characterization directly so as to transmit a signal corresponding directly to liquid volume rather than just liquid level This eliminates the need for an external level computer to perform the necessary characterization The following screenshot was taken from a personal computer running configuration software for a radar level transmitter showing the strapping table data point fields where a technician or engineer would program the vessel s level versus volume piecewise function Setup of CTLR 01C04CHO2 3300 Rev 2 This configuration window actually shows more than just a strapping table It also shows the option of calculating volume for different vessel shapes vertical cylinder is the option selected here including horizontal cylinder and sphere In
386. in the middle between process flow diagrams and loop diagrams A P amp ID shows the layout of all relevant process vessels pipes and machinery but with instruments superimposed on the diagram showing what gets measured and what gets controlled Here one can view the flow of the process as well as the flow of information between instruments measuring and controlling the process SAMA diagrams are used for an entirely different purpose to document the strategy of a control system In a SAMA diagram emphasis is placed on the algorithms used to control a process as opposed to piping wiring or instrument connections These diagrams are commonly found within the power generation industry but are sometimes used in other industries as well 147 148 CHAPTER 6 INSTRUMENTATION DOCUMENTS An instrument technician must often switch between different diagrams when troubleshooting a complex control system There is simply too much detail for any one diagram to show everything Even if the page were large enough a show everything diagram would be so chock full of details that it would be difficult to follow any one line of details you happened to be interested in at any particular time The narrowing of scope with the progression from PFD to loop diagram may be visualized as a process of zooming in as though one were viewing a process through the lens of a microscope at different powers First you begin with a PFD or P amp ID to get an ov
387. in turn will be approximately equal to the diameter of the bubble tube For example a 1 4 inch diameter dip tube will experience pressure oscillations with a peak to peak amplitude of approximately 1 4 inch elevation of process liquid The frequency of this pressure oscillation of course will be equal to the rate at which individual bubbles escape out the end of the dip tube Usually this is a small variation when considered in the context of the measured liquid height in the vessel A pressure oscillation of approximately 1 4 inch compared to a measurement range of 0 to 10 feet for example is only about 0 2 of span Modern pressure transmitters have the ability to filter or dampen pressure variations over time which is a useful feature for minimizing the effect such a pressure variation will have on system performance 13 3 HYDROSTATIC PRESSURE 363 13 3 2 Transmitter suppression and elevation A very common scenario for liquid level measurement is where the pressure sensing instrument is not located at the same level as the 0 measurement point The following photograph shows an example of this where a Rosemount model 3051 differential pressure transmitter is being used to sense hydrostatic pressure of colored water inside a clear vertical plastic tube Consider the example of a pressure sensor measuring the level of liquid ethanol in a storage tank The measurement range for liquid height in this ethanol storage tank is O t
388. indicator via tubing instead of wires 209 210 CHAPTER 9 PNEUMATIC INSTRUMENTATION Indicator Pressure transmitter tube 20 PSI air supply Applied pressure The indicator in this case would be a special pressure gauge calibrated to read in units of process pressure although actuated by the pressure of clean compressed air from the transmitter instead of directly by process fluid The most common range of air pressure for industrial pneumatic instruments is 3 to 15 PSI An output pressure of 3 PSI represents the low end of the process measurement scale and an output pressure of 15 PSI represents the high end of the measurement scale Applied to the previous example of a transmitter calibrated to a range of 0 to 250 PSI a lack of process pressure would result in the transmitter outputting a 3 PSI air signal and full process pressure would result in an air signal of 15 PSI The face of this special receiver gauge would be labeled from 0 to 250 PSI while the actual mechanism would operate on the 3 to 15 PSI range output by the transmitter Just like the 4 20 mA loop the end user need not know how the information gets transmitted from the process to the indicator The 3 15 PSI signal medium is once again transparent to the operator Pneumatic temperature flow and level control systems have all been manufactured to use the same principle of 3 15 PSI air pressure signaling In each case the transmitter and controller are both
389. ing power This form of radiation is the most common used in industrial level measurement One of the most effective methods of shielding against gamma ray radiation is with very dense substances such as lead or concrete This is why the source boxes holding gamma emitting radioactive pellets are lined with lead so that the radiation escapes only in the direction intended Radiation These sources may be locked out for testing and maintenance by moving a lever that hinges a lead shutter over the window of the box This lead shutter acts as an on off switch for the radioactive source The lever actuating the shutter typically has provisions for lockout tagout so that a maintenance person may place a padlock on the lever and prevent anyone else from turning on the source during maintenance The accuracy of radiation based level instruments varies with the stability of process fluid density vessel wall coating source decay rates and detector drift Given these error variables and the additional need for NRC Nuclear Regulatory Commission licensing to operate such instruments at an industrial facility radiation instruments are typically used where no other instrument can possibly function Examples include the level measurement of highly corrosive or toxic process fluids where penetrations into the vessel must be minimized and where piping requirements make weight based measurement impractical as well as processes where the intern
390. int or trip point Some process switches have two adjustments the set point as well as a deadband adjustment The purpose of a deadband adjustment is to provide an adjustable buffer range that must be traversed before the switch changes state To use our 85 PSI low air pressure switch as an example the set point would be 85 PSI but if the deadband were 5 PSI it would mean the switch would not change state until the pressure rose above 90 PSI 85 PSI 5 PSI When calibrating a discrete instrument you must be sure to check the accuracy of the set point in the proper direction of stimulus change For our air pressure switch example this would mean checking to see that the switch changed states at 85 PSI falling not 85 PSI rising If it were not for the existence of deadband it would not matter which way the applied pressure changed during the calibration test However deadband will always be present in a discrete instrument whether that deadband is adjustable or not Given a deadband of 5 PSI for this example switch the difference between verifying a change of state at 85 PSI falling versus 85 PSI rising would mean the difference between the air compressor turning on if the pressure fell below 85 PSI versus turning on if the pressure fell below 80 PSI A procedure to efficiently calibrate a discrete instrument without too many trial and error attempts is to set the stimulus at the desired value e g 85 PSI for our hypothetical low pressure switch
391. ion Q k AP VQ V k AP Q VRAP substituting a new coefficient value kt Q kVAP Students are taught that the differential pressure develops as a consequence of energy conservation in the flowing liquid stream As the liquid enters a constriction its velocity must increase to account for the same volumetric rate through a reduced area This results in kinetic energy increasing which must be accompanied by a corresponding decrease in potential energy i e pressure to conserve total fluid energy Pressure measurements taken in a venturi pipe confirm this 1Since we get to choose whatever k value we need to make this an equality we don t have to keep k inside the radicand and so you will usually see the equation written as it is shown in the last step with k outside the radicand 624APPENDIX A DOCTOR STRANGEFLOW OR HOW I LEARNED TO RELAX AND LOVE REYNOLDS NUMBERS High pressure High pressure Low pressure Flow Flow gt Flow High velocity Low velocity Low velocity In all honesty this did not make sense to me when I heard this My common sense told me the fluid pressure would increase as it became crammed into the constriction not decrease Even more common sense told me that whatever pressure was lost through the constriction would never be regained contrary to the pressure indication of the gauge furthest downstream Accepting this principle was an act of faith on my part putting preconc
392. ion by means of an intentional zero shift of the pressure instrument when it is calibrated 338 CHAPTER 12 CONTINUOUS PRESSURE MEASUREMENT 12 6 6 Purged impulse lines Continuous purge of an impulse line is an option when the line is prone to plugging Consider this example where pressure is measured at the bottom of a sedimentation vessel Pressure transmitter Air supply PV signal Impulse line Purge i Sludge drainage water Supply valve Purge valve Check valve A continuous flow of clean water enters through a purge valve and flows through the impulse line keeping it clear of sediment while still allowing the pressure instrument to sense pressure at 12 6 PRESSURE SENSOR ACCESSORIES 339 the bottom of the vessel A check valve guards against reverse flow through the purge line in case process fluid pressure ever exceeds purge supply pressure Purged systems are very useful but a few details are necessary to consider before deciding to implement such a strategy e How reliable is the supply of purge fluid If this stops for any reason the impulse line may plug e Is the purge fluid supply pressure guaranteed to exceed the process pressure at all times for proper direction of purge flow e What options exist for purge fluids that will not adversely react with the process e What options exist for purge fluids that will not contaminate the process e How expensive will it be to maintain
393. ion for measuring gas flow Proper mounting position for measuring liquid flow Proper mounting position for measuring gas flow Proper mounting position for measuring liquid flow 475 Condensible vapor applications such as steam flow measurement should be treated the same as liquid measurement applications Here condensed liquid will collect in the transmitter s impulse lines so long as the impulse lines are cooler than the vapor flowing through the pipe which is typically the case Placing the transmitter below the pipe allows vapors to condense and fill the 476 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT impulse lines with liquid condensate which then acts as a natural seal protecting the transmitter from exposure to hot process vapors In such applications it is important for the technician to pre fill both impulse lines with condensed liquid prior to placing the flowmeter into service Tee fittings with removable plugs or fill valves are provided to do this Failure to pre fill the impulse lines will likely result in measurement errors during initial operation as condensed vapors will inevitably fill the impulse lines at slightly different rates and cause a difference in vertical liquid column heights within those lines If tap holes must be drilled into the pipe or flanges at the process site great care must be taken to properly drill and de burr the holes A pressure sensing tap hole should be flush w
394. ion is fundamentally piecewise and so nothing but a piecewise characterizing function could possibly linearize the level measurement into a volume measurement 2 There is no theoretical limit to the number of points in a digital computer s characterizer function given sufficient processing power and memory There is however a limit to the patience of the human programmer who must encode all the necessary x y data points defining this function Most of the piecewise characterizing functions I have seen available in digital instrumentation systems provide 10 to 20 x y coordinate points to define the function Fewer than 10 coordinate points risks excessive interpolation errors and more than 20 would just be tedious to set up 17 2 LIQUID VOLUME MEASUREMENT 589 Consider also the case of a spherical vessel with odd shaped objects welded to the vessel walls and or inserted into the vessel s interior A h LY The volumetric space occupied by these structures will introduce all kinds of discontinuities into the transfer function and so once again we have a case where a continuous characterizing function cannot properly linearize the level signal into a volume measurement Here only a piecewise function will suffice To best generate the coordinate points for a proper multi point characterizer function one must collect data on the storage vessel in the form of a strapping table This entails emptying the vessel completely then f
395. ions require drilling into the pipe after installation which is not only labor intensive but may possibly weaken the pipe at the locations of the tap holes Corner taps must be used on small pipe diameters where the vena contracta is so close to the downstream face of the orifice plate that a downstream flange tap would sense pressure in the highly turbulent region too far downstream Corner taps obviously require special i e expensive flange fittings which is why they tend to be used only when necessary 466 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT Care should be taken to avoid measuring downstream pressure in the highly turbulent region following the vena contracta This is why the pipe tap also known as full flow tap standard calls for a downstream tap location eight pipe diameters away from the orifice to give the flow stream room to stabilize for more consistent pressure readings Wherever the taps are located it is vitally important that the tap holes be flush with the inside wall of the pipe or flange Even the smallest recess or burr left from drilling will cause measurement errors For relatively low flow rates an alternative arrangement is the integral orifice plate This is where a small orifice plate is physically attached to the differential pressure sensing element so that no impulse lines are needed A photograph of an integral orifice plate and transmitter is shown here What this means is that a pipe
396. is and where it could potentially fall to Things get interesting when we connect voltage sources in different configurations Consider the following example identical to the previous illustration except the middle battery has been reversed 1 5 volts 1 5 volts 1 5 volts Note the and signs next to the ends of the batteries These signs show the polarity of each battery s voltage Also note how the two voltmeter readings are different from before Here we see an example of negative potential with the middle battery connected in opposition to the other two batteries While the top and bottom batteries are both lifting electric charges to greater potential going from point D to point A the middle battery is decreasing potential from point C to point B It s like taking a step forward then a step back then another step forward Or perhaps more appropriately like lifting a mass 1 5 meters up then setting it down 1 5 meters then lifting it 1 5 meters up again The first and last steps accumulate potential energy while the middle step releases potential energy This explains why it is important to install multiple batteries the same way into battery powered devices such as radios and flashlights The batteries voltages are supposed to add to a make a larger total required by the device If one or more batteries are placed backwards potential will be lost instead of gain
397. is but one of several components that comprise a balancing mechanism in a pneumatic instrument It is this concept of self balancing that we will study next 216 CHAPTER 9 PNEUMATIC INSTRUMENTATION 9 2 Self balancing pneumatic instrument principles A great many precision instruments use the principle of balance to measure some quantity Perhaps the simplest example of a balance based instrument is the common balance beam scale used to measure mass in a laboratory A specimen of unknown mass is placed in one pan of the scale and precise weights are placed in the other pan until the scale achieves a condition of balance When balance is achieved the mass of the sample is known to be equal to the sum total of mass in the other pan An interesting detail to note about the scale itself is that it has no need of routine calibration There is nothing to drift out of spec which would cause the scale to read inaccurately In fact the scale itself doesn t even have a gauge to register the mass of the specimen all it has is a single mark indicating a condition of balance To express this more precisely the balance beam scale is actually a differential mass comparison device and it only needs to be accurate at a single point zero In other words it only has to be correct when it tells you there is zero difference in mass between the specimen and the standard masses piled on the other pan The elegance of this mechanism allows it to be
398. ish it as you would any other book with the full legal right to demand royalties restrict distributions etc This does not compromise the freedom of my original work because that is still available to everyone under the terms and conditions of the Attribution license It does however protect the investment s you make in creating the adaptation by allowing you to release the adaptation under whatever terms you see fit so long as those terms comply with current intellectual property laws of course In summary the following legalese is actually a very good thing for you the reader of my book It grants you permission to do so much more with this text than what you would be legally allowed to do with any other traditionally copyrighted book It also opens the door to open collaborative development so that it might grow into something far better than what I alone could create lYou cannot pass my original work to anyone else under different terms or conditions than the Attribution license That is called sublicensing and the Attribution license forbids it In fact any re distribution of my original work must come with a notice to the Attribution license so anyone receiving the book through you knows their rights B 2 LEGAL CODE 633 B 2 Legal code THE WORK AS DEFINED BELOW IS PROVIDED UNDER THE TERMS OF THIS CREATIVE COMMONS PUBLIC LICENSE CCPL OR LICENSE THE WORK IS PROTECTED BY COPYRIGHT AND OR OTHER APPLICAB
399. iston piston 3 in 27 in Pressure 50 PSI Pressure 50 PSI Pressure Pressure 50 PSI 50 PSI The key assumption we make here is that the only force we need to consider on the fluid is the force exerted on the small piston 150 pounds If this is truly the only force acting on the fluid then it will likewise be the only source of fluid pressure and pressure will simply be equal to force divided by area 150 pounds 3 square inches 50 PSI However when we are dealing with tall columns of fluid and or dense fluids there is another force we must consider the weight of the fluid itself Suppose we took a cubic foot of water which weighs approximately 62 4 pounds and poured it into a tall vertical tube with a cross sectional area of 1 square inch 34 CHAPTER 1 PHYSICS Water column weight 62 4 lbs Cross sectional Pressure gauge tube area 1 in 62 4 PSI Naturally we would expect the pressure measured at the bottom of this tall tube to be 62 4 pounds per square inch since the entire column of water weighing 62 4 pounds has its weight supported by one square inch of area If we placed another pressure gauge mid way up the tube though how much pressure would it register At first you might be inclined to say 62 4 PSI as well because you learned earlier in this lesson that fluids naturally distribute force throughout their bulk However in this case the pressure is not the same mid w
400. it must also be proportional to volumetric flow rate since volumetric flow rate is also proportional to average fluid velocity Thus what we have here is a type of flowmeter based on electromagnetic induction These flowmeters are commonly known as magnetic flowmeters or simply mag flow meters We may state the relationship between volumetric flow rate Q and motional EMF more precisely by algebraic substitution First we will write the formula relating volumetric flow to average velocity and then manipulate it to solve for average velocity Q Av can A Next we re state the motional EMF equation and then substitute Q for v to arrive at an equation relating motional EMF to volumetric flow rate Q magnetic flux density B pipe diameter d and pipe area A Bdv Q Bd A BdQ E A Since we know this is a circular pipe we know that area and diameter are directly related to each other by the formula A ae Thus we may substitute this definition for area into the last equation to arrive at a formula with one less variable only d instead of both d and A BdQ Tra 4 E 23This is an application of the transitive property in mathematics if two quantities are both equal to a common third quantity they must also be equal to each other This property applies to proportionalities as well as equalities if two quantities are proportional to a common third quantity they must also be proporti
401. itch back and forth between those two pressures at will making the task of adjusting an analog instrument with interactive zero and span adjustments much easier than it would have been to precisely adjust a single pressure regulator again and again 284 CHAPTER 11 INSTRUMENT CALIBRATION 11 8 4 Flow standards Most forms of continuous flow measurement are inferential that is we measure flow indirectly by measuring some other variable such as pressure voltage or frequency directly With this in mind we may usually achieve reasonable calibration accuracy simply by calibrating the primary sensor and replacing the flow element if inspection proves necessary In the case of an orifice plate used to measure fluid flow rate this would mean calibrating the differential pressure transmitter to measure pressure accurately and replacing the orifice plate if it shows signs of wear In some cases though direct validation of flow measurement accuracy is needed Most techniques of flow rate validation take the form of measuring accumulated fluid volume over time This may prove to be complicated especially if the fluids in question are hazardous in any way and or the flow rates are large and or the fluid is a gas or vapor For simple validation of liquid flow rates the flow may be diverted from its normal path in the process and into a container where either accumulated volume or accumulated weight may be measured over time If the rate of flow into
402. ith RTD temperature sensors to continuously monitor the process fluid temperature Fluid temperature is important to know because it affects certain properties of the tubes e g spring constant diameter and length The temperature indication is usually accessible as an auxiliary output which means a Coriolis flowmeter may double as a very expensive temperature transmitter Another variable is measured and potentially transmitted by a Coriolis flowmeter and this variable is fluid density The tubes within a Coriolis flowmeter are shaken at their mechanical resonant frequency to maximize their shaking motion with the least amount of applied power to the force coil possible The electronics module continuously varies the force coil s AC excitation frequency to maintain mechanical resonance This resonant frequency happens to change with process fluid density since the effective mass of the fluid filled tubes changes with process fluid density and mass is one of the variables influencing the resonant frequency of any physical object 30Tf you consider each tube as a container with a fixed volume capacity a change in fluid density e g pounds per cubic foot must result in a change of weight for each tube 522 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT Note the mass term in the following formula describing the resonant frequency of a tensed string fess p Where f Fundamental resonant frequency of string Hertz L String
403. ith the inner pipe wall with no rough edges or burrs to create turbulence Also there should be no reliefs or countersinking near the hole on the inside of the pipe Even small irregularities at the tap holes may generate surprisingly large flow measurement errors 15 1 PRESSURE BASED FLOWMETERS 477 15 1 5 High accuracy flow measurement Many assumptions were made in formulating flow equations from physical conservation laws Suffice it to say the flow formulae you have seen so far in this chapter are only approximations of reality Orifice plates are some of the worst offenders in this regard since the fluid encounters such abrupt changes in geometry passing through the orifice Venturi tubes are nearly ideal since the machined contours of the tube ensure gradual changes in fluid pressure and minimize turbulence However in the real world we must often do the best we can with imperfect technologies Orifice plates despite being less than perfect as flow sensing elements are convenient and economical to install in flanged pipes Orifice plates are also the easiest type of flow element to replace in the event of damage or routine servicing In applications such as custody transfer where the flow of fluid represents product being bought and sold flow measurement accuracy is paramount It is therefore important to figure out how to coax the most accuracy from the common orifice plate in order that we may measure fluid flows both accurately and e
404. its 484 lb 1 ft P 2 2 ft 144 in _3 36 lb in P 3 36 PSI 38 CHAPTER 1 PHYSICS 1 8 3 Fluid density expressions Fluid density is commonly expressed as a ratio in comparison to pure water at standard temperature This ratio is known as specific gravity For example the specific gravity of glycerin may be determined by dividing the density of glycerin by the density of water D a e Specific gravity of any liquid awia water Doiycerin 786 lb ft Specific gravity of glycerin H24 1 26 A y Dwater 62 4 lb ft As with all ratios specific gravity is a unitless quantity Note how the identical units of pounds per cubic foot cancel out of both numerator and denominator to leave a quotient with no unit at all Industry specific units of measurement do exist for expressing the relative density of a fluid These units of measurement all begin with the word degree much the same as for units of temperature measurement They are as follows The mathematical relationships between each of these degree units of density versus specific gravity is as follows 141 5 D API 131 5 SERR Specific gravity Degrees Twaddell 200 x Specific gravity 1 Two different formulae exist for the calculation of degrees Baum depending on whether the liquid in question is heavier or lighter than water For lighter than water liquids 140 Degrees Baum light See gravity 130 N
405. ity and function in a context that interests them There do exist many fine references on the subject of industrial instrumentation I only wish I could condense their best parts into a single volume for my students Being able to do so would certainly save me from having to write my own Listed here are some of the best books I can recommend for those wishing to explore instrumentation outside of my own presentation Handbook of Instrumentation and Controls by Howard P Kallen Perhaps the best written textbook on general instrumentation I have ever encountered Too bad it s long out of print my copy dates 1961 Like most American textbooks written during the years immediately following Sputnik it is a masterpiece of practical content and conceptual clarity Industrial Instrumentation Fundamentals by Austin E Fribance Another great post Sputnik textbook my copy dates 1962 Instrumentation for Process Measurement and Control by Normal A Anderson An inspiring effort by someone who knows the art of teaching as well as the craft of instrumentation Too bad the content doesn t seem to have been updated since 1980 Instrument Engineers Handbook series Volumes I II and III edited by B la Lipt k By far my favorite modern references on the subject Unfortunately there is a fair amount of material within that lies well beyond my students grasp Laplace transforms etc and the volumes are incredibly bulky and expensive 1
406. ive circuit analysis much easier The most popular standard of equivalence is based on work and power and we call this the root mean square value of an AC waveform or RMS for short For example an AC voltage of 120 volts RMS means that this AC voltage is capable of producing the exact same amount of power in Watts at an electrical load as a 120 volt DC source powering the exact same load The problem is exactly how to calculate this RMS value if all we know about the AC waveform is its peak value If we compare a sine wave and a DC wave side by side it is clear that the sine wave must peak at a greater value than the constant DC level in order to be equivalent in terms of doing the same work in the same amount of time peak voltage constant voltage g AC circuit DC circuit At first it might seem like the correct approach would be to use calculus to integrate the sine wave over one half of a cycle from 0 to m radians and figure out how much area is under the curve This is close but not fully correct You see the ability of an electrical voltage to produce a power dissipation at a resistor is not directly proportional to the magnitude of that voltage but rather proportional to the square of the magnitude of that voltage In mathematical terms power is predicted by the following equation 2 Pa R If we double the amount of voltage applied to a resistor the power increases four fold If we triple the voltage th
407. ject through convection all other factors being equal 564 CHAPTER 16 CONTINUOUS ANALYTICAL MEASUREMENT in jeopardy Here in the context of chromatograph detectors we exploit the impact specific heat value has on thermal convection using this principle to detect compositional change for a constant flow gas rate The temperature change of a heated RTD or thermistor caused by exposure to a gas mixture with changing specific heat value indicates when a new sample component exits the chromatograph column If we plot the response of the detector on a graph we see a pattern of peaks each one indicating the departure of a component group exiting the column This graph is typically called a chromatogram 1 First component to exit column 5 Last component to exit column Detector signal Time Narrow peaks represent compact bunches of molecules all exiting the column at nearly the same time Wide peaks represent more diffuse groupings of similar or identical molecules In this chromatogram you can see that components 4 and 5 are not clearly differentiated over time Better separation may be achieved by altering the sample volume carrier gas flow rate type of carrier gas column packing material and or column temperature If the relative propagation speeds of each component is known in advance the chromatogram peaks may be used to identify the presence and quantities of those components The quantity of each compon
408. just has a labeled knob allowing for a person to adjust and read its value to a high degree of precision When the ratio of the variable resistance to the specimen resistance equals the ratio of the two fixed resistors the sensitive galvanometer will register exactly zero volts regardless of the excitation source s value This is called a balanced condition for the bridge circuit Ri ne Radjust Ra Rspecimen When the two resistance ratios are equal the voltage drops across the respective resistances will also be equal Kirchhoff s Voltage Law declares that the voltage differential between two equal and opposite voltage drops must be zero accounting for the meter s indication of balance It would not be inappropriate to relate this to the operation of a laboratory balance beam scale comparing a specimen of unknown mass against a set of known masses In either case the instrument is merely comparing an unknown quantity against an adjustable known quantity indicating a condition of equality between the two 102 CHAPTER 3 DC ELECTRICITY Many legacy instruments were designed around the concept of a self balancing bridge circuit where an electric servo motor drove a potentiometer to achieve a balanced condition against the voltage produced by some process sensor Analog electronic paper chart recorders often used this principle Almost all pneumatic process instruments use this principle to translate the force of a sensing element into a
409. k when setting up new formulae for physics and chemistry type problems 1 5 THE INTERNATIONAL SYSTEM OF UNITS 19 1 5 The International System of Units The very purpose of physics is to quantitatively describe and explain the physical world in as few terms as possible This principle extends to units of measurement as well which is why we usually find different units used in science actually defined in terms of more fundamental units The watt for example is one joule of energy transferred per second of time The joule in turn is defined in terms of three base units the kilogram the meter and the second Within the metric system of measurements an international standard exists for which units are considered fundamental and which are considered derived from the fundamental units The modern standard is called SI which stands for Syst me International This standard recognizes seven fundamental or base units from which all others are derived Physical quantity SI unit SI symbol Length meter m Mass kilogram kg Time second s Electric current ampere A Temperature kelvin K Amount of substance mole mol Luminous intensity candela cd An older standard existed for base units in which the centimeter gram and second comprised the first three base units This standard is referred to as the cgs system in contrast to the SI system You will still encounter some derived cgs units us
410. ken in the case of metallic conductors where electrons are the dominant charge carrier This convention was so well established in the electrical engineering realm that it held sway despite the discovery of electrons Engineers who create the symbols used to represent the electronic devices they invent consistently chose to draw arrows in the direction of conventional flow rather than electron flow In each of the following symbols the arrow heads point in the direction that positive charge carriers would move opposite the direction that electrons actually move 84 CHAPTER 3 DC ELECTRICITY E ES NPN bipolar PNP bipolar Diode SCR transistor transistor E E Ea ba m N channel P channel Unijunction Current IGBT IGBT transistor source This stands in contrast to electronics technicians who historically have been taught using electron flow notation I remember sitting in a technical school classroom being told by my teacher to always imagine the electrons moving against the arrows of the devices and wondering why it mattered It is truly a sad situation when the members of two branches within the same field do not agree on something as fundamental as the convention used to denote flow in diagrams It is even worse when people within the field argue over which convention is best So long as one is consistent with their convention and with their thinking it does not matter Many fine technologists may be found on either side of this fence
411. known magnitude against which we compare the instrument being calibrated As with other types of physical calibrations our choices of instruments falls into two broad categories devices that inherently produce known pressures versus devices that accurately measure pressures created by some other adjustable source A deadweight tester sometimes referred to as a dead test calibrator is an example in the former category These devices create accurately known pressures by means of precise masses and pistons of precise area Deadweight tester Mass HL 1 Primary piston Oil or water Pay piston Gauge to be calibrated After connecting the gauge or other pressure instrument to be calibrated the technician adjusts the secondary piston to cause the primary piston to lift off its resting position and be suspended by oil pressure alone So long as the mass placed on the primary piston is precisely known Earth s gravitational field is constant and the piston is perfectly vertical the fluid pressure applied to the instrument under test must be equal to the value described by the following equation F P A Where P Fluid pressure F Force exerted by the action of gravity on the mass Fweignt Mg A Area of piston The primary piston area of course is precisely set at the time of the deadweight tester s manufacture and does not change appreciably throughout the life of the device A very simple deadweight tester unit
412. ks exist to describe things but few really explain things well for students and the field of electronics is no exception I wanted my book s to be different and so they were No one told me how time consuming it was going to be to write them though The next few years worth of my spare time went to developing a set of question and answer worksheets designed to teach electronics theory in a Socratic active engagement style This project proved quite successful in my professional life as an instructor of electronics In the summer of 2006 my job changed from teaching electronics to teaching industrial instrumentation and I decided to continue the Socratic mode of instruction with another set of question and answer worksheets However the field of industrial instrumentation is not as well represented as general electronics and thus the array of available textbooks is not as vast I began to re discover the drudgery of trying to teach with inadequate texts as source material The basis of my active teaching style was that students would spend time researching the material on their own then engage in Socratic style discussion with me on the subject matter when they arrived for class This teaching technique functions in direct proportion to the quality and quantity of the source material at the students disposal Despite much searching I was unable to find a textbook that adequately addressed my students learning needs Many textbooks I found
413. ks socratic sinst book The Creative Commons Attribution license grants you the recipient as well as anyone who might receive my work from you the right to freely use it This license also grants you and others the right to modify my work so long as you properly credit my original authorship My work is copyrighted under United States law but this license grants everyone else in the world certain freedoms that are not customarily available under full copyright This means no one needs to ask my permission or pay any royalties to me in order to read copy distribute publish or otherwise use this book If you choose to modify my work you will have made what legal professionals refer to as a derivative work The Creative Commons license broadly groups derivative works under the term adaptations In simple terms the fundamental restriction placed on you when you do this is that you must properly credit me for the portions of your adaptation that are my original work Otherwise you may treat your adaptation the same way you would treat a completely original work of your own This means you are legally permitted to enjoy full copyright protection for your adaptation up to and including exclusive rights of reproduction and distribution In other words this license does not bind your derivative work under the same terms and conditions that I used to release my original work The practical upshot of this is that you may modify my work and re publ
414. l 611 Reset windup 613 Resistance 87 99 117 Resistor 99 Resonant wire pressure sensor 308 Reverse acting controller 604 Reverse acting pneumatic relay 225 Reverse acting transmitter 154 Reynolds number 51 Richter scale 557 Roots and powers 582 Rosemount Micro Motion Coriolis mass flowmeter 519 Rosemount model 1151 differential pressure transmitter 304 316 358 Rosemount model 3051 differential pressure transmitter 207 306 316 363 481 Rosemount model 309MV multi variable transmitter 482 Rosemount model 3301 guided wave radar transmitter 590 Rosemount model 8700 magnetic flowmeter 509 Rotameter 361 487 RTD 275 422 Salt 72 SAMA diagram 156 Sand bath temperature calibrator 275 Second Law of Motion 21 45 Segmental orifice plate 461 Segmental wedge 471 Self balancing bridge 102 Self balancing system 218 312 Self powered transmitter 198 Sensing line 318 Sensing tube 318 Series PID algorithm 617 Setpoint 130 599 Setpoint tracking 158 Shelf life pH electrode 555 INDEX Sightfeed bubbler 361 Sightglass 348 Silicon resonator pressure sensor 308 Sinking output switch 175 SIP 330 Slack diaphragm 295 Slack tube manometer 283 Slope pH instrument 559 Smart instrument 261 Smart transmitter 207 Snubber pressure 327 Solid 28 Sonic level instrument 390 Source versus load 98 Sourcing output switch 175 Soxhlet degrees 39 Span adjust
415. l controls Both steam and electrical heat tracing are used to protect instruments themselves from cold weather freezing not just the impulse lines In these applications it is important to remember that only the liquid filled portions of the instrument need freeze protection not the electronics portions blow down during warm weather but their popping is much more regular one every minute or less when ambient temperatures drop well below the freezing point of water 342 CHAPTER 12 CONTINUOUS PRESSURE MEASUREMENT 12 6 8 Water traps and pigtail siphons Many industrial processes utilize high pressure steam for direct heating performing mechanical work combustion control and as a chemical reactant Measuring the pressure of steam is important both for its end point use and its generation in a boiler One problem with doing this is the relatively high temperature of steam at the pressures common in industry which can cause damage to the sensing element of a pressure instrument if directly connected A simple yet effective solution to this problem is to intentionally create a low spot in the impulse line where condensed steam water will accumulate and act as a liquid barrier to prevent hot steam from reaching the pressure instrument The principle is much the same as a plumber s trap used underneath sinks creating a liquid seal to prevent noxious gases from entering a home from the sewer system A loop of tube or pipe cal
416. l laws we associate with real exponentials including the differentiation and integration rules of calculus This makes math operations much easier to deal with than if we had to represent AC voltages as trigonometric functions Credit for this mathematical application goes to Charles Proteus Steinmetz the brilliant electrical engineer 1865 1923 At the time Steinmetz simply referred to this representation of AC waveforms as vectors Now we assign them the unique name of phasors so as to not confuse them with other types of vectors The term phasor is quite appropriate because the angle of a phasor represents the phase shift between that waveform and a reference waveform The notation has become so popular in electrical theory that even students who have never been introduced to Euler s Relation use them In this case the notation is altered to make it easier to understand Instead of writing Be the mathematically innocent electronics student would write BO However the real purpose of phasors is to make difficult math easier so this is what we will explore now Consider the problem of defining electrical opposition to current in an AC circuit In DC direct current circuits resistance R is defined by Ohm s Law as being the ratio between voltage V and current 1 v aT There are some electrical components though which do not obey Ohm s Law Capacitors and inductors are two outstanding examples The fundamental rea
417. l measurement If the goal is to separate two liquids of differing densities from one another we need only the light liquid to exit out the overflow pipe and only the heavy liquid to exit out the drain pipe This means we must control the interface level to stay between those two piping points on the vessel If the interface drifts too far up heavy liquid will be carried out the overflow pipe and if we let the interface drift too far down light liquid will flow out of the drain pipe The first step in controlling any process variable is to measure that variable and so here we are faced with the necessity of measuring the interface point between the light and heavy liquids Another way of fixing the total height seen by the transmitter is to use a compensating leg located at a point on the vessel always lower than the total liquid height In this example a transmitter with remote seals is used 13 3 HYDROSTATIC PRESSURE 377 Inlet pipe light liquid out Fill fluid Density Floating pump __ Electronic output signal Pressure Y h F Yhz F Yh Drain pipe heavy liquid out Pressure yhy Y2h3 Since both sides of the differential pressure transmitter see the hydrostatic pressure generated by the liquid column above the top connection point y2h3 this term is naturally canceled q1h1 yaha y2h3 yaha y2h3 vih1 yah2 yah3 yaha Yoho yiha yah2 yaha The hydrostatic
418. l must develop in order to provide the push needed for that deceleration Direction of push Direction of push SS High Acceleration High velocity Low velocity Low velocity A moving mass does not simply slow down on its own There must be some opposing force to decelerate a mass from a high speed to a low speed This is where the pressure recovery downstream of the orifice plate comes from If the pressure differential across an orifice plate originated primarily from friction as I mistakenly assumed when I first learned about orifice plates then there would be no reason for the pressure to ever recover downstream of the constriction The presence of friction means energy lost not energy exchanged Although both inertia and friction are capable of creating pressure drops the lasting effects of these two different phenomena are definitely not the same There is a quadratic square relationship between velocity and differential pressure precisely because there is a quadratic relationship between velocity and kinetic energy as all first quarter 1 physics students learn E 3mv This is why AP increases with the square of flow rate Q 628APPENDIX A DOCTOR STRANGEFLOW OR HOW I LEARNED TO RELAX AND LOVE REYNOLDS NUMBERS and why we must square root the AP signal to obtain a flow measurement This is also why fluid density is so important in the orifice plate flow equation The denser a fluid is the mor
419. l of two flat plates moving past each other with a film of fluid separating them The relationship between the shear stress applied to this fluid film force divided by area and the velocity film thickness ratio is viscosity Force F ag Velocity Y v L A stationary plate _FL 15 Av Where n Absolute viscosity pascal seconds F Force newtons L Film thickness meters typically much less than 1 meter for any realistic demonstration A Plate area square meters v Relative velocity meters per second Another common unit of measurement for absolute viscosity is the poise with 1 poise being equal to 0 1 pascal seconds Both units are too large for common use and so absolute viscosity is often expressed in centipoise Water has an absolute viscosity of very nearly 1 000 centipoise Kinematic viscosity symbolized by the Greek letter nu v includes an assessment of the fluid s density in addition to all the above factors It is calculated as the quotient of absolute viscosity and mass density Where v Kinematic viscosity stokes y Absolute viscosity poises p Mass density grams per cubic centimeter 50 CHAPTER 1 PHYSICS As with the unit of poise the unit of stokes is too large for convenient use so kinematic viscosities are often expressed in units of centistokes Water has an absolute viscosity of very nearly 1 000 centistokes The mechanism of viscosity in liquids is inter molecular
