Index Table of psichrometric functions Group 1, functions of tdb, f and H 17.- Group 2, functions of tdb, twb and H 26.- Psichrometric functions 11.- Absolute humidity x = f(tdb, f, 12.- Specific volume v = f(tdb, f, 13.- density r = f(tdb 14.- Dew point temperature tdp = f(tdb, f, H) 15.- Enthalpy ent = f(tdb, 16.- Wet bulb temperature twb = f(tdb, f, H) 21.- Absolute humidity x = f(tdb, twb 22.- Specific volume v = f(tdb, t 23.- Density r = f(td 24.- Dew point temperature tdp = f(tdb, twb,H) 25.- Enthalpy ent = f(tdb, 27.- Relative humidity f = f(tdb, tw
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Index
Table of psichrometric functions
Group 1, functions of tdb, f and H Group 3, functions of tdb, x and H31.-
17.-
Group 2, functions of tdb, twb and H Group 4, functions of ent, x and H41.-
45.-26.-
Psichrometric functions
11.- Absolute humidity x = f(tdb, f, H)12.- Specific volume v = f(tdb, f, H) 32.- Specific volume v = f(tdb, x, H) 13.- density r = f(tdb, f , H) 33.- density r = f(tdb, x , H)14.- Dew point temperature tdp = f(tdb, f, H) 34.- Dew point temperature tdp = f(tdb, x, H)15.- Enthalpy ent = f(tdb, f, H) 35.- Enthalpy ent = f(tdb, x, H)16.- Wet bulb temperature twb = f(tdb, f, H) 36.- Wet bulb temperature twb = f(tdb, x, H)
37.- Relative humidity f = f(tdb, x, H)
21.- Absolute humidity x = f(tdb, twb ,H)22.- Specific volume v = f(tdb, twb, H) 42.- Specific volume v = f(ent, x ,H)23.- Density r = f(tdb, twb, H) 43.- Density r = f(ent, x ,H)24.- Dew point temperature tdp = f(tdb, twb,H) 44.- Dew point temperature tdp = f(ent, x ,H)25.- Enthalpy ent = f(tdb, twb, H)
46.- Wet bulb temperature twb = f(ent, x, H)27.- Relative humidity f = f(tdb, twb,H) 47.- Relative humidity f = f(ent, x ,H)
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Group 3, functions of tdb, x and H Group 5, functions of tdb, ent and H
51.- Absolute humidity x = f(tdb, ent, H)32.- Specific volume v = f(tdb, x, H) 52.- Specific volume v = f(tdb, ent, H)33.- density r = f(tdb, x , H) 53.- Density r = f(tdb, ent, H)34.- Dew point temperature tdp = f(tdb, x, H) 54.- Dew point temperature tdp = f(tdb, ent, H)35.- Enthalpy ent = f(tdb, x, H)36.- Wet bulb temperature twb = f(tdb, x, H) 56.- Wet bulb temperature twb = f(tdb, ent, H)37.- Relative humidity f = f(tdb, x, H) 57.- Relative humidity f = f(tdb, ent, H)
61.- Air & water properties42.- Specific volume v = f(ent, x ,H) Ref. 1a43.- Density r = f(ent, x ,H) Ref. 1b44.- Dew point temperature tdp = f(ent, x ,H) Ref. 1c
www.piping-tools.net46.- Wet bulb temperature twb = f(ent, x, H)47.- Relative humidity f = f(ent, x ,H)
Dry bulb temperature tdb °C Absolute humidityRelative humidity % Specific volumeHeight above sea level m.a.s.l. Density
In the functions to calculate the wet bulb temperature (functions 16, 36, 46 and 56), some limits to the input values of the dry bulbtemperature, relative humidity and height above sea level habe been set to to obtain an acceptable maximum number of iterations. If required, the maximum values can be changed in the code (functions 16, 36, 46 and 56).The numbers in square brakets indicate the number of the function in the VBA code
GroupsGroup 1 Group 2tdb, f , H tdb, twb, H
tdb ºC tdb 96.00 °C tdb 96.0 °C % 100.0 % #VALUE! [27]
H m s.n.m. H 3.4 m H 3.4 mx kg/kg x #VALUE! [11] x #VALUE! [21]v v #VALUE! [12] v #VALUE! [22]r r #VALUE! [13] r #VALUE! [23]
Note. Some depent variables will not require the three inputs when they arecalculated individually. But because the calculation method with VBAfunctions make use of other functions, the complete set of input variablesis required.
