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ATMOSPHERIC THERMODYNAMICS HP48 Calculator Program

1. Enter P C U W v air saturation enthalpy at water temperature and enthalpy of surface air Dalton Equation plus Im spray term Enthalpy transfer coefficient from CD 0 7 Ooyama 1969 and CBLAST Drag coefficient from Ooyama 1969 CE to CD Ratio 0 7 from CBLAST Drag coefficient according to Dalton 0 0018 from CBLAST Drag coefficient according to Powell 0 002 from CBLAST Spray power of five heat transfer coefficient Hurricane total heat from sea removal rate from ocean cooling in Watt Enter 32 QHU QHV DREN AT Ocean cooling due to hurricane passage C d Depth of cooled layer m w Width of cooled layer m v Velocity of hurricane m s Result is total sea to air heat transfer in watts Assumes all cooling occurs under eyewall Hurricane heat removal rate per unit area of eyewall W m Enter Hurricane total heat from sea removal rate result of QHT Eyewall length w Eyewall width Result is eyewall sea to air heat transfer in W m Hurricane heat required to produce hurricane precipitation Enter rain rate in mm hr and diameter of rain area in meters Heat flux from eddy calculation Enter CE U10 Q0 and Q10 Results are lt w q gt and Qv Used Drennan eddy correlation heat flux calculation in Table 1 of French and Drennan Part1 2007 Heat from sea removal rate RAY GR Rayleigh Number for free convection of air in a tube enter Delta T mean T Diameter Grashof Num
2. GCK TMS PRO2 PRO3 ASA ASW ApA AuW WI THE TCE F1 TPLT RPLT TVL1 Gibb free energy check after running WTUW no parameters required just press SCK entered Results consist of four numbers Gibb free energy of gas phase in final state Gibb free energy of liquid phase in final state Gibb free energy of gas phase in initial state Gibb free energy of liquid phase in final state Change in total Gibb free energy is the maximum energy that would be produced if the mixing process were carried out reversibly Calculates the property of a mixture of mass 1 and of the MM2 water part of mass 2 where MM2 is in vapour state TT2 and MM2 are used to specify the quantity of vaporized water added to the humid air mass PP2 is ignored Surface pressure capability of saturated air water mixture Surface pressure capability of air water mixture Change in entropy of air during mxing Change of entropy of water during Mixing Change in free enthalpy For two air masses mixture Change in free enthalpy For air and condensed water mixture Work loss due to irreversible heating Effective temperature of the hot source Effective temperature of the cold source Fraction air mass 1 Plots the virtual temperature of the mixture array Plots the relative humidity of the mixture array AT5C Margules large air mass ZPO MA Alpha MA Theta W Theta TZ 1 Two forms of the Margules equations for calculating the total en
3. K V 1990 A thermodynamic foundation for modelling the moist atmosphere J Atmos Sci 47 2580 2593 Lilly D K T Gal Chen 1990 Can dryline mixing create buoyancy J Atmos Sci 47 1170 1171 46
4. adiabatid expansion Default 1000 J kg HCU1 Isabel Distant environment surface air conditions 101 1 kPa 27 8 C 75 RH HCU2 Jordan sounding surface air for which WB is zero for P4 12 kPa 101 1 kPa 27 8 C 63 8 RH HCU3 Jordan sounding surface air for which WB is zero for P4 12 kPa 101 1 kPa 28 C 62 63 RH HCM4 Jordan sounding surface air for which T4 T4E for P4 12kPa 101 51 kPa 31 09 C 17 79 g kg HCM5 Jordan sounding surface air for which T4 T4E for P4 13kPa 101 51 kPa 26 25 C 17 79 g kg PC PJ Jordan sounding base pressure AdJ1__ Subdirectory of AT5J Pressure at solar chimney top P200 P1K A5J2 _Subdirectory of AT5J Work correlations moved out of AT5J W2U Equation derived from correlation for calculating work produced when surface air is raised reversibly to the 20 kPa level without need for using slow solver Enter surface air conditions in PCU format 38 W2M Equation derived from correlation for calculating work produced when surface air is raised reversibly to the 20 kPa level without need for using slow slover Enter surface air conditions in PCM format TEE MPI from SST Isabel correlation DEM MPI from SST Isabel correlation EMA MPI from SST Emanuel correlation APE Calculate delta P from CAPE APM Calculate turbine delta P given P1 K1 W12 M1 A5J3 _ Total work calculations VDT Enter upward velocity V at the base of chimney and chimney diameter D ca
5. and press the corresponding key Irrespective of which three parameters are entered the properties are returned to the stack in the PKM format Pressure is stored in variable PP absolute temperature in variable TT and mixing ratio is stored in variable MM MM is the total quantity of water per unit mass of air the mixing ratio MM includes the water in any phase its unit is g water kg air Water beyond the saturation amount is considered to be in a condensed phase and in equilibrium with the air If there is condensed water the water in the vapour phase is the saturation amount The condensed water is in the liquid phase if the temperature is above the freezing temperature TF Properties per unit mass of dry air mixing ratio are used in preference to properties per total mass of substance because in many processes air content is conserved while water content can change for example in processes where condensed water is separated from expanding air pseudo adiabatic expansion Open pseudo adiabatic expansion is handled by removing the condensed water at regular interval Example Pressure P 0 kPa Dry Bulb Temperature C 20 C Dew point D 15 C PP 90 kPA TT 293 15 K MM 12 00 g kg Arguments 3 90 2 20 1 15 Function PCD Results 3 90 2 293 15 1 12 00 Program R recalls the three standard properties to the stack Calculation of the thermodynamic properties is based on having the three standard air property variables on the stack an
6. from Holland 1997 OL Potential temperature PL Lifting condensation level pressure TL Lifting condensation level temperature Expansion temperature is calculated in step of 2 kPa Condensed water is separated after each step Freezing temperature is set to 100 C the condensed water does not freeze A P4 default of 10 kPa is sufficient to reduce water content to negligible level Pseudo adiabatic expansion temperatures at intermediate pressures can be calculated by varying P4 in which case 0e is not valid TPSE calculation requires up to 40 solver operation and can take 30 seconds to run on a fast PC 44 AT5P Sounding array and array conversion programs The AT4 directory contains five arrays of sounding data SNK Sounding data in PKM format SNKU Sounding data in PKU format SNC Raw sounding data in PCD format SNCM Raw sounding data in PCM format SNU Sounding data in PCU format There are five programs to store and generate the five arrays K gt U Generate SNU from SNK KU gt K Generate SNK from SNKU K gt C Generate SNC from SNK C gt K Generate SNK from SNC U gt K Generate SNK from SNU CM gt K Generate SNK from PCM AT6 __ Plot using MLINE AT6 uses program MLINE of AT1 to plot the date in the arrays of AT5 The array to be plotted is stored in array DA The samples in the directory can be copied and modified to plot other properties Plotting range and axis labelling can be redefined The built in plots are PPLT Pseudo a
7. from P1 and p2 Carnot efficiency from Th and Tc in C Carnot efficiency from Th and Tc in K Mole fraction from m Ratio mass of air to total mass from M Mixing ratio to specific humidity Specific humidity to mixing ratio Restrained and unrestrained cylinder piston system Inputs P1 P2 T1 in C Van Ness type analysis Outputs initial temperature isentropic expansion temperature and unrestrained expansion temperature RPN version Same as POP Algebraic version Restrained and unrestrained cylinder piston system Input pressure ratio P2 P1 Output Percent of isentropic expansion work loss as a result of the expansion not being fully restrained Note The loss work is 23 63 for P2 P1 of 0 95 and approaches 22 25 as P2 P1 approaches 1 i e 0 999 Potential temperature lapse rate from P and lapse rate Potential temperature lapse rate from 9 T Vapor pressure of water in kPa slightly more accurate than XVL Affinity A 0 Vapor pressure of water in kPa slightly more accurate than XVI Affinity A 0 Vapor pressure of water in kPa slightly less accurate than PVL Dufour eq 9 87 Vapor pressure of water in kPa slightly less accurate than PVI Dufour eq 9 87 NNN N 21 AT3A_ CLAPEYRON EQUATION COEFFICIENTS from Dufour and Van Mieghem AT3B SOLAR AND INFRARED RADIATION AT3B contains the nominal percent of radiation reflected and absorbed by the atmosphere and the earth surface the solar constant th
8. primary directory AT4 AT2 Thermodynamic constants AT3 Thermodynamic properties of pure air and pure water virtual temperature lapse rate and the distance between sounding pressure AT4 AT5 AT6 levels Thermodynamic properties of moist air The condition of the unit mass of air is specified by entering pressure temperature and a humidity parameter The directory uses the HP48 solver to calculate adiabatic expansion temperature dew point wet bulb and equivalent temperature Thermodynamic properties of complete soundings and work produced when air masses are moved Programs to plot data from arrays 2 3 Side sub directories Side sub directories are used where the data is not likely to be used further down The name of side directories terminates with a letter AT2A AT2B AT2C AT2D ATDAT AT3A AT3B AT3C AT3D AT3E AT4A AT4B AT4C AT5A AT5B A5B1 A5B4 A5B1 A5B2 A5B3 A5B4 A5B6 A5B7 A5B8 AT5C Energy usage and reserves Conversion MPG to Km hr to L 100 km Energy cost Hurricane categories and velocities Atmospheric sounding data Clappeyron equation coefficients calculation Constants relating to the Earth energy budget percent of radiation reflected and absorbed by the atmosphere and the earth surface the solar constant the Stefan Boltzman law and conversion factors from Langley Thermodynamic properties of propane Circulation from earth rotation Lambton College Prototype Paramet
9. properties of a mixture of two air masses or of a mixture of an air mass and of condensed water Mixing is an isenthalpic process The calculation is based on the fact that the enthalpy of the mixture and the water content of the mixture must be equal to the sum of the enthalpy and water content of the initial masses The program is primarily intended air masses initially at the same pressure but can also be used for air masses at different pressures provided M2 has the higher pressure The pressure of the mixture is the lowest of P1 and P2 The higher pressure air mass in expanded isentropically before mixing Air masses can have water in condensed states PCU1 PCU2 PCM1 PCM2 RC1 RC2 RC3 RK1 RK1 PCT1 SIA PCTA DA TMW SAW WTW WTU WTUW Stores properties of air mass 1 in PCU format in PP1 TT1 and MM1 Stores properties of air mass 2 in PCU format in PP2 TT2 and MM2 Stores properties of air mass 1 in PKM format in PP1 TT1 and MM1 Stores properties of air mass 2 in PKM format in PP2 TT2 and MM2 Recall air mass 1 properties in PCM format Recall air mass 2 properties in PCM format Recall air mass 3 properties in PCM format Recall air mass 1 properties in PKM format Recall air mass 2 properties in PKM format Calculates mixture property given percent of mass 1 Calculate mixing internally generated entropy mix air masses 1 and 2 Produces an array DA of mixture properties at 10 mass 1 incre