420. l pressure is non linear a doubling of flow rate will not result in a doubling of differential pressure Rather a doubling of flow rate will result in a quadrupling of differential pressure This quadratic relationship between flow and pressure drop due to fluid acceleration requires us to mathematically condition or characterize the pressure signal sensed by the differential pressure instrument in order to arrive at an expressed value for flow rate The customary solution to this problem is to incorporate a square root function between the transmitter and the flow indicator as shown in the following diagram Differential indicati ressure ndicatin ikstrument Characterizer gauge 4 wires wires 1 1 Direction of flow In the days of pneumatic instrumentation this square root function was performed in a separate device called a square root extractor The Foxboro corporation model 557 pneumatic square root extractor was a classic example of this technology 5Despite the impressive craftsmanship and engineering that went into the design of pneumatic square root extractors their obsolescence is mourned by no one These devices were notoriously difficult to set up and calibrate accurately especially as they aged 15 1 PRESSURE BASED FLOWMETERS 457 The modern solution is to incorporate digital square root computation either in the indicator or in the transmitter itself 458 CHAPTER 15 CON
421. le of pressure balanced by liquid height and this liquid height is always measured parallel to the line of gravitational pull perfectly vertical inclining the manometer tube means that liquid must travel further along the tube to generate the same change in purely vertical height than it would in a vertical manometer tube Thus an inclined manometer tube causes an amplification in liquid motion for a given amount of pressure change allowing measurements of greater resolution Uf you are having difficulty understanding this concept imagine a simple U tube manometer where one of the tubes is opaque and therefore one of the two liquid columns cannot be seen In order to be able to measure pressure just by looking at one liquid column height we would have to make a custom scale where every inch of height registered as two inches of water column pressure because for each inch of height change in the liquid column we can see the liquid column we can t see also changes by an inch A scale custom made for a well type manometer is just the same concept only without such dramatic skewing of scales 12 2 MECHANICAL PRESSURE ELEMENTS 295 12 2 Mechanical pressure elements Mechanical pressure sensing elements include the bellows the diaphragm and the bourdon tube Each of these devices converts a fluid pressure into a force If unrestrained the natural elastic properties of the element will produce a motion proportional to the applied pressure
422. led a pigtail siphon achieves the same purpose Pressure gauge Fill valve Pressure gauge Pigtail siphon Fill valve Isolation block valve 12 6 PRESSURE SENSOR ACCESSORIES 343 12 6 9 Mounting brackets An accessory specifically designed for differential pressure transmitters but useful for other field mounted instruments as well is the 2 inch pipe mounting bracket Such a bracket is manufactured from heavy gauge sheet metal and equipped with a U bolt designed to clamp around any 2 inch black iron pipe Holes stamped in the bracket match mounting bolts on the capsule flanges of most common differential pressure transmitters providing a mechanically stable means of attaching a differential pressure transmitter to a framework in a process area The following photographs show several different instruments mounted to pipe sections using these brackets 344 CHAPTER 12 CONTINUOUS PRESSURE MEASUREMENT 12 7 Process instrument suitability On a fundamental level pressure is universal Regardless of the fluid in question liquid or gas hot or cold corrosive or inert pressure is nothing more than the amount of force exerted by that fluid over a unit area It should come as no surprise then that the common mechanical sensing elements for measuring pressure bellows diaphragm bourdon tube etc are equally applicable to all fluid pressure measurement applications at least in principle It is normally a matter of pro
423. lex for gases than for liquids To begin we must agree on how to standardize volumetric measurement for a gas when the volume is so easily subject to change We can do this by agreeing on standard base line pressures and temperatures under which a particular gas volume is specified For example a gas flow rate of 900 SCFM Standard Cubic Feet per Minute refers to 900 cubic feet of gas flowing per minute of time if that gas flowstream were subjected to atmospheric pressure at 70 F British units The actual volume of gas moving through that pipe each minute under pressurized conditions will likely occupy far less than 900 cubic feet due to physical compression reduction of volume resulting from increased pressure of the gas However the unit of standard cubic feet per minute gives people a common frame of reference 443 444 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT 15 1 Pressure based flowmeters All masses require force to accelerate we can also think of this in terms of the mass generating a reaction force as a result of being accelerated This is quantitatively expressed by Newton s Second Law of Motion iE gt Force Acceleration F F Mass a m Newton s Second Law formula F ma All fluids possess mass and therefore require force to accelerate just like solid masses If we consider a quantity of fluid confined inside a pipe with that fluid quantity having a mass equal to its volume m
424. lf permission to remain ignorant about it and blissfully went on my way Little did I know that Reynolds number held the key to understanding my honey through a straw question of years ago as well as comprehending not just believing how orifice plates actually worked According to Lipt k laminar flowmeters were effective only for low Reynolds numbers typically below 1200 Cross referencing the orifice plate section of the same book told me that Reynolds numbers for typical orifice plate flow streams were much greater 10 000 or higher Furthermore the orifice plate section contained an insightful passage on page 152 which I will now quote here Italicized words indicate my own emphasis locating the exact points of my Aha moments The basic equations of flow assume that the velocity of flow is uniform across a given cross section In practice flow velocity at any cross section approaches zero in the boundary layer adjacent to the pipe wall and varies across the diameter This flow velocity profile has a significant effect on the relationship between flow velocity and pressure difference developed in a head meter In 1883 Sir Osborne Reynolds an English scientist presented a paper before the Royal Society proposing a single dimensionless ratio now known as Reynolds number as a criterion to describe this phenomenon This number Re is expressed as _ VDp u Re where V is velocity D is diameter p is density and y is absol
425. liar to you It has the same form as the total resistance formula for series circuits Just as resistances add in series more series resistance makes the overall resistance to current increase conductances add in parallel more conductive branches makes the overall conductance increase Knowing that resistance is the reciprocal of conductance we may substitute 4 for G wherever we see it in the conductance equation 1 1 1 1 tte Rtotal Ri Ra Rn Now to solve for Rtotal we need to reciprocate both sides 3 4 SERIES VERSUS PARALLEL CIRCUITS 93 Reotal a T T ENTRO oe For both series and parallel circuits total power dissipated by all load devices is equal to the total power delivered by all source devices The configuration of a circuit is irrelevant to the balance between power supplied and power lost because this balance is an expression of the Law of Energy Conservation 94 CHAPTER 3 DC ELECTRICITY 3 5 Kirchhoff s Laws Two extremely important principles in electric circuits were codified by Gustav Robert Kirchhoff in the year 1847 known as Kirchhoff s Laws His two laws refer to voltages and currents in electric circuits respectively Kirchhoff s Voltage Law states that the algebraic sum of all voltages in a closed loop is equal to zero Another way to state this law is to say that for every rise in potential there must be an equal fall if we begin at any point in a circuit and travel in a loop back to that
426. lication as their operation depends on direct contact between process fluid and manometer liquid In the early days of industrial instrumentation liquid mercury was a very common medium for process manometers and it was not unusual to see a mercury manometer used in direct contact with a process fluid such as oil or water to provide pressure indication 14 Although this fluid would not normally contact pure oxygen in the process it could if the isolating diaphragm inside the transmitter were to ever leak 12 7 PROCESS INSTRUMENT SUITABILITY 345 Isolation block valve vent Float Range tube Thankfully those days are gone Mercury chemical symbol Hg is a toxic metal and therefore hazardous to work with Calibration of these manometers was also challenging due to the column height of the process liquid in the impulse line and the range tube When the process fluid is a gas the difference in mercury column height directly translates to sensed pressure by the hydrostatic pressure formula P pgh or P yh When the process fluid is a liquid though the shifting of mercury columns also creates a change in height of the process liquid column which means the indicated pressure is a function of the height difference h and the difference in density between the process liquid and mercury Consequently the indications provided by mercury manometers in liquid pressure applications were subject to correction according
427. ligible compared to the motion of liquid inside the clear viewing tube For all practical purposes the only liquid motion is inside the smaller tube Thus the well manometer provides an easier means of reading pressure 42 CHAPTER 1 PHYSICS no longer does one have to measure the difference of height between two liquid columns only the height of a single column 1 8 FLUID MECHANICS 43 1 8 5 Systems of pressure measurement Pressure measurement is often a relative thing What we mean when we say there is 35 PSI of air pressure in an inflated car tire is that the pressure inside the tire is 35 pounds per square inch greater than the surrounding ambient air pressure It is a fact that we live and breathe in a pressurized environment Just as a vertical column of liquid generates a hydrostatic pressure so does a vertical column of gas If the column of gas is very tall the pressure generated by it will be substantial enough to measure Such is the case with Earth s atmosphere the pressure at sea level caused by the weight of the atmosphere is approximately 14 7 PSI You and I do not perceive this constant air pressure around us because the pressure inside our bodies is equal to the pressure outside our bodies Thus our skin which serves as a differential pressure sensing diaphragm detects no difference of pressure between the inside and outside of our bodies The only time the Earth s air pressure becomes perceptible to us is if we rapidly
428. lity between hydrogen and hydroxyl ions in a pure water sample means that pure water is neutral and that the molarity of hydrogen ions is equal to the square root of Ky Ht VKo V1 0 x 10 4 1 0 x 10 7 M Since we know pH is defined as the negative logarithm of hydrogen ion activity and we can be assured all hydrogen ions present in the solution will be active since there are no other positive ions to interfere with them the pH value for water at 25 degrees Celsius is pH of pure water at 25 C log 1 0 x 1077 M 7 0 pH As the temperature of a pure water sample changes the ionization constant changes as well Increasing temperature causes more of the water molecules to ionize resulting in a larger K value The following table shows Kw values for pure water at different temperatures 70 CHAPTER 2 CHEMISTRY Temperature Kw 0 C 1 139 x 10715 5 C 1 846 x 10715 10 C 2 920 x 105 15 C 4 505 x 10715 20 C 6 809 x 10775 25 C 1 008 x 10 30 C 1 469 x 10717 35 C 2 089 x 104 40 C 2 919 x 10 14 45 C 4 018 x 1071 50 C 5 474 x 1071 55 C 7 296 x 1054 60 C 9 614 x 1071 This means that while any pure water sample is neutral an equal number of positive hydrogen ions and negative hydroxyl ions the pH value does change with temperature and is only equal to 7 0 pH at one particular temperature 25 C Based on the K values shown in the ta
429. lize that the unit definition of a pound is a slug of mass multiplied by the acceleration of gravity in feet per second squared following Newton s Second Law of motion F ma 09 steg 5 Once we make this substitution into the pressure head term the units are revealed to be the same as the other two terms slugs per foot second squared 2 slug s el e ft s2 In order for our British units to be consistent here we must use feet for elevation slugs per cubic foot for mass density feet per second squared for acceleration feet per second for velocity and pounds per square foot for pressure If one wished to use the more common pressure unit of PSI pounds per square inch with Bernoulli s equation instead of PSF pounds per square foot all the other units would have to change accordingly elevation in inches mass density in slugs per cubic inch acceleration in inches per second squared and velocity in inches per second Just for fun we can try dimensional analysis on the second version of Bernoulli s equation this time using metric units ie 29 7 e El Here we see that all three terms end up being cast in simple units of meters That is the fluid s elevation velocity and pressure heads are all expressed as simple elevations In order for our metric units to be consistent here we must use meters for elevation meters per second for velocity meters per second squared for acceleration
430. lled two different ways on the side of a pressure transmitter flange one way to bleed gas out of a liquid process located on top and the other way to bleed liquid out of a gas process located on bottom 10The standard 3 valve manifold for instance does not provide a bleed valve only block and equalizing valves 12 6 PRESSURE SENSOR ACCESSORIES 327 12 6 3 Pressure pulsation dampening A simple way to mitigate the effects of pulsation on a pressure gauge is to fill the inside of the gauge with a viscous liquid such as glycerin or oil The inherent friction of this fill liquid has a shock absorber quality which dampens the gauge mechanism s motion and helps protect against damage from pulsations or from external vibration This method is ineffectual for high amplitude pulsations though A more sophisticated method for dampening pulsations seen by a pressure instrument is called a snubber and it consists of a fluid restriction placed between with the pressure sensor and the process The simplest example of a snubber is a simple needle valve an adjustable valve designed for low flow rates placed in a mid open position restricting fluid flow in and out of a pressure gauge Pressure gauge Needle valve partially open At first the placement of a throttling valve between the process and a pressure measuring instrument seems rather strange because there should not be any continuous flow in or out of the gauge f
431. lly developed turbulent flow that orifice plates need for accurate measurement In a more general sense the lesson we should learn here is that blind faith is no substitute for understanding and that a sense of confusion or disagreement during the learning process is a sign of one or more misconceptions in need of correction If you find yourself disagreeing with what you are being taught either you are making a mistake and or your teacher is Pursuing your questions to their logical end is the key to discovery while making a leap of faith simply believing what you are told is an act of avoidance escaping the discomfort of confusion and uncertainty at the expense of a deeper learning experience This is an exchange no student should feel they have to make 6830 APPENDIX A DOCTOR STRANGEFLOW OR HOW I LEARNED TO RELAX AND LOVE REYNOLDS NUMBERS References Lipt k B la G Instrument Engineers Handbook Process Measurement and Analysis Volume I Third Edition CRC Press New York NY Appendix B Creative Commons Attribution License 631 632 APPENDIX B CREATIVE COMMONS ATTRIBUTION LICENSE B 1 A simple explanation of your rights This is an open source textbook meaning that the digital files used to create the final form PDF printed paper or other are freely available for your perusal reproduction distribution and even modification These files reside at the following website http openbookproject net boo
432. low path of a fluid is disturbed by such a device the velocity profile of that fluid will become asymmetrical e g the velocity gradient from one wall boundary of the pipe to the other will not be orderly Large eddies in the flowstream called swirl will be present This may cause problems for pressure based flow elements which rely on linear acceleration change in velocity in one dimension to measure fluid flow rate If the flow profile is distorted enough the acceleration detected at the element may be too great or too little and therefore not properly represent the full fluid flowstream Large scale disturbances Fluid flow Velocity profile Even disturbances located downstream of the flow element impact measurement accuracy albeit not as much as upstream disturbances Unfortunately both upstream and downstream flow disturbances are unavoidable on all but the simplest fluid systems This means we must devise ways to stabilize a flowstream s velocity profile near the flow element in order to achieve accurate measurements of flow rate A very simple and effective way to stabilize a flow profile is to provide adequate lengths of straight pipe ahead of and behind the flow element Given enough time even the most chaotic flowstream will settle down to a symmetrical profile all on its own The following 9L K Spink mentions in his book Principles and Practice of Flow Meter Engineering that certain tests have shown flow
433. lowing SAMA diagram indicates the presence of setpoint tracking in the controller algorithm a feature that forces the setpoint value to equal the process variable value any time the controller is in manual mode 6 4 SAMA DIAGRAMS 159 Flow transmitter PID controller Flow control valve Here we see a new type of line dashed instead of solid This too has meaning in the world of SAMA diagrams Solid lines represent analog continuously variable signals such as process variable setpoint and manipulated variable Dashed lines represent discrete on off signal paths in this case the auto manual state of the controller commanding the PID algorithm to get its setpoint either from the operator s input A or from the process variable input the flow transmitter FT 160 CHAPTER 6 INSTRUMENTATION DOCUMENTS 6 5 Instrument and process equipment symbols 6 5 1 Line types Process flow line Pneumatic signal continuous HH Electric signal continuous Mechanical link OO Instrument supply or process connection impulse line Pneumatic signal discrete on off HK Electric signal discrete on off o Da Mo Radio link MW N Waveguide oa COO 8S Capillary tube A Data link system internal Sonic or other wave Nu NU 6 5 2 Process Instrument line connections Undefined HA Hydraulic signal Data link between systems Generic Threaded Socket welded Fl
434. lowing into and out of a tee fitting 70 GPM So long as there are no leaks in this piping system every drop of water entering the tee must be balanced by a drop exiting the tee For there to be a continuous mis match between flow rates would imply a violation of the Law of Mass Conservation Let s apply this principle to a real circuit where all currents have been calculated for us 10But not always There do exist positive ground systems particularly in telephone circuits and in some early automobile electrical systems 3 5 KIRCHHOFF S LAWS 97 1kQ 3 B C 4mA D 2m4 Arrows show currents in the direction of conventional flow notation At nodes where just two wires connect such as points A B and C the amount of current going in to the node exactly equals the amount of current going out 4 mA in each case At nodes where three wires join such as points D and E we see one large current and two smaller currents one 4 mA current versus two 2 mA currents with the directions such that the sum of the two smaller currents form the larger current 98 CHAPTER 3 DC ELECTRICITY 3 6 Electrical sources and loads By definition and source is a device that inputs energy into a system while a load is a device that extracts energy from a system Examples of typical electrical sources include generators photovoltaic cells thermopiles and primary cell batteries Examples of typical electrical loads include
435. ly conductive protrusion into a process vessel or pipe that allows a temperature sensitive instrument to detect process temperature without opening a hole in the vessel or pipe Thermowells are critically important for installations where the temperature element RTD thermocouple thermometer etc must be replaceable without de pressurizing the process Thermowells may be made out of any material that is thermally conductive pressure tight and not chemically reactive with the process A simple diagram showing a thermowell in use with a temperature gauge is shown here Thermometer Compression fitting Thermowell Process fluid If the temperature gauge is removed for service or replacement the thermowell maintains pressure integrity of the pipe no process fluid leaking out and no air leaking in 438 CHAPTER 14 CONTINUOUS TEMPERATURE MEASUREMENT Thermometer removed from process Thermowell Process fluid Photographs of a real stainless steel thermowell are shown here the left hand photo showing the entire length of the thermowell and the right hand photo showing the end where the temperature sensing device is inserted A photo of a complete RTD assembly connection head RTD and thermowell appears in the 14 6 TEMPERATURE SENSOR ACCESSORIES 439 next photograph Another photo shows an RTD installed in a thermowell on the side of a commercial freezer using a Rosemount model 3044C temperatu
436. lying the rule that the sum of exponents is the product of powers k nEV ete RT a If k is constant then e will be constant as well calling the new constant C nFV e RT 01 Analytical instruments based on potentiometry must evaluate this inverse function to undo the Nernst equation to arrive at an inferred measurement of ion activity in the sample given the small voltage produced by the sensing membrane These instruments typically have temperature sensors as well built in to the sensing membrane assembly since it is apparent that temperature T also plays a role in the generation of this voltage Once again this mathematical function is typically evaluated in a microprocessor References Lipt k B la G Instrument Engineers Handbook Process Measurement and Analysis Volume I Fourth Edition CRC Press New York NY 2003 Stewart James Calculus concepts and contexts 2nd Edition Brooks Cole Pacific Grove CA 2001 Chapter 18 Continuous feedback control 595 596 CHAPTER 18 CONTINUOUS FEEDBACK CONTROL 18 1 Basic feedback control principles Instrumentation is the science of automated measurement and control Applications of this science abound in modern research industry and everyday living From automobile engine control systems to home thermostats to aircraft autopilots to the manufacture of pharmaceutical drugs automation surrounds us This section explains some of the fundamental principle
437. m value or else the transmitter will not have enough electrical power to continue its normal operation This makes it possible to starve the transmitter of voltage if the loop power supply voltage is insufficient and or if the loop resistance is excessive To illustrate how this can be a problem consider the following 4 20 mA measurement loop where the controller supplies only 20 volts DC to power the loop and an indicator is included in the circuit to provide operators with field located indication of the transmitter s measurement Controller Indicator 2 wire transmitter The indicator contains its own 250 ohm resistor to provide a 1 5 volt signal for the meter mechanism to sense This means the total loop resistance is now 500 ohms plus any wire resistance At full current 20 mA this total resistance will drop at least 10 volts leaving 10 volts or less 8 6 TROUBLESHOOTING CURRENT LOOPS 207 at the transmitter terminals to power the transmitter s internal workings 10 volts may not be enough for the transmitter to successfully operate though The Rosemount model 3051 pressure transmitter for example requires a minimum of 10 5 volts at the terminals to operate However the transmitter will operate just fine at lower loop current levels When the loop current is only 4 mA for example the combined voltage drop across the two 250 ohm resistors will be only 2 volts leaving about 18 volts at the transmitter terminals
438. mA signal will be naturally seen by the controller as a pressure over range condition This is considered dangerous in a compressor system because it predicts a condition of surge Thus the controller will naturally take action to prevent surge by commanding the anti surge control valve to open because it thinks the compressor is about to surge In other words the transmitter is intentionally calibrated to be reverse acting so that any break in the signal wiring will naturally bring the system to its safest condition 156 CHAPTER 6 INSTRUMENTATION DOCUMENTS 6 4 SAMA diagrams SAMA is an acronym standing for Scientific Apparatus Makers Association referring to a unique form of diagram used primary in the power generation industry to document control strategies These diagrams focus on the flow of information within a control system rather than on the process piping or instrument interconnections wires tubes etc The general flow of a SAMA diagram is top to bottom with the process sensing instrument transmitter located at the top and the final control element valve or variable speed motor located at the bottom No attempt is made to arrange symbols in a SAMA diagram to correlate with actual equipment layout these diagrams are all about the algorithms used to make control decisions and nothing more A sample SAMA diagram appears here showing a flow transmitter FT sending a process variable signal to a PID controller which
439. man readable display For a variable speed motor drive the input would be an electronic signal and the output would be electric power to the motor To calibrate am instrument means to check and adjust if necessary its response so that the output accurately corresponds to its input throughout a specified range In order to do this one must expose the instrument to an actual input stimulus of precisely known quantity For a pressure gauge indicator or transmitter this would mean subjecting the pressure instrument to known fluid pressures and comparing the instrument response against those known pressure quantities One cannot perform a true calibration without comparing an instrument s response to known stimuli To range an instrument means to set the lower and upper range values so that it responds with the desired sensitivity to changes in input For example a pressure transmitter set to a range of 0 to 200 PSI could be re ranged to respond on a scale of 0 to 150 PSI In analog instruments re ranging could usually only be accomplished by re calibration since the same adjustments were used to achieve both purposes In digital instruments calibration and ranging are typically separate adjustments so it is important to know the difference 257 258 CHAPTER 11 INSTRUMENT CALIBRATION 11 2 Zero and span adjustments analog transmitters The purpose of calibration is to ensure the input and output of an instrument correspond to one another
440. mbly shakes up and down causing the U bend to twist As mass flow rate through the tube increases so does the degree of twisting By monitoring the amplitude of this twisting motion we may infer the mass flow rate of the fluid passing through the tube 518 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT Shaking motion Shaking 4 motion End view End view In order to reduce the amount of vibration generated by a Coriolis flowmeter and more importantly to reduce the effect any external vibrations may have on the flowmeter two identical U tubes are built next to each other and shaken in complementary fashion always moving in opposite directions Tube twist is measured as relative motion from one tube to the next not as motion between the tube and the stationary housing of the flowmeter This ideally eliminates the effect of any common mode vibrations on the inferred flow measurement 28 For those readers with an automotive bent this is the same principle applied in opposed cylinder engines e g Porsche boxer air cooled 6 cylinder engine Volkswagen air cooled 4 cylinder engine BMW air cooled motorcycle twin engine Citroen 2CV 2 cylinder engine Subaru 4 and 6 cylinder opposed engines etc Opposite piston pairs are always 180 out of phase for the purpose of maintaining mechanical balance both moving away from the crankshaft or both moving toward the crankshaft at any given time
441. me in seconds Since velocity is nothing more than the rate of position change with respect to time the force mass equation may be expressed using the calculus notation of the second derivative acceleration being the derivative of velocity which in turn is the derivative of position dx F m de Where F Force in newtons metric or pounds British m Mass in kilograms metric or slugs British x Position in meters metric or feet British t Time in seconds 1 2 METRIC PREFIXES 9 Mass density p for any substance is the proportion of mass to volume Weight density y for any substance is the proportion of weight to volume Just as weight and mass are related to each other by gravitational acceleration weight density and mass density are also related to each other by gravity Fweight Mg Weight and Mass y pg Weight density and Mass density 1 2 Metric prefixes METRIC PREFIX SCALE T G M k m u n p tera giga mega kilo none milli micro nano pico TOR 0 108 Los 10 405 O o7 T0 10 Ig 10 20 hecto deca deci centi h da d c 10 CHAPTER 1 PHYSICS 1 3 Unit conversions and physical constants Converting between disparate units of measurement is the bane of many science students The problem is worse for students of industrial instrumentation in the United States of America who must work with British Customary units such as the pound the foot the gallon etc World wide adoption of the m
442. me to time A text label printed on the paddle of any orifice plate customarily identifies the upstream side of that plate but in the case of the square edged orifice plate it does not matter The purpose of having a square edge on the hole in an orifice plate is to minimize contact with the fast moving moving fluid stream going through the hole Ideally this edge will be knife sharp If the orifice plate is relatively thick 1 8 or an inch or more it may be necessary to bevel the downstream side of the hole to further minimize contact with the fluid stream 460 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT Square edged concentric orifice plate Paddle with downstream bevel front view side view Looking at the side view of this orifice plate the intended direction of flow is left to right with the sharp edge facing the incoming fluid stream and the bevel providing a non contact outlet for the fluid Beveled orifice plates are obviously uni directional and must be installed with the paddle text facing upstream Other square edged orifice plates exist to address conditions where gas bubbles or solid particles may be present in liquid flows or where liquid droplets or solid particles may be present in gas flows The first of this type is called the eccentric orifice plate where the hole is located off center to allow the undesired portions of the fluid to pass through the orifice rather than build up on the upstream
443. ment 259 Span gas 287 Span shift 267 Specific gravity 38 46 Specific heat 526 Spiral bourdon tube 295 Square root characterizer 456 579 623 625 628 Square root extractor 457 Square root scale 576 Square edged concentric orifice plate 459 Stagnation pressure 447 Standard cell 273 Stationary phase 561 Steam jacket 139 Steam tracing 340 Steam trap 340 Steam In Place 330 Stefan Boltzmann equation 591 Stefan Boltzmann Law 435 Steinmetz Charles Proteus 122 Stem valve 226 Stilling well 409 493 Stoichiometry 64 Stokes 50 Strain gauge 103 300 Strapping table 589 Strouhal number 501 Strouhal Vincenc 501 Superconductivity 87 INDEX Superfluidity 87 Sutro weir 491 Swamping 423 628 Switch 169 Switch process 144 Systeme International 19 Tank expert system 372 Tape and float level measurement 354 Tare weight 403 Target flow element 469 Temperature switch 183 Temperature defined for a gas 415 Test Uncertainty Ratio 272 Thermal conductivity detector GC 564 Thermal energy 415 Thermal imager 435 Thermal mass flowmeter 524 Thermistor 422 Thermocouple 275 427 Thermocouple burnout detection 433 Thermowell 437 Thin layer chromatography 561 Third Law of Motion 21 Three valve manifold 322 Toroidal conductivity cell 546 Torr 44 Torricelli Evangelista 57 Toshiba magnetic flowmeter 509 Transducer 131 Transit time ultrasonic fl
444. mise between two wire and four wire RTD connections is the three wire connection which looks like this 14 3 THERMISTORS AND RESISTANCE TEMPERATURE DETECTORS RTDS 425 10 wire Voltmeter B RTD Current Ri 100 Q source In a three wire RTD circuit voltmeter A measures the voltage dropped across the RTD plus the voltage dropped across the bottom current carrying wire Voltmeter B measures just the voltage dropped across the top current carrying wire Assuming both current carrying wires will have very nearly the same resistance subtracting the indication of voltmeter B from the indication given by voltmeter A yields the voltage dropped across the RTD VrrD Vineter A Vineter B Of course real RTD instruments do not typically employ direct indicating voltmeters Most often the voltage measuring element is an analog to digital converter ADC which sends a digital output to a microprocessor for processing and signal output and or display Analog electronic RTD instruments have also been built using operational amplifiers to convert the RTD s voltage drop into a standard instrument output signal such as 4 20 mA DC The voltmeters shown in the previous diagrams serve only to illustrate the basic concepts One problem inherent to both thermistors and RTD s is self heating In order to measure the resistance of either device we must pass an electric current through it Unfortunately this results
445. mpensating impulse leg Gas pressure with condensible vapors Signal decreases with increasing liquid level Either way of connecting the transmitter to the vessel will suffice for measuring liquid level so long as the instrumentation receiving the transmitter s signal is properly configured to interpret the signal The choice of which way to connect the transmitter to the vessel should be driven by fail safe system design which means to design the measurement system such that the most probably system failures including broken signal wires result in the control system seeing the most dangerous process condition and therefore taking the safest action 372 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT 13 3 4 Tank expert systems An alternative to using a compensating leg to subtract gas pressure inside an enclosed vessel is to simply use a second pressure transmitter and electronically subtract the two pressures in a computing device Gas pressure ae Subtraction iB Pressure Pas x p gt Height gt Pressure P Yh This approach enjoys the distinct advantage of avoiding a potentially wet compensating leg but suffers the disadvantages of extra cost and greater error due to the potential calibration drift of two transmitters rather than just one Such a system is also impractical in applications where the gas pressure is substantial compared to the hydrostatic elevation head pressure If we add a t
446. mplifying 236 CHAPTER 9 PNEUMATIC INSTRUMENTATION relay between the nozzle backpressure chamber and the feedback bellows The purpose of an amplifying relay in a self balancing pneumatic system is the same as the purpose of providing an operational amplifier with an extremely high open loop voltage gain the more internal gain the system has the closer to ideal the balancing effect will be In other words our simplifying assumption of zero baffle nozzle gap change will be closer to the truth in a system where the nozzle pressure gets amplified before going to the feedback bellows Air supply oT gt Pivot Thus adding a relay to a self balancing pneumatic system is analogous to increasing the open loop voltage gain of an opamp 401 by several fold it makes the overall gain closer to ideal The overall gain of the system though is dictated by the ratio of bellows leverage on the force beam just like the overall gain of a negative feedback opamp circuit is dictated by the feedback network and not by the opamp s internal open loop voltage gain 9 5 ANALYSIS OF A PRACTICAL PNEUMATIC INSTRUMENT 237 9 5 Analysis of a practical pneumatic instrument Perhaps one of the most popular pneumatic industrial instruments ever manufactured is the Foxboro model 13 differential pressure transmitter A photograph of one with the cover removed is shown here The following is a functional illustration of this instrument
447. n J The practical import of all this is we can always treat the reference junction s as a single junction made from the same two metal types as the measurement junction so long as all dissimilar metal 432 CHAPTER 14 CONTINUOUS TEMPERATURE MEASUREMENT junctions at the reference location are of equal temperature This fact is extremely important in the age of semiconductor circuitry where the connection of a thermocouple to an electronic amplifier involves many different junctions from the thermocouple wires to the amplifier s silicon Here we see a multitude of reference junctions inevitably formed by the necessary connections from thermocouple wire to the silicon substrate inside the amplifier chip Iron brass copper leadtin kovar gold silicon silicon Constantan brass copper leadin kovar gold It should be obvious that each complementary junction pair cancels if each pair is at the same temperature e g gold silicon junction J 2 cancels with silicon gold junction J 3 because they generate the exact same amount of voltage with opposing polarities The Law of Intermediate Metals goes one step further by telling us junctions J2 through J 3 taken together in series are of the same effect as a single reference junction of iron and constantan Automatic reference junction compensation is as simple as counter acting the voltage produced by this equivalent iron constantan junction at whatever temperature junction
448. n their tendency is to neutralize one another the hydrogen ions liberated by the acid combining and canceling with the hydroxyl ions liberated by the caustic The result of a perfectly balanced mix of acid and caustic is deionized water H20 and a salt Such neutralizations are exothermic owing to the decreased energy states of the hydrogen and hydroxyl ions after combination References Giancoli Douglas C Physics for Scientists amp Engineers Third Edition Prentice Hall Upper Saddle River New Jersey 2000 Weast Robert C Astel Melvin J and Beyer William H CRC Handbook of Chemistry and Physics 64th Edition CRC Press Inc Boca Raton FL 1984 Whitten Kenneth W Gailey Kenneth D and Davis Raymond E General Chemistry Third Edition Saunders College Publishing Philadelphia PA 1988 4Exceptions do exist for strong concentrations where hydrogen ions may be present in solution yet unable to react because of being crowded out by other ions in the solution Chapter 3 DC electricity 74 CHAPTER 3 DC ELECTRICITY 3 1 Electrical voltage Voltage is the amount of specific potential energy available between two points in an electric circuit Potential energy is energy that is potentially available to do work Looking at this from a classical physics perspective potential energy is what we accumulate when we lift a weight above ground level or when we compress a spring Wall Mass m S
449. n 573 17 1 Flow measurement in open channels 0000 eee ee ee 581 17 2 Liquid volume measurement 2 2 a 583 17 3 Radiative temperature measurement 0 000 02 eee ee eee 591 17 4 Analytical measurements aoaaa a 592 CONTENTS 1 18 Continuous feedback control 595 18 1 Basic feedback control principles o e 596 18 2 0n 0ff controle ac ee ek at e e ee Ok EAS ee La ed 602 18 3 Proportional only control 2 0 0 000200020002 2 ee 604 18 4 Proportional only offset 2 2 ee 608 18 5 Integral reset control 2 ee 611 18 6 Derivative rate control ooa ee 614 18 7 PID controllertuning a i 62 2 A ae i le EAA Pa ed BA A a aS 616 A Doctor Strangeflow or how I learned to relax and love Reynolds numbers 621 Creative Commons Attribution License 631 B 1 A simple explanation of your rights o oaoa ee 632 B 2 Tegal code sain Gee u A ee a id oe ee ba ah Sw a a 633 CONTENTS Preface I did not want to write this book honestly My first book project began in 1998 titled Lessons In Electric Circuits and I didn t call quit until six volumes and five years later Even then it was not complete but being an open source project it gained traction on the internet to the point where other people took over its development and it grew fine without me The impetus for writing this first tome was a general dissatisfaction with available electronics textbooks Plenty of textboo
450. n as a strain gauge a folded wire designed to stretch and compress with the object under test altering its electrical resistance accordingly 104 CHAPTER 3 DC ELECTRICITY Test specimen N ciiai When the specimen is stretched along its long axis the metal wires in the strain gauge stretch with it increasing their length and decreasing their cross sectional area both of which work to increase the wire s electrical resistance This stretching is microscopic in scale but the resistance change is measurable and repeatable within the specimen s elastic limit In the above circuit example stretching the specimen will cause the voltmeter to read upscale as defined by the polarity marks Compressing the specimen along its long axis has the opposite effect decreasing the strain gauge resistance and driving the meter downscale Strain gauges are used to precisely measure the strain stretching or compressing motion of mechanical elements One application for strain gauges is the measurement of strain on machinery components such as the frame components of an automobile or airplane undergoing design development testing Another application is in the measurement of force in a device called a load cell A load cell is comprised of one or more strain gauges bonded to the surface of a metal structure having precisely known elastic properties This metal structure will stretch and compress very precisely with applied force as though it wer
451. n economy is to function as an energy storage and transport medium The fundamental principle at work here is the energy stored in chemical bonds invested in the separation of hydrogen from oxygen and later returned in the re combination of hydrogen and oxygen back into water The fact that hydrogen and oxygen as separate gases possess potential energy does not mean they are guaranteed to spontaneously combust when brought together By analogy just because rocks sitting on a hillside possess potential energy by virtue of being elevated above the hill s base does not means all rocks in the world spontaneously roll downhill Some rocks need a push to get started because they are caught on a ledge or resting in a hole Likewise many exothermic reactions require an initial investment of energy before they can proceed In the case of hydrogen and oxygen what is generally needed is a spark to initiate the reaction This initial requirement of input energy is called the activation energy of the reaction Activation energy may be shown in graphical form For an exothermic reaction it appears as a hill that must be climbed before the total energy can fall to a lower than original level 66 CHAPTER 2 CHEMISTRY Exothermic reaction 2m Potential energy Activation energy Energy released by reaction Before After reaction Time gt reaction For an endothermic reaction activation energy is much greater a part of which ne
452. n either case the first aid repair is to pass a welding torch tip cleaner through the plugged hole to break loose the residue or debris plugging it Moisture in compressed air tends to corrode metal parts inside pneumatic mechanisms This corrosion may break loose to form debris that plugs orifices and nozzles or it may simply eat through thin diaphragms and bellows until air leaks develop Grossly excessive moisture will cause erratic operation as plugs of liquid travel through thin tubes orifices and nozzles designed only for air passage A common mistake made when installing pneumatic instruments is to connect them to a general service utility compressed air supply instead of a dedicated instrument service compressed air system Utility air systems are designed to supply air tools and large air powered actuators with pneumatic power These high flow compressed air systems are often seeded with antifreeze and or lubricating chemicals to prolong the operating life of the piping and air consuming devices but the same liquids will wreak havoc on sensitive instrumentation Instrument air supplies should be sourced by their own dedicated air compressor s complete with automatic air dryer equipment and distributed through stainless steel copper or plastic tubing never black iron or galvanized iron pipe The worst example of moisture in an instrument air system I have ever witnessed is an event that happened at an oil refinery
453. n the case of a pneumatic controller an op amp circuit in the case of an analog electronic controller or by a microprocessor running a digital integration algorithm The variable being integrated is error the difference between PV and SP Thus the integral mode of the controller ramps the output either up or down over time the direction of ramping determined by the sign of the error PV greater or less than SP and the rate of ramping determined by the magnitude of the error how far away PV is from SP If proportional action is where the error tells the output how far to move integral action is where the error tells the output how fast to move One might think of integral as being how impatient the controller is with integral action constantly ramping the output as far as it needs to go in order to eliminate error Once the error is zero PV SP of course the integral action stops ramping leaving the controller output valve position at its last value just like a stopped car s odometer holds a constant value If we add an integral term to the controller equation we get something that looks like this m Kye K f edt b 2At least the old fashioned mechanical odometers would Some new cars use a pulse detector on the driveshaft which cannot tell the difference between forward and reverse and therefore their odometers always increment Shades of Ferris Bueller s Day Off 612 CHAPTER 18 CONTINUOUS FEEDBACK CONTROL Where
454. n tips it the other way 3It should be noted that the solution never becomes electrically imbalanced with the addition of an acid or caustic It is merely the balance of hydrogen to hydroxyl ions we are referring to here The net electrical charge for the solution should still be zero after the addition of an acid or caustic because while the balance of hydrogen to hydroxyl ions does change that electrical charge imbalance is made up by the other ions resulting from the addition of the electrolyte anions for acids cations for caustics The end result is still one negative ion for every positive ion equal and opposite charge numbers in the solution no matter what substance s we dissolve into it 72 CHAPTER 2 CHEMISTRY If an electrolyte has no effect on the hydrogen and hydroxyl ion activity of an aqueous solution we call it a salt The following is a list of some common salts showing their respective ions in solution Potassium chloride is a salt produces neither Ht nor OH nor O in solution KCl gt Kt Cl Sodium chloride is a salt produces neither Ht nor OH nor O in solution NaCl gt Nat CI Zinc sulfate is a salt produces neither Ht nor OH nor O in solution ZnSO4 gt Zn SO47 The addition of a salt to an aqueous solution should have no effect on pH because the ions created neither add to nor take away from the hydrogen ion activity When both an acid and caustic are added to an aqueous solutio
455. name implies A Cippoletti weir is much like a rectangular weir except that the vertical sides of the notch have a 4 1 slope rise of 4 run of 1 approximately a 14 degree angle from vertical A V notch weir has a triangular notch customarily measuring either 60 or 90 degrees The following photograph shows water flowing through a Cippoletti weir At a condition of zero flow through the channel the liquid level will be at or below the crest lowest point on the opening of the weir As liquid begins to flow through the channel it must spill over the crest of the weir in order to get past the weir and continue downstream in the channel In order for this to happen the level of the liquid upstream of the weir must rise above the weir s crest 490 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT height This height of liquid upstream of the weir represents a hydrostatic pressure much the same as liquid heights in piezometer tubes represent pressures in a liquid flowstream through an enclosed pipe see page 59 for examples of this The height of liquid above the crest of a weir is analogous to the pressure differential generated by an orifice plate As liquid flow is increased even more a greater pressure head will be generated upstream of the weir forcing the liquid level to rise This effectively increases the cross sectional area of the weir s throat as a taller stream of liquid exits the notch of the weir Greater level ups
456. nce flow profiles are never completely flat any insertion meter element will register a greater flow rate at the center of the pipe than near the walls Wherever the insertion element is placed in the pipe diameter that placement must remain consistent through repeated extractions and re insertions or else the effective calibration of the insertion flowmeter will change every time it is removed and re inserted into the pipe Care must also be taken to insert the flowmeter so that the flow element points directly upstream and not at an angle A unique advantage of insertion instruments is that they may be installed in an operating pipe by using specialized hot tapping equipment A hot tap is a procedure whereby a safe penetration is made into a pipe while the pipe is carrying fluid under pressure The first step in a hot tapping operation is to weld a saddle tee fitting on the side of the pipe 534 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT Next a ball valve is bolted onto the saddle tee flange This ball valve will be used to isolate the insertion instrument from the fluid pressure inside the pipe Ball valve A special hot tapping drill is then bolted to the open end of the ball valve This drill uses a high pressure seal to contain fluid pressure inside the drill chamber as a motor spins the drill bit The ball valve is opened then the drill bit is advanced toward the pipe wall where it cuts a hole into the pipe Flu
457. nd instruments Feed in 3 15 PSI control Signal Steam Reactor 4 20 mA control signal AS Fieldbus digital measurement signal Condensate Product out The purpose of this control system is to ensure the chemical solution inside the reactor vessel is maintained at a constant temperature A steam heated jacket envelops the reactor vessel transferring heat from the steam into the chemical solution inside The control system maintains a constant temperature by measuring the temperature of the reactor vessel and throttling steam from a boiler to the steam jacket to add more or less heat as needed We begin as usual with the temperature transmitter located near the bottom of the vessel Note the different line type used to connect the temperature transmitter TT with the temperature indicating controller TIC solid dots with lines in between This signifies a digital electronic instrument signal sometimes referred to as a fieldbus rather than an analog type such as 4 to 20 mA or 3 to 15 PSI The transmitter in this system is actually a computer and so is the controller The transmitter reports the process variable reactor temperature to the controller using digital bits of information Here there is no analog scale of 4 to 20 milliamps but rather electric voltage current pulses representing the 0 and 1 states of binary data Digital instrument signals are not only capable of tr
458. nd move the control valve just a little bit more so that the PV once again reaches SP then place the controller back into automatic mode In essence this technique adjusts the Bias term of the controller equation The disadvantage of this technique is rather obvious it requires frequent human intervention What s the point of having an automation system that needs periodic human intervention to maintain setpoint A more sophisticated method for eliminating proportional only offset is to add a different control action to the controller one that takes action based on the amount of error between PV and SP and the amount of time that error has existed We call this control mode integral or reset This will be the subject of the next section 18 5 INTEGRAL RESET CONTROL 611 18 5 Integral reset control Integration is a calculus principle but don t let the word calculus scare you You are probably already familiar with the concept of numerical integration even though you may have never heard of the term before Calculus is a form of mathematics that deals with changing variables and how rates of change relate between different variables When we integrate a variable with respect to time what we are doing is accumulating that variable s value as time progresses Perhaps the simplest example of this is a vehicle odometer which accumulates the total distance traveled by the vehicle over a certain time period This stands in con
459. ne or more of the tubes so that distance read along the tube length is a fractional proportion of distance measured along the vertical Inclined manometer 1 8 FLUID MECHANICS Al This way a greater motion of liquid is required to generate the same hydrostatic pressure vertical liquid displacement than in an upright manometer making the inclined manometer more sensitive If even more sensitivity is desired we may build something called a micromanometer consisting of a gas bubble trapped in a clear horizontal tube between two large vertical manometer chambers A simple micromanometer air bubble OOOO Scale Pressure applied to the top of either vertical chamber will cause the vertical liquid columns to shift just the same as any U tube manometer However the bubble trapped in the clear horizontal tube will move much further than the vertical displacement of either liquid column owing to the huge difference in cross sectional area between the vertical chambers and the horizontal tube This amplification of motion makes the micromanometer exceptionally sensitive to small pressures A common form of manometer seen in calibration laboratories is the well type consisting of a single vertical tube and a relatively large reservoir called the well acting as the second column Well manometer Applied pressure Scale Well Due to the well s much larger cross sectional area liquid motion inside of it is neg
460. ne who has ever boiled a pot of water for cooking knows how this process works Making steam continuously however is a little more complicated The fundamental variable to measure and control in a continuous boiler is the level of water in the steam drum the upper vessel in a water tube boiler In order to safely and efficiently produce a continuous flow of steam we must ensure the steam drum never runs too low on water or too high If there is not enough water in the drum the water tubes may run dry and burn through from the heat of the fire If there is too much water in the drum liquid water may be carried along with the flow of steam causing problems downstream In this next illustration you can see the essential elements of a water level control system showing transmitter controller and control valve 5 1 EXAMPLE BOILER WATER LEVEL CONTROL SYSTEM 133 Exhaust stack Steam drum water level control system for an industrial boiler A S Steam Level transmitter Steam drum Riser tubes 3 15 PSI Level a Indicating Downcomer Controller tubes Air operated control valve 3 15 PSI control signal Feedwater lt The first instrument in this control system is the level transmitter or LT The purpose of this device is to sense the water level in the steam drum and report that measurement to the controller in the form of an instrument signal In this case the type of si
461. ng from an external source Here the negative sign represents the spring s reaction force to being displaced the restoring force A spring s reaction force always opposes the direction of displacement compress a spring and it pushes back on you stretch a spring and it pulls back A negative sign is the mathematically symbolic way of expressing the opposing direction of a vector 26 CHAPTER 1 PHYSICS x Displacement of spring in meters metric or feet English Eo The constant of integration representing the amount of energy initially stored in the spring prior to our displacement of it For example if we take a very large spring with a constant k equal to 60 pounds per foot and displace it by 4 feet we will store 480 foot pounds of potential energy in that spring i e we will do 480 foot pounds of work on the spring Graphing the force displacement function on a graph yields a straight line as we would expect because Hooke s Law is a linear function The area accumulated underneath this line from 0 feet to 4 feet represents the integration of that function over the interval of 0 to 4 feet and thus the amount of potential energy stored in the spring 400 300 Force E pounds 2 nan F Displacement x feet Note how the geometric interpretation of the shaded area on the graph exactly equals the result predicted by the equation E ikr the area of a triangle is one half times the base times the heig
462. ng turbine blades the output frequency of a vortex flowmeter is linearly proportional to volumetric flow rate The pressure sensors used in vortex flowmeters are not standard differential pressure transmitters since the vortex frequency is too high to be successfully detected by such bulky instruments Instead the sensors are typically piezoelectric crystals These pressure sensors need not be calibrated since the amplitude of the pressure waves detected is irrelevant Only the frequency of the waves matter for measuring flow rate and so nearly any pressure sensor with a fast enough response time will suffice 15 4 VELOCITY BASED FLOWMETERS 503 Like turbine meters the relationship between sensor frequency f and volumetric flow rate Q may be expressed as a proportionality with the letter k used to represent the constant of proportionality for any particular flowmeter f kQ Where f Frequency of output signal Hz Q Volumetric flow rate e g gallons per second k K factor of the vortex shedding flowtube e g pulses per gallon This means that vortex flowmeters like electronic turbine meters each have a particular K factor relating the number of pulses generated per unit volume passed through the meter Counting the total number of pulses over a certain time span yields total fluid volume passed through the meter over that same time span making the vortex flowmeter readily adaptable for totalizing fluid vol
463. nning speed A detector placed at the outlet of the capillary tube configured to detect any chemical different from the solvent will indicate the different components exiting the tube at different times If the running speed of each chemical component is known from prior tests this device may be used to identify the composition of the original chemical mix and even how much of each component was present in the injected sample This is the essence of chromatography the technique of chemical separation by time delayed travel down the length of a stationary medium called a column In chromatography the chemical solution traveling down the column is called the mobile phase while the solid and or liquid substance residing within the column is called the stationary phase Chromatography was first applied to chemical analysis by a Russian botanist named Tswett who was interested in separating mixtures of plant pigments The colorful bands left behind in the stationary phase by the separated pigments gave rise to the name chromatography which literally means color writing Modern chemists often apply chromatographic techniques in the laboratory to purify chemical samples and or to measure the concentrations of different chemical substances within mixtures Some of these techniques are manual such as in the case of thin layer chromatography where liquid solvents carry liquid chemical components along a flat plate covered with an inert
464. nozzle gap remains constant in order to more easily determine the output pressure response to an input pressure If we simply assume the baffle nozzle gap cannot change with negative feedback in effect we may conclude that the output pressure is exactly equal to the input pressure for the pneumatic system shown since that is what must happen in order for the two pressures to generate exactly opposing forces so that the baffle will not move from its original position The analytical technique of assuming perfect balance in a negative feedback system works just as well for more complicated systems Consider the following opamp circuit 9 4 ANALOGY TO OPAMP CIRCUITS 233 Vout Here negative feedback occurs through a voltage divider from the output terminal to the inverting input terminal so that only one half of the output voltage gets fed back degeneratively If we follow our simplifying assumption that perfect balance zero difference of voltage will be achieved between the two opamp input terminals due to the balancing action of negative feedback we are led to the conclusion that Vout must be exactly twice the magnitude of Vin In other words the output voltage must increase to twice the value of the input voltage in order for the divided feedback signal to exactly equal the input signal Thus feeding back half the output voltage yields an overall voltage gain of two If we make the same analogous change to the pneumatic system
465. nt and use a controller to automatically adjust the chlorine control valve to inject the right amount of chlorine at all times The following P amp ID Process and Instrument Diagram shows how such a control system might look Analytical Chlorine supply indicating 4 20 mA controller control Signal Motor operated 9 P7777 TTT TTT TTT SP control valve j 4 20 MA SSeS measurement 1 signal Analytical transmitter Influent ae Effluent Mixer Chlorine gas coming through the control valve mixes with the incoming water influent then has time to disinfect in the contact chamber before exiting out to the environment The transmitter is labeled AT Analytical Transmitter because its function is to analyze the concentration of chlorine dissolved in the water and transmit this information to the control system The Cl written near the transmitter bubble declares this to be a chlorine analyzer The dashed line coming out of the transmitter tells us the signal is electronic in nature not pneumatic as was the case in the previous boiler control system example The most common and likely standard for electronic signaling in industry is 4 to 20 milliamps DC which represents chlorine concentration in much the same way as the 3 to 15 PSI pneumatic signal standard represented steam drum water level in the previous system Transmitter signal current Chlorine concentration 4mA 0 no chlorin
466. nt to recognize here is that both the process variable sensed by the transmitter and the position of the control valve are proportionately represented by an analog signal The letter M inside the control valve bubble tells us this is a motor actuated valve Instead of using compressed air pushing against a spring loaded diaphragm as was the case in the boiler control system this valve is actuated by an electric motor turning a gear reduction mechanism The gear reduction mechanism allows slow motion of the control valve stem even though the motor spins at a fast rate A special electronic control circuit inside the valve actuator modulates electric power to the electric motor in order to ensure the valve position accurately matches the signal sent by the controller In effect this is another control system in itself controlling valve position according to a setpoint signal sent by another device in this case the AIT controller which is telling the valve what position to go to 5 3 EXAMPLE CHEMICAL REACTOR TEMPERATURE CONTROL 139 5 3 Example chemical reactor temperature control Sometimes we see a mix of instrument signal standards in one control system Such is the case for this particular chemical reactor temperature control system where three different signal standards are used to convey information between the instruments A P amp ID Process and Instrument Diagram shows the inter relationships of the process piping vessels a
467. ntage value and translate it into a milliamp value using the formula previously shown 0 583 58 3 x 16 mA 007 4 mA current 16 mA 38o 4 mA 13 3 mA 100 Ka Therefore the transmitter should output a PV signal of 13 3 mA at a flow rate of 204 GPM 8 2 3 Example calculation temperature transmitter A pneumatic temperature transmitter is ranged 50 to 140 degrees Fahrenheit and has a 3 15 PSI output signal Calculate the pneumatic output pressure if the temperature is 79 degrees Fahrenheit First we convert the temperature value of 79 degrees into a percentage of range based on the knowledge of the temperature range span 140 degrees 50 degrees 90 degrees and lower range value LRV 50 degrees We may do so by manipulating the general formula for any linear measurement to solve for x measured variable Span LRV x 100 measured variable LRV Span 007 0 measured variable LRV lt Span 100 m variable LRV g Span ERA 192 CHAPTER 8 ANALOG ELECTRONIC INSTRUMENTATION 79 F 50 F 1 x 00 F 00 x 32 2 Next we take this percentage value and translate it into a pneumatic pressure value using the formula previously shown x 12 PSI soon 3 PSI pressure 32 2 12 PSI PSI 6 87 PSI s Fa 6 SI 6 87 PS Therefore the transmitter should output a PV signal of 6 87 PSI at a temperature of 79 F 8
468. ntercept form of linear equation y mz b it is more than coincidence Often the response of a proportional controller is shown graphically as a line the slope of the line representing gain and the y intercept of the line representing the output bias point or what value the output signal will be when there is zero error PV precisely equals SP 18 3 PROPORTIONAL ONLY CONTROL 605 100 90 80 70 60 50 40 30 20 10 0 10 20 30 40 50 60 70 80 90 100 Error SP PV In this graph the bias value is 50 and the gain of the controller is 1 Proportional controllers give us a choice as to how sensitive we want the controller to be to changes in process variable PV and setpoint SP With the simple on off bang bang approach there was no adjustment Here though we get to program the controller for any desired level of aggressiveness If the controller could be configured for infinite gain its response would duplicate on off control That is any amount of error will result in the output signal becoming saturated at either 0 or 100 and the final control element will simply turn on fully when the process variable drops below setpoint and turn off fully when the process variable rises above setpoint Conversely if the controller is set for zero gain it will become completely unresponsive to changes in either process variable or setpoint the valve will hold its position at the bias point no matt
469. nturi tube points 1 and 3 are the greatest This is a counter intuitive result but it has a firm grounding in the physics of mass and energy conservation If we assume no energy is added by a pump or lost due to friction as fluid travels through this pipe then the Law of Energy Conservation describes a situation where the fluid s energy must remain constant at all points in the pipe as it travels through If we assume no fluid joins this flowstream from another pipe or is lost from this pipe through any leaks then the Law of Mass Conservation describes a situation where the fluid s mass flow rate must remain constant at all points in the pipe as it travels through So long as fluid density remains fairly constant fluid velocity must increase as the cross sectional area of the pipe decreases as described by the Law of Continuity see section 1 8 10 on page 53 for more details on this concept Av Agve 3This is a very sound assumption for liquids and a fair assumption for gases when pressure changes through the venturi tube are modest 450 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT Rearranging variables in this equation to place velocities in terms of areas we get the following result v2 Aj U1 7 Az This equation tells us that the ratio of fluid velocity between the narrow throat point 2 and the wide mouth point 1 of the pipe is the same ratio as the mouth s area to the throat s area So if the mouth of th
470. number XQ9211 American Gas Association and American Petroleum Institute Washington D C Third Edition October 1992 Second Printing August 1995 Third Printing June 2003 Chow Ven Te Open Channel Hydraulics McGraw Hill Book Company Inc New York NY 1959 Flow Measurement User Manual Form Number A6043 Part Number D301224X012 Emerson Process Management 2005 Fribance Austin E Industrial Instrumentation Fundamentals McGraw Hill Book Company New York NY 1962 General Specifications EJX910A Multivariable Transmitter Document GS 01C25R01 01E 5th edition Yokogawa Electric Corporation Tokyo Japan 2005 Giancoli Douglas C Physics for Scientists amp Engineers Third Edition Prentice Hall Upper Saddle River New Jersey 2000 Hofmann Friedrich Fundamentals of Ultrasonic Flow Measurement for industrial applications Krohne Messtechnik GmbH amp Co KG Duisburg Germany 2000 Hofmann Friedrich Fundamental Principles of Electromagnetic Flow Measurement 3rd Edition Krohne Messtechnik GmbH amp Co KG Duisburg Germany 2003 Kallen Howard P Handbook of Instrumentation and Controls McGraw Hill Book Company Inc New York NY 1961 Keisler H Jerome Elementary Calculus An Infinitesimal Approach Second Edition University of Wisconsin 2000 15 11 PROCESS INSTRUMENT SUITABILITY 539 Lipt k B la G Instrument Engineers Handbook Process Measurement and Analysis Volume I
471. o 40 feet but the transmitter is located 30 feet below the tank 364 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT 100 Measurement span 40 ft 0 This means the transmitter s impulse line contains a 30 foot elevation head of ethanol so that the transmitter sees 30 feet of ethanol when the tank is empty and 70 feet of ethanol when the tank is full A 3 point calibration table for this instrument would look like this assuming a 4 to 20 mA DC output signal range Ethanol level Percent of Pressure Pressure Output in tank range inches of water PSI mA O ft 0 284 W C 10 3 PSI 4 mA 20 ft 50 474 W C 17 1 PSI 12 mA 40 ft 100 663 W C 24 0 PSI 20 mA Another common scenario is where the transmitter is mounted at or near the vessel s bottom but the desired level measurement range does not extend to the vessel bottom 13 3 HYDROSTATIC PRESSURE 365 100 F Measurement span 5 ft 0 4 ft Y In this example the transmitter is mounted exactly at the same level as the vessel bottom but the level measurement range goes from 4 feet to 9 feet a 5 foot span At the level of castor oil deemed 0 the transmitter sees a hydrostatic pressure of 1 68 PSI 46 5 inches of water column and at the 100 castor oil level the transmitter sees a pressure of 3 78 PSI 105 inches water column Thus these two pressure values would define the transmitter s lower and upper
472. o forms of the hydrostatic pressure formula pgh yh pg gt I fe g Armed with the mass density of the liquid inside the tank the computer may now calculate total liquid mass stored inside the tank m pV Dimensional analysis shows how units of mass density and volume cancel to yield only units of mass in this last equation ts E fe Here we see a vivid example of how several measurements may be inferred from just a few actual process in this case pressure measurements Three pressure measurements on this tank allow us to compute four inferred variables liquid density liquid height liquid volume and liquid mass The accurate measurement of liquids in storage tanks is not just useful for process operations but also for conducting business affairs Whether the liquid represents raw material purchased from a supplier or a processed product ready to be pumped out to a customer both parties have a vested interest in knowing the exact quantity of liquid bought or sold Measurement applications such as The details of this math depend entirely on the shape of the tank For vertical cylinders the most common shape for vented storage tanks volume and height are related by the simple formula V ar h where r is the radius of the tank s circular base Other tank shapes and orientations may require much more sophisticated formulae to calculate stored volume from height See section 17 2 beginning on page 583
473. o the positive side of the battery as such Direction of electron flow Unfortunately scientists and engineers had grown accustomed to Franklin s false hypothesis long before the true nature of electric current in metallic conductors was discovered Their preferred notation was to show electric current flowing from the positive pole of a source through the load returning to the negative pole of the source Direction of conventional flow This relationship between voltage polarity marks and conventional flow current makes more intuitive sense than electron flow notation because it is reminiscent of fluid pressure and flow direction 3 2 ELECTRICAL CURRENT 83 Conventional flow current notation Light Voltage bulb source Conventional flow current notation l TE Fluid motion lo DK Fluid motion n If we take the sign to represent more pressure and the sign to represent less pressure it makes perfect sense that fluid should move from the high pressure discharge port of the pump through the hydraulic circuit and back to the low pressure suction port of the pump It also makes perfect sense that the upstream side of the valve a fluid restriction will have a greater pressure than the downstream side of the valve In other words conventional flow notation best honors Mr Franklin s original intent of modeling current as though it were a fluid even though he was later proven to be mista
474. ode so it will not cause an upset in the process by moving the final control element in response to the sudden loss of PV signal Also process alarms should be temporarily disabled so that they do not cause panic If this current signal also drives process shutdown alarms these should be temporarily disabled so that nothing shuts down upon interruption of the signal If the current signal to be interrupted is a command signal from a controller to a final control element the final control element either needs to be manually overridden so as to hold a fixed setting while the signal varies or it needs to be bypasses completely by some other device s If the final control element is a control valve this typically takes the form of opening a bypass valve and closing at least one block valve Control valve Block valve Block valve Bypass valve 8 6 TROUBLESHOOTING CURRENT LOOPS 203 Since the manually operated bypass valve now performs the job that the automatic control valve used to a human operator must remain posted at the bypass valve to carefully throttle it and maintain control of the process From this we see that the seemingly simple task of connecting a milliammeter in series with a 4 20 mA current signal harbors certain risks and can be labor intensive Better ways must exist no One better way to measure a 4 20 mA signal without interrupting it is to do so magnetically using a clamp on milliammeter Modern Hall effect sen
475. oding of the flowtube no gas pockets The flowtube is usually installed with electrodes across from each other horizontally never vertically so that even a momentary gas bubble will not break electrical contact between an electrode tip and the liquid flowstream Electrical conductivity of the process liquid must meet a certain minimum value but that is all It is surprising to some technicians that changes in liquid conductivity have little to no effect on flow measurement accuracy It is not as though a doubling of liquid conductivity will result in a doubling of induced voltage Motional EMF is strictly a function of physical dimensions magnetic field strength and fluid velocity Liquids with poor conductivity simply present a greater electrical resistance in the voltage measuring circuit but this is of little consequence because the input impedance of the detection circuitry is phenomenally high Common fluid types that will 24The colloquial term in the United States for this sort of thing is fudge factor 508 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT not work with magnetic flowmeters include deionized water e g steam boiler feedwater ultrapure water for pharmaceutical and semiconductor manufacturing and oils Proper grounding of the flowtube is very important for magnetic flowmeters The motional EMF generated by most liquid flowstreams is very weak 1 millivolt or less and therefore may be easily overshadowed by noise volta
476. of 25 V and a total resistance of 3500 Q Taking 25 volts and dividing by 3500 ohms you should arrive at a result of 0 007143 amperes or 7 143 milliamperes 7 143 mA One of the most challenging aspect of Ohm s Law is remembering to keep all variables in contect This is a common problem for many students when studying physics as well none of the equations learned in a physics class will yield the correct results unless all the variables relate to the same object or situation For instance it would make no sense to try to calculate the kinetic energy of a moving object E mv by taking the mass of one object m and multiplying it by the square of the velocity of some other object v2 Likewise with Ohm s Law we must make sure the voltage current and resistance values we are using all relate to the same portion of the same circuit If the circuit in question has only one source of voltage one resistance and one path for current there cannot be any mix ups Expressing the previous example in a schematic diagram 3Except in the noteworthy case of superconductivity a phenomenon occurring at extremely low temperatures 4Except in the noteworthy case of superfluidity another phenomenon occurring at extremely low temperatures 88 CHAPTER 3 DC ELECTRICITY Current 7 143 mA Resistor 25 V Es Voltage 3500 Q source 5 7 143 mA Current Note arrows point in the direction of electron motion However if we look at
477. of pressure where the mechanism changes direction of motion due to mechanism friction and deadband errors due to backlash looseness in mechanical connections You are likely to encounter this sort of pressure instrument design in direct reading gauges equipped with electronic transmitting capability An instrument manufacturer will take a proven product line of pressure gauge and add a motion sensing device to it that generates an electric signal proportional to mechanical movement inside the gauge resulting in an inexpensive pressure transmitter that happens to double as a direct reading pressure gauge 312 CHAPTER 12 CONTINUOUS PRESSURE MEASUREMENT 12 4 Force balance pressure transmitters An important legacy technology for all kinds of continuous measurement is the self balancing system A self balance system continuously balances an adjustable quantity against a sensed quantity the adjustable quantity becoming an indication of the sensed quantity once balance is achieved A common manual balance system is the type of scale used in laboratories to measure mass Known masses Unknown mass Here the unknown mass is the sensed quantity and the known masses are the adjustable quantity A human lab technician applies as many masses to the left hand side of the scale as needed to achieve balance then counts up the sum total of those masses to determine the quantity of the unknown mass Such a system is perfectly linear which is
478. of range Pressure at transmitter Transmitter output 4 5 ft 0 16 2 W C 4 mA 5 25 ft 25 13 32 W C 8 mA 6 ft 50 10 44 W C 12 mA 6 75 ft 75 7 56 W C 16 mA 7 5 ft 100 4 68 W C 20 mA When the time comes to bench calibrate this instrument in the shop the easiest way to do so will be to set the two remote diaphragms on the workbench at the same level then apply 16 2 to 4 68 inches of water column pressure to the low remote seal diaphragm with the other diaphragm at atmospheric pressure to simulate the desired range of negative differential pressures11 The more mathematically inclined reader will notice that the span of this instrument URV LRV is equal to the span of the interface level 3 feet or 36 inches multiplied by the difference in specific gravities 1 1 0 78 Span in W C 36 inches 1 1 0 78 11Remember that a differential pressure instrument cannot tell the difference between a positive pressure applied to the low side an equal vacuum applied to the high side or an equivalent difference of two positive pressures with the low side s pressure exceeding the high side s pressure Simulating the exact process pressures experienced in the field to a transmitter on a workbench would be exceedingly complicated so we cheat by simplifying the calibration setup and applying the equivalent difference of pressure only to the low side 13 3 HYDROSTAT
479. of the line in units of mA over the total span in mA 8 2 RELATING 4 TO 20 MA SIGNALS TO INSTRUMENT VARIABLES 195 17PSI mA 30 PSI 40 mA Solving for the unknown current by cross multiplication and division yields a value of 22 67 mA Of course this value of 22 67 mA only tells us the length of the line segment on the number line it does not directly tell us the current signal value To find that we must add the live zero offset of 10 mA for a final result of 32 67 mA 12 PSI 5 PSI 25 PSI 10 PS 17 5 PSI 25 PSI ps fem 10 mA 20 mA 30 40 mA 50 mA 32 67 mA Thus an applied pressure of 12 PSI to this transmitter should result in a 32 67 mA output signal 196 CHAPTER 8 ANALOG ELECTRONIC INSTRUMENTATION 8 3 Controller output current loops The simplest form of 4 20 mA current loop is the type used to represent the output of a process controller sending a command signal to a final control element Here the controller both supplies the electrical power and regulates the DC current to the final control element which acts as an electrical load To illustrate consider the example of a controller sending a 4 20 mA signal to an I P current to pressure signal converter which then pneumatically drives a control valve Controller Control valve 20 PSI instrument air supply air tubing air tubing VN il 2 wire cable AI UY Transducer Current to Pressure converter
480. of two identical metals which does not generate a temperature dependent voltage at all The presence of this second voltage generating junction J2 helps explain why the voltmeter registers 0 volts when the entire system is at room temperature any voltage generated by the iron copper junctions will be equal in magnitude and opposite in polarity resulting in a net series total voltage of zero It is only when the two junctions J and Jz are at different temperatures that the voltmeter registers any voltage at all 428 CHAPTER 14 CONTINUOUS TEMPERATURE MEASUREMENT Thus thermocouple systems are fundamentally differential temperature sensors That is they provide an electrical output proportional to the difference in temperature between two different points For this reason the wire junction we use to measure the temperature of interest is called the measurement junction while the other junction which we cannot get rid of is called the reference junction Multiple techniques exist to deal with the influence of the reference junction s temperature One technique is to physically fix the temperature of that junction at some constant value so it is always stable This way any changes in measured voltage must be due to changes in temperature at the measurement junction since the reference junction has been rendered incapable of changing temperature This may be accomplished by immersing the reference junction in a bath of ice and water Jun
481. ograph extending from 0 to 1 5 inches on the scale reading left to right 294 CHAPTER 12 CONTINUOUS PRESSURE MEASUREMENT Note that venting one side of a manometer is standard practice when using is as a gauge pressure indicator responding to pressure in excess of atmospheric Both pressure ports will be used if the manometer is applied to the measurement of differential pressure just as in the case of the U tube manometer first shown in this section Absolute pressure may also be measured by a manometer if one of the pressure ports connects to a sealed vacuum chamber This is how a mercury barometer is constructed for the measurement of absolute ambient air pressure by sealing off one side of a manometer and removing all the air in that side so that the applied atmospheric pressure is always compared against a vacuum Manometers incorporating a well have the advantage of single point reading one need only compare the height of one liquid column not the difference in height between two liquid columns The cross sectional area of the liquid column in the well is so much greater than that within the transparent manometer tube that the change in height within the well is usually negligible In cases where the difference is significant the spacing between divisions on the manometer scale may be skewed to compensate Inclined manometers enjoy the advantage of increased sensitivity Since manometers fundamentally operate on the princip
482. oil Secondary coil voltage therefore is directly proportional to liquid conductivity The equivalent electrical circuit for a toroidal conductivity probe looks like a pair of transformers with the liquid acting as a resistive path for current to connect the two transformers together wire i wire liquid AC voltage AC source voltmeter liquid wire wire Toroidal conductivity cells are whenever possible due to their ruggedness and virtual immunity to fouling However they are not sensitive enough for conductivity measurement in high purity applications such as boiler feedwater treatment and ultra pure water treatment necessary for pharmaceutical and semiconductor manufacturing As always the manufacturer s specifications are the best source of information for conductivity cell applicability in any particular process The following photograph shows a toroidal conductivity probe along with a conductivity transmitter to both display the conductivity measurement in millisiemens per centimeter and also transmit the measurement as a 4 20 mA analog signal TNote that this is opposite the behavior of a direct contact conductivity cell which produces less voltage as the liquid becomes more conductive 548 CHAPTER 16 CONTINUOUS ANALYTICAL MEASUREMENT 16 4 PH MEASUREMENT 549 16 4 pH measurement pH is the measurement of the hydrogen ion activity in a liquid solution It is one of the most common forms of analytical measurement in
483. ol Academic Press New York NY 1978 Shinskey Francis G Process Control Systems Application Design Adjustment Second Edition McGraw Hill Book Company New York NY 1979 St Clair David W Controller Tuning and Control Loop Performance a primer Straight Line Control Company Newark DE 1989 620 CHAPTER 18 CONTINUOUS FEEDBACK CONTROL Appendix A Doctor Strangefiow or how I learned to relax and love Reynolds numbers Of all the non analytical non chemistry process measurements students encounter in their Instrumentation training flow measurement is one of the most mysterious Where else would we have to take the square root of a transmitter signal just to measure a process variable in the simplest case Since flow measurement is so vital to many industries it cannot go untouched in an Instrumentation curriculum Students must learn how to measure flow and how to do it accurately The fact that it is a fundamentally complex thing however often leads to oversimplification in the classroom Such was definitely the case in my own education and it lead to a number of misunderstandings that were corrected after a lapse of 15 years in a sudden Aha moment that I now wish to share with you The orifice plate is to flow measurement what a thermocouple is to temperature measurement an inexpensive yet effective primary sensing element The concept is disarmingly simple Place a restriction in a pipe then measure th
484. oles and solution concentration see section 2 3 beginning on page 63 286 CHAPTER 11 INSTRUMENT CALIBRATION After preparing the buffer solution in a cup the pH probe is inserted into the buffer solution and given time to stabilize One stabilized the pH instrument may be adjusted to register the proper pH value Buffer solutions should not be exposed to ambient air for any longer than necessary especially alkaline buffers such as 10 0 pH due to contamination Pre mixed liquid buffer storage containers should be capped immediately after pouring into working cups Used buffer solution should be discarded rather than re used at a later date Analyzers designed to measure the concentration of certain gases in air must be calibrated in a similar manner Oxygen analyzers for example used to measure the concentration of free oxygen in the exhaust gases of furnaces engines and other combustion processes must be calibrated against known standards of oxygen concentration An oxygen analyzer designed to measure oxygen concentration over a range of ambient 20 9 oxygen to 0 oxygen may be calibrated with ambient air as one of the standard values and a sample of pure nitrogen gas containing 0 oxygen as the 3Carbon dioxide gas in ambient air will cause carbonic acid to form in an aqueous solution This has an especially rapid effect on high pH alkaline buffers 4It is assumed that the concentration of oxygen in ambient air is a stable
485. oltage and current phasors do In electric circuit theory there is a special name we give to such a quantity being a ratio of voltage to current but possessing a complex value We call this quantity impedance rather than resistance and we symbolize it using the letter Z When we do this we arrive at a new form of Ohm s Law for AC circuits V V Z V IZ l 3 I Z With all quantities expressed in the form of phasors we may apply nearly all the rules of DC circuits Ohm s Law Kirchhoff s Laws etc to AC circuits What was old is new again References Boylestad Robert L Introductory Circuit Analysis 9th Edition Prentice Hall Upper Saddle River New Jersey 2000 Steinmetz Charles P Theory and Calculation of Alternating Current Phenomena Third Edition McGraw Publishing Company New York NY 1900 128 CHAPTER 4 AC ELECTRICITY Chapter 5 Introduction to Industrial Instrumentation Instrumentation is the science of automated measurement and control Applications of this science abound in modern research industry and everyday living From automobile engine control systems to home thermostats to aircraft autopilots to the manufacture of pharmaceutical drugs automation surrounds us This chapter explains some of the fundamental principles of industrial instrumentation The first step naturally is measurement If we can t measure something it is really pointless to try to control it This something usually
486. oltmeter and not register accurately Fortunately modern operational amplifier circuits with field effect transistor input stages are sufficient for this task Equivalent electrical circuit of a pH probe and instrument pH probe assembly R Cable pH instrument glass The voltage sensed by the pH instrument very nearly equals V because Rass Ref lt lt R nput Even if we use a high input impedance pH instrument to sense the voltage output by the pH probe assembly we may still encounter a problem created by the impedance of the glass electrode an RC time constant created by the parasitic capacitance of the probe cable connecting the electrodes to the sensing instrument The longer this cable is the worse the problem becomes due to increased capacitance 1 Glass is a very good insulator of electricity With a thin layer of glass being an essential part of the sensor circuit the typical impedance of that circuit will lie in the range of hundreds of mega ohms 12Operational amplifier circuits with field effect transistor inputs may easily achieve input impedances in the tera ohm range 1 x 1012 Q 558 CHAPTER 16 CONTINUOUS ANALYTICAL MEASUREMENT pH probe assembly R Cable pH instrument glass This time constant value may be significant if the cable is long and or the probe resistance is abnormally large Assuming a combined measurement and reference electrode resistance of 700 MO and a 30 foot length of RG 58
487. olumn A typical gas chromatograph column appears in the next photograph It is nothing more than a stainless steel tube packed with an inert porous filling material 568 CHAPTER 16 CONTINUOUS ANALYTICAL MEASUREMENT This particular GC column is 28 feet long with an outside diameter of only 1 8 inch the tube s inside diameter is even less than that Column geometry and packing material vary greatly with application The many choices intrinsic to column design are best left to specialists in the field of chromatography not the average technician or even the average process engineer Arguably the most important component of a process gas chromatograph is the sample valve Its purpose is to inject the exact same sample quantity into the column at the beginning of each cycle A common form of sample valve uses a rotating element to switch port connections between the sample gas stream carrier gas stream and column 16 5 CHROMATOGRAPHY Position 1 Fluid path LI Position 2 569 Three slots connect three pairs of ports together When the rotary valve actuates the port connections switch redirecting gas flows Connected to a sample stream carrier stream and column the rotary sample valve operates in two different modes The first mode is a loading position where the sample stream flows through a short length of tubing called a sample loop and exits to a waste discharge port while the carrier gas flows thr
488. ome point on the mountain as having a specific altitude unless we assume a point of reference to measure from If we say the mountain summit is 9 200 feet high we usually mean 9 200 feet higher than sea level with the level of the sea being our common reference point However our hiking adventure 96 CHAPTER 3 DC ELECTRICITY where we climbed 8 500 feet in two days did not imply that we climbed to an absolute altitude of 8 500 feet above sea level Since I never specified the sea level altitude at the base of the mountain it is impossible to calculate our absolute altitude at the end of day 2 All you can tell from the data given is that we climbed 8 500 feet above the mountain base wherever that happens to be with reference to sea level So it is with electrical voltage as well most circuits have a point labeled as ground where all other voltages are referenced In DC powered circuits this ground point is often the negative pole of the DC power source Voltage is fundamentally a quantity relative between two points a measure of how much potential has increased or decreased moving from one point to another Kirchhoff s Current Law is a much easier concept to grasp This law states that the algebraic sum of all currents at a junction point called a node is equal to zero Another way to state this law is to say that for every electron entering a node one must exit somewhere An analogy for visualizing Kirchhoff s Current Law is water f