10. temperature TF Freezing temperature TF default 273 15 K and freezing band FB default 20 K are stored in constant directory AT2 and can be changed to check their effect The freezing band must be at least 5 K to avoid solver singularity problem AT4 HP48SX SOLVERS The HP48 solver is used to solve for variables that cannot be isolated and to avoid having to manipulate equations Program S EQ is an equation calculating the total entropy from PP TT and MM The temperature during true adiabatic expansion is calculated by entering PP and solving for TT Program TSOL invokes the solver to solve for TT given PP The MEQ directory contains the following equations A EQ Entropy moisture is condensed E EQ Enthalpy moisture content condensed EM EQ Enthalpy Emanuel PKM equation EU EQ Enthalpy Emanuel PKU equation G EQ Gas Law H EQ Enthalpy L EQ Humidity minus 100 Used by LCL3 to calcualte lifting condensation level M EQ Entropy for two conditons equation S EQ Entropy TV EQ Virtual temperature equation V EQ Vapour Pressure W EQ Enthalpy at Wet Bulb W2 EQ Enthalpy amp wet bulb The solver will solve for any missing variable The following programs invoke the solver directly to calculate frequently need variables ASOL Isentropic desiccation temperature enter P Solve A EQ DSOL Dew Point Temperature enter partial pressure of water Solve the V EQ HSOL Mixture temperatures Enter P Solve H EQ for TT USOL So
11. 37 m AD Area of 8 6 x 24 tangential deflector entry slots 0 74 m AF1 Heat capacity of small salamander 44 000 W AF2 Heat capacity of large salamander 110 000 W ARD Ratio of diamerter 3 89 ARV Ratio of velocity 0 15 AS1 Area of 8 6 x 24 tangential deflector entry slots AT4 MAIN PROGRAM See description at beginning of program description AT4A_ Subsidence velocity AT4B 23 AT4C_ EFFICIENCY OF COMBINED CYCLES Efficiency calculations for three stages combined cycle Gas turbine steam AVE Cycles can be omitted by making hot and cold source temperatures the same TSTO Store up to four source temperatures in C Example 1600 600 30 50 TRCL Recall up to four source temperatures in C COTA Calculate actual cycle efficiency initiates COMN COMT Calculate Carnot efficiency initiates COMN COMP Calculate percent contribution of each cycle and percent increment due to AVE cycle COMW Display W1 W2 W3 W4 COMN Calculate percent contribution of each cycle from individual efficiency enter the three efficiencies from COTA or COMT delete x Also calculate W1 W2 W3 W4 EFF Carnot efficiency Enter Th and Tc in C EFF2 Carnot efficiency Enter Th and Tc in C with exchanger Delta T EFH Carnot efficiency Enter Th in K and use default TH EFF Carnot efficiency Enter Tc in K and use default TC EFU Ultimate efficiency when work is dissipated at hot source temperature E
12. 5 TQ Triple point temperature 273 16 Flags 1 and 2 are used to set Freezing Temperature Flag 3 is used to set Freezing Band Flags are used because the flag status is visible in the calculator screen and because flags can be changed from any directory while objects can only be stored in the current directory Toggle between freezing temperature of 273 15 K Ice Flags 1 and 2 clear and 173 15 K No Ice Flags 1 and 2 set II Toggle between freezing bans of 20 K flag 3 clear and freezing band of 5 K Flag 3 set SFT Set Freezing Temperature TF Freezing temperature 273 15 K F1 F2 TF SFT argument Clear Clear 0 C 0 Set Clear 10 C 10 Clear Set 40 C 40 Set Set 100 C 100 The Freezing Temperature can be selected by setting the flags manually or by preceding the the SFT object with the argument of the above table FB Freezing band 20 K The Freezing Band can be selected by setting flag 3 manually or toggled by pressing the SFB without argument The default FB with flag 3 clear is 20 FB is 5 when flag 3 is set CPA Specific heat of air at constant pressure CVA Specific heat of air at constant volume RA Gas constant for air KA RA CPA MA Molecular weight of air CPV Specific heat of water vapour at constant pressure RV Gas constant for water vapour CW Specific heat of water CI Specific heat of ice LVO Latent heat of vaporization at TO LVQ Latent heat of vaporization at the triple point of water LFO Latent h
13. ATMOSPHERIC THERMODYNAMICS HP48 Calculator Program Documentation Louis Michaud Revised October 2015 1 0 PROGRAM DESCRIPTION HP48 calculator program Atmospheric Thermodynamics AT1 calculates the properties of air containing water in any phase given pressure temperature and a humidity parameter The program can calculate a wide range of parameters including Thermodynamic properties for individual air masses or of complete sounding Work produced when small air masses are moved isentropically Work produced when large masses of dry air change position Properties of mixtures of air and water Pressure drop and work loss for laminar and turbulent flow in tubes work loss and terminal velocity for bubble flow OIE The program uses the power and versatility of the Hewlett Packard HP48 object oriented programming language The HP48SX calculator came out in 1990 and is now out of production The HP48SX is a programmable scientific calculator using object oriented programming programmable keys Reverse Polish Notation RPN or Algebraic Notation When it came out the HP48SX was the leading scientific calculator and has not been surpassed A community of HP48SX adepts developed When HP stopped producing the calculator the community developed an HP48SX emulator for PC s which is available free of charge on the internet The PC emulator runs approximately 100 times faster than the original calculator on a medium speed desktop A calculation
14. D PTAZ PCAZ TPTA Z EQ PX1 PX2 CX1 ax Partial pressure of water from P and M Partial pressure of air from P and T dew point Saturation mixing ratio from P and T Vapor in equilibrium with liquid or ice Saturation mixing ratio from P and T Vapor in equilibrium with liquid Density of pure air from P and T Density of pure water from P and T Entropy of air from P and T per kg air Entropy of vapour from P and T per kg vapour Entropy of liquid water from T per kg liquid water lower case to distinguish from built in shift left Entropy of liquid water from P T M per kg of water Uses sL and throws out P and Entropy of ice from T per kg of ice Entropy of condensed water from T per kg liquid water Entropy of condensed water from P T M per kg of water Uses SC and throws out P and M Enthalpy of air from T per kg air Enthalpy of vapour from T per kg water Enthalpy of liquid water from T per kg water Enthalpy of ice from T per kg ice Enthalpy of condensed waater from T per kg water Enthalpy of condensed water from P T M per kg of water Uses HC and throws out P and M Free enthalpy of air from P and T per kg air Free enthalpy of vapour from P and T per kg vapor Free enthalpy of liquid water from T per kg water Free enthalpy of ice from T per kg ice Affinity of liquid water from P and T Virtual temperature from T and M Latent heat of vaporization from t Latent heat of sublima
15. ELZARA 10000 25 m 20 C 40 m s ZARA ELZARA 150 60 m 20 C 8 m s GR1 Grotvlei 120 m 83 m 31 5 C 2 07 m s 9 75 C km GR2 Grotvlei 120 m 83 m 31 5 C 2 07 m s 6 5 C km GR20 Grotvlei 2400 m 83 m 31 5 C 2 07 m s 6 5 C km GR21 Grotvlei 2400 m 17 m 30 5 C 50 m s 6 5 C km GR21 Grotvlei 2400 m 30 m 15 C 30 m s 6 5 C km GT Grptvlei 120 m 58 m 31 5 C 4 24 m s 6 5 C km AT5N_ PSEUDO ADIABATIC EXPANSION TEMPERATURE AND EQUIVALENT TEMPERATURE PKM1 Enter initial air properties in PKM format store in P1 T1 M1 PCM1 Enter initial air properties in PCM format store in P1 T1 M1 PCU1 Enter initial air properties in PCU format store in P1 T1 M1 P4 Enter final pressure default 10 kPa TOEN Calculate pseudo adiabatic expansion temperature and equivalent temperature No argument required Results are final temperature in C in K and 0e No freezing of condensed water Freezing temperature 173 15 K TOEF Calculate pseudo adiabatic expansion temperature and equivalent temperature No argument required Results are final temperature in C in K and 8e With With freezing of condensed water Freezing temperature 273 15 K 0 33 Equivalent temperature based on raising air to 10 kPa level Os eq Equivalent potential temperature equation no separation SL3 Entropy when water is in liquid phase BOL3 Equivalent temperature using Bolton equation BOL4 Bolton equation
16. I Note that T4 is higher in the irreversible case than in the reversible case by Wosrev Cpa Convection Energy with heater humidifier WA2 _ Calculate P3 given T3 and U3 WA Calculate reversible work for entered for P3 guess given T3 and U3 Wet heat TU Enter temperature and relative humidity downstream of heater humidifier before running WA or WA2 WA2 Calculate P3 using two guesses method given T3 and U3 Provide one P3 guess WD2_ Calculate P3 given T3 and M3 WD Calculate reversible work for entered for P3 guess given T3 and M3 Dry heat TM Enter temperature and mixing ratio humidity downstream of heater humidifier before running WD or WD2 WD2 Calculate P3 using two guesses method given T3 and M3 Provide one P3 guess WTA2 Calculate C3 required to produce work given WO and U3 WTA Calculate work for temperature C3 in C given WO and U3 Provide C3 guess WU Enter work of buoyancy WO and relative humidity RH3 in state 3 before running WTA or WTA2 Set WO to zero to find datum temperature for which W 0 WTA2 Calculate C3 required to make the work zero given U3 using two guesses method Provide C3 guess OK for zero work Needs fixing when work gt 0 WUA2 Calculate relative humidity required to produce work given WO and T3 WUA Calculate relative humidity given WO and C3 Provide relative humidity guess WC Enter work of buoyancy WO and temperatrue T3 in state 3 before running WUA or WUA2 Set WO0 to zero
17. JR DJV ATMC MAN MAN2 EMI EMI2 Enter height and base temperature in C caculates efficiency from simple solar chimney equation Enter chimney height Z chimney base temperature C and chimney base delta T AT Calculate ideal work per unit mass J kg from simple solar chimney equation Ex Manzanares 200 m 30 C 17 C gt 109 91 J kg Pressure kPa Temperature K Mixing ratio g kg Adrian Bejan Work equation Adrian Bejan Power equation Flatness Factor used in DJV Diameter of Rankine vortex based on radial delta P Input Conditons for various cases Manzanares 200 m 10 m 20 C 8 m s Manzanares 1000 m 10 m 3 4 C 8 m s EnviroMission 1000 m 150 m 28 C 16 m s EnviroMission 1000 m 180 m 20 C 16 m s 43 DEV2 Dust Devil 1000 m 2 m 5 C 12 m s DEV10 Dust Devil 1000 m 10 m 5 C 12 m s FWH Fire Whirl 1000 m 2 m 100 C 20 m s ESC Eskom AVE 10 000 m 50 m 20 C 20 m s DCT Dry cooling tower 10 000 m 35 m 20 C 20 m s DCT8 Dry cooling tower 10 000 m 18 m 20 C 80 m s DCT Dry cooling tower 10 000 m 35 m 20 C 20 m s 8 09 C km DCT Dry cooling tower 10 000 m 18 m 20 C 80 m s 8 09 C km DCTs Dry cooling tower 2 000 m 35 m 20 C 20 m s 5 C km KEN Kendall Eskom 165 m 145 m 20 C 4 m s GAR Garage prototype 2 m 0 05 m 100 C 1 m s LAM Lambton College 5 m 0 25 m 30 C 5 m s ZARV