489. on and cylinder mechanism used to precisely measure a quantity of liquid over time Process flow is diverted through the prover moving the piston over time Sensors on the prover mechanism detect when the piston has reached certain positions and time measurements taken at those different positions enable the calculation of average flow ay 11 8 PRACTICAL CALIBRATION STANDARDS 285 11 8 5 Analytical standards An analyzer measures intrinsic properties of a substance sample such as its density chemical content or purity Whereas the other types of instruments discussed in this chapter measure quantities incidental to the composition of a substance pressure level temperature and flow rate an analyzer measures something related to the nature of substance being processed As previously defined to calibrate an instrument means to check and adjust if necessary its response so that the output accurately corresponds to its input throughout a specified range In order to do this one must expose the instrument to an actual input stimulus of precisely known quantity This is no different for an analytical instrument In order to calibrate an analyzer we must exposed it to known quantities of substances with the desired range of properties density chemical composition etc A classic example of this is the calibration of a pH analyzer pH is the measurement of hydrogen ion activity in an aqueous solution The standard range of measurement i
490. on factor C Discharge coefficient accounts for energy losses Reynolds number corrections pressure tap locations etc A Cross sectional area of mouth A gt Cross sectional area of throat Zs Compressibility factor of gas under standard conditions Zf1 Compressibility factor of gas under flowing conditions upstream Gy Specific gravity of gas T Absolute temperature of gas Upstream pressure absolute P Downstream pressure absolute This equation implies the continuous measurement of gas pressure P and temperature T inside the pipe in addition to the differential pressure produced by the orifice plate P Pa These measurements may be taken by three separate devices their signals routed to a gas flow computer 480 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT Flow signal to a Yancscdaao flow indicator Computer i flow controller etc Orifice plate Note the location of the RTD thermowell positioned downstream of the orifice plate so that the turbulence it generates will have negligible impact on the fluid dynamics at the orifice plate The American Gas Association AGA allows for upstream placement of the thermowell but only if located at least three feet upstream of a flow conditioner This photograph shows an AGA3 compliant installation of several orifice plates to measure the flow of natural gas 12Specified in Part 2 of the AGA Report 3 section 2 6 5 page 22 15 1 P
491. onal to each other 15 4 VELOCITY BASED FLOWMETERS 507 pz BdQ 4 1 xd 4BQ ES Td If we wish to have a formula defining flow rate Q in terms of motional EMF we may simply manipulate the last equation to solve for Q rdE Q 4B This formula will successfully predict flow rate only for absolutely perfect circumstances In order to compensate for inevitable imperfections a proportionality constant k is usually included in the formula TdE ar 3 Note the linearity of this equation Nowhere do we encounter a power root or other non linear mathematical function in the equation for a magnetic flowmeter This means no special characterization is required to calculate volumetric flow rate A few conditions must be met for this formula to successfully infer volumetric flow rate from induced voltage The liquid must be a reasonably good conductor of electricity Both electrodes must contact the liquid e The pipe must be completely filled with liquid e The flowtube must be properly grounded to avoid errors caused by stray electric currents in the liquid The first condition is met by careful consideration of the process liquid prior to installation Magnetic flowmeter manufacturers will specify the minimum conductivity value of the liquid to be measured The second and third conditions are met by correct installation of the magnetic flowtube in the pipe The installation must be done in such a way as to guarantee full flo
492. ond F Force of gravity acting on the weighed belt section e g pounds S Belt speed e g feet per second d Length of weighed belt section e g feet 15 9 CHANGE OF QUANTITY FLOW MEASUREMENT 529 15 9 Change of quantity flow measurement Flow by definition is the passage of material from one location to another over time So far this chapter has explored technologies for measuring flow rate en route from source to destination However a completely different method exists for measuring flow rates measuring how much material has either departed or arrived at the terminal locations over time Mathematically we may express flow as a ratio of quantity to time Whether it is volumetric flow or mass flow we are referring to the concept is the same quantity of material moved per quantity of time We may express average flow rates as ratios of changes Am AV a JSA W Where W Average mass flow rate Q Average volumetric flow rate Am Change in mass AV Change in volume At Change in time Suppose a water storage vessel is equipped with load cells to precisely measure weight which is directly proportional to mass with constant gravity Assuming only one pipe entering or exiting the vessel any flow of water through that pipe will result in the vessel s total weight changing over time Support structure 530 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT If the measured mass of this vessel decreased from 7
493. one sees a strong preference in industry for conventional flow notation 3 2 ELECTRICAL CURRENT 85 e Conventional flow notation makes sense of the descriptive terms sourcing and sinking This last point merits further investigation The terms sourcing and sinking are often used in the study of digital electronics to describe the direction of current in a switching circuit A circuit that sources current to a load is one where the direction of conventional flow points outward from the sourcing circuit to the load device For example here are two schematic diagrams showing two different kinds of electronic proximity switch The first switch sinks current in from the LED through its output terminal through its transistor and down to ground The second switch sources current from the positive supply terminal through its transistor and out to the LED through its output terminal note the direction of the thick arrow near the output screw terminal in each circuit Sinking output Current sinks down to proximity switch ground through the switch Sourcing output Switch sources current proximity switch out to the load device These terms simply make no sense when viewed from the perspective of electron flow notation If you were to actually trace the directions of the electrons you would find that a device sourcing current has electrons flowing nto its connection terminal while a device sinking current s
494. onic 4 to 20 mA flow transmitter or a digital fieldbus temperature transmitter alike Each and every instrument has an input and an output and there is always a predictable and testable correlation from one to the other Another interesting detail seen on this loop diagram is the action of each instrument You will notice a box and arrow pointing either up or down next to each instrument bubble An up arrow T represents a direct acting instrument one whose output signal increases as the input stimulus increases A down arrow represents a reverse acting instrument one whose output signal decreases as the input stimulus increases All the instruments in this loop are direct acting with the exception of the pressure differential transmitter PDT 42 0 200 PSID G3 6 3 LOOP DIAGRAMS 155 Here the down arrow tells us the transmitter will output a full range signal 20 mA when it senses zero differential pressure and a 0 signal 4 mA when sensing a full 200 PSI differential While this calibration may seem confusing and unwarranted it serves a definite purpose in this particular control system Since the transmitter s current signal decreases as pressure increases and the controller must be correspondingly configured a decreasing current signal will be interpreted by the controller as a high differential pressure If any wire connection fails in the 4 20 mA current loop for that transmitter the resulting 0
495. or instance use laminar restrictors as part of the derivative and integral calculation modules the combination of resistance from the restrictor and capacitance from volume chambers forming a sort of pneumatic time constant 7 network 15 This includes elaborate oil bath systems where the laminar flow element is submerged in a temperature controlled oil bath the purpose of which is to hold temperature inside the laminar element constant despite sudden changes in the measured fluid s temperature 15 3 VARIABLE AREA FLOWMETERS 487 15 3 Variable area flowmeters An Variable area flowmeter is one where the fluid must pass through a restriction whose area increases with flow rate The simplest example of a variable area flowmeter is the rotameter which uses a solid object called a plummet or float as a flow indicator suspended in the midst of a tapered tube Pipe Flow gt Clear tapered Scale glass tube Plummet or float Flow mp Stop Pipe As fluid flows upward through the tube a pressure differential develops across the plummet This pressure differential acting on the effective area of the plummet body develops an upward force F 2 If this force exceeds the weight of the plummet the plummet moves up As the plummet moves further up in the tapered tube the area between the plummet and the tube walls through which the fluid must travel grows larger This increased flowing area allows the fluid to make
496. or both systems The simplest expression of negative feedback is a condition of 100 negative feedback where the whole strength of the output signal gets fed back to the amplification system in degenerative fashion For an opamp this simply means connecting the output terminal directly to the inverting input terminal out V We call this negative or degenerative feedback because its effect is counteractive in nature If the output voltage rises too high the effect of feeding this signal to the inverting input will be to bring the output voltage back down again Likewise if the output voltage is too low the inverting input will sense this and act to bring it back up again Self correction typifies the very nature of negative feedback Having connected the inverting input directly to the output of the opamp leaves us with the noninverting terminal as the sole remaining input Thus our input voltage signal is a ground referenced voltage just like the output The voltage gain of this circuit is unity 1 meaning that the output will assume whatever voltage level is present at the input within the limits of the opamp s power supply If we were to send a voltage signal of 5 volts to the noninverting terminal of this opamp circuit it would output 5 volts provided that the power supply exceeds 5 volts in potential from ground Let s analyze exactly why this happens First we will start with the equation representing the o
497. or mass ooa 13 1 3 6 Conversion factors for force o e 13 1 3 7 Conversion factors for area e 13 1 3 8 Conversion factors for pressure either all gauge or all absolute 13 1 3 9 Conversion factors for pressure absolute pressure units only 14 1 3 10 Conversion factors for energy or work 0 e 14 1 3 11 Conversion factors for power e 14 1 3 12 Terrestrial constants 14 1 3 13 Properties of water a s iee a an e E A a a ee 15 1 3 14 Properties of dry air at sea level 0 15 1 3 15 Miscellaneous physical constants sooo 00 ee ee 15 1 3 16 Weight densities of common materials 16 1 4 Dimensional analysis s s os ae ee dea Grae ee a a a e ee 18 1 5 The International System of Units aoaaa e e 19 1 6 Conservation Laws s sosai eiii 222542446 blk Bae e ee Pe ER a a Oe PS 20 Lt SVlassical mechanics ot anata teri Bol BS GOS Ro A Pe he Eee Eg ek 20 1 7 1 Newton s Laws of Motion 0 0 200000 eee ee 21 17 2 Work and Energy oree ee hs A Se e EE Fe a A 22 fa Mechanical springs ro te ae ec A A Ee Re 2 25 1 9 Elid mechanics usario ets Bo ee ie he So oe ee eee oS 27 L851 Press re sh eo geist a OE a Ge id Dado A ae puta 28 1 8 2 Pascal s Principle and hydrostatic pressure o o e 33 1 8 3 Fluid density expressions 38 1 8 4
498. or my grade to just go along with what the teacher said than to press for answers he couldn t give In other words I swept my doubts under the carpet of learning and made a leap of faith After that we studied different types of orifice plates different types of pressure tap locations and other inferential primary sensing elements annubars target meters pipe elbows etc They all worked on Bernoulli s principle of decreased pressure through a restriction and they all required square root extraction of the pressure signal to obtain a linearized flow measurement In fact this became the sole criterion for determining whether or not we needed square root extraction on the signal did the flow measurement originate from a differential pressure instrument If so then we needed to square root the signal If not we didn t A neat and clean distinction separating AP based flow measurements from all the others magnetic vortex shedding Coriolis effect thermal etc Nice clean simple neat and only 95 correct as I was to discover later Fast forward fifteen years I was now a teacher in a technical college teaching Instrumentation to students just like myself a decade and a half ago It was my first time preparing to teach flow measurement and so I brushed up on my knowledge by consulting one of the best technical references I could get my hands on B la Lipt k s Process Measurement and Analysis third edition Part of t
499. or such a valve to throttle However a pulsing pressure causes a small amount of alternating flow in and out of the pressure instrument owing to the expansion and contraction of the mechanical pressure sensing element bellows diaphragm or bourdon tube The needle valve provides a restriction for this flow which when combined with the fluid capacitance of the pressure instrument combine to form a low pass filter of sorts By impeding the flow of fluid in and out of the pressure instrument that instrument is prevented from seeing the high and low peaks of the pulsating pressure Instead the instrument registers a much steadier pressure over time An electrical analogy for a pressure snubber is an RC low pass filter circuit dampening voltage pulsations from reaching a voltmeter 328 CHAPTER 12 CONTINUOUS PRESSURE MEASUREMENT Voltmeter needle vibrates with AC ia pulsations N Pulsing voltage source DC AC no longer Low pass filter Voltmeter needle preterea e pice mpera ninsa vibrates E Pulsing voltage source DC AC One potential problem with the needle valve idea is that the small orifice inside the valve may plug up over time with debris or deposits from dirty process fluid This of course would be bad because if that valve were to ever completely plug the pressure instrument would stop responding to any changes in process pressure at all or perhaps just become too slow in responding to major ch
500. or you need to find a finely adjustable temperature source and use an accurate thermometer to compare your instrument under test against This scenario is analogous to the use of a high accuracy voltmeter and an adjustable voltage source to calibrate a voltage instrument Laboratory grade thermometers are relatively easy to secure Variable temperature sources suitable for calibration use include oil bath and sand bath calibrators These devices are exactly what they sound like small pots filled with either oil or sand containing an electric heating element and a temperature control system using a laboratory grade NIST traceable thermal sensor In the case of sand baths a small amount of compressed air is introduced at the bottom of the vessel to fluidize the sand so that the grains move around much like the molecules of a liquid helping the system reach thermal equilibrium To use a bath type calibrator place the temperature instrument to be calibrated so that the sensing element dips into the bath then wait for the bath to reach the desired temperature An oil bath temperature calibrator is shown in the following photograph with sockets to accept seven temperature probes into the heated oil reservoir lThe Celsius scale used to be called the Centigrade scale which literally means 100 steps I personally prefer Centigrade to Celsius because it actually describes something about the unit of measurement In the same vein
501. orce exactly equals the weight of the submarine and the remaining 46 CHAPTER 1 PHYSICS water stored in the ballast tanks so that the submarine is able to hover in the water with no vertical acceleration or deceleration An interesting application of Archimedes Principle is the quantitative determination of an object s density by submersion in a liquid For instance copper is 8 96 times as dense as water with a mass of 8 96 grams per cubic centimeter 8 96 g cm as opposed to water at 1 00 gram per cubic centimeter 1 00 g cm If we had a sample of pure solid copper exactly 1 cubic centimeter in volume it would have a mass of 8 96 grams Completely submerged in pure water this same sample of solid copper would appear to have a mass of only 7 96 grams because it would experience a buoyant force equivalent to the mass of water it displaces 1 cubic centimeter 1 gram of water Thus we see that the difference between the dry mass mass measured in air and the wet mass mass measured when completely submerged in water is the mass of the water displaced Dividing the sample s dry mass by this mass difference dry wet mass yields the ratio between the sample s mass and the mass of an equivalent volume of water which is the very definition of specific gravity The same calculation yields a quantity for specific gravity if weights instead of masses are used since weight is nothing more than mass multiplied by the acceleration
502. ot possible or practical to ensure complete submersion of the stilling well an alternative technique is to drill holes or cut slots in the well to allow interface levels to equalize inside and outside of the well tube 412 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT Stilling well Slots cut into stilling well tube Such equalization ports are commonly found as a standard design feature on coaxial probes for guided wave radar level transmitters where the outer tube of the coaxial transmission line acts as a sort of stilling well for the fluid Coaxial probes are typically chosen for liquid liquid interface radar measurement applications because they do the best job of preventing dispersion of the radio energy but the stilling well property of a coaxial probe practically necessitates these equalization ports to ensure the interface level within the probe always matches the interface level in the rest of the vessel 13 11 Process instrument suitability 2280 much of the incident power is lost as the radar signal partially reflects off the gas liquid interface then the liquid liquid interface then again through the gas liquid interface on its return trip to the instrument that every care must be taken to ensure optimum received signal strength While twin lead probes have been applied in liquid liquid interface measurement service the coaxial probe design is still the best for maintaining radar signal integrity 13 11 PROCESS INSTR
503. otating vector instead of a graph over time it is easier to see how multiple waveforms will interact with each other Quite often in alternating current AC circuits we must deal with voltage waveforms that add with one another by virtue of their sources being connected in series This sinusoidal addition becomes confusing if the two waveforms are not perfectly in step which is often the case However out of step sinusoids are easy to represent and easy to sum when drawn as vectors in a crank diagram Consider the following example showing two sinusoidal waveforms 60 degrees 5 radians out of step with each other 120 CHAPTER 4 AC ELECTRICITY 1 2 37 2 0 n 2 T 37 2 27 Graphically computing the sum of these two waves would be quite difficult in the standard graph right hand side but it is as easy as stacking vectors tip to tail in the crank diagram Pa T 2 i a 3n 2 of The length of the dashed line vector A B radius of the dashed line circle represents the amplitude of the resultant sum waveform while the phase shift is represented by the angles between 4 4 PHASOR MATHEMATICS 121 this new vector and the original vectors A and B This is all well and good but we need to have a symbolic means of representing this same information if we are to do any real math with AC voltages and c
504. ote that pure water would measure 10 Baum on the light scale As liquid density decreases the light Baum value increases For heavier than water liquids 145 Specific gravity Degrees Baum heavy 145 Note that pure water would measure 0 Baum on the heavy scale As liquid density increases the heavy Baum value increases Just to make things confusing there are different standards for the heavy Baum scale Instead of the constant value 145 shown in the above equation used throughout the United States of America an older Dutch standard used the same formula with a constant value of 144 The Gerlach heavy Baum scale uses a constant value of 146 78 144 Specific gravity Degrees Baum heavy old Dutch 144 Usually this standard temperature is 4 degrees Celsius the point of maximum density for water However sometimes the specific gravity of a fluid will be expressed in relation to the density of water at some other temperature 10 For each of these calculations specific gravity is defined as the ratio of the liquid s density at 60 degrees Fahrenheit to the density of pure water also at 60 degrees Fahrenheit 1 8 FLUID MECHANICS 39 146 78 Specific gravity Degrees Baum heavy Gerlach scale 146 78 There exists a seemingly endless array of degree scales used to express liquid density scattered throughout the pages of history For the measurement of sugar concentrations in the food
505. ote the differences in the instrument bubbles as shown on this P amp ID Some of the bubbles are just open circles where others have lines going through the middle Each of these symbols has meaning according to the ISA Instrumentation Systems and Automation society standard Panel mounted Panel mounted Field mounted main control room auxiliary location Front of panel Front of panel Rear of panel Rear of panel The type of bubble used for each instrument tells us something about its location This obviously is quite important when working in a facility with many thousands of instruments scattered over acres of facility area structures and buildings The rectangular box enclosing both temperature recorders shows they are part of the same physical instrument In other words this indicates there is really only one temperature recorder instrument and that it plots both suction and discharge temperatures most likely on the same trend graph This suggests that each bubble may not necessarily represent a discrete physical instrument but rather an instrument function that may reside in a multi function device Details we do not see on this P amp ID include cable types wire numbers terminal blocks junction boxes instrument calibration ranges failure modes power sources and the like To examine this level of detail we must go to the loop diagram we are interested in 6 3 LOOP DIAGRAMS 153 6 3 Loop diagrams Finally
506. ough the column to wash the last sample through The second mode is a sampling position where the volume of sample gas held in the sample loop tubing gets injected into the column by a flow of carrier gas behind it 570 CHAPTER 16 CONTINUOUS ANALYTICAL MEASUREMENT Sample loop Loading position Sample in To column To waste Carrier gas Sample loop Sampling position Sample in To column To waste Carrier gas The purpose of the sample loop tube is to act as a holding reservoir for a fixed volume of sample gas When the sample valve switches to the sample position the carrier gas will flush the contents of the sample loop into the front of the column This valve configuration guarantees that the injected sample volume does not vary with inevitable variations in sample valve actuation time The sample valve need only remain in the sampling position long enough to completely flush the sample loop tube and the proper volume of injected sample gas is guaranteed While in the loading position the stream of gas sampled from the process continuously fills the sample loop and then exits to a waste port This may seem unnecessary but it is in fact essential for practical sampling operation The volume of process gas injected into the chromatograph column during each cycle is so small typically measured in units of microliters that a continuous flow of sample gas to waste is necessary to purge the impulse line connecting the analyzer to the pro
507. ount of power dissipated by a resistance may be calculated as a function of either voltage or current and is known as Joule s Law P IV P P PR 100 CHAPTER 3 DC ELECTRICITY 3 8 Bridge circuits A bridge circuit is basically a pair of voltage dividers where the circuit output is taken as the difference in potential between the two dividers Bridge circuits may be drawn in schematic form in an H shape or in a diamond shape although the diamond configuration is more common V excitation N exciton The voltage source powering the bridge circuit is called the excitation source This source may be DC or AC depending on the application of the bridge circuit The components comprising the bridge need not be resistors either capacitors inductors lengths of wire sensing elements and other component forms are possible depending on the application Two major applications exist for bridge circuits which will be explained in the following subsections 3 8 BRIDGE CIRCUITS 101 3 8 1 Component measurement Bridge circuits may be used to test components In this capacity one of the arms of the bridge circuit is comprised of the component under test while at least one of the other arms is made adjustable The common Wheatstone bridge circuit for resistance measurement is shown here V acatar Galvanometer specimen Fixed resistors Ri and Ra are of precisely known value and high precision Variable resistor Rad
508. ourced by the instrument s internal milli voltage source or low temperature grounded depending on what failure mode we deem safest for the application 14 5 OPTICAL TEMPERATURE SENSING 435 14 5 Optical temperature sensing Virtually any mass above absolute zero temperature will emit electromagnetic radiation photons or light as a function of that temperature The Stefan Boltzmann Law of radiated energy tells us that the rate of heat lost by radiant emission from a hot object is proportional to the fourth power of the absolute temperature dQ eo AT dt Where ag Radiant heat loss rate watts e Emissivity factor unitless o Stefan Boltzmann constant 5 67 x 1078 W m K A Surface area square meters T Absolute temperature Kelvin This phenomenon provides us a way to infer an object s absolute temperature by sensing the radiation it emits Such a measurement technique holds obvious advantages perhaps the greatest being the lack of need for direct contact to the process with a sensing element such as an RTD or thermocouple Using an array of radiation sensors it is possible to build a thermal imager providing a graphic display of objects in its view according to their temperatures Each object is artificially colored in the display on a chromatic scale that varies with temperature hot objects typically registering as red tones and cold objects typically registering as blue tones Thermal imaging is very usef
509. ow range of water level near the middle of the drum Thus 3 PSI 0 will not represent an empty drum and neither will 15 PSI 100 represent a completely full drum Calibrating the transmitter like this helps avoid the possibility of actually running the drum completely empty or completely full in the case of an operator incorrectly setting the setpoint value near either extreme end of the measurement scale An example table showing this kind of realistic transmitter calibration is shown here 136 CHAPTER 5 INTRODUCTION TO INDUSTRIAL INSTRUMENTATION Transmitter air signal pressure Actual steam drum water level 3 PSI 40 6 PSI 45 9 PSI 50 12 PSI 55 15 PSI 60 5 2 EXAMPLE WASTEWATER DISINFECTION 137 5 2 Example wastewater disinfection The final step in treating wastewater before releasing it into the natural environment is to kill any harmful bacteria in it This is called disinfection and chlorine gas is a very effective disinfecting agent However just as it is not good to mix too little chlorine in the outgoing water effluent because we might not disinfect the water thoroughly enough there is also danger of injecting too much chlorine in the effluent because then we might begin poisoning animals and beneficial micro organisms in the natural environment To ensure the right amount of chlorine injection we must use a dissolved chlorine analyzer to measure the chlorine concentration in the efflue
510. owmeter 512 Transmitter 131 Trap 342 Trap steam 340 Trend recorder 142 Tuning controller 616 TUR 272 Turbine flow element 496 Turbulent flow 52 Turndown 271 Twaddell degrees 38 U tube manometer 291 Ullage 390 Ultrasonic flowmeter 512 Ultrasonic level instrument 390 645 Unit conversions 10 Unity fraction 10 Up down calibration test 265 Upper range value 131 262 283 URV 131 262 283 V cone flow element 470 V notch weir 489 Variable area flowmeter 487 Velocity of approach factor 483 Velocity PID algorithm 617 Vena contracta 458 622 Venturi tube 58 449 Viscosity 49 Viscosity absolute 49 Viscosity kinematic 49 Viscosity temperature dependence 50 Viscous flow 51 Volt 75 Volta Alessandro 75 Voltage 74 Volumetric flow 443 von K rm n Theodore 501 Vortex flowmeter 502 Vortex street 501 Wallace amp Tiernan 283 Wally box 283 Wastewater disinfection 137 601 Weighfeeder 528 Weight density 9 Weight based level instrument 403 Weir 489 581 Well manometer 291 Weston cell 273 Wet leg 368 Wild variable 600 Wind up controller 613 Work 75 Yokogawa DPharp pressure transmitter 308 Yokogawa model EJA110 differential pressure transmitter 308 316 Zero adjustment 259 Zero energy state 326 646 INDEX Zero shift 267 Zirconium oxide 592
511. ows them to be manufactured in very small sizes The following photograph shows a small device that is not only a mass flow meter but also a mass flow controller with its own built in throttling valve mechanism and control electronics To give you a sense of scale the tube fittings seen on the left and right hand sides of this device are 1 4 inch making this photograph nearly full size MASS FLOW CONTROLLER UN Btetiia AA 10 Ste 526 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT An important factor in the calibration of a thermal mass flowmeter is the specific heat of the process fluid Specific heat is a measure of the amount of heat energy needed to change the temperature of a standard quantity of substance by some specified amount3 Some substances have much greater specific heat values than others meaning those substances have the ability to absorb or release a lot of heat energy without experiencing a great temperature change Fluids with high specific heat values make good coolants because they are able to remove much heat energy from hot objects without experiencing great increases in temperature themselves Since thermal mass flowmeters work on the principle of convective cooling this means a fluid having a high specific heat value will elicit a greater response from a thermal mass flowmeter than the exact same mass flow rate of a fluid having a lesser specific heat value i e a fluid that is not as good of a coolant T
512. ozzle mechanism responds to slight out of balance conditions the more precise will be the relationship between measured variable mass and output signal air pressure to the gauge A plain baffle nozzle mechanism may be made extremely sensitive by reducing the size of the orifice However a problem caused by decreasing orifice size is a corresponding decrease in the nozzle s ability to provide increasing backpressure to fill a bellows of significant volume In other words a smaller orifice will result in greater sensitivity to baffle motion but it also limits the air flow rate available to fill the bellows which makes the system slower to respond Another disadvantage of smaller orifices is that they become more susceptible to plugging due to impurities in the compressed air An alternative technique to making the baffle nozzle mechanism more sensitive is to amplify its output pressure using some other pneumatic device This is analogous to increasing the sensitivity of a voltage generating electrical detector by passing its output voltage signal through an electronic amplifier Small changes in detector output become bigger changes in amplifier output which then causes our self balancing system to be even more precise What we need then is a pneumatic amplifier a mechanism to amplify small changes in air pressure and convert them into larger changes in air pressure In essence we need to find a pneumatic equivalent of the electronic transi
513. pect the two current signals to be equal for they represent entirely different things In fact if the controller is reverse acting it is entirely normal for the two current signals to be inversely related as the PV signal increases going to a reverse acting controller the output signal will decrease If the controller is placed into manual mode by a human operator the output signal will have no automatic relation to the PV signal at all instead being entirely determined by the operator s whim 190 CHAPTER 8 ANALOG ELECTRONIC INSTRUMENTATION 8 2 Relating 4 to 20 mA signals to instrument variables Calculating the equivalent milliamp value for any given percentage of signal range is quite easy Given the linear relationship between signal percentage and milliamps the equation takes the form of the standard slope intercept line equation y mu b Here y is the equivalent current in milliamps x is the desired percentage of signal m is the span of the 4 20 mA range 16 mA and b is the offset value or the live zero of 4 mA current 16 mA 4 mA x 100 This equation form is identical to the one used to calculate pneumatic instrument signal pressures the 3 to 15 PSI standard pressure 12 PSI 007 3 PSI 0 The same mathematical relationship holds for any linear measurement range Given a percentage of range x the measured variable is equal to measured variable Span LRV dE 100
514. pedance Resistance R is the dissipative opposition to an electric current analogous to friction encountered by a moving object Reactance X is the opposition to an electric current resulting from energy storage within circuit components analogous to inertia of a moving object Impedance Z is the combined total opposition to an electric current Reactance comes in two opposing types capacitive Xc and inductive Xz Each one is a function of frequency f in an AC circuit o 1 InfC Xc Xr 2rfL 4 3 Series and parallel circuits Impedance in a series circuit is the orthogonal sum of resistance and reactance Z yf R X2 X2 Equivalent series and parallel circuits are circuits that have the exact same total impedance as one another one with series connected resistance and reactance and the other with parallel connected resistance and reactance The resistance and reactance values of equivalent series and parallel circuits may be expressed in terms of those circuits total impedance R series X i parallel R parallel X series If the total impedance of one circuit either series or parallel is known the component values of the equivalent circuit may be found by algebraically manipulating these equations and solving for the desired R and X values 2 2 a Rseries parallel Z X series X parallel 118 CHAPTER 4 AC ELECTRICITY 4 4 Phasor mathematics Something every beginning t
515. pen loop output of an opamp as a function of its differential input voltage Vout AoL Vin Vin 230 CHAPTER 9 PNEUMATIC INSTRUMENTATION As stated before the open loop voltage gain of an opamp is typically very large Aoz 200 000 or more Connecting the opamp s output to the inverting input terminal simplifies the equation Vout may be substituted for Vin _ and Vin simply becomes Vin since it is now the only remaining input Reducing the equation to the two variables of Vouz and Vin and a constant Aoz allows us to solve for overall voltage gain Fut as a function of the opamp s internal voltage gain Aoz The following sequence of algebraic manipulations shows how this is done Vout AoL Vin Vout Vout AoLVin p AoL Vout AOL Vout Vout AoLVin Vout Aor 1 AoLVin Vout _ _Aoz Vin Aor 1 If we assume an internal opamp gain of 200 000 the overall gain will be very nearly equal to unity 0 999995 Moreover this near unity gain will remain quite stable despite large changes in the opamp s internal open loop gain The following table shows the effect of major Aoz changes on overall voltage gain Ay Overall gain AoL Ay Internal gain Overall gain 100 000 0 99999 200 000 0 999995 300 000 0 999997 500 000 0 999998 1 000 000 0 999999 Note how an order of magnitude change in Aoz from 100 000 to 1 000 000 results is a miniscule change in overall voltage gain from 0
516. pening the control valve thus introducing more heat energy into the process thus raising the temperature to the new setpoint level If the process fluid flow rate an uncontrolled or wild variable were to suddenly increase the heat exchanger outlet temperature would fall due to the physics of heat transfer but once this drop was detected by the transmitter and reported to the controller the controller would automatically call for additional steam flow to compensate for the temperature drop thus bringing the process variable back in agreement with the setpoint Ideally a well designed and well tuned control loop will sense and compensate for any change in the process or in the setpoint the end result being a process variable value that always holds steady at the setpoint value Many types of processes lend themselves to feedback control Consider an aircraft autopilot system keeping an airplane on a steady course heading reading the plane s heading process variable from an electronic compass and using the rudder as a final control element to change the plane s yaw An automobile s cruise control is another example of a feedback control system with the process variable being the car s velocity and the final control element being the engine s throttle Steam boilers with automatic pressure controls electrical generators with 18 1 BASIC FEEDBACK CONTROL PRINCIPLES 601 automatic voltage and frequency controls and water
517. per material selection and element strength material thickness to make a pressure instrument suitable for any range of process fluids Fill fluids used in pressure instruments whether it be the dielectric liquid inside a differential capacitance sensor the fill liquid of a remote or chemical seal system or liquid used to fill a vertical section of impulse tubing must be chosen so as to not adversely react with or contaminate the process Pure oxygen processes require that no system component have traces of hydrocarbon fluids present While oxygen itself is not explosive it greatly accelerates the combustion and explosive potential of any flammable substance Therefore a pressure gauge calibrated using oil as the working fluid in a deadweight tester would definitely not be suitable for pure oxygen service The same may be said for a differential pressure transmitter with a hydrocarbon based fill inside its pressure sensing capsule Pharmaceutical medical and food manufacturing processes require strict purity and the ability to disinfect all elements in the process system at will Stagnant lines are not allowed in such processes as microbe cultures may flourish in such dead end piping Remote seals are very helpful in overcoming this problem but the fill fluids used in remote systems must be chosen so that a leak in the isolating diaphragm will not contaminate the process Manometers of course are rather limited in their app
518. personally witnessed the confusion and wasted time that results from trying to calibrate a field instrument to a tighter tolerance than what the calibrating equipment is capable of In one case an instrument technician attempted to calibrate a pneumatic pressure transmitter to a tolerance of 0 5 of span using a test gauge that was only good for 1 of the same span This poor technician kept going back and forth adjusting zero and span over and over again trying to stay within the stated specification of 0 5 After giving up he tested the test gauges by comparing three of them one against the other When it was realized no two test gauges would agree with each other to within the tolerance he was trying to achieve in calibrating the transmitter it became clear what the problem was The lesson to be learned here is to always ensure the equipment used to calibrate industrial instruments is reliably accurate enough No piece of test equipment will ever be perfectly accurate but perfection is not what we need Our goal is to be accurate enough that the final calibration will be reliable within specified boundaries The next few subsections describe various standards used in instrument shops to calibrate industrial instruments 11 8 PRACTICAL CALIBRATION STANDARDS 273 11 8 1 Electrical standards Electrical calibration equipment used to calibrate instruments measuring voltage current and resistance must be periodically calibra
519. phisticated pressure transmitter may be corrupted despite perfect calibration of both analog digital converter circuits and perfect range settings in the microprocessor The microprocessor thinks the applied pressure is only 96 PSI and it responds accordingly with a 19 36 mA output signal The only way anyone would ever know this transmitter was inaccurate at 100 PSI is to actually apply a known value of 100 PSI fluid pressure to the sensor and note the incorrect response The lesson here should be clear digitally setting a smart instrument s LRV and URV points does not constitute a legitimate calibration of the instrument For this reason smart instruments always provide a means to perform what is called a digital trim on both the ADC and DAC circuits to ensure the microprocessor sees the correct representation of the applied stimulus and to ensure the microprocessor s output signal gets accurately converted into a DC current respectively I have witnessed some technicians use the LRV and URV settings in a manner not unlike the zero and span adjustments on an analog transmitter to correct errors such as this Following this methodology we would have to set the URV of the fatigued transmitter to 96 PSI instead of 100 PSI so that an applied pressure of 100 PSI would give us the 20 mA output signal we desire In other words we would let the microprocessor think it was only seeing 96 PSI then skew the URV so that it output the correc
520. physical difference between the solutes sample components dissolved within the carrier gas and the carrier gas itself which acts as a gaseous solvent Flame ionization detectors work on the principle of ions liberated in the combustion of the sample components A permanent flame usually fueled by hydrogen gas which produces negligible ions in combustion serves to ionize any gas molecules exiting the chromatograph column that are not carrier gas Common carrier gases used with FID sensors are helium and nitrogen Gas molecules containing carbon easily ionize during combustion which makes the FID sensor well suited for GC analysis in the petrochemical industries where hydrocarbon content analysis is the most common form of analytical measurement Thermal conductivity detectors work on the principle of heat transfer by convection gas cooling Recall the dependence of a thermal mass flowmeter s calibration on the specific heat value of the gas being measured This dependence upon specific heat meant that we needed to know the specific heat value of the gas whose flow we intend to measure or else the flowmeter s calibration would be l5In fact FID sensors are sometimes referred to as carbon counters since their response is almost directly proportional to the number of carbon atoms passing through the flame 16See section 15 6 on page 526 The greater the specific heat value of a gas the more heat energy it can carry away from a hot ob
521. ponents is also an expression of a more fundamental law of physics the Conservation of Energy in this case the conservation of specific potential energy which is the definition of voltage In order for voltage to differ between parallel connected components the potential energy of charge carriers would have to somehow appear and disappear to account for lesser and greater voltages It would be the equivalent of having a high spots and low spots of water mysteriously appear on the quiet surface of a lake which we know cannot happen because water has the freedom to move meaning any high spots would rush to fill any low spots The sum of all component currents must equal the total current in a parallel circuit and total resistance will be less than the smallest individual resistance value TAn ideal conductor has no resistance and so there is no reason for a difference of potential to exist along a pathway where nothing stands in the way of charge motion If ever a potential difference developed charge carriers within the conductor would simply move to new locations and neutralize the potential 8 Again interesting exceptions do exist to this rule on very short time scales such as in cases where we examine the a transient pulse signal nanosecond by nanosecond and or when very high frequency AC signals exist over comparatively long conductor lengths The exceptional cases mentioned in the previous footnote exist only because
522. pression fitting 318 Condensate boot 382 Conductance 92 99 639 Conductivity cell 543 Conductivity sensor 543 Conical entrance orifice plate 463 Conservation of Electric Charge 90 Conservation of Energy 20 23 30 55 91 93 449 Conservation of Mass 20 53 64 96 449 Constant of proportionality 453 Control algorithm 601 Controller 131 Controller gain 604 Conventional flow 175 Coriolis force 515 Coriolis mass flowmeter 516 Corner taps orifice plate 465 Coulomb 75 80 Counterpropagation ultrasonic flowmeter 512 cps 275 Crank diagram 119 Crest weir 490 Current 79 80 Curved manometer 578 Custody transfer 375 477 499 523 527 Cycles per second 275 Dall flow tube 469 DC excitation magnetic flowmeter 511 Dead test unit 278 Deadweight tester 278 Deadweight tester pneumatic 280 Degrees API 38 Degrees Balling 39 Degrees Bark 39 Degrees Baum 38 Degrees Brix 39 Degrees Oleo 39 Degrees Soxhlet 39 Degrees Twaddell 38 Density influence on hydrostatic level measurement accuracy 358 Dependent current source 196 Derivative control 614 Derivative notation calculus 530 Derived unit 19 Diaphragm 223 295 Diaphragm isolating 301 303 306 330 640 Dielectric constant 397 Dielectric constant influence on radar level measurement accuracy 401 Differential 614 Differential capacitance pressure sensor 303 Differential notation
523. pring ei Elastic force kx gt Weight Height raised Distance mg h compressed x Ground level In either case potential energy is calculated by the work done in exerting a force over a parallel distance In the case of the weight potential energy Ep is the simple product of weight gravity g acting on the mass m and height h Ep mgh For the spring things are a bit more complex The force exerted by the spring against the compressing motion increases with compression F kx where k is the elastic constant of the spring It does not remain steady as the force of weight does for the lifted mass Therefore the potential energy equation is nonlinear 1 Ep ake Releasing the potential energy stored in these mechanical systems is as simple as dropping the mass or letting go of the spring The potential energy will return to the original condition zero when the objects are at rest in their original positions If either the mass or the spring were attached to a machine to harness the return motion that stored potential energy could be used to do useful tasks Potential energy may be similarly defined and quantified for any situation where we exert a force over a parallel distance regardless of where that force or the motivating distance comes from For instance the static cling you experience when you pull a cotton sock out of a dryer is an example of a force By pulling that sock away from another article of
524. produced across membrane due to ion exchange volts R Universal gas constant 8 315 J mol K T Absolute temperature Kelvin n Number of electrons transferred per ion exchanged unitless F Faraday constant 96 485 coulombs per mole a Activity of ion in measured sample az Activity of ion in reference sample on other side of membrane A practical application for this technology is in the measurement of oxygen concentration in the flue gas of a large industrial burner such as what might be used to heat up water to generate steam The measurement of oxygen concentration in the exhaust of a combustion heater or boiler is very important both for maximizing fuel efficiency and for minimizing pollution specifically the production of NO molecules Ideally a burner s exhaust gas will contain no oxygen having consumed it all in the process of combustion with a perfect stoichiometric mix of fuel and air In practice the exhaust gas of an efficiently controlled burner will be somewhere near 2 as opposed to the normal 21 of ambient air One way to measure the oxygen content of hot exhaust is to use a high temperature zirconium oxide detector This detector is made of a sandwich of platinum electrodes on either side of a solid zirconium oxide electrolyte One side of this electrochemical cell is exposed to the exhaust gas process while the other side is exposed to heated air which serves as a reference 17 4 ANALYTICAL M
525. quid height e g inches of water inches of mercury As you can see a manometer is fundamentally an instrument of differential pressure measurement indicating the difference between two pressures by a shift in liquid column height U tube manometer pplied pplied a Bee greater lesser T Transparent Head tube allows liquid columns to be seen Liquid Liquid column height in a manometer should always be interpreted at the centerline of the liquid column regardless of the shape of the liquid s meniscus the curved air liquid interface 12 1 MANOMETERS 291 Read here Manometers come in a variety of forms the most common being the U tube well sometimes called a cistern raised well and inclined U tube manometer Well manometer gt vented vented Applied pressure Applied pressure 292 CHAPTER 12 CONTINUOUS PRESSURE MEASUREMENT o Pressure f Raised well inclined manometer input Raised well manometer vented Well Well U tube manometers are very inexpensive and are generally made from clear plastic see the left hand photo Cistern style manometers are the norm for calibration bench work and are typically constructed from metal cisterns and glass tubes see the right hand photo 12 1 MANOMETERS 293 Inclined manometers are used to measure very low pressures owing to their exceptional sensitivity note the fractional scale for inches of water column in the following phot
526. quite accurate The only real limitation to accuracy is the certainty to which we know the masses of the balancing weights Imagine being tasked with the challenge of automating this laboratory scale Suppose we grew weary of having to pay a lab technician to place standard weights on the scale to balance it for every new measurement and we decided to find a way for the scale to balance itself Where would we start Well we would need some sort of mechanism to tell when the scale was out of balance and another mechanism to change weight on the other pan whenever an out of balance condition was detected The baffle nozzle mechanism previously discussed would suffice quite well as a detection mechanism Simply attach a baffle to the end of the pointer on the scale and attach a nozzle adjacent to the baffle at the zero position where the pointer should come to a rest at balance 9 2 SELF BALANCING PNEUMATIC INSTRUMENT PRINCIPLES 217 Tube Air supply ad Orifice Now we have a highly sensitive means of indicating when the scale is balanced but we still have not yet achieved full automation The scale cannot balance itself at least not yet What if instead of using precise machined brass weights placed on the other pan to counter the mass of the specimen we used a pneumatically actuated force generator operated by the backpressure of the nozzle An example of such a force generator is a bellows a device made of thin sheet
527. r 16 6 x 1078 per degree C Iron 12 x 10 per degree C e Tin 20 x 107 per degree C e Titanium 8 5 x 107 per degree C As you can see the values for a are quite small This means the amount of expansion or contraction for modest temperature changes are almost too small to see unless the sample size lo is huge We can readily see the effects of thermal expansion in structures such as bridges where expansion joints must be incorporated into the design to prevent serious problems due to changes in ambient temperature However for a sample the size of your hand the change in length from a cold day to a warm day will be microscopic One way to amplify the motion resulting from thermal expansion is to bond two strips of dissimilar metals together such as copper and iron If we were to take two equally sized strips of copper and iron lay them side by side and then heat both of them to a higher temperature we would see the copper strip lengthen slightly more than the iron strip lt INN COPE Expansion MH iron If we bond these two strips of metal together this differential growth will result in a bending motion that greatly exceeds the linear expansion This device is called a bi metal strip Bending copper J iron 418 CHAPTER 14 CONTINUOUS TEMPERATURE MEASUREMENT This bending motion is significant enough to drive a pointer mechanism activate an electromechanical switch or perform any numbe
528. r but in actuality the situation is as simple as before A principle we apply in thermocouple circuit analysis called the Law of Intermediate Metals helps us simplify the situation According to this law intermediate metals in a series of junctions are of no consequence to the overall net voltage so long as those intermediate junctions are all at the same temperature Representing this pictorially the net effect of having four different metals A B C and D joined together in series is the same as just having the first and last metal in that series A and D joined with one junction if all intermediate junctions are at the same temperature 14 4 THERMOCOUPLES 431 xo A If all junctions are at the same temperature it is equivalent to A D In our Type J thermocouple circuit where iron and constantan both join to copper we see copper as an intermediate metal so long as junctions Jo and J3 are at the same temperature Since those two junctions are located next to each other on the indicating instrument identical temperature is a reasonable assumption and we may treat junctions J2 and J3 as a single iron constantan reference junction In other words the Law of Intermediate Metals tells us we can treat these two circuits identically Junction Iron R Junction Ji Constantan mu Junction J Junction Iron y 2 Voltmeter made of constantan wire Junction Ji Constantan Constantan no voltage Junctio
529. r will actually return to the transceiver antenna Any dissipative losses between the transceiver and the interface s of concern will weaken the radio signal to the point where it may become difficult to distinguish from noise Another important factor in maximizing reflected power is the degree to which the microwaves spread out on their way to the liquid interface s and back to the transceiver Guided wave radar instruments receive a far greater percentage of their transmitted power than non contact radar instruments because the metal rod s used to guide the microwave signal pulses help prevent the waves from spreading and therefore weakening throughout the liquids as they propagate In other words the metal rod s function as a transmission line to direct and focus the microwave energy ensuring a straight path from the instrument into the liquid and a straight echo return path from the liquid back to the instrument This is why guided wave radar is the only practical radar technology for measuring liquid liquid interfaces 13 5 ECHO 401 A critically important factor in accurate level measurement using radar instruments is that the relative permittivity of the upper substance s all media between the radar instrument and the interface of interest be accurately known The reason for this is rooted in the dependence of electromagnetic wave propagation velocity to relative permittivity Recalling the wave velocity formula shown earlier
530. r more Collections and to Reproduce the Work as incorporated in the Collections 2 to create and Reproduce Adaptations provided that any such Adaptation including any translation in any medium takes reasonable steps to clearly label demarcate or otherwise identify that changes were made to the original Work For example a translation could be marked The original work was translated from English to Spanish or a modification could indicate The original work has been modified 3 to Distribute and Publicly Perform the Work including as incorporated in Collections and 4 to Distribute and Publicly Perform Adaptations 5 For the avoidance of doubt 1 Non waivable Compulsory License Schemes In those jurisdictions in which the right to collect royalties through any statutory or compulsory licensing scheme cannot be waived the Licensor reserves the exclusive right to collect such royalties for any exercise by You of the rights granted under this License 2 Waivable Compulsory License Schemes In those jurisdictions in which the right to collect royalties through any statutory or compulsory licensing scheme can be waived the Licensor waives the exclusive right to collect such royalties for any exercise by You of the rights granted under this License and B 2 LEGAL CODE 635 3 Voluntary License Schemes The Licensor waives the right to collect royalties whether individually or in the event that the Licensor is a member of a
531. r of other mechanical tasks making this a very simple and useful primary sensing element for temperature If a bi metallic strip is twisted over a long length it will tend to un twist as it heats up This twisting motion may be used to directly drive the needle of a temperature gauge This is the operating principle of the temperature gauge shown in the following photograph 14 2 FILLED BULB TEMPERATURE SENSORS 419 14 2 Filled bulb temperature sensors Filled bulb systems exploit the principle of fluid expansion to measure temperature If a fluid is enclosed in a sealed system and then heated the molecules in that fluid will exert a greater pressure on the walls of the enclosing vessel By measuring this pressure and or by allowing the fluid to expand under constant pressure we may infer the temperature of the fluid Class I and Class V systems use a liquid fill fluid class V is mercury Here the volumetric expansion of the liquid drives an indicating mechanism to show temperature Pivot Pointer Scale Bellows Class I or Class V Bulb Class III systems use a gas fill fluid instead of liquid Here the change in pressure with temperature as described by the Ideal Gas Law allows us to sense the bulb s temperature 420 CHAPTER 14 CONTINUOUS TEMPERATURE MEASUREMENT Pivot Pointer Scale Bellows Class III Bulb Gas In these systems it is quite critical that the tube connecting the sensing b
532. r values If the voltage range is 1 5 volts and the current range is 4 20 mA the precision resistor value must be 250 ohms Since this is a digital controller the input voltage at the controller terminals is interpreted by an analog to digital converter ADC circuit which converts the measured voltage into a digital number that the controller s microprocessor can work with In some installations the transmitter power is supplied through additional wires in the cable from a power source located in the same panel as the controller 8 4 4 WIRE SELF POWERED TRANSMITTER CURRENT LOOPS 199 Controller Power source 4 wire transmitter AN A Ll wrocabo 4 PA The obvious disadvantage of this scheme is the requirement of two more conductors in the cable More conductors means the cable will be larger diameter and more expensive for a given length Cables with more conductors will require larger electrical conduit to fit in to and all field wiring panels will have to contain more terminal blocks to marshal the additional conductors If no suitable electrical power source exists at the transmitter location though a 4 wire cable is necessary to service a 4 wire transmitter 200 CHAPTER 8 ANALOG ELECTRONIC INSTRUMENTATION 8 5 2 wire loop powered transmitter current loops It is possible to convey electrical power and communicate analog information over the same two wires using 4 to 20 milliamps DC if we desi
533. range values LRV and URV respectively The term for describing either of the previous scenarios where the lower range value LRV of the transmitter s calibration is a positive number is called zero suppression If the zero offset is reversed e g the transmitter mounted at a location higher than the 0 process level it is referred to as zero elevation If the transmitter is elevated above the process connection point it will most likely see a negative pressure vacuum with an empty vessel owing to the pull of liquid in the line leading down from the instrument to the vessel It is vitally important in elevated transmitter installations to use a remote seal rather than an open impulse line so that liquid cannot dribble out of this line and into the vessel 2Or alternatively zero depression 3There is some disagreement among instrumentation professionals as to the definitions of these two terms According to B la G Lipt k s Instrument Engineers Handbook Process Measurement and Analysis Fourth Edition page 67 suppressed zero range refers to the transmitter being located below the 0 level the LRV being a positive pressure value while suppression suppressed range and suppressed span mean exactly the opposite LRV is a negative value The Yokogawa Corporation defines suppression as a condition where the LRV is a positive pressure Autolevel Application Note as does the Michael M
534. re becomes a representation of mass air flow rate past the wire Most mass air flow sensors used in automotive engine control applications employ this principle It is important for engine control computers to measure mass air flow and not just volumetric air flow because it is important to maintain proper air fuel ratio even if the air density changes due to changes in altitude In other words the computer needs to know how many air molecules are entering the engine per second in order to properly meter the correct amount of fuel into the engine for complete and efficient combustion The hot wire mass air flow sensor is simple and inexpensive to produce in quantity which is why it finds common use in automotive applications Industrial thermal mass flowmeters usually consist of a specially designed flowtube with two temperature sensors inside one that is heated and one that is unheated The heated sensor acts as the mass flow sensor cooling down as flow rate increases while the unheated sensor serves to compensate for the ambient temperature of the process fluid A typical thermal mass flowtube appears in the following diagrams note the swirl vanes in the close up photograph designed to introduce large scale turbulence into the flowstream to maximize the convective cooling effect of the fluid against the heated sensor element 15 6 THERMAL BASED MASS FLOWMETERS 525 The simple construction of thermal mass flowmeters all
535. re Transmitter output O ft 0 0 PSI 4mA 3 ft 25 0 833 PSI 8mA 6 ft 50 1 67 PSI 12 mA 9 ft 75 2 50 PSI 16 mA 12 ft 100 3 33 PSI 20 mA 13 3 HYDROSTATIC PRESSURE 361 13 3 1 Bubbler systems An interesting variation on this theme of direct hydrostatic pressure measurement is the use of a purge gas to measure hydrostatic pressure in a liquid containing vessel This eliminates the need for direct contact of the process liquid against the pressure sensing element which can be advantageous if the process liquid is corrosive Such systems are often called bubble tube or dip tube systems the former name being appropriately descriptive for the way purge gas bubbles out the end of the tube as it is submerged in process liquid A key detail of a bubble tube system is to provide a means of limiting gas flow through the tube so that the purge gas backpressure properly reflects hydrostatic pressure at the end of the tube with no additional pressure due to frictional losses along the length of the tube Most bubble tube systems therefore are provided with some means of monitoring purge gas flow typically with a rotameter or with a sightfeed bubbler Purge supply Purge supply Pressure Pressure regulator regulator WA Needle Needle valve valve Rotameter Sight feed bubbler If the purge gas flow is not too great gas pressure measured anywhere in the tube system downstream of the needle valve will
536. re is no mechanism in an orifice to dissipate energy and so with no energy lost there must be full pressure recovery as the fluid returns to its original speed e Pressure tap location makes a difference to ensure that the downstream tap is actually sensing the pressure at a point where the fluid is moving significantly faster than upstream the vena contracta and not just anywhere downstream of the orifice If the pressure drop were due to friction alone it would be permanent and the downstream tap location would not be as critical e Standard orifice plates have knife edges on their upstream sides to minimize contact area friction points with the high speed flow e Care must be taken to ensure Reynolds number is high enough to permit the use of an orifice plate if not the linear Q AP relationship for viscous flow will assert itself along with the quadratic potential kinetic energy relationship causing the overall Q AP relationship to be polynomial rather than purely quadratic and thereby corrupting the measurement accuracy e Sufficient upstream pipe length is needed to condition flow for orifice plate measurement not to make it laminar as is popularly and wrongly believed but to allow natural turbulence to flatten the flow profile for uniform velocity Laminar flow is something that only happens when viscous forces overshadow inertial forces e g flow at low Reynolds numbers and is totally different from the fu
537. re preferred over mechanical cables or gears for the simple reason of less resistance to rotation Cables and gears always present some degree of friction to the turbine s rotation causing the flowmeter to register less flow than there actually is Magnetic pickup sensors however are frictionless The rotational speed of the turbine wheel directly relates to fluid velocity which is proportional to volumetric flow rate If a magnetic pickup is used to detect the turbine blades as they pass by the sensor the frequency of the AC voltage signal output by the sensor relates directly to fluid velocity and volumetric flow 19 For instance a blade angle of 45 degrees would make blade tip speed equal to fluid velocity A blade angle of only 30 degrees from the turbine shaft centerline would result in a blade tip speed of about one half fluid velocity 498 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT Since volumetric flow and pickup coil output frequency are directly proportional to each other we may express this relationship in the form of an equation f kQ Where f Frequency of output signal Hz Q Volumetric flow rate e g gallons per second k K factor of the turbine element e g pulses per gallon Dimensional analysis confirms the validity of this equation Using units of GPS gallons per second and pulses per gallon we see that the product of these two quantities is indeed pulses per second equivalent to cycles p
538. re transmitter to output a 4 20 mA signal to an operator display 440 CHAPTER 14 CONTINUOUS TEMPERATURE MEASUREMENT As useful as thermowells are they are not without their caveats First and foremost is the first order time lag they add to the temperature measurement system by virtue of their mass and specific heat value It should be intuitively obvious that one or more pounds of metal will not heat up and cool down as fast as a few ounces worth of RTD or thermocouple and therefore that the presence of a thermowell will decrease the response time of any temperature sensing element A potential problem with thermowells is incorrect installation of the temperature sensing element The element must be inserted with full contact at the bottom of the thermowell s blind hole If any air gap is allows to exist between the end of the temperature element and the bottom of the thermowell s hole this will add a second time lag to the measurement system Some thermowells include a spring clip in the bottom of the blind hole to help maintain constant metal to metal contact between the sensing element and the thermowell wall 2The air gap acts as a thermal resistance while the mass of the element itself acts as a thermal capacitance Thus the inclusion of an air gap forms a thermal RC time constant delay network secondary to the thermal delay incurred by the thermowell 14 7 PROCESS INSTRUMENT SUITABILITY 441 14 7 Process instrument
539. red 32 to 1600 F K chromel yellow alumel red 32 to 2300 F S Pt90 Rh10 black Platinum red 32 to 2700 F B Pt70 Rh30 black Pt94 Rh6 red 32 to 3380 F It is critical to realize that the phenomenon of a reference junction is an inevitable effect of having to close the electric circuit loop in a circuit made of dissimilar metals This is true regardless of the number of metals involved In the last example only two metals were involved iron and copper This formed one iron copper junction J at the measurement end and one iron copper junction J2 at the indicator end Recall that the copper copper junction J3 was of no consequence because its identical metallic composition generates no thermal voltage 430 CHAPTER 14 CONTINUOUS TEMPERATURE MEASUREMENT Junction Iron Jy Voltmeter Copper Junction J Junction Js The same thing happens when we form a thermocouple out of two metals neither one being copper Take for instance this example of a type J thermocouple Junction Iron E Voltmeter Copper Junction Ji Constantan oe Junction J3 Here we have three voltage generating junctions J of iron and constantan J2 of iron and copper and J3 of copper and constantan which just happens to be the metallic combination for a type T thermocouple Upon first inspection it would seem we have a much more complex situation than we did with just two metals iron and coppe
540. resulting in a pressure value of 480 pounds per square foot PSF To convert into the more common pressure unit of pounds per square inch we may multiply by the proportion of square feet to square inches eliminating the unit of square feet by cancellation and leaving square inches in the denominator 480 Ib 12 ft e ir ft 122 in 480 lb 1 ft Pe Gat ft 144 in 3 33 Ib _ in 3 33 PSI Thus a pressure gauge attached to the bottom of the vessel holding a 12 foot column of this oil would register 3 33 PSI It is possible to customize the scale on the gauge to read directly in feet of oil height instead of PSI for convenience of the operator who must periodically read the gauge Since the mathematical relationship between oil height and pressure is both linear and direct the gauge s indication will always be proportional to height Any type of pressure sensing instrument may be used as a liquid level transmitter by means of this principle In the following photograph you see a Rosemount model 1151 pressure transmitter being used to measure the height of colored water inside a clear plastic tube The critically important factor in liquid level measurement using hydrostatic pressure is liquid density One must accurately know the liquid s density in order to have any hope of measuring that liquid s level using hydrostatic pressure since density is an integral part of the height pressure relationship P pgh and P
541. rforms some sort of processing on that signal Examples I P converter converts 4 20 mA electric signal into 3 15 PSI pneumatic signal P I converter converts 3 15 PSI pneumatic signal into 4 20 mA electric signal square root extractor calculates the square root of the input signal Note in general science parlance a transducer is any device that converts one form of energy into another such as a microphone or a thermocouple In industrial instrumentation however we generally use primary sensing element to describe this concept and reserve the word transducer to specifically refer to a conversion device for standardized instrumentation signals Transmitter A device that translates the signal produced by a primary sensing element PSE into a standardized instrumentation signal such as 3 15 PSI air pressure 4 20 mA DC electric current Fieldbus digital signal packet etc which may then be conveyed to an indicating device a controlling device or both Lower and Upper range values abbreviated LRV and URV respectively the values of process measurement deemed to be 0 and 100 of a transmitter s calibrated range For example if a temperature transmitter is calibrated to measured a range of temperature starting at 300 degrees Celsius and ending at 500 degrees Celsius 300 degrees would be the LRV and 500 degrees the URV Controller A device that receives a process variable PV signal from a primary sensing element
542. riation on this theme is the so called hydraulic load cell which is a piston and cylinder mechanism designed to translate vessel weight directly into hydraulic liquid pressure A normal pressure transmitter then measures the pressure developed by the load cell and reports it as material weight stored in the vessel Hydraulic load cells completely bypass the electrical problems associated 13 7 WEIGHT 405 with resistive load cells but are more difficult to network for the calculation of total weight using multiple cells to measure the weight of a large vessel 406 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT 13 8 Capacitive Capacitive level instruments measure electrical capacitance of a conductive rod inserted vertically into a process vessel As process level increases capacitance increases between the rod and the vessel walls causing the instrument to output a greater signal The basic principle behind capacitive level instruments is the capacitance equation EA d Where C Capacitance e Permittivity of dielectric insulating material between plates A Overlapping area of plates d Distance separating plates The amount of capacitance exhibited between a metal rod inserted into the vessel and the metal walls of that vessel will vary only with changes in permittivity e area A or distance d Since A is constant the interior surface area of the vessel is fixed as is the area of the rod once installed only changes in e
543. rigonometry student learns or should learn is how a sine wave is derived from the polar plot of a circle 1 2 37 2 0 n 2 T 31 2 27 This translation from circular motion to a lengthwise plot has special significance to electrical circuits because the circular diagram represents how alternating current AC is generated by a rotating machines while the lengthwise plot shows how AC is generally displayed on a measuring instrument The principle of an AC generator is that a magnet is rotated on a shaft past stationary coils of wire When these wire coils experience the changing magnetic field produced by the rotating magnet a sinusoidal voltage will be induced in the coils Vo coil Veoil 0 Veoil Vo cos O While sine and cosine wave graphs are quite descriptive there is another type of graph that is even more descriptive for AC circuits the so called crank diagram A crank diagram represents 4 4 PHASOR MATHEMATICS 119 the sinusoidal wave not as a plot of instantaneous amplitude versus time but rather as a plot of peak amplitude versus generator shaft angle This is basically the polar circular plot seen earlier which beginning trigonometry students often see near the beginning of their studies i Direction of y vector rotation 37 2 By representing a sinusoidal voltage as a r
544. rithm 617 Potential energy 22 74 Power reflection factor 398 Powers and roots 582 ppm 287 Preamplifier pH probe 558 Predictive maintenance 270 Pressure 27 29 344 643 Pressure gauge mechanism typical 295 Pressure recovery 58 Pressure snubber 327 Pressure switch 179 Pressure absolute 43 Pressure differential 43 Pressure gauge 43 Pressure hydrostatic 36 Pressure based flowmeters 444 Primary sensing element 131 Process 130 596 Process switch 144 Process variable 130 597 Programming chromatograph 571 Projectile physics 23 Proportional band controller 616 Proportional control 603 Proportional weir 491 Proportional only offset 610 Proximity switch 175 Purge flow rate 339 361 Purged impulse line 339 Quadrant edge orifice plate 463 Quarter active bridge circuit 106 Radar detection of liquid interfaces 399 Radar level instrument 395 Radioactivity 62 Raised well manometer 291 Range wheel 239 Rangeability 557 Rangedown 271 Ranging 257 Rate control 614 Reactance 117 Real Gas Law 48 Receiver gauge 214 Recorder 142 Rectangular weir 489 Reference electrode 552 Reference junction compensation 428 Reference junction thermocouple 428 Reflection factor 398 Relative permittivity 397 644 Relative permittivity influence on radar level measurement accuracy 401 Remote seal 331 Repeats per minute 616 Repose angle of 392 Reset contro
545. rmal energy from one sample to another by way of conduction direct contact convention transfer via a moving fluid or radiation emitted energy although you will often find the terms thermal energy and heat used interchangeably Temperature is a more easily detected quantity than heat There are many different ways to measure temperature from a simple glass bulb mercury thermometer to sophisticated infra red optical sensor systems Like all other areas of measurement there is no single technology that is best for all applications Each temperature measurement technique has its own strengths and weaknesses One responsibility of the instrument technician is to know these pros and cons so as to choose the best technology for the application and this knowledge is best obtained through understanding the operational principles of each technology 14 1 BEMETAL TEMPERATURE SENSORS 417 14 1 Bi metal temperature sensors Solids tend to expand when heated The amount that a solid sample will expand with increased temperature depends on the size of the sample the material it is made of and the amount of temperature rise The following formula relates linear expansion to temperature change 1 1Ip 1 AT Where l Length of material after heating lo Original length of material a Coefficient of linear expansion AT Change in temperature Here are some typical values of a for common metals e Aluminum 25 x 1076 per degree C e Coppe
546. roblem was the fact the controller was having some difficulty maintaining setpoint Other than that it seemed to operate adequately I doubt any electronic device would have fared as well unless completely potted in epoxy 244 CHAPTER 9 PNEUMATIC INSTRUMENTATION causing problems within the sensitive instrument mechanisms References Patrick Dale R and Patrick Steven R Pneumatic Instrumentation Delmar Publishers Inc Albany NY 1993 Chapter 10 Digital electronic instrumentation 245 246 CHAPTER 10 DIGITAL ELECTRONIC INSTRUMENTATION 10 1 The HART digital analog hybrid standard A technological advance introduced in the late 1980 s was HART an acronym standing for Highway Addressable Remote Transmitter The purpose of the HART standard was to create a way for instruments to digitally communicate with one another over the same two wires used to convey a 4 20 mA analog instrument signal In other words HART is a hybrid communication standard with one variable channel of information communicated by the analog value of a 4 20 mA DC signal and another channel for digital communication whereby many other variables could be communicated using pulses of current to represent binary bit values of O and 1 The HART standard was developed with existing installations in mind The medium for digital communication had to be robust enough to travel over twisted pair cables of very long length and unknown characteristic impedan
547. rom a distance This brings us to the final and most critical component of the heat exchanger temperature control system the controller This is a device designed to interpret the transmitter s process variable signal and decide how far open the control valve needs to be in order to maintain that process variable at the desired value 18 1 BASIC FEEDBACK CONTROL PRINCIPLES 599 Steam in 4 y Steam out Here the circle with the letters TC in the center represents the controller Those letters stand for Temperature Controller since the process variable being controlled is the process fluid s temperature Usually the controller consists of a computer making automatic decisions to open and close the valve as necessary to stabilize the process variable at some predetermined setpoint Note that the controller s circle has a solid line going through the center of it while the transmitter and control valve circles are open An open circle represents a field mounted device according to the ISA standard for instrumentation symbols and a single solid line through the middle of a circle tells us the device is located on the front of a control panel in a main control room location So even though the diagram might appear as though these three instruments are located close to one another they in fact may be quite far apart Both the transmitter and the valve must be located near the heat exchanger out in the field area rather
548. rrent as was the case with measurements taken in parallel with the precision resistor Take for example this 4 20 mA loop where a controller sends a command signal to an I P transducer Controller Control valve _ 20 PSI instrument air supply air tubing air tubing OA il 2 wire cable Oe Transducer Current to Pressure converter 8 6 TROUBLESHOOTING CURRENT LOOPS 205 There is no standardized resistance value for I P transducer coils and so the amount of voltage dropped across the I P terminals for any given amount of loop current will be unique for every different model of I P The Fisher model 567 I P transducer built for 4 20 mA signals has a nominal coil resistance of 176 ohms Thus we would expect to see a voltage drop of approximately 0 7 volts at 4 mA and a drop of approximately 3 5 volts at 20 mA across the I P terminals Since the controller output terminals are directly in parallel with the I P terminals we would expect to see approximately the same voltage there as well slightly greater due to wire resistance The lack of known precision in the I P coil resistance makes it difficult to tell exactly how much current is in the loop for any given voltage measurement we take with a voltmeter However if we do know the approximate coil resistance of the I P we can at least obtain an estimate of loop current which is usually good enough for diagnostic purposes If the I P coil resistance
549. rry it over to the table and release it there Since now it can only fall half a meter it will only release 4 9 joules in the process How much potential energy did the mass have while suspended above that table What if we carry it over to the edge of the cliff and release it there Falling 301 meters it will release 2 95 kilojoules kJ of energy How much potential energy did the mass have while suspended over the cliff As you can see potential energy is a relative quantity We must know the mass s position relative to its falling point before we can quantify its potential energy Likewise we must know an electric charge s position relative to its return point before we can quantify the voltage it has Consider a series of batteries connected as shown A 1 5 volts 1 5 volts 1 5 volts The voltage as measured between any two points directly across a single battery will be 1 5 volts Va 1 5 volts Vgc 1 5 volts Vop 1 5 volts If however we span more than one battery with our voltmeter connections our voltmeter will register more than 1 5 volts Vac 3 0 volts Vep 3 0 volts Vap 4 5 volts 3 1 ELECTRICAL VOLTAGE 77 There is no such thing as voltage at a single point in a circuit The concept of voltage has meaning only between pairs of points in a circuit just as the concept of potential energy for a mass has meaning only between two physical locations where the mass
550. rs and position characterized control valves Every nonlinear instrument will have its own recommended calibration procedure so I will defer you to the manufacturer s literature for your specific instrument I will however offer one piece of advice When calibrating a nonlinear instrument document all the adjustments you make e g how many turns on each calibration screw just in case you find the need to re set the instrument back to its original condition More than once I have struggled to calibrate a nonlinear instrument only to find myself further away from good calibration than where I originally started In times like these it is good to know you can always reverse your steps and start over 266 CHAPTER 11 INSTRUMENT CALIBRATION 11 4 3 Discrete instruments The word discrete means individual or distinct In engineering a discrete variable or measurement refers to a true or false condition Thus a discrete sensor is one that is only able to indicate whether the measured variable is above or below a specified setpoint Examples of discrete instruments are process switches designed to turn on and off at certain values A pressure switch for example used to turn an air compressor on if the air pressure ever falls below 85 PSI is an example of a discrete instrument Discrete instruments need regular calibration just like continuous instruments Most discrete instruments have but one calibration adjustment the set po
551. rtain minimum amount of electrical power available on which to operate while regulating current to signal the process measurement Internally the loop powered transmitter circuitry looks something like this 8 5 2 WIRE LOOP POWERED TRANSMITTER CURRENT LOOPS 201 Loop powered 4 20 mA transmitter lt 4mA Voltage in regulator e e Sensor YTa Sensing nd scaling out circuitry Additional current as needed All sensing scaling and output conditioning circuitry inside the transmitter must be designed to run on less then 4 mA of DC current and at a modest terminal voltage In order to create loop currents exceeding 4 mA as the transmitter must do in order to span the entire 4 to 20 milliamp signal range the transmitter circuitry uses a transistor to shunt bypass extra current from one terminal to the other as needed to make the total current indicative of the process measurement For example if the transmitter s internal operating current is only 3 8 mA and it must regulate loop current at a value of 16 mA to represent a condition of 75 process measurement the transistor will bypass 12 2 mA of current Early current based industrial transmitters were not capable of operating on such low levels of electrical power and so used a different current signal standard 10 to 50 milliamps DC Loop power supplies for these transmitters ranged upwards of 90 volts to provide enough power
552. rtial vacuum provided by the compressor The compressor then transports the vapors to a knockout drum where some of them condense into liquid form As a typical PFD this diagram shows the major interconnections of process vessels and equipment but omits details such as instrument signal lines and auxiliary instruments N 2 Knockout gt 4 M Compressor E N LEEN y 5 EG Evaporator Water VES A ya Ba Steam es Pca Bad Brine One might guess the instrument interconnections based on the instruments labels For instance a good guess would be that the level transmitter LT on the bottom of the knockout drum might send the signal that eventually controls the level valve LV on the bottom of that same vessel One might also guess that the temperature transmitter TT on the top of the evaporator might be part of the temperature control system that lets steam into the heating jacket of that vessel Based on this diagram alone one would be hard pressed to determine what control system if 150 CHAPTER 6 INSTRUMENTATION DOCUMENTS any controls the compressor itself All the PFD shows relating directly to the compressor is a flow transmitter FT on the suction line This level of uncertainty is perfectly acceptable for a PFD because its purpose is merely to show the general flow of the process itself and only a bare minimum of control instrumentation 6 2 PROCESS AND INSTRUMENT DIAGRAMS 151 6 2 Proces
553. rub past the walls of the pipe past the face of the orifice plate and through the constriction of the orifice at a very high speed in order to make it through to the other side I memorized what my teacher told us about energy exchange and how pressure had to drop as velocity increased but I never really internalized it because I still held to my faulty assumption of friction being the dominant mechanism of pressure drop in an orifice plate In other words while I could parrot the doctrine of kinetic and potential energy exchange I was still thinking in terms of friction which is a totally different phenomenon The difference between these two phenomena is the difference between energy exchanged and energy dissipated To use an electrical analogy it is the difference between reactance X and resistance R Incidentally many electronics students experience the same confusion when they study reactance mistakenly thinking it is the same thing as resistance where in reality it is quite different in terms of energy but that is a subject for another essay In a frictionless flow stream fluid pressure decreases as fluid velocity increases in order to conserve energy Another way to think of this is that a pressure differential must develop in order to provide the push needed to accelerate the fluid from a low speed to a high speed Conversely as the fluid slows back down after having passed through the constriction a reverse pressure differentia
554. ructions whatsoever in the path of the flow This translates to nearly zero permanent pressure loss along the length of the tube and therefore Thermal mass and straight tube Coriolis flowmeters are nearly obstructionless while vortex and turbine meters are only slightly worse 538 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT References AGA Report No 3 Orifice metering of natural gas and other related hydrocarbon fluids Part 1 General Equations and Uncertainty Guidelines Catalog number XQ9017 American Gas Association and American Petroleum Institute Washington D C Third Edition October 1990 Second Printing June 2003 AGA Report No 8 Orifice metering of natural gas and other related hydrocarbon fluids Part 2 Specification and Installation Requirements Catalog number XQ0002 American Gas Association and American Petroleum Institute Washington D C Fourth Edition April 2000 Second Printing June 2003 AGA Report No 3 Orifice metering of natural gas and other related hydrocarbon fluids Part 3 Natural Gas Applications Catalog number XQ9210 American Gas Association and American Petroleum Institute Washington D C Third Edition August 1992 Second Printing June 2003 AGA Report No 3 Orifice metering of natural gas and other related hydrocarbon fluids Part 4 Background Development Implementation Procedure and Subroutine Documentation for Empirical Flange Tapped Discharge Coefficient Equation Catalog
555. rument technician mistaking a conical entrance orifice plate for a square edged beveled orifice plate and installing it backward Several standards exist for pressure tap locations Ideally the upstream pressure tap will detect fluid pressure at a point of minimum velocity and the downstream tap will detect pressure at the vena contracta maximum velocity In reality this ideal is never perfectly achieved An overview of the most popular tap locations for orifice plates is shown in the following illustration 15 1 PRESSURE BASED FLOWMETERS 465 Flange taps Vena contracta taps Pipe sg threads Orifice plate In a Orifice plate hoes eis L x x D D vena contracta u point of maximum constriction i ODO Radius taps Corner taps ID 14D Pi g ji thr ads Orifice plate thr ads thr ads x A gt T tors coors O ts Pipe taps or Full flow taps 2 5D 8D Flange taps are the most popular tap location in the United States Flanges may be manufactured with tap holes pre drilled and finished before the flange is even welded to the pipe making this a very convenient pressure tap configuration Most of the other tap configurat
556. s The speed of sound through liquid is irrelevant in these applications since most of the acoustic energy reflects off the liquid surface and therefore never travels through it 13 5 ECHO 395 13 5 2 Radar level measurement Radar level instruments measure the distance from the transmitter located at some high point to the surface of a process material located further below in much the same way as ultrasonic transmitters The fundamental difference between a radar instrument and an ultrasonic instrument is the use of radio waves instead of sound waves Radio waves are electromagnetic in nature comprised of alternating electric and magnetic fields and very high frequency in the microwave frequency range GHz Sound waves are mechanical vibrations transmitted from molecule to molecule in a fluid or solid substance and of much lower frequency tens or hundreds of kilohertz still too high for a human being to detect as a tone than radio waves Some radar level instruments use waveguide probes to guide the radio waves into the process liquid while others send radio waves out through open space to reflect off the process material The instruments using waveguides are called guided wave radar instruments whereas the radar instruments relying on open space for signal propagation are called non contact radar The differences between these two varieties of radar instruments is shown in the following illustration Non contact radar G
557. s of course suffer no such problem because there is no liquid in the capillary tube to generate a pressure 422 CHAPTER 14 CONTINUOUS TEMPERATURE MEASUREMENT 14 3 Thermistors and Resistance Temperature Detectors RTDs One of the simplest classes of temperature sensor is one where temperature effects a change in electrical resistance With this type of primary sensing element a simple ohmmeter is able to function as a thermometer interpreting the resistance as a temperature measurement Ohmmeter lt lt Thermistor a or RTD Thermistors are devices made of metal oxide which either increase in resistance with increasing temperature a positive temperature coefficient or decrease in resistance with increasing temperature a negative temperature coefficient RTDs are devices made of pure metal usually platinum or copper which always increase in resistance with increasing temperature The major different between thermistors and RTDs is linearity thermistors are highly sensitive and nonlinear whereas RTDs are relatively insensitive but very linear For this reason thermistors are typically used where high accuracy is unimportant Many consumer grade devices use thermistors for temperature sensors Resistive Temperature Detectors RTDs relate resistance to temperature by the following formula Rr Ref 1 a T Ter Where Rr Resistance of RTD at given temperature T ohms Ref Resistance of RTD at the reference temperatur
558. s 0 pH to 14 pH the number representing a negative power of 10 approximately describing the hydrogen ion molarity of the solution how many moles of active hydrogen ions per liter of solution The pH of a solution is typically measured with a pair of special electrodes immersed in the solution which generate a voltage proportional to the pH of the solution In order to calibrate a pH instrument you must have a sample of liquid solution with a known pH value For pH instrumentation such calibration solutions are called buffers because they are specially formulated to maintain stable pH values even in the face of slight levels of contamination pH buffers may be purchased in liquid form or in powder form Liquid buffer solutions may be used directly out of the bottle while powdered buffers must be dissolved in appropriate quantities of de ionized water to generate a solution ready for calibration use Pre mixed liquid buffers are convenient to use but have a fairly limited shelf life Powdered buffer capsules are generally superior for long term storage and also enjoy the advantage of occupying less storage space in their dry state than a liquid buffer solution The following photograph shows a few 7 00 pH 0 02 pH buffer capsules ready to be mixed with water to form a usable buffer solution 2For example a solution with a pH value of 4 7 has a concentration of 10747 moles of active hydrogen ions per liter For more information on m