18. L RE REW FL FT FTW FLW Work loss J kg for turbulent and laminar flows Enter DVZp Work per unit mass loss through friction in a horizontal tube for laminar air From d v z rho Work per unit mass loss through friction in a horizontal tube for turbulent air From d v z rho Circular conduit area from d Volumetric flow m3 s from d v Mass flow kg s from d v rho Reynold number for turbulent air From d v rho Reynold number for water From d v rho Friction Factor laminar flow Friction Factor turbulent flow air From d v rho Friction Factor turbulent water From d v rho Friction Factor laminar water From d v rho Buoyant air bubble flow FBUO FDRG DDRG WDRG VTER VJS SVOL SMAS CD CK HFX HFS HFSA CEO CDO CEDR CDD CDP CS QHT Buoyancy force from d rho ambient b b rho ambient rho parcel Drag force from d v rho Drag work from d v Z Terminal velocity from d b Sphere volume Sphere mass Drag coefficient constant 0 5 Sea to Air heat transfer coefficient Enter v Sea to Air heat transfer in W m Enter p air density hs air saturation enthalpy at water temperature ha air enthalpy v velocity Dalton equation Sea to Air heat transfer in W m Enter p air density hs air saturation enthalpy at water temperature ha air enthalpy v velocity Dalton equation plus Im spray term Sea to Air heat transfer in W m
19. N WX WF and WT FF Vortex mode friction loss multiplier default 10 VF Vortex mode exit velocity divider default 10 THP Calculate enthalpy and entropy ENR Calculate heat work average source temperatures and efficiency HYD Calculate air density Z4 Chimney height T Lapse rate VCH Upward velocity at the bottom of the chimney DCH Chimney diameter DCO Diameter of collector ie 244 m FCO Heat flux on collector ie 800 W m2 NCO Efficiency of collector ie 31 NT Turbine efficiency in default 80 p2 Density of air at the base of the collector outlet P1 P4 Pressures kPa T1 T4 Temperatures K H1 H4 Enthalpies J kg 1 S2 Entropy J K kg u3 u4Moist static energy Specific work wl Specific work ideal reversible J kg wX Specific work Turbine loss J kg wF Specific work Friction loss J kg wT Specific work Turbine loss J kg wC Specific work Work of compression J kg wE Specific work Work of expansion J kg Total work QQI Heat input W WI Ideal work W WN Net work W WX Exit losses W WF Friction losses W WT Turbine losses W Specific heat QI Heat in J kg QO Heat out J kg EF Efficiency TCA Effective temperature of the cold source THA Effective temperature of hot source D400 Manzanares velocity delta T correlation at 400 W m insolation D800 Manzanares velocity delta T correlation at 800 W m insolation 42 HT HTAT PP MM BJW BJP D
20. PB5 GST GSP ZB WKT o EQ oSOL AVS AVH AVM Kinetic Energy produced when a parcel from base level is raised true adiabatically to pressure P Enter upper level P Kinetic energy equals total energy minus WPP Kinetic Energy when the parcel is moved to another sounding level Enter upper level row number Kinetic energy equals total energy minus WPP Kinetic Energy produced when a parcel recalled using Alpha GET is raised true adiabatically to pressure P The work becomes positive at the Level of Free Convection LFC Kinetic energy equals total energy minus WPP Potential energy of condensed water for typical pseudo adiabatic expansion default value 1000 J kg Total Mechanical Energy produced when a parcel from base level is raised true adiabatically to pressure P Enter upper level P Total Mechanical Energy produced when the parcel is moved to another sounding level Enter upper level row number Total Mechanical Energy produced when a parcel recalled using Alpha GET is raised true adiabatically to pressure P The work becomes positive at the Level of Free Convection LFC Sounding in PCD format Sounding in PKM format Sounding in PKM plus elevation Sounding True adiabatic expansion Sounding Pseudo adiabatic expansion Generate soundings al GST GSP I Generate sounding heights Toggle between reversible constant entropy and irreversible constant static energy expansion by setting flag 4 Pressure
21. YPPH PPH steam to Watt ZPPH Watt to PPH steam YQPY Quadrillion BTU yr to Watt ZQPY Watt to quadrillion BTU yr YTR Ton of refrigerant to Watt ZTR Watt to Ton of refrigerant YHR Heat Rate to Efficiency ZHR Efficiency to Heat Rate BTU kW hr Energy Conversion YMO Cubic meter of crude oil to Joule ZMO Joule to cubic meter of crude oil YMG Cubic meter of natural gas to Joule ZMG Joule to cubic meter of natural gas YBBL Barrel of crude to Joule ZBBL Joule to barrel of crude oil 12 YTOE ZTOE YTC ZTC ZTNT YTNT Tonne of crude oil to Joule Joule to tonne of crude oil Tonne of coal to Joule Joule to tonne of coal Joule to tonne of TNT Tonne of TNT to Joule Miscellaneous conversions TO B B TO G KG KG gt G GP PG KS gt G GM gt K CF gt KG KG KCF pM plo Tonne of crude oil to barrel Barrel of crude oil to tonne US gallons to kilogram of water Kilogram of water to US gallon US gallon of water to pound Pound of water to US gallon Kilogram per second water to US gallon per minute US gallon per minute water to kilogram per second Standard cubic feet of air to kilogram Kilogram of air to standard cubic feet Density lb ft to kg m Density kg m to lb ft Conversion Factors WPH WQ WTR BKH GP JMO JMG JTOE JBBL JTC JTT TOB Watts per pound per hour steam Watts per quadrillion BTU per year Watt per ton of refrigerant BTU per kilowatt hour Pound per Gallon Joule per cubic meter of o
22. a QO O Z 3 5 OF a Oli Gas Content Pressure kPa Temperature K Mixing ratio g kg Entropy J kg K Virtual Temperature K Lapse rate to next level down K m Distance to the next level down m Height of current level m SNT contains data relating to work produced when a parcel from the base level is raised true adiabatically to the current level Pit TS Pressure kPa True adiabatic expansion temperature K Potential energy of condensed water J kg air Total mechanical energy WB Kinetic energy WK WB WPP SNP contains data relating to work produced when a parcel from the base level is raised pseudo adiabatically to the current level pa Pressure KPA Pseudo Adiabatic expansion temperature K Water vapour content g kg Entropy of parcel excluding condensed water J kg K 26 5 Water condensed in current expansion step g kg 6 Accumulated potential energy of condensed water WP 7 Enthalpy of condensed water 8 Enthalpy of vapour phase 9 Height z 10 Work of buoyancy AWB in current step 11 Cummulative work of buoyancy WB 12 Work of buoyancy minus potential energy of concensed water WK WB WP AT5A_ADIABATIC EXPANSION TEMPERATURES The condition of the air to be expanded is stored in Matrix Beta and moved to the stack with Beta GET GTA generates the adiabatic expansion temperatures for 6 types of expansion and puts the result in a seven column array The array ends up o
23. air but limits the number of properties that can be specified to two for saturated air When the air is dry the third property is zero When the air is saturated the third property is used to determine the quantity of condensed water The program checks if MM is beyond the saturation amount if so the water beyond the saturated amount is taken to be all in the liquid phase if the temperature is above freezing temperature TF or to be all in the ice phase if the temperature is below freezing temperature TF minus the freezing band FB The calculations are based on the air and the water in any phase being at equilibrium The calculated properties include the contribution of the condensed water Air masses can have water in two condensed phases Once the required two or three properties are known all other thermodynamic properties of the air mass are readily calculated Example of program structure Visiting U3 shows that P T M must be on the stack to calculate relative humidity and that the program MVS is used in calculating the saturation mixing ratio Visiting MVS in AT3 shows that pressure and temperature must be on the stack to calculate saturation mixing ratio and that the program PV is used in calculating the vapour pressure Visiting PV shows temperature must be on the stack to calculate vapour pressure and that the program PVL or PVI are used to calculate vapour pressure depending on whether the temperature is above or below the freeze point
24. array Pressure array with 5 kPa intervals Generate sounding temperatures true adiabatic expansion Generate sounding temperatures pseudo adiabatic expansion Calculates the height of any pressure from the SNZ data Calculates the virtual temperature at any pressure from the SNZ data Calculates work produced when a parcel is lifted from h1 h2 mv z Calculates potential energy of condensed water from m1 mv z Moist static energy equation Solve moist static energy equation for temperature Average sounding entropy Total and Average sounding enthalpy Total and Average sounding water mm H20 25 ZZ4 to ZZ8 WT1 to WT5 PD2 to PD9 Results array reversible no separation true adiabatic constant entropy Results array irreversible no separation constant static energy Results array reversible with separation Pseudo adiabatic constant entropy Results array reversible with separation constant static energy Copy result arrays SNT and SNP in SNTs and SNPs Copy result arrays SNT and SNP in SNTo and SNPo Generate parcel properties parcel properties in PCU format Generate parcel properties parcel properties in PKM format Generate parcel properties relative to sounding base enter AT and AM Parcel Presure Parcel Temperature Parcel mixing ratio Parcel entropy Parcel enthalpy Subsoutines used in calculating SNZ Subroutines used in calculating SNT Subroutines used in calculating SNP SNZ contains the following sounding dat
25. ber for free convection of air in a tube enter Delta T mean T Diameter Calculations Calculate all output data from input data Calculate Delta pressure for turbulent flow Calculate Delta pressure for laminar flow Calculate Delta pressure using friction factor F5 Calculate Work loss per unit mass turbulent flow Calculate Work loss per unit mass laminar flow Calculate Reynolds Number Calculate Friction factor turbulent flow Calculate Friction factor laminar flow Calculate Tube cross sectional area Calculate Volumetric flow Calculate Mass flow Calculate Total work loss turbulent flow Calculate Total work loss laminar flow Calculate Ideal work from T delta T Z5 adiabatic lapse rate Calculate Ideal delta P from PCE Input Data Tube diameter Velocity Tube length 33 u5 Fluid viscosity p5 Fluid density F5 Friction factor Output data PT6 Pressure drop turbulent flow PL6 Pressure drop laminar flow WT6 Work loss per unit mass turbulent flow WL6 Work loss per unit mass laminar flow FT6 Friction factor turbulent flow FL6 Friction factor laminar flow FR6 Ratio of Turbulent to Laminar friction factors Re6 Reynolds Number A6 Tube area QV6 Volumetric flow QM6 Mass flow TWT6 Total work loss turbulent flow TWL6 Total work loss laminar flow AT5F Properties with unit AT5F contains one program called PROP PROP calculates the properties of the air specified in AT4 and tags each property with a na