559. s J2 through J 3 happen to be at Previously it was suggested this automatic compensation could be accomplished by intentionally inserting a temperature dependent voltage source in series with the circuit oriented in such a way as to oppose the reference junction s voltage Compensating for the effects of J using a reference junction compensation circuit to generate a counter voltage Junction Iron Junction Jj This technique is known as hardware compensation A stand alone circuit designed to do this is sometimes called an ice point because it electrically accomplishes the same thing as physically placing the reference junction s in a bath of ice water 14 4 THERMOCOUPLES 433 A more modern technique for reference junction compensation is called software compensation This is applicable only where the indicating device is microprocessor based and where an additional analog input channel exists Compensating for the effects of J using a second input channel to sense ambient temperature and correcting mathematically in the computer Junction Jj 4 20 mA output Instead of canceling the effect of the reference junction electrically we can cancel the effect mathematically inside the microprocessor Perhaps the greatest advantage of software compensation is flexibility Being able to re program the compensation function means we may use this device with different thermocouple types With hardware based compen
560. s a maximum calibration range of 0 to 300 pounds per square inch PSI and a turndown of 20 1 This means that a technician may adjust the span anywhere between 300 PSI and 15 PSI This is important to know in order to select the proper transmitter for any given measurement application The odds of you finding a transmitter with just the perfect factory calibrated range for your measurement application may be quite small meaning you will have to adjust its range to fit your needs The turndown ratio tells you how far you will be able to practically adjust your instrument s range 272 CHAPTER 11 INSTRUMENT CALIBRATION 11 8 Practical calibration standards Within the context of a calibration shop environment where accurate calibrations are important yet intrinsic standards are not readily accessible we must do what we can to maintain a workable degree of accuracy in the calibration equipment used to calibrate field instruments It is important that the degree of uncertainty in the accuracy of a test instrument is significantly less than the degree of uncertainty we hope to achieve in the instruments we calibrate Otherwise calibration becomes an exercise in futility This ratio of uncertainties is called the Test Uncertainty Ratio or TUR A good rule of thumb is to maintain a TUR of at least 4 1 ideally 10 1 or better the test equipment being many times more accurate less uncertain than the field instruments we calibrate with them I have
561. s and Instrument Diagrams The next level of detail is the Process and Instrument Diagram or P amp ID Here we see a zooming in of scope from the whole evaporator process to the compressor as a unit The evaporator and knockout vessels almost fade into the background with their associated instruments absent from view Knockout drum Evaporator Now we see there is more instrumentation associated with the compressor than just a flow transmitter There is also a differential pressure transmitter PDT a flow indicating controller FIC and a recycle control valve that allows some of the vapor coming out of the compressor s discharge line to go back around into the compressor s suction line Additionally we have a pair of temperature transmitters that report suction and discharge line temperatures to an indicating recorder Some other noteworthy details emerge in the P amp ID as well We see that the flow transmitter flow controller pressure transmitter and flow valve all bear a common number 42 This common loop number indicates these four instruments are all part of the same control system An instrument 152 CHAPTER 6 INSTRUMENTATION DOCUMENTS with any other loop number is part of a different control system measuring and or controlling some other function in the process Examples of this include the two temperature transmitters and their respective recorders bearing the loop numbers 41 and 43 Please n
562. s less conductive than it actually is 16 3 3 Four electrode conductivity probes A very old electrical technique known as the Kelvin or four wire resistance measuring method is a practical solution for this problem Commonly employed to make precise resistance measurements 5The use of alternating current forces the ions to switch directions of travel many times per second thus reducing the chance they have of bonding to the metal electrodes 16 3 CONDUCTIVITY MEASUREMENT 545 for scientific experiments in laboratory conditions as well as measuring the electrical resistance of strain gauges and other resistive sensors the four wire technique uses four conductors to connect the resistance under test to the measuring instrument 4 wire ohmmeter 4 wire cable f I 4 V er wire resistance Voltmeter indication Current source R specimen Only the outer two conductors carry substantial current The inner two conductors connecting the voltmeter to the test specimen carry negligible current due to the voltmeter s extremely high input impedance and therefore drop negligible voltage along their lengths Voltage dropped across the current carrying outer wires is irrelevant since that voltage drop is never detected by the voltmeter Since the voltmeter only measures voltage dropped across the specimen the resistor under test and not the test resistance plus wiring resistance the resulting resistance measurement is
563. s may be represented by the symbol customarily reserved for wavelength the Greek letter lambda A The proportionality between object width d and vortex street wavelength A is called the Strouhal number S approximately equal to 0 17 d AS d AR 7 If a differential pressure sensor is installed immediately downstream of the stationary object in such an orientation that it detects the passing vortices as pressure variations an alternating signal will be detected 502 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT Pressure sensor Pressure signal The frequency of this alternating pressure signal is directly proportional to fluid velocity past the object since the wavelength is constant This follows the classic frequency velocity wavelength formula common to all traveling waves Af v Since we know the wavelength will be equal to the bluff body s width divided by the Strouhal number approximately 0 17 we may substitute this into the frequency velocity wavelength formula to solve for fluid velocity v in terms of signal frequency f and bluff body width d v Af d ar F 2 0 17 Thus a stationary object and pressure sensor installed in the middle of a pipe section constitute a form of flowmeter called a vortez flowmeter Like a turbine flowmeter with an electronic pickup sensor to detect the passage of rotati
564. s of automatic process control Before we begin our discussion on process control we must define a few key terms First we have what is known as the process This is the physical system we wish to monitor and control For the sake of illustration consider a heat exchanger that uses high temperature steam to transfer heat to a lower temperature liquid Heat exchangers are used frequently in the chemical industries to maintain the necessary temperature of a chemical solution so that the desired blending separation or reactions can occur A very common design of heat exchanger is the shell and tube style where a metal shell serves as a conduit for the chemical solution to flow through while a network of smaller tubes runs through the heating space carrying steam or some other heating medium The hotter steam flowing through the tubes transfers heat energy to the cooler process fluid surrounding the tubes inside the shell of the heat exchanger Steam in y Shell and Tube heat exchanger Shell Warm process fluid out Cool process fluid in gt l Steam out In this case the process is the entire heating system consisting of the fluid we wish to heat the heat exchanger and the steam delivering the required heat energy In order to maintain steady control of the process fluid s exiting temperature we must find a way to measure it and represent that measurement in signal form so that it may be interpreted by oth
565. s typically exceed 200 000 over 100 dB and we have already seen how just a few thousandths of an inch of baffle motion is enough to drive the backpressure of a nozzle nearly to its limits supply pressure and atmospheric pressure respectively Gain is always defined as the ratio between output and input for a system Mathematically it is the quotient of output change and input change with change represented by the triangular Greek capital letter delta AOutput in A a Alnput Normally gain is a unitless ratio We can easily see this for the opamp circuit since both output and input are voltages any unit of measurement for voltage would cancel in the quotient leaving a unitless quantity This is not so evident in the baffle nozzle system with the output represented in units of pressure and the input represented in units of distance If we were to add a bellows to the baffle nozzle mechanism we would have a system that inputs and outputs fluid pressure allowing us to more formally define the gain of the system as a unitless 3 APout ratio of AP 9 4 ANALOGY TO OPAMP CIRCUITS 229 Orifice Air supply _ gt gt lt P Baffle The general effect of negative feedback is to decrease the gain of a system and also make that system s response more linear over the operating range This is not an easy concept to grasp however and so we will explore the effect of adding negative feedback in detail f
566. same starting point An analogy for visualizing Kirchhoff s Voltage Law is hiking up a mountain Suppose we start at the base of a mountain and hike to an altitude of 5 000 feet to set up camp for an overnight stay Then the next day we set off from camp and hike further up another 3 500 feet Deciding we ve climbed high enough for two days we set up camp again and stay the night The next day we hike down 6 200 feet to a third location and camp once gain On the fourth day we hike back to our original starting point at the base of the mountain We can summarize our hiking adventure as a series of rises and falls like this Day Path Altitude gain loss Day 1 AB 5 000 feet Day 2 BC 3 500 feet Day 3 CD 6 200 feet Day 4 DA 2 300 feet Total ABCDA 0 feet Of course no one would brag to their friends that they spent four days hiking a total altitude of 0 feet so people generally speak in terms of the highest point reached in this case 8 500 feet However if we track each day s gain or loss in algebraic terms maintaining the mathematical sign either positive or negative we see that the end sum is zero and indeed must always be zero if we finish at our starting point If we view this scenario from the perspective of potential energy as we lift a constant mass from point to point we would conclude that we were doing work on that mass i e investing energy in it by lifting it higher on days 1 and 2 b
567. sation an ice point circuit re wiring or replacement is necessary to accommodate different thermocouple types Another consideration for thermocouples is burnout detection The most common failure mode for thermocouples is to fail open otherwise known as burning out An open thermocouple is problematic for any voltage measuring instrument with high input impedance because the lack of a complete circuit on the input makes it possible for electrical noise from surrounding sources power lines electric motors variable frequency motor drives to be detected by the instrument and falsely interpreted as a wildly varying temperature For this reason it is prudent to design into the thermocouple instrument some provision for generating a consistent state in the absence of a complete circuit This is called the burnout mode of a thermocouple instrument Burnout mode The resistor in this circuit provides a path for current in the event of an open thermocouple 434 CHAPTER 14 CONTINUOUS TEMPERATURE MEASUREMENT It is sized in the mega ohm range so that its effect is minimal during normal operation when the thermocouple circuit is complete Only when the thermocouple fails open will the miniscule current through the resistor have any substantial effect on the voltmeter s indication The SPDT switch provides a selectable burnout mode in the event of a burnt out thermocouple we can configure the meter to either read high temperature s
568. se including without limitation any production in the literary scientific and artistic domain whatever may be the mode or form of its expression including digital form such as a book pamphlet and other writing a lecture address sermon or other work of the same nature a dramatic or dramatico musical work a choreographic work or entertainment in dumb show a musical composition with 634 APPENDIX B CREATIVE COMMONS ATTRIBUTION LICENSE or without words a cinematographic work to which are assimilated works expressed by a process analogous to cinematography a work of drawing painting architecture sculpture engraving or lithography a photographic work to which are assimilated works expressed by a process analogous to photography a work of applied art an illustration map plan sketch or three dimensional work relative to geography topography architecture or science a performance a broadcast a phonogram a compilation of data to the extent it is protected as a copyrightable work or a work performed by a variety or circus performer to the extent it is not otherwise considered a literary or artistic work 7 You means an individual or entity exercising rights under this License who has not previously violated the terms of this License with respect to the Work or who has received express permission from the Licensor to exercise rights under this License despite a previous violation 8 Publicly Perform means to perform public
569. se tubes or water in a steam system this fill fluid will be lost Also if the process fluid is dangerously hot or radioactive a combination of open equalizing and block valves will let that dangerous fluid reach the transmitter and manifold possibly causing damage or creating a personal hazard Speaking from personal experience I once made this mistake on a differential pressure transmitter connected to a steam system causing hot steam to flow through the manifold and overheat the equalizing valve so that it seized open and could not be shut again The only way I was able to stop the flow of hot steam through the manifold was to locate and shut 12 6 PRESSURE SENSOR ACCESSORIES 325 a sliding gate hand valve between the impulse tube and the process pipe Fortunately this cast iron valve was not damaged by the heat and was still able to shut off the flow Pressure transmitter valve manifolds also come in single block and bleed configurations for gauge pressure applications Here the low pressure port of the transmitter is vented to atmosphere with only the high pressure port connected to the impulse line pal Bleed valve Block valve Impulse line to process The following photograph shows a bank of eight pressure transmitters seven out of the eight being equipped with a single block and bleed manifold The eighth transmitter bottom row second from left sports a 5 valve manifold 326 CHAPTER 12 CONTINUOUS PRESS
570. senting any type of two terminal electrical component Series circuit Parallel circuit Equipotential points uauno 10 yjed aun Equipotential points The defining characteristic of a series electrical circuit is that it has just one path for current This means there can be only one value for current anywhere in the circuit the exact same current for all components at any given time The principle of current being the same everywhere in a series circuit is actually an expression of a more fundamental law of physics the Conservation of Charge which states that electric charge cannot be created or destroyed In order for current to have different values at different points in a series circuit indefinitely electric charge would have to somehow appear and disappear to account for greater rates of charge flow in some areas than in others It would be the equivalent of having different rates of water flow at different locations along one length of pipe Series circuits are defined by having only one path for current and this means the steady state current in a series circuit must be the same at all points of that circuit It also means that the sum of all voltages dropped by load devices must equal the sum total of all source voltages and that the total resistance of the circuit will be the sum of all individual resistances Interesting exceptions do exist to this rule but only on very short time scales such as in cases where we ex
571. simplest form of coil excitation is when the coil is energized by 60 Hz AC power taken from the line power source Since motional EMF is proportional to fluid velocity and to the flux density of the magnetic field the induced voltage for such a coil will be a sine wave whose amplitude varies with volumetric flow rate Unfortunately if there is any stray electric current traveling through the liquid to produce erroneous voltage drops between the electrodes chances are it will be 60 Hz AC as well With the coil energized by 60 Hz AC any such noise voltage may be falsely interpreted as fluid flow because the sensor electronics has no way to distinguish between 60 Hz noise in the fluid and a 60 Hz motional EMF caused by fluid flow A more sophisticated solution to this problem uses a pulsed excitation power source for the flowtube coils This is called DC excitation by magnetic flowmeter manufacturers which is a bit 15 4 VELOCITY BASED FLOWMETERS 511 misleading because these DC excitation signals often reverse polarity appearing more like an AC square wave on an oscilloscope display The motional EMF for one of these flowmeters will bear the same waveshape with amplitude once again being the indicator of volumetric flow rate The sensor electronics can more easily reject any AC noise voltage because the frequency and waveshape of the noise 60 Hz sinusoidal will not match that of the flow induced motional EMF signal 512 CHAPTER 15 CONTIN
572. sition algorithm controller makes a sudden jump in its output value Most digital electronic controllers also have provision for process variable filtering the purpose of which is to dampen unwanted noise from the PV signal Over enthusiastic use of filtering however can cause major problems with PID control Too much filtering and the PID algorithm does not see the real time value of the PV and consequently will begin to control a sluggish version of the PV instead of the real PV There is much that may be said about controller tuning The first and most significant point to be made about tuning is this don t unless you know what you are doing Poor control caused by improper tuning is very wasteful of product and energy in a manufacturing operation and can even be dangerous to operations if too unstable Far too many control loops run erratically because someone decided to mess with the controller s PID settings when they did not understand how or why to do so When a formerly robust control system gets out of tune the cause is almost always due to problems in the process or field instrumentation Unfortunately what a lot of good intended technicians do is go straight to the controller and try adjusting the P I and D settings because it 618 CHAPTER 18 CONTINUOUS FEEDBACK CONTROL looks easy and it will make them look really smart to be able to fix the problem just by making a few technical adjustments No amount of
573. smitted power at any interface of materials is called the power reflection factor R This may be expressed as a unitless ratio or more often as a decibel figure The relationship between dielectric permittivity and reflection factor is as follows p Vav Vez Vert Where R Power reflection factor at interface as a unitless ratio r1 Relative permittivity dielectric constant of the first medium 13 5 ECHO 399 r2 Relative permittivity dielectric constant of the second medium The fraction of incident power transmitted through the interface Pforwara is of course the mathematical complement of the power reflection factor 1 R For situations where the first medium is air or some other low permittivity gas the formula simplifies to the following form with e being the relative permittivity of the reflecting substance 2 ac Esa Va 1 In the previous illustration the two media were air e 1 and water e 80 a nearly ideal scenario for strong signal reflection Given these relative permittivity values the power reflection factor has a value of 0 638 63 8 or 1 95 dB This means that well over half the incident power gets reflected by the air water interface with the remaining 0 362 36 2 of the wave s power making it through the air water interface and propagating into water If the liquid in question is gasoline rather than water having a rather low relative permittivity value of approximately
574. soil by the violet color of its blossoms 8 Truth be told the color of a hydrangea blossom is only indirectly determined by soil pH Soil pH affects the plant s uptake of aluminum which is the direct cause of color change Interesting the pH color relationship of a hydrangea plant is exactly opposite that of common laboratory litmus paper red litmus paper indicates an acidic solution while blue litmus paper indicates an alkaline solution whereas red hydrangea blossoms indicate alkaline soil while blue or violet hydrangea blossoms indicate acidic soil 550 CHAPTER 16 CONTINUOUS ANALYTICAL MEASUREMENT 16 4 2 Potentiometric pH measurement Color change is a common pH test method used for manual laboratory analyses but it is not well suited to continuous process measurement By far the most common pH measurement method in use is electrochemical special pH sensitive electrodes inserted into an aqueous solution will generate a voltage dependent upon the pH value of that solution Like all other potentiometric voltage based analytical measurements electrochemical pH measurement is based on the Nernst equation which describes the electrical potential generated by a difference in ionic concentration between two different solutions separated by an ion permeable membrane O RT Q vip in E Where V Voltage produced across membrane due to ion exchange in volts V R Universal gas constant 8 315 J mol K T Absolute tempera
575. son why these two components do not follow Ohm s Law is because they do not dissipate energy like resistances do Rather than dissipate energy in the form of heat and or light capacitors and inductors store and release energy from and to the circuit in which they are connected The contrast between resistors and these components is remarkably similar to the contrast between friction and inertia in mechanical systems Whether pushing a flat bottom box across a floor or pushing a heavy wheeled cart across a floor work is required to get the object moving However the flat bottom box will immediately stop when you stop pushing it while the wheeled cart will continue to coast because it has kinetic energy stored in it 4 4 PHASOR MATHEMATICS 123 The relationships between voltage and current for capacitors C and inductors L are as follows dV dI I C Ti V L qi Expressed verbally capacitors pass electric current proportional to how quickly the voltage across them changes over time Conversely inductors produce a voltage drop proportional to how quickly current through them changes over time The symmetry here is beautiful capacitors which store energy in an electric field oppose changes in voltage Inductors which store energy in a magnetic field oppose changes in current When either type of component is placed in an AC circuit and subjected to sinusoidal voltages and currents it will appear to have a resistance Given the amplit
576. sors are sensitive and accurate enough to now monitor the weak magnetic fields created by the passage of small DC currents in wires Thus a clamp on milliammeter is very simple and non intrusive to use Not all technicians have access to these wonderful test instruments though and even if they do there are certain precautions one must take to ensure their indications will not be thrown into error by external magnetic fields Another way to measure a 4 20 mA signal without interrupting it involves the use of a rectifying diode originally installed in the loop circuit when it was commissioned The diode may be placed anywhere in series within the loop in such a way that it will be forward biased During normal operation the diode will drop approximately 0 7 volts as is typical for any silicon rectifying diode when forward biased The following schematic diagram shows such a diode installed in a 2 wire transmitter loop circuit Power Transmitter supply If someone connects a milliammeter in parallel with this diode however the very low input resistance of the ammeters shorts past the diode and prevents any substantial voltage drop from forming across it Without the necessary forward voltage drop the diode effectively turns off and conducts 0 mA leaving the entire loop current to pass through the ammeter All current goes through the milliammeter Power Transmitter supply When the milliammeter is disconnected the requisit
577. specific percentage points chosen for checking the goal is to ensure that minimum accuracy is maintained at all points along the scale so that the instrument s response may be trusted when placed into service Yet another improvement over the basic five point test is to check the instrument s response at five calibration points decreasing as well as increasing Such tests are often referred to as Up down calibrations The purpose of such a test is to determine if the instrument has any significant hysteresis a lack of responsiveness to a change in direction Some linear instruments provide a means to adjust linearity This adjustment should be moved only if absolutely necessary Quite often these linearity adjustments are very sensitive and prone to over adjustment by zealous fingers The linearity adjustment of an instrument should be changed only if the required accuracy cannot be achieved across the full range of the instrument Otherwise it is advisable to adjust the zero and span controls to split the error between the highest and lowest points on the scale and leave linearity alone 11 4 2 Nonlinear instruments The calibration of inherently nonlinear instruments is much more challenging than for linear instruments No longer are two adjustments zero and span sufficient because more than two points are necessary to define a curve Examples of nonlinear instruments include expanded scale electrical meters square root characterize
578. ss becomes necessary only when multiple devices are connected to the same network wiring and there arises a need to digitally distinguish one device from another on the same network This is a functionality the designers of HART intended from the beginning although it is frequently unused in industry Multiple HART instruments may be connected directly in parallel with one another along the same wire pair and information exchanged between those instruments and a host system if the HART address numbers are set to non zero values between 1 and 15 Address 4 Address 13 Address 10 Address 5 Setting an instrument s HART address to a non zero value is all that is necessary to engage multidrop mode The address numbers themselves are irrelevant as long as they fall within the range of 1 to 15 and are unique to that network The major disadvantage of using HART instruments in multidrop mode is its slow speed Due to HART s slow data rate 1200 bits per second it may take several seconds to access a particular instrument s data on a multidropped network For some applications such as temperature measurement this slow response time may be acceptable For inherently faster processes such as liquid flow control it would not be nearly fast enough to provide up to date information for the control system to act upon 10 1 THE HART DIGITAL ANALOG HYBRID STANDARD 253 10 1 2 HART multi variable transmitters Some smart instruments have t
579. st common pressure sensing device used in this capacity to infer liquid level within a vessel In the hypothetical case of the oil vessel just considered the transmitter would connect to the vessel in this manner with the high side toward the process and the low side vented to atmosphere Transmitter e Electronic output signal vented Impulse tube Connected as such the differential pressure transmitter functions as a gauge pressure transmitter responding to hydrostatic pressure exceeding ambient atmospheric pressure As liquid level increases the hydrostatic pressure applied to the high side of the differential pressure transmitter also increases driving the transmitter s output signal higher Some pressure sensing instruments are built specifically for hydrostatic measurement of liquid level in vessels doing away with impulse tubing altogether in favor of a special kind of sealing diaphragm that protrudes slightly into the vessel through a flanged pipe entry commonly called a nozzle A photograph of such a level transmitter is shown here 360 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT The calibration table for a transmitter close coupled to the bottom of an oil storage tank would be as follows assuming a zero to twelve foot measurement range for oil height an oil density of 40 pounds per cubic foot and a 4 20 mA transmitter output signal range Oil level Percent of range Hydrostatic pressu
580. stems a vertical offset is guaranteed to produce a pressure offset because fill fluids are always liquid and liquids generate pressure in direct proportion to the vertical height of the liquid column and to the density of that liquid A similar problem unique to isolated fill pressure instruments is measurement error caused by 336 CHAPTER 12 CONTINUOUS PRESSURE MEASUREMENT temperature extremes Suppose the liquid filled capillary tube of a remote seal pressure instrument comes too near a hot steam pipe furnace or some other source of high temperature The expansion of the fill fluid may cause the isolation diaphragm to extend to the point where it begins to tense and add a pressure to the fill fluid above and beyond that of the process fluid Cold temperatures may wreak havoc with filled capillary tubes as well if the fill fluid congeals or even freezes such that it no longer flows as it should Proper mounting of the instrument and proper selection of the fill fluid will help to avoid such problems All in all the potential for trouble with remote and chemical seal pressure instruments is greatly offset by their benefits in the right applications 12Most pressure instrument manufacturers offer a range of fill fluids for different applications Not only is temperature a consideration in the selection of the right fill fluid but also potential contamination of or reaction with the process if the isolating diaphragm ever suffers a leak
581. stor a device that lets one signal control another First let us analyze the following pneumatic mechanism and its electrical analogue as shown on the right 9 3 PILOT VALVES AND PNEUMATIC AMPLIFYING RELAYS 221 Pneumatic mechanism Equivalent electrical circuit Compressed air supply V Output pressure Vout t 2u vent vent Control rod moves up and down As the control rod is moved up and down by an outside force the distance between the plug and the seat changes This changes the amount of resistance experienced by the escaping air thus causing the pressure gauge to register varying amounts of pressure There is little functional difference between this mechanism and a baffle nozzle mechanism Both work on the principle of one variable restriction and one fixed restriction the orifice dividing the pressure of the compressed air source to some lesser value The sensitivity of this pneumatic mechanism may be improved by extending the control rod and adding a second plug seat assembly The resulting mechanism with dual plugs and seats is known as a pneumatic pilot valve An illustration of a pilot valve is shown here along with its electrical analogue on the right 222 CHAPTER 9 PNEUMATIC INSTRUMENTATION Pneumatic pilot valve Equivalent electrical circuit Compressed air rid Output pressure Control _ 1 knob i Vout vent vent eye rod moves up and down As the control rod is move
582. stressed it fails 3For a simple demonstration of metal fatigue and metal flow simply take a metal paper clip and repeatedly bend it back and forth until you feel the metal wire weaken Gentle force applied to the paper clip will cause it to deform in such a way that it returns to its original shape when the force is removed Greater force however will exceed the paper clip s elastic limit causing permanent deformation and also altering the spring characteristics of the clip 123 ELECTRICAL PRESSURE ELEMENTS 301 completely rather than flows as is the case with metal strain gauges This is generally considered a better result as it clearly indicates the need for sensor replacement whereas a metallic strain sensor may give the false impression of continued function after an over stress event Thus most modern piezoresistive based pressure instruments use silicon strain gauge elements to sense deformation of a diaphragm due to applied fluid pressure A simplified illustration of a diaphragm strain gauge pressure sensor is shown here Diaphragm Strain gauge Applied pressure In some designs a single silicon wafer serves as both the diaphragm and the strain gauge so as to fully exploit the excellent mechanical properties of silicon high linearity and low fatigue However silicon is not chemically compatible with many process fluids and so pressure must be transferred to the silicon diaphragm sensor via a non reactiv
583. such circumstance is in the presence of a lighter liquid layer existing between the connection ports of the gauge If a lighter less dense liquid exists above a heavier denser liquid in the process vessel the level gauge may not show the proper interface if at all ye Water only 350 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT Here we see how a column of water in the sightglass shows less total level than the combination of water and oil inside the process vessel Since the oil lies between the two level gauge ports into the vessel sometimes called nozzles it cannot enter the sightglass tube and therefore the level gauge will continue to show just water If by chance some oil does find its way into the sightglass tube either by the interface level dropping below the lower nozzle or the total level rising above the upper nozzle the oil water interface shown inside the level gauge may not continue to reflect the true interface inside the vessel once the interface and total levels return to their previous positions In effect the level gauge and vessel together form a U tube manometer So long as the pressures from each liquid column are the same the columns balance each other The problem is many different liquid liquid interface columns can have the same hydrostatic pressure without being identical to one another Oil Oil Oil Water lt Water Water The only way to ensure proper two p
584. suitability The primary consideration for selecting a proper temperature sensing element for any application is the expected temperature range Mechanical bi metal and filled system temperature sensors are limited to relatively low process temperatures and cannot relay signals very far from the point of measurement Thermocouples are by far the most rugged and wide ranging of the contact type temperature sensors Accuracies vary with thermocouple type and installation quality RTDs are more fragile than thermocouples but they require no reference compensation and are inherently more linear Optical sensors lack the ability to measure temperature of fluids inside vessels unless a transparent window is provided in the vessel for light emissions to reach the sensor Otherwise the best an optical sensor can do is report the skin temperature of a vessel For monitoring surface temperatures of solid objects especially objects that would be impractical or even dangerous to contact e g electrical insulators on high voltage power lines optical sensors are the only appropriate solution Chemical reactivity is a concern for contact type sensors If the sensing element is held inside a thermowell that thermowell must be selected for minimum reaction with the process fluid s Bare thermocouples are particularly vulnerable to chemical reactions given the nature of most thermocouple metals iron nickel copper etc and must be carefully chosen for the
585. sure caused by the flow rate manifests itself as a difference in liquid height at different points in the channel Thus weirs and flumes allow the indirect measurement of liquid flow by sensing liquid height An interesting feature of weirs and flumes is that although they are nonlinear primary sensing elements their nonlinearity is quite different from that of an orifice Note the following transfer functions for different weirs and flumes relating the rate of liquid flow through the device Q to the level of liquid rise upstream of the device called head or H 582 CHAPTER 17 SIGNAL CHARACTERIZATION Q 2 48 ten 5 H V notch weir Q 3 367LH Cippoletti weir Q 0 992H 3 inch wide throat Parshall flume Q 3 07H 53 9 inch wide throat Parshall flume Where Q Volumetric flow rate cubic feet per second CFS L Width of notch crest or throat width feet V notch angle degrees H Head feet It is important to note these functions provide answers for flow rate Q with head H being the independent variable In other words they will tell us how much liquid is flowing given a certain head In the course of calibrating the head measuring instruments that infer flow rate however it is important to know the inverse transfer function how much head there will be for any given value of flow Here algebraic manipulation becomes important to the technician For example here is the solution for H in the function for
586. suring mechanism Vessel valves displacer Displacer cage The following photograph shows a Fisher LevelTrol model pneumatic transmitter measuring condensate level in a knockout drum for natural gas service The instrument itself appears on the right hand side of the photo topped by a grey colored head with two pneumatic pressure gauges visible The displacer cage is the vertical pipe immediately behind and below the head unit Note that a sightglass level gauge appears on the left hand side of the knockout chamber or condensate boot for visual indication of condensate level inside the process vessel 13 4 DISPLACEMENT 383 Two photos of a disassembled LevelTrol displacer instrument appear here showing how the displacer fits inside the cage pipe 384 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT The cage pipe is coupled to the process vessel through two block valves allowing isolation from the process A drain valve allows the cage to be emptied of process liquid for instrument service and zero calibration Full range calibration may be done by flooding the cage with process liquid a wet calibration or by suspending the displacer with a string and precise scale a dry calibration pulling upward on the displacer at just the right amount to simulate buoyancy at 100 liquid level 13 4 DISPLACEMENT 385 Pull up on string until scale registers the desired force Dry calibration Scale
587. t as that output is increased and decreased in steps Ls PV 25 Output Time gt Notice the time delay between when the output signal is stepped to a new value and when the process variable responds to the change This sort of delay is generally not good for a control system Imagine trying to steer an automobile whose front wheels respond to your input at the steering wheel only after a 5 second delay This would be a very challenging car to drive because the steering is grossly delayed The same problem plagues any industrial control system with a time lag between the final control element and the transmitter Typical causes of this problem include transport delay where there is a physical delay resulting from transit time of a process medium from the point of control to the point of measurement and mechanical problems in the final control element This next example shows another type of problem revealed by a trend recording during manual mode testing 144 CHAPTER 5 INTRODUCTION TO INDUSTRIAL INSTRUMENTATION PV 30 Output Time gt Here we see the process quickly responding to all step changes in controller output except for those involving a change in direction This problem is usually caused by mechanical friction in the final control element e g sticky valve stem packing in a pneumatically actuated control valve and is analogous to loose steering in an automobile where the driver must turn the steerin
588. t kinds of flow measurement technologies When the pipe carrying process fluid is large in size it may be impractical or cost prohibitive to install a full diameter flowmeter to measure fluid flow rate A practical alternative for many applications is the installation of an insertion flowmeter a probe that may be inserted into or extracted from a pipe to measure fluid velocity in one region of the pipe s cross sectional area usually the center A classic example of an insertion flowmeter element is the Annubar a form of averaging pitot tube pioneered by the Dieterich Standard corporation The Annubar flow element is inserted into a pipe carrying fluid where it generates a differential pressure for a pressure sensor to measure Compression nut a Gland nut Handle The Annubar element may be extracted from the pipe by loosening a gland nut and pulling the assembly out until the end passes through a hand ball valve Once the element has been extracted this far the ball valve may be shut and the Annubar completely removed from the pipe 15 10 INSERTION FLOWMETERS 533 Loosen this nut to lt extract the Annubar Close this ball valve Ball valve when the Annubar is clear Other flowmeter technologies manufactured in insertion form include vortex turbine and thermal mass If the flow detection element is compact rather than distributed care must be taken to ensure correct positioning within the pipe Si
589. t loss However if there is even a slight breeze of air moving past your body your body will come into contact with more cool unheated air molecules than it would otherwise causing a greater rate of heat loss Thus your perception of the surrounding temperature will be cooler than if there were no breeze We may exploit this principle to measure mass flow rate by placing a heated object in the midst of a fluid flowstream and measuring how much heat the flowing fluid convects away from the heated object The wind chill experienced by that heated object is a function of true mass flow rate and not just volumetric flow rate because the mechanism of heat loss is the rate at which fluid molecules contact the heated object with each of those molecules having a definite mass The simplest form of thermal mass flowmeter is the hot wire anemometer used to measure air speed This flowmeter consists of a metal wire through which an electric current is passed to heat it up An electric circuit monitors the resistance of this wire which is directly proportional to wire temperature because most metals have a definite temperature coefficient of resistance If air speed past the wire increases more heat will be drawn away from the wire and cause its temperature to drop The circuit senses this temperature change and compensates by increasing current through the wire to bring its temperature back up to setpoint The amount of current sent through the wi
590. t proportional gain influences both P and I terms which is quite common One could also express that controller s integral action as 0 2 repeats per minute instead of 5 minutes per repeat just to be confusing Derivative is the most consistent tuning parameter of them all always being expressed directly in units of time usually minutes or seconds A controller with a derivative time setting of 2 minutes will generate an output offset of 10 if it sees the error changing at a steady rate of 5 per minute That is unless the proportional gain of the controller also affects derivative action in which case the amount of offset introduced by derivative action will be multiplied by the gain value Oh but the fun doesn t end here In addition to having multiple units of measurement to express PID settings we also have multiple algorithms for calculating the controller output The version I ve been showing you thus far in this section is called the parallel algorithm with the P I and D terms all separate 18 7 PID CONTROLLER TUNING 617 dt If only things were always this simple As luck would have it the best algorithm for tuning real processes called the ISA algorithm uses Kp as a multiplier for all three terms and so the resulting equation looks different d m Kye K edt Ka b de m K erro fears Ku b Back in the days when pneumatic controllers were the norm it was expensive to build PID controllers to implement eith
591. t signal anyway Such an approach will work to an extent but any digital 264 CHAPTER 11 INSTRUMENT CALIBRATION queries to the transmitter e g using a digital over analog protocol such as HART will result in conflicting information as the current signal represents full scale 100 PSI while the digital register inside the transmitter shows 96 PSI The only comprehensive solution to this problem is to trim the analog to digital converter so that the transmitter s microprocessor knows the actual pressure value applied to the sensor Once digital trims have been performed on both input and output converters of course the technician is free to re range the microprocessor as many times as desired without re calibration This capability is particularly useful when re ranging is desired for special conditions such as process start up and shut down when certain process variables drift into uncommon regions An instrument technician may use a hand held digital communicator device to re set the LRV and URV range values to whatever new values are desired by operations staff without having to re check calibration by applying known physical stimuli to the instrument So long as the ADC and DAC trims are both fine the overall accuracy of the instrument will still be good with the new range With analog instruments the only way to switch to a different measurement range was to change the zero and span adjustments which necessitated the re
592. t technicians were often referred to as instrument mechanics for these air powered devices were mechanically complex and in frequent need of adjustment to maintain high accuracy Pneumatic instruments still find wide application in industry although it is increasingly rare to encounter completely pneumatic control loops One of the most common applications for pneumatic control system components is control valve actuation where pneumatic technology still dominates Not only is compressed air used to create the actuation force in many control valve mechanisms it is still often the signal medium employed to command the valve s position Quite often this pneumatic signal originates from a device called an I P transducer or current to pressure converter taking a 4 20 mA control signal from the output of an electronic controller and translating that information as a pneumatic 3 15 PSI signal to the control valve s positioner or actuator 9 1 PNEUMATIC SENSING ELEMENTS 213 9 1 Pneumatic sensing elements Most pneumatic instruments use a simple but highly sensitive mechanism for converting mechanical motion into variable air pressure the baffle and nozzle assembly sometimes referred to as a flapper and nozzle assembly A baffle is nothing more than a flat object obstructing the flow of air out of a small nozzle by close proximity Pressure gauge Clearance Nozzle gt From compressed air supply gt 20 PSI Baf
593. t where it was prior to the load change Unfortunately it will not although the reason for this may not be evident upon first inspection In order to prove that the PV will never go back to SP as long as the incoming feed temperature has dropped let us imagine for a moment that somehow it did According to the proportional controller equation this would mean that the steam valve would resume its old pre load change position only letting through the original flow rate of steam to heat the process fluid Obviously if the incoming process fluid is colder than before and the flow rate is unchanged the same amount of heat input from steam will result in a colder outlet temperature In other words if the steam valve goes back to its old position the outlet temperature will fall just as it did when the incoming flow suddenly became colder This tells us the controller cannot bring the outlet temperature back up to setpoint by proportional action alone What will happen is that the controller s output will increase with falling outlet temperature until there is enough steam flow admitted to the heat exchanger to prevent the temperature from falling any further But in order to maintain this greater flow rate of steam for greater heating effect an error must develop between PV and SP In other words the process variable temperature must fall a bit in order for the controller to call for more steam in order that the process variable does not fall
594. takes one of the following forms in industry e Fluid pressure e Fluid flow rate e The temperature of an object e Fluid volume stored in a vessel e Chemical concentration e Machine position motion or acceleration e Physical dimension s of an object e Count inventory of objects e Electrical voltage current or resistance Once we measure the quantity we are interested in we usually transmit a signal representing this quantity to an indicating or computing device where either human or automated action then takes place If the controlling action is automated the computer sends a signal to a final controlling device which then influences the quantity being measured This final control device usually takes one of the following forms 129 130 CHAPTER 5 INTRODUCTION TO INDUSTRIAL INSTRUMENTATION e Control valve for throttling the flow rate of a fluid e Electric motor e Electric heater Both the measurement device and the final control device connect to some physical system which we call the process To show this as a general block diagram Decides Senses Influences The common home thermostat is an example of a measurement and control system with the home s internal air temperature being the process under control In this example the thermostat usually serves two functions sensing and control while the home s heater adds heat to the home to increase temperature and or the home s air conditioner extracts
595. tal to master if one hopes to be able to manipulate algebraic literal expressions For example to solve for time t in this exponential formula you must know that the natural logarithm function directly un does the exponential e This is the only way to unravel the equation and get t isolated by itself on one side of the equals sign V 12e Divide both sides by 12 Take the natural logarithm of both sides n 5 ne The natural logarithm cancels out the exponential 573 574 CHAPTER 17 SIGNAL CHARACTERIZATION Multiply both sides by negative one In industry there exist a great many practical problems where inverse functions play a similar role Just as inverse functions are useful for manipulating literal expressions in algebra they are also useful in inferring measurements of things we cannot directly measure Many continuous industrial measurements are inferential in nature meaning that we actually measure some other variable in order to quantify the variable of interest More often than not the relationship between the primary variable and the inferred variable is nonlinear necessitating some form of mathematical processing to complete the inferential measurement Take for instance the problem of measuring fluid flow through a pipe To the layperson this may seem to be a trivial problem However there is no practical way to directly and continuously measure the flow rate of a fluid especially when we
596. tandard pH measurement electrode produces no potential when the process solution s pH value is exactly 7 0 pH equal in hydrogen ion activity to the buffer solution trapped within the bulb Actually measuring this voltage however presents a bit of a problem while we have a convenient electrical connection to the solution inside the glass bulb we do not have any place to connect the 552 CHAPTER 16 CONTINUOUS ANALYTICAL MEASUREMENT other terminal of a sensitive voltmeter to the solution outside the bulb In order to establish a complete circuit from the glass membrane to the voltmeter we must create a zero potential electrical junction with the process solution To do this we use another special electrode called a reference electrode wire connection point Reference electrode Glass or plastic body silver wire Filled with potassium chloride silver chloride puffer solution tip Porous junction Together the measurement and reference electrodes provide a voltage generating element sensitive to the pH value of whatever solution they are submerged in Remember that voltage is always measured between two points 16 4 PH MEASUREMENT 553 Voltmeter Measurement Reference electrode electrode Sik a The most common configuration for modern pH probe sets is what is called a combination electrode which combines both the glass measurement electrode and the porous reference electrode in a single unit This
597. tap installation is actually measuring permanent pressure loss which also happens to scale with the square of flow rate because the primary mechanism for energy loss in turbulent flow conditions is the translation of linear velocity to angular swirling velocity in the form of eddies This kinetic energy is eventually dissipated in the form of heat as the eddies eventually succumb to viscosity 15 1 PRESSURE BASED FLOWMETERS 467 15 1 3 Other differential producers Other pressure based flow elements exist as alternatives to the orifice plate The Pitot tube for example senses pressure as the fluid stagnates comes to a complete stop against the open end of a forward facing tube A shortcoming of the classic single tube Pitot assembly is sensitivity to fluid velocity at just one point in the pipe so a more common form of Pitot tube seen in industry is the averaging Pitot tube consisting of several stagnation holes sensing velocity at multiple points across the width of the flow Averaging Pi itot tube pitot tube A variation on the latter theme is the Annubar flow element a trade name of the Dieterich Standard corporation An Annubar is an averaging pitot tube consolidating high and low pressure sensing ports in a single probe assembly 468 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT Annubar Divider internal Holes A less sophisticated realization of the stagnation principle is the targ
598. ted against higher tier standards maintained by outside laboratories In years past instrument shops would often maintain their own standard cell batteries often called Weston cells as a primary voltage reference These special purpose batteries produced 1 0183 volts DC at room temperature with low uncertainty and drift but were sensitive to vibration and non trivial to actually use Now electronic voltage references have all but displaced standard cells in calibration shops and laboratories but these references must be checked and adjusted for drift in order to maintain their NIST traceability One enormous benefit of electronic calibration references is that they are able to generate accurate currents and resistances in addition to voltage and not just voltage at one fixed value either Modern electronic references are digitally controlled as well which lends themselves well to automated testing in assembly line environments and or programmed multi point calibrations with automatic documentation of as found and as left calibration data If a shop cannot afford one of these versatile references for benchtop calibration use an acceptable alternative in some cases is to purchase a high accuracy multimeter and equip the calibration bench with adjustable voltage current and resistance sources These sources will be simultaneously connected to the high accuracy multimeter and the instrument under test and adjusted until the high accuracy meter re
599. the controller s aggressiveness in terms of how much input change is necessary in units of percent to produce a full scale 100 change in output signal Thus a gain of 2 would be expressed as a proportional band of 50 A gain of 5 would be equivalent to a proportional band of 20 A gain of 0 4 is the same as a proportional band of 250 These are just two different reciprocal ways of saying the same thing Integral isn t any better We have two reciprocal again ways of expressing how fast a controller will ramp its output integrate given a constant input error The first way is in units of time usually minutes or seconds An integral only controller with a tuning constant value of 2 minutes and a constant error difference between SP and PV of 10 will ramp the output at a constant rate of 10 every 2 minutes or 5 per minute Often we find integral action included with proportional in the same controller and so the integral constant is sometimes expressed in minutes per repeat instead of just minutes referring to how many minutes the integral action will repeat proportional s action Thus a PI controller with a proportional gain of 1 an integral constant of 5 minutes per repeat and a constant error of 10 will take 5 minutes to ramp the output 10 or 2 per minute The same controller with twice the proportional gain will only take 2 5 minutes to ramp the output the same amount 4 per minute if the algorithm is such tha
600. the electrical property of inductance allows potential energy to be stored in a magnetic field manifesting as a voltage different along the length of a conductor Even then the law of energy conservation is not violated because the stored energy re emerges at a later time 92 CHAPTER 3 DC ELECTRICITY Parallel circuit resistors connected across each other Voltage is the same throughout Vio Vi V2 Va Currents add up to equal the total Lota 1 b 1 Resistances diminish to equal the total Roa Rt R R The rule for calculating total resistance in a parallel circuit perplexes many students with its weird compound reciprocal notation There is a more intuitive way to understand this rule and it involves a different quantity called conductance symbolized by the letter G Conductance is defined as the reciprocal of resistance that is a measure of how easily electrical charge carriers may move through a substance If the electrical resistance of an object doubles then it now has half the conductance it did before 1 C It should be intuitively apparent that conductances add in parallel circuits That is the total amount of conductance for a parallel circuit must be the sum total of all individual conductances because the addition of more conductive pathways must make it easier overall for charge carriers to move through the circuit Thus Giotal Gi G2 Gn The formula shown here should be fami
601. the impulse lines and how cold the weather gets in that geographic location One safeguard against impulse line freezing is to trace the impulse lines with some form of active heating medium steam and electrical being the most common Steam tracing consists of a copper tube carrying low pressure steam bundled alongside one or more impulse tubes enclosed in a thermally insulating jacket Isolation block valve 15 PSI steam supply __Steam traced impulse tube Pressure gauge lt Steam trap Vent Steam flows through the shutoff valve through the tube in the insulated bundle transferring heat to the impulse tube as it flows past Cooled steam condenses into water and collects in the steam trap device located at the lowest elevation on the steam trace line When the water level builds up to a certain level inside the trap a float operated valve opens to vent the water This allows more steam to flow into the tracing tube keeping the impulse line continually heated The steam trap naturally acts as a sort of thermostat as well even though it only senses condensed water level and not temperature The rate at which steam condenses into water depends on how cold the impulse tube is The colder the impulse tube caused by colder ambient conditions the more heat energy drawn from the steam and consequently the faster condensation rate of steam into water This means water will accumulate faster in the steam trap
602. the input terminals together forcing Vinput to be equal to 0 millivolts and note the pH indication on the instrument s display When calibrating a pH instrument you should choose buffers that most closely bracket the expected range of pH measurement in the process The most common buffer pH values are 4 7 and 10 nominal For example if you expect to measure pH values in the process ranging between 7 5 and 9 you should calibrate that pH instrument using 7 and 10 buffers 13 With all modern pH instruments being digital in design this standardization process usually entails pressing a pushbutton on the faceplate of the instrument to tell it that the probe is stabilized in the buffer solution 16 5 CHROMATOGRAPHY 561 16 5 Chromatography Imagine a major marathon race where hundreds of runners gather in one place to compete When the starting gun is fired all the runners begin running the race starting from the same location the starting line at the same time As the race progresses the faster runners distance themselves from the slower runners resulting in a dispersion of runners along the race course over time Now imagine a marathon race where certain runners share the exact same running speeds Suppose a group of runners in this marathon all run at exactly 8 miles per hour MPH while another group of runners in the race run at exactly 6 miles per hour and another group runs at exactly 5 miles per hour What would
603. the landscape so continuously subject to change that life long learning for the technician is a matter of professional survival Chapter 6 Instrumentation documents Every technical discipline has its own standardized way s of making descriptive diagrams and instrumentation is no exception The scope of instrumentation is so broad however that no one form of diagram is sufficient to capture all we might need to represent This chapter will discuss three different types of instrumentation diagrams e Process Flow Diagrams PFDs e Process and Instrument diagrams P amp IDs e Loop diagrams e SAMA diagrams At the highest level the instrument technician is interested in the interconnections of process vessels pipes and flow paths of process fluids The proper form of diagram to represent the big picture of a process is called a process flow diagram Individual instruments are sparsely represented in a PFD because the focus of the diagram is the process itself At the lowest level the instrument technician is interested in the interconnections of individual instruments including all the wire numbers terminal numbers cable types instrument calibration ranges etc The proper form of diagram for this level of fine detail is called a loop diagram Here the process vessels and piping are sparsely represented because the focus of the diagram is the instruments themselves Process and instrument diagrams P amp IDs lie somewhere
604. the pressure gauge in units of grams mass instead of PSI or kPa pressure 9 2 SELF BALANCING PNEUMATIC INSTRUMENT PRINCIPLES 219 Gauge Tube Air supply A Orifice Although it may seem as though we are done with the task of fully automating the laboratory scale we can go a step further Building this pneumatic negative feedback balancing system provides us with a capability the old manually operated scale never had remote indication There is no reason why the indicating gauge must be located near the scale Nothing prevents us from locating the receiver gauge some distance from the scale and using long lengths of tubing to connect the two Gauge e Along ways away gt Tube Air supply ge Orifice By equipping the scale with a pneumatic self balancing apparatus we have turned it into a pneumatic mass transmitter capable of relaying the mass measurement in pneumatic analog form to an indicating gauge far away This is the basic force balance principle used in most pneumatic industrial transmitters to convert some process measurement into a 3 15 PSI pneumatic signal 220 CHAPTER 9 PNEUMATIC INSTRUMENTATION 9 3 Pilot valves and pneumatic amplifying relays Self balancing mechanisms such as the fictitious pneumatic laboratory scale in the previous section are most accurate when the imbalance detection mechanism is most sensitive In other words the more aggressively the baffle n
605. the square root of both sides we arrive at our final answer 1 V V2 So for a sinusoidal voltage with a peak value of 1 volt the DC equivalent or RMS voltage value would be a volts or approximately 0 707 volts In other words a sinusoidal voltage of 1 volt peak will produce just as much power dissipation at a resistor as a steady DC battery voltage of 0 7071 volts applied to that same resistor Therefore this 1 volt peak sine wave may be properly called a 0 7071 volt RMS sine wave or a 0 7071 volt DC equivalent sine wave This factor for sinusoidal voltages is quite useful in electrical power system calculations where the wave shape of the voltage is nearly always sinusoidal or very close In your home for example the voltage available at any wall receptacle is 120 volts RMS which translates to 169 7 volts peak Electricians and electronics technicians often memorize the wi conversion factor without realizing it only applies to sinusoidal voltage and current waveforms If we are dealing with a non sinusoidal wave shape the conversion factor between peak and RMS will be different The mathematical procedure for obtaining the conversion factor will be identical though integrate the wave shape s function squared over an interval sufficiently long to capture the essence of the shape and set that equal to V times that same interval span 4 2 RESISTANCE REACTANCE AND IMPEDANCE 117 4 2 Resistance Reactance and Im
606. then sends a manipulated variable signal to a flow control valve FCV Flow transmitter PID controller A cascaded control system where the output of one controller acts as the setpoint for another controller to follow appears in SAMA diagram form like this 6 4 SAMA DIAGRAMS 157 Level Flow transmitter transmitter EAS PID controller FCV Flow control valve In this case the primary controller senses the level in a vessel commanding the secondary flow controller to maintain the necessary amount of flow either in or out of the vessel as needed to maintain level at some setpoint SAMA diagrams may show varying degrees of detail about the control strategies they document For example you may see the auto manual controls represented as separate entities in a SAMA diagram apart from the basic PID controller function In the following example we see a transfer block T and two manual adjustment blocks A providing a human operator the ability to separately adjust the controller s setpoint and output manipulated variables and to transfer between automatic and manual modes 158 CHAPTER 6 INSTRUMENTATION DOCUMENTS Flow transmitter PID controller Flow control valve Rectangular blocks such as the A P I and D shown in this diagram represent automatic functions Diamond shaped blocks such as the A and T blocks are manual functions which must be set by a human operator Showing even more detail the fol
607. ther at one end a voltage is produced at the other end that is approximately proportional to temperature That is to say the junction of two different metals behaves like a temperature sensitive battery This form of electrical temperature sensor is called a thermocouple Iron Fe wire Junction Voltage Copper Cu wire PS This phenomenon provides us with a simple and direct way to electrically infer temperature simply measure the voltage produced by the junction and you can tell the temperature of that junction And it would be that simple if it were not for an unavoidable consequence of electric circuits when we connect any kind of electrical instrument the iron and copper wires we inevitably produce another junction of dissimilar metals The following schematic shows this fact Junction Iron 42 Voltmeter Copper Junction J Junction Js Junction J is a junction of iron and copper two dissimilar metals which will generate a voltage related to temperature Note that junction J2 which is necessary for the simple fact that we must somehow connect our copper wired voltmeter to the iron wire is also a dissimilar metal junction which will generate a voltage related to temperature Note also how the polarity of junction J2 stands opposed to the polarity of junction J iron positive copper negative A third junction J3 also exists between wires but it is of no consequence because it is a junction
608. third law describes how forces always exist in pairs between two objects The rotating blades of a helicopter for example exert a downward force on the air accelerating the air but the air in turn exerts an upward force on the helicopter suspending it in flight These two forces are equal in magnitude but opposite in direction Such is always the case when forces exist between objects 22 CHAPTER 1 PHYSICS 1 7 2 Work and Energy Work is the expenditure of energy resulting from exerting a force over a parallel displacement motion W Fr Where W Work in joules metric or foot pounds English F Force doing the work in newtons metric or pounds English x Displacement over which the work was done in meters metric or feet English Potential energy is energy existing in a stored state having the potential to do useful work If we perform work in lifting a mass vertically against the pull of earth s gravity we store potential energy which may later be released by allowing the mass to return to its previous altitude The equation for potential energy in this case is just a special form of the work equation W Fx where work is now expressed as potential energy W Ep force is now expressed as a weight caused by gravity acting on a mass F mg and displacement is now expressed as a height x h W Fr Ep mgh Where E Potential energy in joules metric or foot pounds British m Mass of o
609. this constant flow of purge fluid into the process Also it is important to limit the flow of purge fluid to a rate that will not create a falsely high pressure measurement due to restrictive pressure drop across the length of the impulse line yet flow freely enough to achieve the goal of plug prevention In many installations a visual flow indicator is installed in the purge line to facilitate optimum purge flow adjustment Such flow indicators are also helpful for troubleshooting as they will indicate if anything happens to stop the purge flow In the previous example the purge fluid was clean water Many options exist for purge fluids other than water though Gases such as air nitrogen or carbon dioxide are often used in purged systems for both gas and liquid process applications Purged impulse lines just like filled lines and diaphragm isolated lines will generate hydrostatic pressure with vertical height If the purge fluid is a liquid this elevation dependent pressure may be an offset to include in the instrument s calibration If the purge fluid is a gas such as air however any height difference may be ignored because the density of the gas is negligible 340 CHAPTER 12 CONTINUOUS PRESSURE MEASUREMENT 12 6 7 Heat traced impulse lines If impulse lines are filled with liquid there may exist a possibility for that liquid to freeze in cold weather conditions This possibility depends of course on the type of liquid filling
610. this container is constant the accumulated volume or weight should increase linearly over time The actual flow rate may then be calculated by dividing the change in volume AV by the time interval over which the change in volume was measured At The resulting quotient is the average flow rate between those two points in time which is an approximation of instantaneous flow rate A Average flow AV z a Instantaneous flow At d i If a suitable vessel exists in the process with level measuring capability e g a liquid storage vessel equipped with a level transmitter you may apply the same mathematical technique use that vessel as an accumulator for the flow in question tracking the accumulated or lost volume over time and then calculating a The accuracy of this technique rests on some additional factors though e The accuracy of the level transmitter as a volume measuring instrument e The ability to ensure only one flow path in or out of that vessel The first condition listed here places significant limitations on the flow calibration accuracy one can achieve with this method In essence you are using the level instrument as the test gauge for the flow instrument so it needs to be high accuracy in order to achieve even reasonable accuracy for the flowmeter being calibrated A more sophisticated approach for direct flow validation is the use of a device called a flow prover A flow prover is a precision pist
611. tial pressure applied to the transmitter in this condition is the difference between the high and low port pressures which becomes the lower range value LRV for calibration Prrv 101 52 W C 117 72 W C 16 2 W C As the second step in our thought experiment we imagine what the process would look like with the interface at the URV level calculating hydrostatic pressures seen at each side of the transmitter Interface level URV Fill fluid 5G 71 09 am e ei poe Electronic output signal 380 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT Phigh 7 5 feet of heavy liquid 1 5 feet of light liquid Phigh 90 inches of heavy liquid 18 inches of light liquid Prigh W C 90 inches of heavy liquid 1 1 18 inches of light liquid 0 78 Phign W C 99 W C 14 04 W C Phigh 113 04 W C The hydrostatic pressure of the compensating leg is exactly the same as it was before 9 feet of fill fluid having a specific gravity of 1 09 which means there is no need to calculate it again It will still be 117 72 inches of water column Thus the differential pressure at the URV point is Pury 113 04 W C 117 72 W C 4 68 W C Using these two pressure values and some interpolation we may generate a 5 point calibration table assuming a 4 20 mA transmitter output signal range for this interface level measurement system Interface level Percent
612. titutes a command to the rest of the drive circuitry telling it to modulate the power going to the electric motor in order to drive it at the desired speed Controller To source of 3 phase AC power OA i Two wire cable MO Y 198 CHAPTER 8 ANALOG ELECTRONIC INSTRUMENTATION 8 4 4 wire self powered transmitter current loops DC electric current signals may also be used to communicate process measurement information from transmitters to controllers indicators recorders alarms and other input devices The simplest form of 4 20 mA measurement loop is one where the transmitter has two terminals for the 4 20 mA signal wires to connect and two more terminals where a power source connects These transmitters are called 4 wire or self powered The current signal from the transmitter connects to the process variable input terminals of the controller to complete the loop Controller 4 wire transmitter YF ji 2 wire cable JE MO Y Power source Typically process controllers are not equipped to directly accept milliamp input signals but rather voltage signals For this reason we must connect a precision resistor across the input terminals to convert the 4 20 mA signal into a standardized analog voltage signal that the controller can understand A voltage signal range of 1 to 5 volts is standard although some models of controller use different voltage ranges and therefore require different precision resisto
613. to as pH Free hydrogen ions Ht are rare in a liquid solution and are more often found attached to whole water molecules to form a positive ion called hydronium H30 However process control professionals usually refer to these positive ions simply as hydrogen even though the truth is a bit more complicated pH is mathematically defined as the negative common logarithm of hydrogen ion activity in a solution Hydrogen ion activity is expressed as a molarity number of moles of active ions per liter of solution with pH being the unit of measurement for the logarithmic result pH log H For example an aqueous solution with an active hydrogen concentration of 0 00044 M has a pH value of 3 36 pH Water is a covalent compound and so there is little separation of water molecules in liquid form Most of the water molecules remain as whole molecules H20 while a very small percentage ionize into positive hydrogen ions Ht and negative hydroxyl ions OH The mathematical product of hydrogen and hydroxyl ion molarity in water is known as the ionization constant Kw and its value varies with temperature At 25 degrees Celsius room temperature the value of Ky is 1 0 x 10714 Since each one of the water molecules that does ionize in this absolutely pure water sample separates into exactly one hydrogen ion Ht and one hydroxyl ion OH the molarities of hydrogen and hydroxyl ions must be equal to each other The equa
614. to liquid volume However if the vessel in question does not have a constant cross sectional area throughout its height the relationship between liquid height and liquid volume will not be linear For example there is a world of difference between the height volume functions for a vertical cylinder versus a horizontal cylinder her F m ame The volume function for a vertical cylinder is a simple matter of geometry height h multiplied by the cylinder s cross sectional area mr V nrh 584 CHAPTER 17 SIGNAL CHARACTERIZATION Calculating the volume of a horizontal cylinder as a function of liquid height h is a far more complicated matter because the cross sectional area is also a function of height For this we need to apply calculus First we begin with the mathematical definition of a circle then graphically represent a partial area of that circle as a series of very thin rectangles r h r r In this sketch I show the circle filling from left to right rather than from bottom to top I have done this strictly out of mathematical convention where the x horizontal axis is the independent variable No matter how the circle gets filled the relationship of area A to fill distance A will be the same If x y r the mathematical definition of a circle then the area of each rectangular slice comprising the accumulated area between r and h r is equal to 2y dx In other words the total
615. to process liquid density 346 CHAPTER 12 CONTINUOUS PRESSURE MEASUREMENT References Beckerath Alexander von Eberlein Anselm Julien Hermann Kersten Peter and Kreutzer Jochem WIKA Handbook Pressure and Temperature Measurement WIKA Alexander Wiegand GmbH amp Co Klingenberg Germany 1995 Digital Sensor Technology PowerPoint slideshow presentation Yokogawa Corporation of America Fribance Austin E Industrial Instrumentation Fundamentals McGraw Hill Book Company New York NY 1962 Kallen Howard P Handbook of Instrumentation and Controls McGraw Hill Book Company Inc New York NY 1961 Lipt k B la G Instrument Engineers Handbook Process Measurement and Analysis Volume I Fourth Edition CRC Press New York NY 2003 Patrick Dale R and Patrick Steven R Pneumatic Instrumentation Delmar Publishers Inc Albany NY 1993 Technical Note Rosemount 1199 Fill Fluid Specifications Rosemount Emerson Process Management 2005 Chapter 13 Continuous level measurement Many industrial processes require the accurate measurement of fluid or solid powder granule etc height within a vessel Some process vessels hold a stratified combination of fluids naturally separated into different layers by virtue of differing densities where the height of the interface point between liquid layers is of interest A wide variety of technologies exist to measure the level of substances in a
616. trast to a speedometer which indicates how far the vehicle is traveling per unit of time Imagine a car moving along at exactly 30 miles per hour How far will this vehicle travel after 1 hour of driving this speed Obviously it will travel 30 miles Now how far will this vehicle travel if it continues for another 2 hours at the exact same speed Obviously it will travel 60 more miles for a total distance of 90 miles since it began moving If the car s speed is a constant calculating total distance traveled is a simple matter of multiplying that speed by the travel time The odometer mechanism that keeps track of the mileage traveled by the car may be thought of as integrating the speed of the car with respect to time In essence it is multiplying speed times time continuously to keep a running total of how far the car has gone When the car is traveling at a high speed the odometer integrates at a faster rate When the car is traveling slowly the odometer integrates slowly If the car travels in reverse the odometer will decrement count down rather than increment count up because it sees a negative quantity for speed The rate at which the odometer decrements depends on how fast the car travels in reverse When the car is stopped zero speed the odometer holds its reading and neither increments nor decrements Now imagine how this concept might apply to a process controller Integration is provided either by a mechanism i
617. tream of the weir Zero flow Liquid spilling over weir crest Effective notch area Effective notch area l Zero flow Some flow More flow This dependence of notch area on flow rate creates a very different relationship between flow rate and liquid height measured above the crest than the relationship between flow rate and differential pressure in an orifice plate Q 3 33 L 0 2H H Rectangular weir Q 3 367LH Cippoletti weir 17Orifice plates are variable pressure constant area flowmeters Rotameters are constant pressure variable area flowmeters Weirs are variable pressure variable area flowmeters As one might expect the mathematical functions describing each of these flowmeter types is unique 15 3 VARIABLE AREA FLOWMETERS 491 Q 2 48 tan 5 4 V notch weir Where Q Volumetric flow rate cubic feet per second CFS L Width of crest feet 9 V notch angle degrees H Head feet As you can see from a comparison of characteristic flow equations between these three types of weirs the shape of the weir s notch has a dramatic effect on the mathematical relationship between flow rate and head liquid level upstream of the weir measured above the crest height This implies that it is possible to create almost any characteristic equation we might like just by carefully shaping the weir s notch in some custom form A good example of this is the so called proportional or Sutro weir
618. trons These positive charge carriers are repelled by any positive pole and attracted to any negative pole Viewed in this light we see the exact same principle at work the source device is seen to motivate the flow of these positive charge carriers while the load device resists the flow 3 7 RESISTORS 99 Shown using conventional flow notation Source l Load Generator C Resistor Positive charge carriers are repelled by the poles and attracted to the poles In later sections we encounter devices with the ability to act as sources and loads at different times Both capacitors see section 3 9 starting on page 108 and inductors see section 3 10 starting on page 110 have the ability to temporarily contribute to and extract energy from electrical circuits both having the ability to act as energy storage devices 3 7 Resistors Resistance is dissipative opposition to the flow of charge carriers All conductors except superconductors possess some electrical resistance The relationship between voltage current and resistance is known as Ohm s Law V IR Conductance G is the reciprocal of resistance 1 G R Resistors are devices expressly designed and manufactured to possess electrical resistance They are constructed of a partially conductive material such as carbon or metal alloy Resistors have power dissipation ratings as well as resistance ratings Here are some schematic symbols for resistors The am
619. tube Annubar Divider internal pem Holes The following subsections in this flow measurement chapter explore different primary sensing elements PSE s used to generate differential pressure in a moving fluid stream Despite their very different designs they all operate on the same fundamental principle causing a fluid to accelerate or decelerate by changing its flow path and thus generating a measurable pressure difference The following subsection will introduce a device called a venturi tube used to measure fluid flow rates and derive mathematical relationships between fluid pressure and flow rate starting from basic physical conservation laws 15 1 PRESSURE BASED FLOWMETERS 449 15 1 1 Venturi tubes and basic principles The standard example used to demonstrate pressure change in a fluid stream is the venturi tube a pipe purposefully narrowed to create a region of low pressure If the fluid going through the venturi tube is a liquid under relatively low pressure we may vividly show the pressure at different points in the tube by means of piezometers which are transparent tubes allowing us to view liquid column heights The greater the height of liquid column in the piezometer the greater the pressure at that point in the flowstream Point 1 Point 2 Point 3 Ground level As indicated by the piezometer liquid heights pressure at the constriction point 2 is the least while pressures at the wide portions of the ve
620. ture in Kelvin K n Number of electrons transferred per ion exchanged unitless F Faraday constant in coulombs per mole 96 485 C mol e C Concentration of ion in measured solution in moles per liter of solution M C2 Concentration of ion in reference solution on other side of membrane in moles per liter of solution M We may also write the Nernst equation using of common logarithms instead of natural logarithms which is usually how we see it written in the context of pH measurement V _2303RT A nF 5 Ca In the case of pH measurement the Nernst equation describes the amount of electrical voltage developed across a special glass membrane due to hydrogen ion exchange between the process liquid solution and a buffer solution inside the bulb formulated to maintain a constant pH value of 7 0 pH Special pH measurement electrodes are manufactured with a closed end made of this glass with the buffer solution contained within the glass bulb 16 4 PH MEASUREMENT 551 wire connection point Measurement electrode glass body silver wire Bulb filled with potassium chloride buffer solution 7 0 pH Very thin glass bulb Voltage produced across thickness of glass membrane Any concentration of hydrogen ions in the process solution differing from the hydrogen ion concentration in the buffer solution H 1 x 1077 M will cause a voltage to develop across the thickness of the glass Thus a s
621. ude of the circuit voltage and the frequency of oscillation how rapidly the waveforms alternate over time each type of component will only pass so much current It would be nice then to be able to express the opposition each of these components offers to alternating current in the same way we express the resistance of a resistor in ohms Q To do this we will have to figure out a way to take the above equations and manipulate them to express each component s behavior as a ratio of K I will begin this process by using regular trigonometric functions to represent AC waveforms then after seeing how ugly this gets I will switch to using phasors and you will see how much easier the math becomes Let s start with the capacitor Suppose we impress an AC voltage across a capacitor as such AC voltage source Capacitor V sin t It is common practice to represent the angle of an AC signal as the product wt rather than as a static angle O with w representing the angular velocity of the circuit in radians per second If a circuit has a w equal to 27 it means the generator shaft is making one full rotation every second Multiplying w by time t will give the generator s shaft position at that point in time For example in the United States our AC power grid operates at 60 cycles per second or 60 revolutions of our ideal generator every second This translates into an angular velocity w of 1207 radians per second or approximately 377 radians p
622. ue to pressure existing in the vapor space above the liquid Unless a way can be found to compensate for any non hydrostatic pressure in the vessel this extra pressure will be interpreted by the transmitter as additional liquid level Moreover this error will change as gas pressure inside the vessel changes so it cannot simply be calibrated out by a static zero shift within the instrument The only way to hydrostatically measure liquid level inside an enclosed non vented vessel is to continuously compensate for gas pressure Fortunately the capabilities of a differential pressure transmitter make this a simple task All we need to do is connect a second impulse line called a compensating leg from the Low port of the transmitter to the top of the vessel so that the Low side of the transmitter experiences nothing but the gas pressure enclosed by the vessel while the High side experiences the sum of gas and hydrostatic pressures Since a differential pressure transmitter responds only to differences in pressure between High and Low sides it will naturally subtract the gas pressure Pyas to yield a measurement based solely on hydrostatic pressure yh 368 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT Gas pressure E Compensating a leg gt Electronic Pressure P yh Pressure P Pas Pias Yh The amount of gas pressure inside the vessel now becomes completely irrelevant to the
623. uided wave radar liquid level measurement liquid level measurement Non contact radar transmitters are always mounted on the top side of a storage vessel Modern radar transmitters are quite compact as this photograph shows 14 Radar is an acronym RAdio Detection And Ranging First used as a method for detecting enemy ships and aircraft at long distances over the ocean in World War II this technology is used for detecting the presence distance and or speed of objects in a wide variety of applications 396 CHAPTER 13 CONTINUOUS LEVEL MEASUREMENT Probes used in guided wave radar instruments may be single metal rods parallel pairs of metal rods or a coaxial metal rod and tube structure Single rod probes radiate the most energy whereas coaxial probes do the best job guiding the microwave energy to the liquid interface and back However single rod probes are much more tolerant of process fouling where sticky masses of viscous liquid and or solid matter cling to the probe Such fouling deposits may cause radio energy reflections of sufficient magnitude to be misinterpreted by the radar instrument as a liquid level Non contact radar instruments rely on an antenna to direct microwave energy into the vessel and to receive the echo return energy These antennae must be kept clean and dry which may be a problem if the liquid being measured emits condensible vapors For this reason non contact radar instruments are often separated
624. uitable flow measurement and in some cases even integrate that flow measurement with respect to time to arrive at a value for total liquid volume passed through the element in accordance with the calculus relationship V f Q dt C A technique for providing a clean and quiet still liquid surface to measure the level of is called a stilling well This is an open top chamber connected to the weir flume channel by a pipe so that the liquid level in the stilling well matches the liquid level in the channel The following illustration shows a stilling well connected to a weir flume channel with the direction of liquid flow in the channel being perpendicular to the page i e either coming toward your eyes or going away from your eyes 494 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT ultrasonic Water in weir flume channel To discourage plugging of the passageway connecting the stilling well to the channel a small flow rate of clean water may be introduced into the well This forms a constant purge flow into the channel flushing out debris that might otherwise find its way into the connecting passageway to plug it up Note how the purge water enters the stilling well through a submerged tube so it does not cause splashing on the water s surface inside the well which could cause measurement problems for the ultrasonic sensor ultrasonic Water in weir flume channel Sediment flushed out of passagew
625. ul in the electric power distribution industry where technicians can check power line insulators and other objects at elevated potential for hot spots without having to make physical contact with those objects Thermal imaging is also useful in performing energy audits of buildings and other heated structures providing a means of revealing points of heat escape through walls windows and roofs Perhaps the main disadvantage of optical temperature sensors is their inaccuracy The emissivity factor e in the Stefan Boltzmann equation varies with the composition of a substance but beyond that there are several other factors surface finish shape etc that affect the amount of radiation an optical sensor will receive from an object For this reason emissivity is not a very practical way to gauge the effectiveness of an optical temperature sensor Instead a more comprehensive measure of an object s thermal optical measureability is emittance A perfect emitter of thermal radiation is known as a blackbody Emittance for a blackbody is unity 1 while emittance figures for any real object is a value between 1 and 0 The only certain way to know the emittance of an object is to test that object s thermal radiation at a known temperature This assumes we have the ability to measure that object s temperature by direct contact which of course renders void one of the major purposes of optical thermometry to be able to measure an obje
626. ulb to the indicating element be of minimal volume so that the fluid expansion is primarily due to changes in temperature at the bulb rather than changes in temperature along the length of the tube It is also important to realize that the fluid volume contained by the bellows or bourdon tube or diaphragm is also subject to expansion and contraction due to temperature changes at the indicator This means the temperature indication varies somewhat as the indicator temperature changes which is not desirable since we intend the device to measure temperature exclusively at the bulb Various methods of compensation exist for this effect for example a bi metal spring inside the indicator mechanism to automatically offset the indication as ambient temperature changes but it may be permanently offset through a simple zero adjustment provided that the ambient temperature at the indicator does not change much A fundamentally different class of filled bulb system is the Class II which uses a volatile liquid vapor combination to generate a temperature dependent fluid expansion 14 2 FILLED BULB TEMPERATURE SENSORS 421 Pivot Pointer Scale Pivot Pointer Scale Pivot Pointer Scale Bellows Bellows Bellows Nonvolatile liquid Class IIA Class IIB Class IID Vapor Vapor Bulb Bulb Volatile liquid Bulb Volatile Volatile liquid Nonvolatile liquid liquid Given that the liquid and vapor are in direct contact with
627. ultiplied by its mass density m pV where p is the fluid s mass per unit volume the force required to accelerate that fluid plug would be calculated just the same as for a solid mass A volume of fluid Pipe m iE gt Force F Acceleration a Mass m pV Newton s Second Law formula F ma F pVa Since this accelerating force is applied on the cross sectional area of the fluid plug we may express it as a pressure the definition of pressure being force per unit area F pVa FV At A Sometimes referred to as a plug of fluid 15 1 PRESSURE BASED FLOWMETERS 445 P pZa Since the rules of algebra required we divide both sides of the force equation by area it left us with a fraction of volume over area 4 on the right hand side of the equation This fraction has a physical meaning since we know the volume of a cylinder divided by the area of its circular face is simply the length of that cylinder v P p7 P pla When we apply this to the illustration of the fluid mass it makes sense the pressure described by the equation is actually a differential pressure drop from one side of the fluid mass to the other with the length variable l describing the spacing between the differential pressure ports Length 1 He gt Pipe a gt Acceleration a Pressure drop P This tells us we can accelerate a plug of fluid by applying a difference of pressure across its length