26. c The freezing temperature and the freezing bands are 0 C and 20 C by default but can be changed AT5J can calculate the maximum intensity MPI of hurricanes and the work produced in an atmospheric Vortex Engine AVE work based on ideal process including a heater humidifier AT5J calculation prerequisites include entering the properties of ambient air at state 1 using either PCM1 or PCU1 entering the upper level pressure and level with PZ4 PCM1 Enter surface air conditions in PCM format PCU1 Enter surface air conditions in PCU format PJ4 Enter pressure gt Jordan Caribbean sounding hurricane height from lookup table PJ4S Enter pressure gt Jordan Caribbean sounding hurricane height by interpolation P4 Upper level pressure Z4 upper level elevation R1 Recall state 1 conditions in PCM format Several of the objects use the two guesses method wherein the user enters one guess and the program provides a second guess and then extrapolates to find the solution Program using the two guess method are identified with a 2 in their names Results show the extrapolated value and the residual error The two guess programs can be rerun to reduce the residual error Convection Energy wirhout heater humidifier The following four CE Convection Energy programs are for a three states process where there is no heater humidifier Results are stored in parameters X1 X3 and X4 There is no state 2 The calculation can usually be carried out d
27. d then pressing the key for the desired property The ending digit 3 in the program name is used to indicate properties calculated from the three standard parameters R Recall PP TT and MM to stack TT in K PKM format C Recall PP TT and MM to stack Display in C PCM format MOOXK lt gt Ww A1 PV3 UP3 UIS MS3 MV3 ML3 MI3 p3 pD3 pL3 TV3 TV3S ST3 SM3 SE3 AA3 HT3 HM3 EE3 HW4 u3 uAL3 T 9 0 gt T 63D 63M Oe e3 oWw3 L3 Toggle temperature in level 2 from C to K Recall PP TT and MM to stack Display in C PCU format Convert 3 stack properties from PKM format to PCU format Convert 3 stack properties from PCU format to PKM format Equivalent temperature air expanded to 10 kPa and compressed 100 kPa isentropically Backup PP TT MM in PPP TTT MMM Store PP TT MM in PPP TTT MMM Calculate and store SS Recall PPP TTT MMM to the stack Vapour pressure kPa Relative humidity from mass ratio saturation value relative to water Relative humidity from partial pressure ratio Relative humidity from mass ratio saturation value relative to ice Mixing ratio at saturation g kg Mixing ratio of water in the vapour phase g kg Mixing ratio of water in the liquid phase g kg Mixing ratio of water in the ice phase g kg Density kg m3 Valid for moist air and for saturated air containing condensed water Density kg m3 Moist air onl
28. diabatic expansion work RPLT True adiabatic expansion work SPLT Sounding Temperature Entropy Diagram WPLT Virtual Temperature Excess of the parcel TPLT Sounding Pressure Entropy Plot XPLT Potential and Equivalent Potential Temperatures YPLT Virtual and Potential Virtual Temperatures ZPLT Double Potential Temperature AT6A_Plot using HP48 parametric plot AT6B plots equations based on the data in arrays The result of the equation must be a complex number the real part is plotted on the horizontal axis and the complex part is plotted on the vertical axis The complex number may be taken directly from arrays or calculated from array data Plot is more flexible than MLINE the X and Y can come from different arrays the data plotted not need to be in an array it can be calculated from data in arrays You can invoke the plotter edit the equation and add more line to a plot Parametric plot is slower than MLINE MLINE takes 10 seconds to plot a single line Parametric plot can take 1 minute to plot a line from an array without any calculation calculating and plotting a property can take 5 minutes The plots can be exported to a PC and printed with Word Perfect 45 1 REFERENCES Dufour L et J Van Mieghem 1975 Thermodynamique de l Atmosphere Institut Royal Meteorologique de Belgique Bruxelles Randall D A J Wang 1992 The moist available energy of a conditionally unstable atmosphere J Atmos Sci 49 240 255 Ooyama
29. e HP48SX The calculations were independently checked on an equivalent MathCad program and on chemical engineering process simulator PROII HP48SX programs are called objects Calculator programs are difficult to document and therefore are rarely shared The labelled programmable key features of the HP48SxX facilitate the use of the calculator The directories and the programmable keys of the directory are organized to help one remember the name of function and sequence of use The programs can be viewed using the VISIT key as a supplements to this documentation Objects are usually kept short to make it easier to understand the programs Parameters required to run a program are usually listed at the beginning of the program code RPN and algebraic programming mode are both used The algebraic mode is used to show equations their familiar form Using the HP48SX calculator requires an understanding of its two volumes User Manual Using the search function of your file reader can be an effective way of finding the topic or the object you are looking for in this program documentation The AT program can be modified to test scenarios not anticipated when the program was conceived The program and its documentation are a work in progress The purpose of infrequently used old objects may no longer be clear to the author An attempt has been made to remove unused and duplicate objects Some of the objects whose usefulness is in doubt or that may be used by othe
30. e Stefan Boltzman law and earth surface area Source Earth s Annual Global Mean Energy Budget J T Kiehl and Kevin E Trenberth Bulletin of the American Meteorological Society Volume 78 Issue 2 February 1997 pp 197 208 Units are in W m SCON Solar constant 342 W m STR Solar radiation reflected by atmosphere and earth s surface 107 SAR Solar radiation reflected by air and clouds 77 SGR Solar radiation reflected by ground 30 SAB Solar radiation absorbed by air and clouds 67 SGB Solar radiation absorbed by ground 168 IGE Infrared emitted by the earth s surface 390 IGB Infrared absorbed by the earth s surface 324 IGN Infrared net from the earth s surface 66 CVT Convection from then earth s surface 102 LGC Latent from ground 78 HGE Sensible from ground 24 IRT Infrared total 235 IGU Infrared upward from the earth s surface 40 ICU Infrared upward from cloud 30 IAU Infrared upward from air 165 W gt P Watts to percent P gt W Percent to Watt SBC Stefan Boltzman constant WR Radiative flux from temperature TR Temperature from Watts ESUR Earth s surface ERAD Earth radius km R A Radius km to area km FDO Forcing as a result of doubling CO concentration 4 W m FBB Forcing for Black Body 0 3 C W m FHA Forcing including all feedback from James Hansen 0 75 C W m AT3C_ THERMODYNAMIC PROPERTIES OF PROPANE pV Density of propane gas in kg m3 ent
31. e updraft Work calculated Using Michaud enthalpy reversible updraft of given temperature and RH Work calculated Using Michaud enthalpy irreversible updraft Miscellaneous AT5J objects SAB T2C EXT SST AAP BAP Enter Sea surface temperature SST temperature approach AAP and humidity approach BAP Store in SST AAP and BAP This is an alternate to PZ4 Calculate temperature T2 and net work Store W12 and Q23 Interpolate using work for two P3 guesses to determine P3 which makes W34 0 Sea surface temperature in C Air temperature approach to SST in C Air humidity approach to 100 in PCaP Z4 calculation based on P1 T1 C and lapse rate a C m and P4 Results are stored in P4 and Z4 PCa Z Z4 calculation based on P1 T1 C and lapse rate a C m and Z4 Results are PS4 PW4 PE4 W95 HM HMO T4 T4E BUO stored in P4 and Z4 Enter pressure gt Standard atmosphere height Enter pressure gt Standard winter atmosphere height enter pressure gt Standard equatorial atmosphere height Work calculation based on 95 RH Enter SST Michaud enthalpy Enthalpy of air producing zero work 66900 J kg when air is raised to Jordan 12 kPa level 15500m Michaud enthalpy Enthalpy of air producing zero work 59500 J kg when dry air is raised to Jordan 12 kPa level 15500m Temperature of parcel at level 4 Temperature of parcel at level 4 from P4JS Buoyancy of parcel at lev
32. e values can be changed by the user For the default values condensed water is all liquid temperatures above 0 C all ice at temperatures under 20 C and 50 liquid at 10 C Objects MV3 ML3 and MI3 in AT4 can be used to calculate how much of the water is in each of the three phases A freezing band is equivalent to the transition phase suggested by Ooyama both approaches eliminates a singularity solver problem when all the condensate freezes suddenly If the condensate were to all to freeze suddenly during adiabatic expansion the air temperature would rise and some of the condensate would have to re evaporate to conserve entropy The freezing band can be removed by setting FB to zero Using a freezing band is preferable to using sudden freezing even if the point where freezing starts or end is not known A freezing band of 5 K is sufficient to eliminate the solver singularity problems The program assumes that water in the vapour phase is in equilibrium with liquid water if the temperature is above the bottom of the freezing band and in equilibrium with ice otherwise AT2 DIRECTORY TAT4 Make sub directory AT4 the current directory Directory AT2 contains constants Z Converts degK to degC and vice versa formerly named KC If the number on the stack is less than 150 TO 273 15 is added if the number on the stack is greater than 150 TO is subtracted Pressing KC repeatedly toggles between degK and degC 14 TO Temperature base 273 1
33. eat of fusion at TO LSQ Latent heat of sublimation at the triple point of water MW Molecular weight of water G Acceleration of gravity 9 8 m s GM Accelleration of gravity 9 80665 m s D Dry adiabatic lapse rate G CPV RA RV K Kilo One thousand 1000 15 PO PVO PQ PU PW1 PW2 PE2 TS TW1 TE1 TE2 KAIR aAIR aW pAIR VAIR HVC HVL Base pressure for air 100 kPa Standard pressure 101 325 kPa Base pressure for water vapour 0 61070 kPa Triple point pressure 0 61114 kPa Standard atmosphere tropopause 11 000 m pressure 22 65kPa Winter standard atmosphere tropopause 8000 m pressure 77 37 KPA Winter standard atmosphere pressure 2000 m 32 29 kPA Equatorial standard atmosphere tropopause 15 000 m pressure 12 95 kPA Standard atmosphere bottom temperature 288 15 K Standard atmosphere top temperature 216 65 K Standard Winter atmosphere bottom temperature 253 15 K Equatorial standard atmosphere bottom temperature 301 15 K Equatorial standard atmosphere top temperature 203 15 K Standard Atmosphere Lapse Rate 0 00650 K m Winter Atmosphere lapse rate 0 00608 K m Equatorial Atmosphere lapse rate 0 00653 K m Elevation of the top of the Standard Troposphere 11 000 m Winter Atmosphere height 2000 m Winter Atmosphere height 8000 m Equatorial Atmosphere height 15000 m Clapeyron equation coefficient for saturation with respect to liquid water Clapeyron equation coefficie
34. efficient CK Heat transfer coefficient RO Outer radius km FK Coriolis factor UC Central relative humidity DEMA DeMaria 1994 hurricane velocity correlation enter SST in C AT5M_ _ SOLAR CHIMNEY ATMC ATT VT Q down CHI VOR LOR ZDD P1T7T FNN MU Solar chimney cases see list of case at ene of this section Enter chimney base delta AT Calculate ideal work per unit mass J kg Ex Manzanares 17 C gt 109 91 J kg Enter upward velocity V at the base of chimney calculate power Ex Manzanares 8 m s gt power ideal 75147 W actual power 41802 W Exit losses 21879 W Friction losses 3952 W Turbine losses 7514 W Ex Manzanares 8 Calculate heat input from chimney flow and from collector area Chimney mode power calculation Vortex mode power calculation Friction loss increased by a factor of 5000 per Lorenz Enter chimney height Z chimney diameter and collector diameter Ex Manzanares 200 10 244 Enter chimney base pressure P1 default 100 kPa base ambient temperature in C and lapse rate T default 0 00975 C m stored in variable D EX Manzanares 100 30 0 00975 Enter Insolation heat flux F collector efficiency N in percent and turbine efficiency in percent Calculate total heat received and collector delta T Ex Manzanares 10800 W m2 31 80 Calculated upward mass flow of air in kg s 41 VUD DDD Calculate turbine loss WT and display QQo WI W
35. el 4 with condensed water in and out Extrapolation subroutine EXT variables 37 PY P3 for guess 1 WY Work 34 for guess 1 PZ P3 for guess 2 WZ Work 34 for guess 2 Work and heat calculated in T2C and used in WA2 and WD2 W12 Work of expansion process 12 for CE1R Q01 Heat input required to reach state 1 assuming that the water is initially in the condensed state and that the air and water are initially at temperature tO Enter tO the temperature of air and water in C typically 20 C This is a good representation of the heat input for deep atmospheric cycle wherein essentially all the water separates from the air Relevant to CE1R Q03 Heat input required to reach state 3 assuming that the water is initially in the condensed state and that the air and water are initially at temperature tO Enter tO the temperature of air and water in C typically 20 C This is a good representation of the heat input for deep atmospheric cycle wherein essentially all the water separates from the air and where in the air is subsequently sprayed with sea water Q23 Heat received in process 23 for reversible expansion CE1R Q13I Heat received in process 23 for irreversible expansion CE11 Work calculated in CE1R WB Work of buoyancy Convective Energy CE corresponds to CAPE MV Maximum velocity from WB WP Potential energy of condensed water for true adiabatic expansion WPP Potential energy of condensed water for pseudo
36. er P in kPa and T in K PC Vapor pressure of propane in kPa Enter T in K RC Propane gas constant 188 7 22 HC Propane heat of combustion 50 292 000 J kg LVO Propane heat of vaporization 430 310 J kg MW Propane molecular weight CW Propane liquid sensible heat CP Propane gas specific heat at constant pressure pL Propane liquid density 510 kg m3 aC Propane vapour pressure equation coefficient 6C Propane vapour pressure equation coefficient yC Propane vapour pressure equation coefficient AT3D CIRCULATION PRODUCED FROM THE EARTH S ROTATION R1 Enter annulus radius to initiate calculation V1 Enter annulus velocity for storage in V1 R1 Result annulus radius V1 Result annulus velocity R2 Result radial distance where C2 C1 V2 Tangential velocity at radius where C2 C1 C1 Circulation C1 R1 V1 R2 V2 RAT Radius and velocity ration RAT V2 V1 R2 R1 a1 vorticity at radius 1 1S__ vorticity at radius 1 solid body rotation 2 vorticity at radius 2 2S vorticity at radius 2 solid body rotation FQ Coriolis factor from latitude MOM Angular momentum absolute MOMR Angular momentum relative to earth surface MOME Angular momentum earth surface POTR Potential Radius Emanuel 1999 AT3E LAMBTON COLLEGE PROTOTYPE PARAMETERS AA8 Area of central 8 diameter hot air inlet 0 0324 m A24 Area of central 24 diameter circle 0 29 m AAS1 Area of one 6 x 48 deflector slot 0
37. er kg of air Calculates to quantity of water that must be mixed with air mass 1 to produce saturated air of relative humidity U at temperature T with water at temperature W Enter air mass 1 properties using PCU1 or PCM1 prior to running WTUW Tthe temperature of the liquid water in the mixture is the wet bulb temperature of the air mixture Enter W the temperature of the water T the temperature of the mixture U the relative humidity of the mixture P3 the pressure of the mixture The mixture is assumed to be at pressure P3 M1 air is expanded isentropically to from P1 to P3 prior to mixing Result in mass of water MM2 in grams of water per kg air Enthalpy check after running WTUW no parameters required just press HCK Results consist of four numbers Enthalpy of gas phase in final state Enthalpy of liquid phase in final state Enthalpy of gas phase in initial state Enthalpy of liquid phase in final state Total enthalpy in the final state equals total enthalpy in the initial state Entropy check after running WTUW no parameters required just press SCK entered Results consist of four numbers Entropy of gas phase in final state Entropy of liquid phase in final state Entropy of gas phase in initial state Entropy of liquid phase in final state Total entropy in the final state is greater than total entropy in the initial state because internally generated entropy is generated during the irreversible mixing process 29
38. ers Subsidence velocity required to compensate for radiative cooling Carnot efficiency and ultimate efficiency Efficiency of aimple and combined cycles Tables of adiabatic temperatures for both true and pseudo adiabatic expansion the freezing temperatures is adjustable Properties of isenthalpically mixed air and water Data for the four cases described in Thermodynamic Cycle of the Atmospheric process Case 1 air column with an adiabatic lapse rate pure air Case 2 air column with a 6 5 K km lapse rate pure air Case 3 and 4 air column with a 6 5 K km lapse rate moist parcel Properties of air rising with entrainment and detrainment Used for Tellus paper currently broken Marqules type air masses change of position AT5D AT5E ATE1 AT5F AT5G AT5H AT5J AT5J1 AT5J2 AT5J3 AT5K AT5L AT5M AT5N AT5P AT5Q AT6A AT6B AT6C AT6D AT6E Independent check of adiabatic expansion temperature using a standard equation for the entropy of moist air during adiabatic expansion not used Pressure drop and work loss for continuous flow in a tube Drag terminal velocity and work loss for spherical air parcels Air to sea heat transfer Tube flow calculations with stored data Thermodynamic properties with tags symbol and units HP48 differentiation function test unused CAPE from sounding data Hurricane intensity AVE Ideal process Total energy equation Sarnia constants Emperical ener
39. erves WGR World gas reserves WCR World coal reserves WUR World uranium reserves AT2B Car mileage conversions GALC Toggle between Litres per 100 km to miles per Canadian gallon GALU Toggle between Litres per 100 km to miles per US gallon KPM Toggle between Litres per 100 km and kilometres per Litre AT2C Energy price Values based on September 2013 EIA GJE Electricity per Giga Joule 33 33 JE Electricity per Joule 33 33E 9 KE Electricity per kilowatt hour used to calculate others 0 12 GJO Crude oil per Giga Joule 15 5 JO Crude oil per Joule 15 5E 9 MTO Crude oil per metric ton 650 BO Crude oil per Barrel used to calculate others 95 GJG Natural gas per Giga Joule 5 29 JG Natural Gas oil per Joule 5 29E 9 17 MG Natural gas per standard cubic meter 0 203 TFG Natural gas per standard thousand cubic feet used to calculate others 5 74 GJC Coal per Giga Joule 1 74 JC Coal per Joule 1 74E 9 MTC Coal per metric ton 45 10 TC Coal per US ton used to calculate others 41 00 GJZ Gasoline per Giga Joule 26 5 JZ Gasoline per Joule 26 5E 9 LZ Gasoline per litre 0 92 GZ Gasoline per US gallon used to calculate others 3 50 AT2D Hurricane categories minimum velocity in m s VTS Tropical storm VH1 Category 1 hurricane VH2 Category 2 hurricane VH3 Category 3 hurricane VH4 Category 4 hurricane VH5 Category 5 hurricane KPH Convert m s to km hr MPH Co
40. gy equations Hurricane amp AVE total work Exergy Hurricane intensity Emanuel method Solar chimney Pseudoadiabatic expansion temperatures Equivalent Potential temperatures by step and by Bolton Sounding arrays and array conversion programs AT5J with addition of WK WB WPP recognises that WP reduces WB Plots array data using the HP48 parametric plot rather than MLINE Sounding CAPE Subsidence Average properties of a sounding AT4 PROGRAMS DESCRIPTION Directory AT4 is described first because it is the most important and most frequently used directory Pressing ATM in the HOME directory makes AT4 the current directory AT4 makes use of the constants in AT2 and of the pure air properties of AT3 Air properties can be entered in many ways PKM Pressure in kPa dry bulb in K and mixing ratio in g kg PKU Pressure in kPa dry bulb in K and relative humidity in PCD Pressure in kPa dry bulb and dew point in degC with respect to liquid water PCM Pressure in kPa dry bulb in C and mixing ratio in g kg PCU Pressure in kPa dry bulb in degC and RH in PCW Pressure in kPa dry and wet bulb in degC PCDF Pressure in kPa dry bulb and dew point in degC with respect to ice POM Pressure in kPa potential temperature in K and mixing ratio in g kg dry air POQ Pressure in kPa potential temperature in K and humidity in g kg substance To specify the air property put the appropriate three properties on the stack
41. il Joules per cubic meter natural gas Joules per ton of crude oil Joules per barrel of oil Joules per ton of coal Joules per tonne of TNT Ton of oil per barrel Time Conversion Factors Seconds per day Seconds per sidereal day Minutes per day Hours per year Seconds per year Miscellaneous Utilities TICK DONE MLINE GRAPHER AUTHOR SYMB Short audible Long audible Plotting program A program to transform an array to a string for transfer to a PC Program author name Calculator keyboard index 13 AT1 Custom Menu The converts between SI and traditional units and works like the calculator s built in unit converter To use the converter enter the value and press the key for the old unit To convert to an other unit press the left shift key and the key for the new unit Press UVAL to remove the unit tag The AT1 custom menu has the following user defined keys Conversion only works within a category Category UVAL Energy Units J KW H BTU Power Units W BTU H Temperature Units C K F R Volumetric flow L S GPM Density KG M LB FT Energy Density G GJ T GW h AT2 _ _ FREEZING BAND Condensed water can freeze between 0 C K and 40 C Condensed water can be made to freeze over a band of temperature FB starting at a specified freezing temperature TF Freezing temperature TF and freezing band FB are stored in directory AT2 Default freezing temperature is 273 15 K default freezing band is 20 K but thes