628. ume just like turbine meters Since vortex flowmeters have no moving parts they do not suffer the problems of wear and lubrication facing turbine meters There is no moving element to coast as in a turbine flowmeter if fluid flow suddenly stops which means vortex flowmeters are better suited to measuring erratic flows The following photograph shows a vortex flow transmitter manufactured by Rosemount The next two photographs show close up views of the flowtube assembly front left and rear right 21This K factor is empirically determined for each flowmeter by the manufacturer using water as the test fluid a factory wet calibration to ensure optimum accuracy 504 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT 15 4 VELOCITY BASED FLOWMETERS 505 15 4 3 Magnetic flowmeters When an electrical conductor moves perpendicular to a magnetic field a voltage is induced in that conductor perpendicular to both the magnetic flux lines and the direction of motion This phenomenon is known as electromagnetic induction and it is the basic principle upon which all electro mechanical generators operate In a generator mechanism the conductor in question is typically a coil or set of coils made of copper wire However there is no reason the conductor must be made of copper wire Any electrically conductive substance in motion is sufficient to electromagnetically induce a voltage even if that substance is a liquid or a gas
629. ument is nearly two to one just from the upper liquid having the lesser of two identical e values Of course in real life you do not have the luxury of choosing which liquid will go on top of the other but you do have the luxury to choose the appropriate liquid liquid interface level measurement technology and as you can see here certain orientations of e values are less detectable with radar than others Another factor working against radar as a liquid liquid interface measurement technology for interfaces where the upper liquid has a greater dielectric constant is that fact that many high e liquids are aqueous in nature and water readily dissipates microwave energy This fact is exploited in microwave ovens where microwave radiation excites water molecules in the food dissipating energy in the form of heat For a radar based level measurement system consisting of gas vapor over water over some other heavier liquid the echo signal will be extremely weak because the signal must pass through the lossy water layer twice before it returns to the radar instrument Radio energy losses are important to consider in radar level instrumentation even when the detected interface is simply gas or vapor over liquid The power reflection factor formula only predicts the ratio of reflected power to incident power at an interface of substances Just because an air water interface reflects 63 8 of the incident power does not mean 63 8 of the incident powe
630. unds lb of force per square inch in of area Pressure is often expressed in units of kilo pascals kPa when metric units are used because one pascal is a rather low pressure in most engineering applications The even distribution of force throughout a fluid has some very practical applications One application of this principle is the hydraulic lift which functions somewhat like a fluid lever 30 CHAPTER 1 PHYSICS Resulting force Applied force Hydraulic lift y Small piston Large piston Applied force Resulting y Lever and fulcrum force Leve Fulcrum Ground Force applied to the small piston creates a pressure throughout the fluid That pressure exerts a greater force on the large piston than what is exerted on the small piston by a factor equal to the ratio of piston areas If the large piston has five times the area of the small piston force will be multiplied by five Just like with the lever however there must be a trade off so we do not violate the Conservation of Energy The trade off for increased force is decreased distance whether in the lever system or in the hydraulic lift system If the large piston generates a force five times greater than what was input at the small piston it will move only one fifth the distance that the small piston does In this way energy in equals energy out remember that work which is equivalent to energy is calculated by multiplying force by parallel distance trav
631. ure regulator Manometer The difference in liquid column heights h within the manometer shows the pressure applied to the gauge As with the deadweight tester the accuracy of this pressure measurement is bound by just a few physical constants none of which are liable to spurious change So long as the manometer s liquid density is precisely known Earth s gravitational field is constant and the manometer tubes are perfectly vertical the fluid pressure indicated by the manometer must be equal to the value described by the following equation two different forms given Where P pgh or P gt h P Fluid pressure p Mass density of fluid y Weight density of fluid g Acceleration of gravity h Height difference between manometer liquid columns Of course with pressure measuring test instruments of suitable accuracy preferably NIST traceable the same sort of calibration jig may be used for virtually any desired range of pressures From air source 11 8 PRACTICAL CALIBRATION STANDARDS 283 Gauge to be o calibrated _ Precision D pressure regulator From air source When the electronic test gauge is designed for very low pressures inches of water column they are sometimes referred to as electronic manometers Instrument calibrations performed in the field i e in locations near or at the intended point of use rather than in a professionally equipped shop are almost always done this way
632. ure into an electrical signal response These technologies form the basis of electronic pressure transmitters devices designed to measure fluid pressure and transmit that information via electrical signals such as the 4 20 mA analog standard or in digital form such as HART or FOUNDATION Fieldbus A brief survey of electronic pressure transmitters in contemporary use reveals a diverse representation of electrical pressure sensing elements Manufacturer Model Pressure sensor technology ABB Bailey PTSD Differential reluctance ABB Bailey PTSP Piezoresistive strain gauge Foxboro IDP10 Piezoresistive strain gauge Honeywell ST3000 Piezoresistive strain gauge Rosemount 1151 Differential capacitance Rosemount 3051 Differential capacitance Rosemount 3095 Differential capacitance Yokogawa EJX series Mechanical resonance As of this writing 2008 300 CHAPTER 12 CONTINUOUS PRESSURE MEASUREMENT 12 3 1 Piezoresistive strain gauge sensors Piezoresistive means pressure sensitive resistance or a resistance that changes value with applied pressure The strain gauge is a classic example of a piezoresistive element Test specimen R excitation As the test specimen is stretched or compressed by the application of force the conductors of the strain gauge are similarly deformed Electrical resistance of any conductor is proportional to the ratio of length over cross sectional area
633. urrents There is one way to do this if we take the leap of labeling the axes of the crank diagram as the axes of a complex plane real and imaginary numbers imaginary real real imaginary If we do this we may symbolically represent each vector as a complex number For example vector B in the above diagram could be represented as the complex number x jy using j as the symbol for an imaginary quantity instead of so as to not confuse it with current imaginary jy real real imaginary Alternatively we could express this complex quantity in polar form as an amplitude B and an angle O using the cosine and sine functions to translate this amplitude and angle into rectangular 122 CHAPTER 4 AC ELECTRICITY terms B cosO j sin O This is where things get really elegant As you may recall Euler s Relation relates complex exponential functions to trigonometric functions as such e cosO sin O With this critical piece of information we have a truly elegant way to express all the information contained in the crank diagram vector in the form of an exponential term Be In other words this AC voltage which is really a sinusoidal function over time may be symbolized as a constant amplitude B representing the peak voltage of the waveform multiplied by a complex exponential e What makes this representation really nice is that the complex exponential obeys all the mathematica
634. ut letting the mass do work on us i e releasing energy by 3 5 KIRCHHOFF S LAWS 95 lowering it on days 3 and 4 After the four day hike the net potential energy imparted to the mass is zero because it ends up at the exact same altitude it started at Let s apply this principle to a real circuit where total current and all voltage drops have already been calculated for us TV Arrow shows current in the direction of conventional flow notation If we trace a path ABCDEA we see that the algebraic voltage sum in this loop is zero Path Voltage gain loss AB 4 volts BC 6 volts CD 5 volts DE 2 volts EA 7 volts ABCDEA 0 volts We can even trace a path that does not follow the circuit conductors or include all components such as EDCBE and we will see that the algebraic sum of all voltages is still zero Path Voltage gain loss ED 2 volts DC 5 volts CB 6 volts BE 3 volts EDCBE 0 volts Kirchhoff s Voltage Law is often a difficult subject for students precisely because voltage itself is a difficult concept to grasp Remember that there is no such thing as voltage at a single point rather voltage exists only as a differential quantity To intelligently speak of voltage we must refer to either a loss or gain of potential between two points Our analogy of altitude on a mountain is particularly apt We cannot intelligently speak of s
635. ut signal that each input has An increasing voltage applied to the input drives the op amp s output positive while an increasing voltage applied to the input drives the op amp s output negative In a similar manner an increasing pressure applied to the high port of a DP transmitter will drive the output signal to a greater level up while an increasing pressure applied to the low port of a DP transmitter will drive the output signal to a lesser level down 8 As far as I have been able to determine the labels D P and DP cell were originally trademarks of the Foxboro Company Those particular transmitter models became so popular that the term DP cell came to be applied to nearly all makes and models of differential pressure transmitter much like the trademark Vise Grip is often used to describe any self locking pliers or Band Aid is often used to describe any form of self adhesive bandage 318 CHAPTER 12 CONTINUOUS PRESSURE MEASUREMENT 4 20 mA signal Pressure here drives output toward 4 mA Pressure here drives output toward 20 mA High Low side side We can use metal or plastic tubes or pipes to connect one or more ports of a pressure transmitter to points in a process These tubes are commonly called impulse lines or gauge lines or sensing lines This is equivalent to the test wires used to connect a voltmeter to points in a circuit for measuring
636. ute viscosity Reynolds number expresses the ratio of inertial forces to viscous forces At a very low Reynolds number viscous forces predominate and the inertial forces have little effect Pressure difference approaches direct proportionality to average flow velocity and to viscosity At high Reynolds numbers inertial forces predominate and viscous drag effects become negligible What the second paragraph is saying is that for slow moving viscous fluids such as honey in a straw the forces of friction fluid dragging against the pipe walls are far greater than the forces of inertia fluid momentum This means that the pressure difference required to move such a fluid through a pipe primarily works to overcome the friction of that fluid against the walls of the pipe For most industrial flows where the flow velocities are fast and the fluids have little viscosity like clean water flow through an orifice plate is assumed to be frictionless Thus the pressure dropped across a constriction is not the result of friction between the fluid and the pipe but rather it is a consequence of having to accelerate the fluid from a low velocity to a high velocity through the narrow orifice 627 My mistake years ago was in assuming that water flowing through an orifice generated substantial friction and that this is what created the AP across an orifice plate This is what my common sense told me In my mind I imagined the water having to
637. vanes installed inside the pipe parallel to the direction of flow These tubes or vanes force the fluid molecules to travel in straighter paths thus stabilizing the flowstream prior to entering a flow element Flow conditioner Velocity profile Velocity profile asymmetrical symmetrical Another common source of trouble for pressure based flowmeters is improper transmitter location Here the type of process fluid flow being measured dictates how the pressure sensing instrument should be located in relation to the pipe For gas and vapor flows it is important that no stray liquid droplets collect in the impulse lines leading to the transmitter lest a vertical liquid column begin to collect in those lines and generate an error producing pressure For liquid flows it is important that no gas bubbles collect in the impulse lines or else those bubbles may displace liquid from the lines and thereby cause unequal vertical liquid columns which would again generate an error producing differential pressure In order to let gravity do the work of preventing these problems we must locate the transmitter above the pipe for gas flow applications and below the pipe for liquid flow applications 10However there are disadvantages to using small beta elements one of them being increased permanent pressure loss which usually translates to increased operating costs due to energy loss 15 1 PRESSURE BASED FLOWMETERS Proper mounting posit
638. variable Finding the derivative of a function differentiation is the inverse operation of integration With integration we calculated accumulated value of some variable s product with time With derivative we calculate the ratio of a variable s change per unit of time Whereas integration is fundamentally a multiplicative operation products differentiation always involves division ratios A controller with derivative or rate action looks at how fast the process variable changes per unit of time and takes action proportional to that rate of change In contrast to integral reset action which represents the impatience of the controller derivative rate action represents the cautious side of the controller If the process variable starts to change at a high rate of speed the job of derivative action is to move the control valve in such a direction as to counteract this rapid change and thereby moderate the speed at which the process variable changes What this will do is make the controller cautious with regard to rapid changes in process variable If the process variable is headed toward the setpoint value at a rapid rate the derivative term of the equation will diminish the output signal thus slowing tempering the control response and slowing the process variable s approach toward setpoint To use an automotive analogy it is as if a driver driving a very heavy vehicle preemptively applies the brakes to slow the
639. variable air pressure Modern bridge circuits are mostly used in laboratories for extremely precise component measurements Very rarely will you encounter a Wheatstone bridge circuit used in the process industries 3 8 BRIDGE CIRCUITS 103 3 8 2 Sensor signal conditioning A different application for bridge circuits is to convert the output of an electrical sensor into a voltage signal representing some physical measurement This is by far the most popular use of bridge measurement circuits in industry and here we see the same circuit used in an entirely different manner from that of the balanced Wheatstone bridge circuit V excitation output 5 ra Here the bridge will be balanced only when Rsensor is at one particular resistance value Unlike the Wheatstone bridge which serves to measure a component s value when the circuit is balanced this bridge circuit will probably spend most of its life in an unbalanced condition The output voltage changes as a function of sensor resistance which makes that voltage a reflection of the sensor s physical condition In the above circuit we see that the output voltage increases positive on the top wire negative on the bottom wire as the resistance of Rsensor increases One of the most common applications for this kind of bridge circuit is in strain measurement where the mechanical strain of an object is converted into an electrical signal The sensor used here is a device know
640. ve 4 20MA i measurement 1 signal Analytical transmitter Contact chamber Effluent Influent Mixer Now that we have seen the basic elements of a feedback control system we will concentrate on the algorithms used in the controller to maintain a process variable at setpoint For the scope of this topic an algorithm is a mathematical relationship between the process variable and setpoint inputs of a controller and the output manipulated variable Control algorithms determine how the manipulated variable quantity is deduced from PV and SP inputs and range from the elementary to the very complex In the most common form of control algorithm the so called PID algorithm calculus is used to determine the proper final control element action for any combination of input signals 602 CHAPTER 18 CONTINUOUS FEEDBACK CONTROL 18 2 On off control Once while working as an instrument technician in a large manufacturing facility a mechanic asked me what it was that I did I began to explain my job which was essentially to calibrate maintain troubleshoot document and modify as needed all automatic control systems in the facility The mechanic seemed puzzled as I explained the task of tuning loop controllers especially those controllers used to maintain the temperature of large gas fired industrial furnaces holding many tons of molten metal Why does a controller have to be tuned he asked
641. vehicle s approach to an intersection knowing that the vehicle doesn t stop on a dime The heavier the vehicle the sooner a wise driver will apply the brakes to avoid overshoot beyond the stop sign and into the intersection If we modify the controller equation to incorporate differentiation it will look something like this de ee m Kye K edt Ka Where m Controller output e Error difference between PV and SP K Proportional gain K Integral gain Kq Derivative gain t Time b Bias The term of the equation expresses the rate of change of error e over time t The lower case letter d symbols represent the calculus concept of differentials which may be thought of in this context as very tiny increments of the following variables In other words g refers to the ratio of a very small change in error de over a very small increment of time dt On a graph this is interpreted as the slope of a curve at a specific point slope being defined as rise over run It should be mentioned that derivative mode should be used with caution Since it acts on rates of change derivative action will go crazy if it sees substantial noise in the PV signal Even small amounts of noise possess extremely large rates of change defined as percent PV change per minute 18 6 DERIVATIVE RATE CONTROL 615 of time owing to the relatively high frequency of noise compared to the timescale of physical
642. ven in its solid form an ionic compound is already ionized with its constituent atoms held together by an imbalance of electric charge Being in a liquid state simply gives those atoms the physical mobility needed to dissociate 3Covalent compounds are formed when neutral atoms bind together by the sharing of valence electrons Such compounds are not good conductors of electricity in their pure liquid states 16 3 CONDUCTIVITY MEASUREMENT 543 a fair estimate of ionic impurity concentration Conductivity is therefore an important analytical measurement for certain water purity applications such as the treatment of boiler feedwater and the preparation of high purity water used for semiconductor manufacturing It should be noted that conductivity measurement is a very non specific form of analytical measurement The conductivity of a liquid solution is a gross indication of its ionic content but it tells us nothing specific about the type or types of ions present in the solution Therefore conductivity measurement is meaningful only when we have prior knowledge of the particular ionic species present in the solution or when the purpose is to eliminate all ions in the solution such as in the case of ultra pure water treatment in which case we do not care about types of ions because our ideal goal is zero conductivity 16 3 2 Two electrode conductivity probes Conductivity is measured by an electric current passed through the solution The most
643. ver it is a very practical solution for acquiring multiple channels of data over a single pair of wires 254 CHAPTER 10 DIGITAL ELECTRONIC INSTRUMENTATION 10 2 Fieldbus standards The general definition of a fieldbus is any digital network designed to interconnect field located instruments By this definition HART multidrop is a type of industrial fieldbus However HART is too slow to function as a practical fieldbus for many applications so other fieldbus standards exist Here is a list showing many popular fieldbus standards e FOUNDATION Fieldbus Profibus PA Profibus DP Profibus FMS e Modbus e AS I e CANbus ControlN ET DeviceNet e BACnet The utility of digital fieldbus instruments becomes apparent through the host system these instruments are connected to typically a distributed control system or DCS Fieldbus aware host systems usually have means to provide instrument information including diagnostics in very easy to navigate formats For example the following screenshot shows the field instrument devices connected to a small scale DCS used in an educational lab Each instrument appears as an icon which may be explored further simply by pointing and clicking with the mouse lThe host system in this case is an Emerson DeltaV DCS and the device manager software is Emerson AMS 10 3 WIRELESS INSTRUMENTATION 255 of AMS Suite Intelligent Device Manager Device Connection iew F File
644. ver the purpose of this example is to show you how the technique of unity fractions works not to get an answer to a problem First we set up the original quantity as a fraction in this case a fraction with 1 as the denominator 35 qt 1 Next we multiply this fraction by another fraction having a physical value of unity or 1 This means a fraction comprised of equal measures in the numerator and denominator but with different units of measurement arranged in such a way that the undesired unit cancels out leaving only the desired unit s In this particular example we wish to cancel out quarts and end up with gallons so we must arrange a fraction consisting of quarts and gallons having equal quantities in numerator and denominator such that quarts will cancel and gallons will remain 35 qt 1 gal 1 4 qt lAn interesting point to make here is that the United States did get something right when they designed their monetary system of dollars and cents This is essentially a metric system of measurement with 100 cents per dollar The founders of the USA wisely decided to avoid the utterly confusing denominations of the British with their pounds pence farthings shillings etc The denominations of penny dime dollar and eagle 10 gold coin comprised a simple power of ten system for money Credit goes to France for first adopting a metric system of general weights and measures as their national standard 1 3 UNIT CONVERSIONS AND
645. ver returns but is stored in the reaction products as potential energy Endothermic reaction Activation energy Potential ener gy Energy stored by reaction Before After reaction Time gt reaction A catalyst is a substance that works to minimize activation energy in a chemical reaction without being altered by the reaction itself Catalysts are popularly used in industry to accelerate both exothermic and endothermic reactions reducing the gross amount of energy that must be initially input to a process to make a reaction occur A common example of a catalyst is the catalytic 2 5 ENERGY IN CHEMICAL REACTIONS 67 converter installed in the exhaust pipe of an automobile engine helping to reduce oxidize unburnt fuel molecules and certain combustion products such as carbon monoxide CO to compounds which are not as polluting Without a catalytic converter the exhaust gas temperature is not hot enough to overcome the activation energy of these reactions and so they will not occur at least not at the rate necessary to make a significant difference The presence of the catalyst allows the reactions to take place at standard exhaust temperatures The effect of a catalyst on activation energy may be shown by the following graphs the dashed line curve showing the energy progression with a catalyst and the solid line curve showing the reaction progressing without the benefit of a catalyst Exothermic reaction Endothermic reaction
646. verted the displacer dimensions into feet to arrive at a displacer volume in units of cubic feet 13 4 DISPLACEMENT 387 13 4 1 Displacement interface level measurement Displacer level instruments may be used to measure liquid liquid interfaces just the same as hydrostatic pressure instruments One important requirement is that the displacer always be fully submerged If this rule is violated the instrument will not be able to tell the difference between a low total liquid level and a low interface level If the displacer instrument has its own cage it is important that both pipes connecting the cage to the process vessel sometimes called nozzles be submerged This ensures the liquid interface inside the cage matches the interface inside the vessel If the upper nozzle ever goes dry the same problem can happen with a caged displacer instrument as with a sightglass level gauge see page 350 for a detailed explanation of this problem Calculating buoyant force on a displacer element due to a combination of two liquids is not as difficult as it may sound Archimedes Principle still holds that buoyant force is equal to the weight of the fluid s displaced All we need to do is calculate the combined weights and volumes of the displaced liquids to calculate buoyant force For a single liquid buoyant force is equal to the weight density of that liquid y multiplied by the volume displaced V Fouoyant yV For a
647. vidual device with its own terminals for connecting wires Note that dashed lines now represent individual copper wires instead of whole cables Terminal blocks where these wires connect to are represented by squares with numbers in them Cable numbers wire colors junction block numbers panel identification and even grounding points are all shown in loop diagrams The only type of diagram at a lower level of abstraction than a loop diagram would be an electronic schematic diagram for an individual instrument which of course 154 CHAPTER 6 INSTRUMENTATION DOCUMENTS would only show details pertaining to that one instrument Thus the loop diagram is the most detailed form of diagram for a control system as a whole and thus it must contain all details omitted by PFDs and P amp IDs alike To the novice it may seem excessive to include such trivia as wire colors in a loop diagram To the experienced instrument technician who has had to work on systems lacking such documented detail this information is highly valued The more detail you put into a loop diagram the easier it makes the inevitable job of maintaining that system at some later date When a loop diagram shows you exactly what wire color to expect at exactly what point in an instrumentation system and exactly what terminal that wire should connect to it becomes much easier to proceed with any troubleshooting calibration or upgrade task An interesting detail seen on this loop diagram
648. w measurement along 20 Custody transfer refers to measurement applications where a product is exchanging ownership In other words someone is selling and someone else is buying quantities of fluid as part of a business transaction It is not difficult to understand why accuracy is important in such applications as both parties have a vested interest in a fair exchange 15 4 VELOCITY BASED FLOWMETERS 499 with the associated mathematics for precisely calculating flow rate based on turbine speed gas pressure and gas temperature The following photograph shows three AGA7 compliant installations of turbine flowmeters for measuring the flow rate of natural gas Note the pressure sensing and temperature sensing instrumentation installed in the pipe reporting gas pressure and gas temperature to a flow calculating computer along with turbine pulse frequency for the calculation of natural gas flow rate Less critical applications may use a compensated turbine flowmeter that mechanically performs the same pressure and temperature compensation functions on turbine speed to achieve true gas flow measurement as shown in the following photograph 500 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT The particular flowmeter shown in the above photograph uses a filled bulb temperature sensor note the coiled armored capillary tube connecting the flowmeter to the bulb and shows total gas flow by a series of pointers rather than
649. w one of the square rooted p terms cancels out the one in the denominator of the fraction W kypvy Pi Pa Re writing the two roots as one W ky p Pi Pa As with the volumetric flow equation all we need in order to arrive at a suitable k value for any particular venturi tube is a set of values taken from a real venturi tube in service expressed in whatever units of measurement we desire For example if we had a venturi tube generating a differential pressure of 2 30 kilo Pascals kPa at a mass flow rate of 500 kilograms per minute of naphtha a petroleum product having a density of 0 665 kilograms per liter we could solve for the k value of this venturi tube as such W ky p P Po 500 ky 0 665 2 3 500 0 665 2 3 k 404 Now that we know a value of 404 for k will yield kilograms per minute of liquid flow through this venturi tube given pressure in kPa and density in kilograms per liter we may readily predict the mass flow rate through this tube for any other pressure drop we might happen to measure j sou 155 ura 6 1 kPa of differential pressure generated by a flow of sea water density 1 03 kilograms per liter in this particular venturi tube gives us the following mass flow rate W 404 1 03 6 1 456 CHAPTER 15 CONTINUOUS FLUID FLOW MEASUREMENT W 1012 kg m It should be apparent by now that the relationship between flow rate whether it be volumetric or mass and differentia
650. w rate This is the basis of a Coriolis mass flowmeter As you might guess it can be difficult to engineer a tubing system capable of spinning in circles while carrying a flowstream of pressurized fluid To bypass the practical difficulties of building a spinning tube system Coriolis flowmeters are instead built on the principle of a flexible tube that oscillates back and forth producing the same effect in an intermittent fashion rather than continuously The effect is not unlike wiggling a hose side to side as it carries a stream of water 27This is an example of a vector cross product where all three vectors are perpendicular to each other and the directions follow the right hand rule 15 5 INERTIA BASED TRUE MASS FLOWMETERS 517 Fulcrum elbow Y Motion of hand Arc of rotation 2 Coriolis force XxX This illustration is from a vertical view looking down The Coriolis force acts laterally bending the hose to the side ie ic A il We cannot build a Coriolis flowmeter exactly like the water hose illustration shown above unless we are willing to let the process fluid exit the tubing so a common Coriolis flowmeter design uses a U shaped tube that redirects the fluid flow back to the center of rotation The curved end of the flexible U tube is forced to shake back and forth while the tube ends anchor to a stationary manifold The two parallel tubes will experience opposite Coriolis forces as the U tube asse
651. we see the same effect Air supply gt Small bellows Large bellows Area A nie Pivot Here the feedback bellows has been made smaller exactly half the surface area of the input bellows This results in half the amount of force applied to the force beam for the same amount of pressure If we follow our simplifying assumption that perfect balance zero baffle motion will be achieved due to the balancing action of negative feedback we are led to the conclusion that Pout must be exactly twice the magnitude of Pin In other words the output pressure must increase to twice the value of the input pressure in order for the divided feedback force to exactly equal the input force and prevent the baffle from moving Thus our pneumatic mechanism has a pressure gain of two just like the opamp circuit with divided feedback 234 CHAPTER 9 PNEUMATIC INSTRUMENTATION We could have achieved the same effect by moving the feedback bellows to a lower position on the force beam instead of changing its surface area Fog Air supply O b Esi Pivot This arrangement effectively reduces the feedback force by placing the feedback bellows at a mechanical disadvantage to the input bellows If the distance between the feedback bellows tip and the force beam pivot is exactly half the distance between the input bellows tip and the force beam pivot the effective force ratio will be one half Pneumatic instruments built such that bellows forc
652. where I worked as an instrument technician Someone on the operations staff decided they would use 100 PSI instrument air to purge a process pipe filled with acid Unfortunately the acid pressure in the process pipe exceeded 100 PSI and as a result acid flushed backward into the instrument air system Within days most of the pneumatic instruments in that section of the refinery failed due to accelerated corrosion of brass and aluminum components inside the instruments The total failure of multiple instruments over such a short time could have easily resulted in a disaster but fortunately the crisis was minimal Once the first couple of faulty instruments were disassembled after removal the cause of failure became evident and the technicians took action to purge the lines of acid before too many more instruments suffered the same fate Pneumatic instruments must be fed compressed air of the proper pressure as well Just like electronic circuits which require power supply voltages within specified limits pneumatic instruments do not operate well if their air supply pressure is too low or too high If the supply pressure is too low the instrument cannot generate a full scale output signal If the supply pressure is too high internal failure may result from ruptured diaphragms seals or bellows Many pneumatic instruments are equipped with their own local pressure regulators directly attached to ensure each instrument receives the correct pressure despite
653. why these balance scales are popularly used for scientific work The scale mechanism itself is the very model of simplicity and the only thing the pointer needs to accurately sense is a condition of balance equality between masses If the task of balancing is given to an automatic mechanism the adjustable quantity will continuously change and adapt as needed to balance the sensed quantity thereby becoming a representation of that sensed quantity In the case of pressure instruments pressure is easily converted into force by acting on the surface area of a sensing element such as a diaphragm or a bellows A balancing force may be generated to exactly cancel the process pressure s force making a force balance pressure instrument Like the laboratory balance scale an industrial instrument built on the principle of balancing a sensed quantity with an adjustable quantity will be inherently linear which is a tremendous advantage for measurement purposes Here we see a diagram of a force balance pneumatic pressure transmitter balancing a sensed differential pressure with an adjustable air pressure which becomes a pneumatic output signal 5Based on the design of Foxboro s popular model 13A pneumatic DP cell differential pressure transmitter 12 4 FORCE BALANCE PRESSURE TRANSMITTERS 313 Air i su Relay Py adjustable Range wheel fulcrum Force sensed Force adjustable
654. will achieve a rotating tip speed that equalizes with the linear velocity of the fluid Cable Turbine wheel Turbine blades side view Turbine shaft Fluid flow Direction of wheel rotation A cut away demonstration model of a turbine flowmeter is shown in the following photograph The blade sensor may be seen protruding from the top of the flowtube just above the turbine wheel 15 4 VELOCITY BASED FLOWMETERS 497 Note the sets of flow conditioner vanes immediately before and after the turbine wheel in the photograph As one might expect turbine flowmeters are very sensitive to swirl in the process fluid flowstream In order to achieve high accuracy the flow profile must not be swirling in the vicinity of the turbine lest the turbine wheel spin faster or slower than it should to represent the velocity of a straight flowing fluid Each blade on the turbine acts as an inclined plane for the fluid molecules as they pass by The angle of the blades determines the ratio of tip speed to fluid velocity Turbine speed may be transmitted to an indicator mechanically by means of cables and or gears electronically by means of magnetic sensor using a pickup coil to generating voltage pulses as the turbine blades rotate underneath or even optically in some applications by reflecting light off the specific locations on the turbine wheel the light pulses conveyed to and from the wheel via fiber optic cables Pickup coils a
655. xample a capacitance having a value of 33 microfarads charged to a voltage of 5 volts would store an electric charge of 165 microcoulombs Capacitance is a non dissipative quantity Unlike resistance a pure capacitance does not dissipate energy in the form of heat rather it stores and releases energy from and to the rest of the circuit Capacitors are devices expressly designed and manufactured to possess capacitance They are constructed of a sandwich of conductive plates separated by an insulating dielectric Capacitors have voltage ratings as well as capacitance ratings Here are some schematic symbols for capacitors Nonpolarized Polarized Lo T FP sl BE T ae A capacitor s capacitance is related to the electric permittivity of the dielectric material symbolized by the Greek letter epsilon e the cross sectional area of the overlapping plates A and the distance separating the plates d EA TS Capacitance adds when capacitors are connected in parallel It diminishes when capacitors are connected in series 1 Cparallel Cl Ca Fe Ch Cseries AL pe E C t a 7 The relationship between voltage and current for a capacitor is as follows I C dt As such capacitors oppose changes in voltage over time by creating a current This behavior makes capacitors useful for stabilizing voltage in DC circuits One way to think of a capacitor 3 9 CAPACITORS 109 in a DC circuit is as a temporary voltag
656. xchanger which causes the outlet temperature to rise As the temperature re approaches setpoint the error becomes smaller and thus the integral action proceeds at a slower rate like a car s odometer ticking by at a slower rate when the car s speed decreases So long as the PV is below SP the outlet temperature is still too cool the controller will continue to integrate upwards driving the control valve further and further open Only when the PV rises to exactly meet SP does integral action finally rest holding the valve at a steady position Integral is a highly effective mode of process control In fact some processes respond so well to integral controller action that it is possible to operate the control loop on integral action alone without proportional Typically though process controllers are designed to operate as proportional only P proportional plus integral PI Just as too much proportional gain will cause a process control system to oscillate too much integral gain will also cause oscillation If the integration happens at too fast a rate the controller s output will saturate either high or low before the process variable can make it back to setpoint Once this happens the only condition that will unwind the accumulated integral quantity is for an error to develop of the opposite sign and remain that way long enough for a canceling quantity to accumulate Thus the PV must cross over the SP guaranteeing at
657. y 1 Volt 1 Coulomb of electric charge In other words if we forced 1 Coulomb s worth of electrons 6 24 x 1018 of them to be exact away from a positively charged place and did one Joule s worth of work in the process we would have generated one Volt of electric potential Electric potential voltage and potential energy share a common yet confusing property both quantities are fundamentally relative between two physical locations There is really no such thing as specifying a quantity of potential energy at a single location The amount of potential energy in any system is always relative between two different points If I lift a mass off the ground I can specify its potential energy but only in relation to its former position on the ground The amount of energy that mass is potentially capable of releasing by free fall depends on how far it could possibly fall To illustrate imagine lifting a 1 kilogram mass 1 meter off the ground That 1 kilo mass weighs 9 8 Newtons on Earth and the distance lifted was 1 meter so the potential energy stored in the mass is 9 8 joules right Consider the following scenario Mass m 1 kg Weight UNE PASEO Height raised h 1 meter Table 0 5 meters tall Cliff 300 meters to bottom i 76 CHAPTER 3 DC ELECTRICITY If we drop the mass over the spot we first lifted it from it will release all the potential energy we invested in it 9 8 joules But what if we ca
658. y a coiled capillary tube a long tube with a very small inside diameter The small inside diameter of such a tube makes wall boundary effects dominant such that the flow regime will remain laminar over a wide range of flow rates The extremely restrictive nature of a capillary tube of course limits the use of such flow elements to very low flow rates such as those encountered in the sampling networks of certain analytical instruments A unique advantage of the laminar flowmeter is its linear relationship between flow rate and developed pressure drop It is the only pressure based flow measurement device for filled pipes that exhibits a linear pressure flow relationship This means no square root characterization is necessary to obtain linear flow measurements with a laminar flowmeter The big disadvantage of this meter type is its dependence on fluid viscosity which in turn is strongly influenced by fluid temperature Thus all laminar flowmeters require temperature compensation in order to derive accurate measurements and some even use temperature control systems to force the fluid s temperature to be constant as it moves through the element gt Laminar flow elements find their widest application inside pneumatic instruments where a linear pressure flow relationship is highly advantageous behaving like a resistor for instrument air flow and the viscosity of the fluid instrument air is relatively constant Pneumatic controllers f
659. y or take other derogatory action in relation to the Work which would be prejudicial to the Original Author s honor or reputation Licensor agrees that in those jurisdictions e g Japan in which any exercise of the right granted in Section 3 b of this License the right to make Adaptations would be deemed to be a distortion mutilation modification or other derogatory action prejudicial to the Original Author s honor and reputation the Licensor will waive or not assert as appropriate this Section to the fullest extent permitted by the applicable national law to enable You to reasonably exercise Your right under Section 3 b of this License right to make Adaptations but not otherwise 5 Representations Warranties and Disclaimer UNLESS OTHERWISE MUTUALLY AGREED TO BY THE PARTIES IN WRITING LICENSOR OFFERS THE WORK AS IS AND MAKES NO REPRESENTATIONS OR WARRANTIES OF ANY KIND CONCERNING THE WORK EXPRESS IMPLIED STATUTORY OR OTHERWISE INCLUDING WITHOUT LIMITATION WARRANTIES OF TITLE MERCHANTIBILITY FITNESS FOR A PARTICULAR PURPOSE NONINFRINGEMENT OR THE ABSENCE OF LATENT OR OTHER DEFECTS ACCURACY OR THE PRESENCE OF ABSENCE OF ERRORS WHETHER OR NOT DISCOVERABLE SOME JURISDICTIONS DO NOT ALLOW THE EXCLUSION OF IMPLIED WARRANTIES SO SUCH EXCLUSION MAY NOT APPLY TO YOU 6 Limitation on Liability EXCEPT TO THE EXTENT REQUIRED BY APPLICABLE LAW IN NO EVENT WILL LICENSOR BE LIABLE TO YOU ON ANY LEGAL THEORY FOR ANY SPECIAL I
660. ymbol is enclosed by a diamond shape indicating a powered active device Proximity switch symbols prox prox _ A A Normally open Normally closed NO NC Many proximity switches though do not provide dry contact outputs Instead their output elements are transistors configured either to source current or sink current The terms sourcing and sinking are best understood by visualizing electric current in the direction of conventional flow rather than electron flow The following schematic diagrams contrast the two modes of switch operation using red arrows to show the direction of current conventional flow notation In both examples the load being driven by each proximity switch is a light emitting diode LED 176 CHAPTER 7 DISCRETE PROCESS MEASUREMENT Sinking output Current sinks down to proximity switch ground through the switch Sourcing output Switch sources current proximity switch out to the load device 7 4 PROXIMITY SWITCHES 177 This switch detects the passing of teeth on the chain sprocket generating a slow square wave electrical signal as the sprocket rotates Such a switch may be used as a rotational speed sensor 178 CHAPTER 7 DISCRETE PROCESS MEASUREMENT sprocket speed proportional to signal frequency or as a broken chain sensor when sensing the rotation of the driven sprocket NIP POINTS INSID HOT COMPONENTS I SIDE INJURY COULD RESULT
661. ype whose ball and stem valves could never close simultaneously and thus would always bleed some compressed air to atmosphere so long as the output pressure remained somewhere between saturation limits 228 CHAPTER 9 PNEUMATIC INSTRUMENTATION 9 4 Analogy to opamp circuits Self balancing pneumatic instrument mechanisms are very similar to negative feedback operational amplifier circuits in that negative feedback is used to generate an output signal in precise proportion to an input signal This section compares simple operational amplifier opamp circuits with analogous pneumatic mechanisms for the purpose of illustrating how negative feedback works and learning how to generally analyze pneumatic mechanisms In the following illustration we see an opamp with no feedback open loop next to a baffle nozzle mechanism with no feedback open loop V Clearance Air supply Orifice Nozzle Vig Vion Se Baffle V For each system there is an input and an output For the opamp input and output are both electrical voltage signals V is the differential voltage between the two input terminals and Vout is the single ended voltage measured between the output terminal and ground For the baffle nozzle the input is the physical gap between the baffle and nozzle in while the output is the backpressure indicated by the pressure gauge Pout Both systems have very large gains Operational amplifier open loop gain
662. ystem has no way to regulate how warm or cold the process fluid is before it enters the heat exchanger This is precisely the definition of a load 18 4 PROPORTIONAL ONLY OFFSET 609 Of course it is the job of the controller to counteract any tendency for the outlet temperature to stray from setpoint but as we shall soon see this cannot be perfectly achieved with proportional control alone Let us carefully analyze the scenario of sudden inlet fluid temperature decrease to see how a proportional controller would respond Imagine that previous to this sudden drop in feed temperature the controller was controlling outlet temperature exactly at setpoint PV SP and everything was stable Recall that the equation for a proportional controller is as follows m Kpe b Where m Controller output e Error difference between PV and SP Kp Proportional gain b Bias We know that a decrease in feed temperature will result in consequent a decrease of outlet temperature with all other factors remaining the same From the equation we can see that a decrease in process variable PV will cause the Output value in the proportional controller equation to increase This means a wider open steam valve admitting more heating steam into the heat exchanger All this is good as we would expect the controller to call for more steam as the outlet temperature drops But will this action be enough to bring the outlet temperature back up to setpoin

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