42. irectly without any guess indicated by the 1 in the program name or by providing one guess indicated by 2 in the program name R stands for reversible expansion and I stands for irreversible expansion There is no separation of the condensate in either case Convective Energy reversible process CE1R Calculate the work produced when surface air is raised reversibly Results shown are T4 P3 thetaE and WB Calculates P3 and T3 only valid if there is no condensation at state 3 Convective Energy irreversible process Convective Energy reversible process CE1 Calculate the work produced when surface air is semi reversibly Enter turbine efficiency Results shown are T4 P3 and WB Calculates P3 and T3 only valid if there is no condensation at state 3 CE11 Calculate the work produced when surface air is raised irreversibly Result T4 and P3 CER Subroutine used by CE2R CE2R Calculate the work produced when surface air is raised reversibly Enter a P3 guess Results P3 and residual error Can be rerun to reduce residual minor bug run CE1R first to correct 35 CE1R and CE2R results correspond to the CAPE of a true adiabatic updraft When there is no condensation at state 3 the two programs give the same result CEI Subroutine used by CE2l CE2I Calculate the work produced when surface air is raised irreversibly Enter a P3 guess Results P3 and residual error Can be rerun to reduce residual CE1I and CE2
43. l temperature of air with no condensed water content 93M uses the solver to calculate the potential temperature of air containing condensed water Potential temperature can also be calculated using TSOL TSOL uses the solver to calculate the temperature at the end of an isentropic process 93D is much faster than TSOL but TSOL is more fundamental entropy is conserved in isentropic processes 63M is valid for any kind of air including air containing condensed water 63D is only valid when there is no water in a condensed phase TSOL is valid for compression or expansion The program makes extensive use of Gibb s rule that states that knowing three properties is sufficient to calculate all thermodynamic properties of a two component system The three properties need not be one of the set listed at the beginning of section 3 1 For example the three properties can be entropy mixing ratio and pressure TSOL calculates temperature from entropy mixing ratio and pressure When TSOL is used it is only necessary to enter the pressure PP because the values of entropy and the mixing ratio are taken from the calculator memory SS MM The high resolution of the HP48SX makes possible to reverse a calculation to get back the originals input AT4 Miscellaneous objects SET Store stack in PP TT MM IS Initialize by calculating entropy and storing it in SS GF Accelleration of gravity factor of air water mixture enter MM KM Poisson ratio of air water
44. lculate power Calculates 01 and MU CHI Work calculation Press after VTDT L osses based on turbulent flow W Based on AT5J WB in J kg Results are WR WX WF and WT VOR Work Calculation Press after VTDT Losses based on laminar flow W Based on AT5J WB in J kg Results are WR WX WF and WT DDD Calculate turbine loss WT and display WII WAA WX WF and WT DVZp Friction loss calculation for turbulent and laminar flow J kg Enter diameter velocity length and density VCH Upward velocity at base of updraft m s DCH Diameter of updraft or solar chimney m pi Density of air at state 1 kg m MU _Updraft flow kg s WR Reversible process work W WX Exit velocity losses W WF Friction losses W WT Turbine losses W EF Exit kinetic energy loss divider Default 10 FF Laminar flow friction multiplier Default 10 NT Turbine efficiency Total work WI Ideal work W WN Net work W WX Exit losses W WF Friction losses W WT Turbine losses W 39 Specific work wl Specific work ideal reversible J kg wX Specific work Turbine loss J kg wF Specific work Friction loss J kg wT Specific work Turbine loss J kg wC Specific work Work of compression J kg wE Specific work Work of expansion J kg AT5K Energy calculations using Exergy IRR Given p t m pj tj and z Calculates loss work WEX6 Given p t m pj tj and z Calculates delta h delta h mg
45. lve H EQ for MM Enter HH MSOL Mixing ratio from wet bulb Solve W EQ PSOL Isentropic expansion pressure Enter T Solve S EQ for P given S T and M SSOL Isentropic expansion temperature Enter P Solve S EQ Solve for T given S P and M 10 TCAL Isentropic expansion temperature equation no condensation allowed TSOL Isentropic expansion temperature Enter P Invoke SSOL after calculating SS Solve for T given S P and M VSOL Temperature from Virtual temperature Enter TV Solve TV EQ WSOL Wet bulb temperature Solve W EQ The following xxx 3 properties programs invoke the solver TAS 0A3 TE3 0E3 663 LCL3 LFZ3 Properties calculated using the solver which require up to a minute to calculate on the original HP48SX calculator can be calculated in under 1 second on the emulator The solver adds variables to the current directory The use of the solver should be restricted to the directories where the variables PP TT and MM exist namely AT4 AT5 AT5B AT5F The solver can overwrite the values of PP TT MM SS and HH Results are always stored in the current directory New variables appear at the front of the current directory before the name of the first sub directory and can be purged once they are no longer required Programs B Backup and R Restore can be used to restore the standard properties before the next calculations 63D calculates potential temperature using a formula for the potentia
46. me and unit It is a quick way to check units used by the program 12 2 AT5G 12 3 AT5H Upflow process calculations WC Work Calculate Enter P3 and Z3 HC Enthalpy calculate Calculate air conditions at the base of the updraft in PCD format Calculates P1 T1 and H1 ZC Height Calculate Calculate Z1 the height of the P1 level Used to calculate the elevation at the base of a sounding when the station elevation is not provided AT5J Hurricane intensity Total Energy Equation method AT5J contains objects for calculating work production when air is raised both reversibly and irreversibly for a variety for conditions Calculations are based on the total energy equation method and on the four state ideal process shown in Fig 1 of the Isabel intensity paper Calculation results at the four states are stored in variables P1 P4 T1 T4 M1 M3 S1 S3 H1 H4 Other results include WB work of buoyancy WP potential energy of condensed water Q heat received and maximum hurricane intensity in kPa and m s The AT5J directory contains valuable programs AT5J can be used to show that work is equal to heat received times Carnot efficiency AT5J can be used to calculate the final temperature of 34 air raised reversibly and irreversibly and to show that the final temperature is slightly higher for irreversible upflow than for reversible upflow All calculation are based on updraft without separation commonly called true adiabati
47. ments Cloumns PCTA C M U TV entropy increase Mixing result array Calculates the property of a mixture of mass 1 and of the MM2 water part of mass 2 where MM2 is in liquid state TT2 and MM2 must be entered prior to pressing TMW and are used to specify the temperature and quantity of condensed water added to the humid air mass Entropy of air water mixture Calculates to quantity of water required to saturate mass 1 air at T by mixing with water at temperature W Enter the temperature of the water W and air mass 3 temperature T prior to pressing WTW Calculates to quantity of water required to produce saturated air of relative humidity U at T with water at temperature W Water outlet temperature equal to final air dry bulb temperature Enter the temperature of the water W air mass 3 temperature T and relative humidity U prior to pressing WTU Calculates to quantity of water that must be mixed with air mass 1 to produce saturated air of relative humidity U at temperature T with water at temperature 28 WTUP HCK SCK W Enter air mass 1 properties using PCU1 or PCM1 prior to running WTUW The temperature of the liquid water in the mixture is the wet bulb temperature of the air mixture Enter W the temperature of the water T2 T the temperature of the mixture U the relative humidity of the mixture The mixture is assumed to be at pressure P1 there is no change in pressure Result in mass of water MM2 in grams p
48. mixture enter MM RM Gas constant of air water mixture enter MM CPM Specific heat at constant pressure of air water mixture enter MM CST Custom menu 11 AT4 CUSTOM MENU CST The custom menu provides access to the most commonly used functions by using the A to F keys in the unshifted left shifted and right shifted mode KEY LABEL UNSHIFTED LEFT SHIFTED RIGHT SHIFTED A RUM R PCU PCM B SHp ST3 HT3 03 C SCF MS3 LCL3 LFZ3 D PUV PV3 U3 TV3 E Dwe DSOL WSOL TSOL F KCF Z ZF ZC There are two custom menus CST one in AT1 and one in AT4 The AT1 custom menu is available in all subdirectory of AT1 down to AT4 The AT4 custom menu is available from all subdirectory of AT4 The AT1 custom menu converts between non SI and SI units The AT4 custom menu can be accessed from the AT1 directory with the TAT4 key and pressing CST The TAT4 key switches to directory AT4 Pressing SAT4 is a good way to get in the program it puts you in the middle of the program where the commonly used functions and no more then two directories away AT1 Conversion factors times and utilities The purpose of the conversion factors is primarily to replace incoherent units into rational SI unit Energy units should be converted to the base energy SI unit the Joules Prefixes are not used Prefixes can be seen by going to engineering mode and looking at the exponent Temperature Conversion ZC Degree F to C ZF Degree C to F Power Conversion
49. n the stack but is moved to AT6A and called VT for plotting The array columns are Col Number Parameter Pressure True adiabatic freezing at 0 degC True adiabatic freezing at 40 degC True adiabatic no freezing Pseudo adiabatic freezing at 0 degC Pseudo adiabatic freezing at 10 degC Pseudo adiabatic no freezing NOOR WOD GTA uses GT1 GT2 and GT3 GT1 produces the pressure column GT2 produces true adiabatic expansion temperatures GT3 produces pseudo adiabatic expansion temperatures GTA calculates expansion temperatures at 5 kPa pressure interval PT Delta in AT6A plots the differences between the various adiabatic expansion temperatures in VT ET delta equation can be edited plot the difference between any two type of expansion lines can be added to the plot Programs TAT TAP and PAP list adiabatic expansion temperatures on the stack for a single type of expansion TAT True adiabatic at specified pressure interval TAP Pseudo adiabatic at specified pressure interval PAP Pseudo adiabatic at specified temperature interval Sample arrays are stored in the program name preceded by a left arrow PAP produces an array that correspond to the Smithsonian Pseudo expansion tables Theta WB calculates the potential pseudo wet bulb temperature which is stored at the bottom of the array The Potential Pseudo wet bulb are in agreement with the Smithsonian tables within 0 2 K 27 AT5B MIXTURE PROPERTIES AT5B calculates the
50. nctions are available The name of the current directory and the path from the Home directory are indicated at the top of the calculator screen The name of the left hand key after you press VAR is the next directory down When you see the AT5 key you are in the AT4 directory Sub directories AT2 AT3 AT4 AT5 and AT6 form a chain The objects in the upper level directories are available from any underlying directory The constants in AT2 are available in AT3 AT4 and AT5 the data in AT5 can be plotted in AT6 The objects not in in line directories are not accessible without changing directory The functions in AT4 can be accessed from AT5 AT5B can access the objects in AT4 AT3 and AT2 but not the objects in AT5A When the program encounters a new object it looks for it first in the current directory and then in its parent directories The constant values are entered only once usually in AT2 therefore results are consistent and repeatable Directory Structure Parent Sub Directories Directories HOME AT1 AT1 AT2 AT2A AT2B AT2C AT2D ATDAT AT2 AT3 AT3A AT3B ATSC ATSD AT3E AT3 AT4 AT4A AT4B AT4C AT4 AT5 AT5A AT5B AT5C AT5D AT5E AT5F AT5G AT5H AT5J AT5K AT5L AT5M AT5P AT5Q AT5 AT6 AT6A AT6B AT6C ATED AT6E AT6 AT7 2 2 Main In Line directories HOME Complete AT1 Program Atmospheric Themodynamics Program AT1 AT1 Conversion between customary units and base SI unit and energy content of common fuels Press ATM to jump directly to
51. nt for saturation with respect to liquid water Clapeyron equation coefficient for saturation with respect to liquid water Clapeyron equation coefficient for saturation with respect to ice Clapeyron equation coefficient for saturation with respect to ice Clapeyron equation coefficient for saturation with respect to ice User keys No longer used Coriolis Factor 2 n N Viscosity of air Viscosity of water Prandt Number of air Prandt Number of water Conductivity of air Conductivity of water Diffusivity of air Diffusivity of water Density of air at standard conditions Kinematic viscosity of air at standard conditions Heating value of coal J kg Heating value of liquid fuel J kg 16 AT2A Energy usage and reserves in Joules All values are in Joules the base SI unit Unit with SI prefixes can easily be inferred by going to ENG mode WPY World primary energy usage per year WEY World electrical energy usage per year WOY World oil energy usage per year WGY World gas energy usage per year WCY World coal energy usage per year USEY US electrical energy usage per year USOY US oil energy usage per year USGY US gas energy usage per year SUNS Solar radiation received by the earth per second SUND Solar radiation received by the earth per day SUNY Solar radiation received by the earth per year HHS Hurricane thermal energy heat per second HHD Hurricane thermal energy per day WFR World fuel reserves WOR World oil res
52. nter Carnot efficiency from 7 terms of series EFL Ultimate efficiency when work is dissipated at hot source temperature Enter Carnot efficiency from series ultimate limit TH Default hot source temperature TC Default cold source temperature ATH Steam cycle hot source Delta T ATC Steam cycle cold source Delta T Q1 Q2 Q3 Q4 Heat input to each cycle and waste heat Joule or Watt W1 W2 W3 W123 Work from each cycle and total work _ Joule or Watt A1 A2 A3 Actual efficiency to Carnot efficiency ratio AT5 PROGRAM DESCRIPTION AT5 contains programs to calculate properties for a whole sounding including how much work is produced when a parcel is raised true adiabatically or pseudo adiabatically Caution parcel properties PP TT MM SS etc use in AT5 are not the same as used in AT4 aGET Gets the original sounding data in PKM format for the specified sounding level BGET Gets the properties of pseudo adiabatic expanded air in PKM format for the specified sounding level GET Gets the properties of true adiabatic expanded air in PKM format for the specified expansion level pGET Get parcel properties MIX Mixing calculator 63 Calculates the static energy per unit mass of air ZB and SNZ are used to calculate height oM3 Calculates the static energy per unit mass of substance ZB and SNZ are used to calculate height 24 NW1 NW2 NW4 WPP W1 W2 W4 SNC SNK SNZ SNT SNP GSA GSZ So PB
53. nvert m s to mph KT Convert m s to knot VIA 76 m s VIM 170 m s EFO Enhanced Fujita category 0 EF1 Enhanced Fujita category 1 EF2 Enhanced Fujita category 2 EF3 Enhanced Fujita category 3 EF4 Enhanced Fujita category 4 EF5 Enhanced Fujita category 5 FUJ Old Fujita tornado class to m s TOC Tropical Cyclone 135 m s AT1 ATDAT Data directory ATDAT contains data relating to specific soundings STDA Standard atmosphere EQUA Standard equatorial atmosphere POLE Standard high latitude atmosphere WILLIS Willis island sounding JOR Jordan mean Caribbean hurricane season sounding BRA1 Roscoe Braham pre lake Michigan sounding FM3 Fawbush and Miller type 3 tornado sounding GATE GATE sounding 18 HAW Sounding LEE Lee s convergence line sounding LEMO LeMoyne sounding LUCAS Lucas sounding MK1 Makung pre severe squall sounding PFLD Plainfield tornado sounding RW Randal and Wang sounding TEL TELLUS sounding TRIER Trier sounding WAT Watonga pre tornado sounding WEI WEI sounding WSPO sounding AEXP Expansion data generated in AT5A PAP TAT TAP The data directories can contains arrays of raw sounding data SNC SNK SNU and arrays of calculated data SNZ SNT SNP The arrays have the same names as the arrays of AT5 There are programs in AT4 to convert raw data arrays from one format to another You can store the SNC data in AT5 and recalculate the other arrays or move all five arrays back to AT5 Program SAV
54. o show that the result is the same as the simpler ST3 program approach SD2W Entropy of air containing water in the liquid phase SD2l Entropy of air containing water in the ice phase Four equations are required to calculate the adiabatic expansion temperature of rising air one for the moist air stage one for the stage where the air contains water in the liquid phase one for the transition from liquid to ice and one for the ice stage The constant entropy approach used in AT4 is simpler a single equation covers all four stages AT5E TUBULAR AND SPHERICAL FLOW Tubular flow A5E1 TUBULAR FLOW USING STORED DATA Input data identified with suffix 5 Output data identified with suffix 6 APF Pressure drop due to friction when fluid flows in a horizontal tube From d v z rho f APTA Frictional delta P for turbulent air From d v z rho DPL Frictional delta P laminar air APLA Frictional delta P for laminar air From d v z rho APTW Frictional delta P turbulent water APLW Frictional delta P laminar water DVZW Delta P turbulent and laminar water flow APW Calculate pressure reduction at the base of a vertical tube from pressure the temperature and the work p k w APA Calculate pressure reduction at the base of a vertical tube from the work only w approximation WF Work per unit mass loss through friction when a fluid flows in a horizontal tube From d v z f 31 DVZp WLA WTA AREA TVFL TMF
55. or true adiabatic expansion with water separation at the 10 kPa level 000 Equivalent Temperature using 003 enter PCU 00E3 Equivalent Temperature using 003 uses PP TT MM HUX Canadian Humidex Equation taken from Wikipedia EMA3 Equivalent Temperature based on an equation from Emanuel enter PKM EMAU Equivalent Temperature based on an equation from Emanuel enter PKU t4 Isentropic expansion temperature for moist air not valid for saturated air LCL3 Level of Condensation kPa LFZ3 Freezing pressure kPa Q3 Specific humidity g kg AFFK Affinity of air at PKM for liquid water at the temperature of the air AFFC Affinity of air at PCU for liquid water at the temperature of the air AC Affinity of pure water vapour at pressure FF for water at temperature in C FF Vapor pressure in kPa FF calculated by either AFFK or AFFC Example Arguments 1 90 2 293 15 3 12 00 Function ST3 Result 212 47 Entropy is 212 47 J kg K The program is valid for 3 kinds of air 1 Dry air where the moisture content is zero 2 Moist air where the moisture is less than the saturated amount 3 Saturated air where the water content is equal or greater than the saturation amount The three standard properties are used for the three kinds of air Two properties are required to describe dry air three properties are required to describe moist or saturated air The phase rule allows three properties be specified to describe humid
56. r objects have been retained Questions marks are used for the descriptions of objects that have not yet been documented Calculated thermodynamic properties list Partial Pressure of Water Partial Pressure of Air Mixing Ratio for Water in any Phase Specific Humidity Mole fraction of water Relative Humidity Wet Bulb Temperature Density Virtual Temperature Potential Virtual Temperature Entropy Enthalpy Free Enthalpy Potential Temperature at 100 kPa Double Potential Temperature potential temperature at 10 kPa Isentropic Desiccation Temperature Potential Isentropic Desiccation Temperature Equivalent Temperature Isenthalpic Desiccation Temperature Equivalent Potential Temperature Lifting Condensation Pressure Freezing Level Level of Free Convection True Adiabatic Expansion Temperatures Pseudo Adiabatic Expansion Temperature Potential pseudo wet bulb Temperature Affinity Static Energy The calculations are based on Thermodynamique de I Atmosph re by Louis Dufour and Jacques Van Mieghem Thermodynamic functions are generally based on the equations listed in http vortexengine ca misc AT1_Equations pdf The program uses rigorous definitions of thermodynamic properties and avoids algebraic approximations The HP48 solver is used to calculate properties that cannot be isolated by algebraic manipulation rather than by using approximate equations As a result running the calculation backwards reproduce
57. recall the five arrays and their names to the stack To move all arrays back to the AT5 directory recall SAV to the stack and press EVAL switch to the AT5 directory FM3 and press STO 5 times The opposite procedure can be used to move the arrays from AT5 to ATDAT Arrow down AT5 changes to the AT5 directory SEN Arrays Summarizing the result of sensitivity analysis for the sounding The second third and fourth columns contain the potential energy of the condensed water the residual work and the total work The number in the first column is a code indicating the type of expansion the freezing temperature the parcel temperature excess and the parcel mixing ratio excess Column 1 code 1 true adiabatic expansion 2 pseudo adiabatic expansion Column 2 code 0 freezing at 0 C 1 freezing at 10 C 4 freezing at 40 C 9 no freezing Column 3 code parcel temperature excess K beyond base of sounding value Column 4 code parcel mixing ratio excess beyond base of sounding value g kg or 1 10 g kg AT3 PROGRAM DESCRIPTION Directory AT3 contains programs to calculate the thermodynamic properties of pure air and pure water the virtual temperature of moist air lapse rate and distance between two sounding levels PV Partial pressure of water from T PVL Partial pressure of liquid water from T same as PGL PVI Partial pressure of ice from T same as PGI 19 PV2 MVS MVL pA SA SV sL SL3 SI SC3 ZTA ZPT ZPTA ZPT
58. s the original inputs HP48 functions are written in algebraic notation so that the user can see the equations used to calculate a property and the parameters required by the program by visiting the program Calculator programs can be extremely useful but are notoriously difficult to document For this reason the use of calculator programs is frequently limited to the program creator This documentation is an attempt to explain the major features of the program This documentation is organized by directory Object in directories are usually listed in the order they appear in the calculator A good way to find what you are looking for is to use your pdf reader search function The program and its documentation are works in progress The program uses SI units Directory AT1 contains objects for converting non SI units to the base SI unit Calculations are usually based on absolute temperature in degree Kelvin Temperature can be entered in degree Celsius or Kelvin Extensive properties are per unit mass of dry air Enthalpy of moist air is in Joules per kilogram of dry air and includes the enthalpy of the air and its water content in any phase Engineering multiples of the basic SI unit are used when appropriate pressure is in kPa mixing ratio is in g water kg air Units are not shown except in directory AT5F Program PROP in AT5F calculates 28 properties of the air mass defined in AT4 and tag the values with the appropriate SI unit The program can plo
59. t arrays of properties calculated from atmospheric soundings The program is designed so that the calculated properties can be used in subsequent calculations including plots based on arrays of sounding properties Entropy calculations were checked against Randall mixing calculations were checked against Lilly 2 0 PROGRAM INSTALLATION The compete Atmospheric Thermodynamics program is contained in object AT1 The program is installed by putting object AT1 on the stack and saving it as AT1 in the Home directory AT1 requires 155 kbytes of memory A real HP48SX calculator requires at least one 128 kbytes memory card This memory card must be merged in the built in 32 kBytes main memory to give a total memory of 160 kbytes An HP48SxX can have up to 290 kbytes of memory by merging two 128 kbytes memory card with its basic 30 kbytes of memory The HP48SX emulator should be set up with 290 kbytes of memory The AT1 program will run on either the HP48SX or the HP48GX or on their PC emulators AT1 was written for the HP48SX The HP48SX has a more consistent user interface than the HP48GX and is recommended On a PC the use of the Casey touch screen HP48SxX skin is recommended 2 1 DIRECTORY ORGANIZATION Sub directory AT2 is accessed by pressing the AT1 key in the home directory The left hand key in each directory is usually the next directory down The TAT4 key in sub directory AT2 gets one directly to the AT4 directory from which most of the fu
60. taking 10 minutes on the original calculator can be completed in less than 2 seconds on a PC HP48 emulators for IPod and IPad are now available for 15 at the Apple Application store On the IPod IPad emulators the key can be pressed directly like on the original calculators In addition the IPad emulator provides visual and audible feedback when key are pressed resulting in a fabulous user interface HP48 emulators are also available for Android devices For some unexplained reason the skin for the PC version of the HP48SX calculator reversed the color of the orange and blue shift keys The skin for the HP48SX IPad emulator reverted to the original colors which match those of the HP48SX Manual The AT1 program can be run on the HP48SX or HP48GX original calculators on windows PC s on IPod on IPad and on Android devices AT1 requires 160 kBytes of memory HP48SX PC emulator memory can be increased from 30 kB to 292 kB by merging two 128 kB memory cards HP48GX PC emulator memory can be increased from 128 kB to 259 kB by merging one 128 kB memory card The IPod IPad applications now support the second memory card and therefore their maximum memory is 292 kB for the HP48SX app and 256 kB for the HP48GX app According to Vaclav Smil a well programmed calculator is probably the most cost and time effective investment an inquisitive mind can make in a life time Calculations relating to the Atmospheric Vortex Engine AVE can be carried out on th
61. thalpy of large air masses 2 Programs to calculate the work produced when thin layer of dry air are raised including the efficiency of the process and the height of air columns of uniform potential temperature Calculate the height of a layer of air of uniform potential temperature Enter P1 P2 and 9 Margules equation for the total enthalpy of large air masses from bottom and top pressure bottom temperature and lapse rate Margules equation for the total enthalpy of large air masses from bottom and top pressure and potential temperature Work produced when a thin layer of dry air is raised from potential 30 temperature parcel temperature and height WP Theta T Work produced when a thin layer of dry air is raised from bottom and top pressure potential temperature and parcel temperature N Theta Z Efficiency from potential temperature and height ZP Theta Height from bottom and top pressure and potential temperature Subdirectory AT5C1 contains a program for calculating the area that two air equal air masses of different potential temperature would require so that they have the same height Invoke the solver enter Theta 1 Theta 2 and PT the pressure at the top of the air mass Solve for height ZZ press A1 and P1 to obtain the area of air mass 1 and the pressure at the base of A1 10 0 AT5D contains the equation given by Dufour and also by Iribarne and Godson for the entropy of humid air expanding isentropically t
62. tion from t Height from T1 T2 and lapse rate Height from P1 P2 T1 T2 Height from P1 P2 T1 and lapse rate Height from P2 and T1 P1 100 kPa Lapse rate adiabatic P2 from P1 T1 in K lapse rate and height solar chimney P2 from P1 T1 in C lapse rate and height solar chimney Temperature from P1 P2 T1 and lapse rate Equation relating PX1 PX2 CX1 aX ZX Ambient Conduit bottom pressure Ambient Conduit top pressure Ambient bottom temperature C Ambient lapse rate K km 20 ZX a4 y4 yxa axy NXy yXN CNa CNy ZS ZTS AZS ZTW AZW ZTE AZE NCC NCK MOL R gt Q Q gt R POP POPA POP1 OZPO 6ZOT PGL PGI XVL XVI BV tBV TAU ER Ambient Conduit top pressure Lapse rate from P1 P2 TV1 TV2 Poison exponent from P1 P2 TV1 TV2 Poison exponent from Lapse rate Lapse rate from Poison ratio N from Poison ratio poison ratio rate from N Specific heat from lapse rate Specific heat from Poison ratio Height in the Standard Atmosphere from P2 Height and temperature in the Standard Atmosphere from P2 Height difference in the Standard Atmosphere from P1 and P2 Height in the Winter Atmosphere from P2 Height and temperature in the Winter Atmosphere from p2 Height difference in the Winter Atmosphere from P1 and p2 Height in the Summer Atmosphere from p2 Height and temperature in the Summer Atmosphere from p2 Height difference in the Summer Atmosphere
63. to find datum relative humidity for which W 0 WUA2 Calculate relative humidity U3 required to make the work zero given C3 using two guesses method Provide relative humidity guess OK for zero work Needs fixing when work gt 0 WPU2 Calculate temperature C3 required to produce pressure P3 at relative humidity RH3 WPU Calculate work for U3 given T3 PU Enter Pressure P3 and relative humidity RH3 in state 3 before running WPU or WPU WPU2 Calculate T3 required to make the work zero given C3 using two guesses method Provide one C3 guess Note The four W 2 solvers give result in y register error in x register The error can be deleted 36 S97 S100 SSA SSI SSW X1 X2 WM3 WM4 WM5 and W 2 can be pressed again to produce more accuracy Results can be displayed in more detail by deleting the results and pressing X1 or X2 Hurricane Maximum Potential Intensity MPI from SST 97 eyewall relative humidity amp with freezing Hurricane Maximum Potential Intensity MPI from SST 100 eyewall relative humidity amp without freezing PROII equivalent Hurricane air temperature from SST T3 24 5 SST SSI SSW Hurricane Intercept SST at which T3 24 5 C default 27 C used in SSA SST Weighing Delta T3 Delta SST default 0 75 used in SSA Hurricane Potential Intensity T3 WP WB WT Hurricane Potential Intensity T3 P3 Pc WB v Work calculated Using Michaud enthalpy reversibl
64. y Dufour and Van Mieghen equation 8 63 Density kg m3 Moist air only Leonard density of air plus density of water Virtual temperature K Valid for moist air and for saturated air containing condensed water Virtual temperature of saturated air without condensed water K Entropy per unit mass of air J kg K Entropy per unit mass of substance J kg K Entropy from a common equation equation possibly from Emanuel Equivalent to ST3 Enter PKM Entropy if water is in condensed phase Enter PKM Enthalpy per unit mass of air J kg Enthalpy per unit mass of substance J kg Enthalpy when water is in condensed state Dufour Equivalent Temperature 12 39 Enthalpy at wet bulb temperature Free enthalpy H TS J kg Free enthalpy all water in liquid phase J kg Temperature to Potential Temperature Potential temperature to Temperature Potential Temperature of dry or unsaturated air Potential Temperature of any air including air with condensed water solver Equivalent Temperature from Memory PTM Equivalent Temperature from entered PTM Wet bulb from entered PTM Liquid water potential temperature 6V3 Virtual potential temperature K TA3 Isentropic Desiccation Temperature K 6A3 Potential Isentropic Desiccation Temperature Dufour 14 23 K 6E3 Equivalent Potential Temperature TE3 Equivalent Isenthalpic Desiccation Temperature K 003 Temperature at 10 kPa K and equivalent potential temperature f
65. z exergy WEXZ Given p t m pj and z Calculates work from delta h mgz EXR5 Given p t m pj and tj Calculates exergy EXRZ Given p t m pj tj and z Calculates delta h tj delta s ideal work GIBB gt Givenp t m Calculates Gibb free energy AT5L Hurricane Intensity Renno Emanuel equations Renno Equation A simple theory for Dust Devils 1998 eq 16 POC Calculate base pressure PCUc Enter base pressure temperature and humidity Poa Far Environment Pressure Ta Far environment Temperature TO Central Temperature C To SST temperature C Mo Far Environment mixing ratio Mas Far environment saturation mixing ratio MO Central mixing ratio Ua Far environment Relative Humidity AN Efficiency multiplied by fractional dissipation in boundary layer PCUA Enter surface condition in PCU format Use SST for C VK Maximum velocity without frictional reheat K Kerry VKB Maximum velocity with frictional reheat KB Kerry Bister Bister and Emanuel 1998 eq 21 Emanuel 1999 eq 1 EK Efficiency without frictional reheat 40 EKB Efficiency with frictional reheat V86 Maximum velocity Emanuel 1986 eq 43 VKD V86 denominator term VKN V86 Numerator term B86 V86 beta term PC Central pressure Emanuel 1986 eq 26 LPA LPB LPC LPD PC terms PE TE ME MES UE Surface conditions HS Enthalpy of saturated air at SST HE Enthalpy of surface air TO Outflow temperature CD Drag co

ATMOSPHERIC THERMODYNAMICS HP48 Calculator Program

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