f or fH
f f f
m3/kgkg/m3
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Psychrometric Functions [1] & [2]
x kg w/kg da Dew point temperature ºCv Specific enthalpy ent kJ/kg dar Wet bulb temperature twb ºC
In the functions to calculate the wet bulb temperature (functions 16, 36, 46 and 56), some limits to the input values of the dry bulb Maximum values for the input parameterstemperature, relative humidity and height above sea level habe been set to to obtain an acceptable maximum number of iterations. 96 °CIf required, the maximum values can be changed in the code (functions 16, 36, 46 and 56). 100 %
5300 m.a.s.l.
GroupsGroup 3 Group 4 Group 5tdb, x, H ent, x, H tdb, ent, H
H 3.4 m H 3.4 m H 3.4 mx #VALUE! kg/kg x #VALUE! kg/kg x #VALUE! [51]v #VALUE! [32] v #VALUE! [42] v #VALUE! [52]r #VALUE! [33] r #VALUE! [43] r #VALUE! [53]
v = #VALUE! m³/kg daSpecific volume [1] Eq.(28) x = #VALUE! kg/kg
0.62198 * Pvap / (Patm - Pvap) r = #VALUE! kg/m³
v = Rair*T/Patm *(1+1.6078*x) Using function 13287.06 J/(kg*K) r = Density_twb_f_H
T = 313.15 K tdb = 40.0 °C98,945 Pa f = 30.0 %
x = #VALUE! kg/kg H = 200.0 mv = #VALUE! m³/kg da r = #VALUE! kg/m³
Using function 12v = Specific_volume_tdb_twb_H
tdb = 40.0 ºCf 30.0 %
H = 200.0 mv = #VALUE! m³/kg da
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12.- Specific volume v = f(tdb, f, H) and 13.- density r = f(tdb,f , H)
Rair = Rgen / MMair
Rgen:MMair =Rair =
Rair =
Patm =
v=Rair⋅TPatm
⋅(1+1.6078⋅x ) (28 )
Microsoft Editor de ecuaciones 3.0
ρ=1v⋅(1+x ) (11)
14.- Dew point temperature tdp = f(tdb, f, H)
Data Relative humiditytdb = 37.8 °C fi = f / 100
f = 31.5 % f = 31.5H = 3.353 m fi = 0.315
Saturation pressure of water at dry bulb temperature Vapor pressuretdb = 37.8 °C [2]
Psat =(1/100)* Exp(ca / tK + cb + cc * tK + cd * tK ^ 2 + ce * tK ^ 3 + cf * Ln(tK)) [bar] 0.0655tK = t + 273.15 °C fi = 0.315tK = 310.9277778 K 0.02065ca = -5800.22006 2065cb = -5.516256cc = -0.04864024cd = 4.17648E-05 Dew point temperaturece = -1.4452E-08 -35.97 - 1.8726 * Ln(Pvap) + 1.1689 * (Ln((Pvap) )^2cf = 6.5459673 Pvap = 2065
0.0655 bar 17.84
Using function 14Using function 1 [2] tdp = Sicro_Dew_Point_tdb_f_H
Sicro_Saturated_vapor_pressure_t tdb = 37.8t = 37.8 °C twb = 31.5
#VALUE! bar H = 3.4tdp = #VALUE!
Using equation (35) from Ashrae 1985, the resulting dew point temperature isUsing equation (39) from Ashrae 20055, the resulting dew point temperature is
(see next page)Result when using ther VBA function
The enthalpy of a mixture of perfectgases equals the sum of the individualpartial enthalpies of the components .Therefore, the enthalpy of the moistair can be written:h=ha+ hvh=ha+ x ⋅ hg (27 )whereha : specific enthalpy of dry air kJ/kg da
hv : specific enthalpy of vapor kJ/kg da
x: moisture content kg w /kgda
hg :specific enthalpy of saturated vaporat the temperature of the mixture kJ/kg wh: specific enthalpy of mixture kJ/kg da
Microsoft Equation 3.0
Moist air as an ideal gas [1 ] , page 6 . 8
The enthalpy of a mixture of perfectgases equals the sum of the individualpartial enthalpies of the components .Therefore, the enthalpy of the moistair can be written:h=ha+ hvh=ha+ x ⋅ hg (27 )whereha : specific enthalpy of dry air kJ/kg da
hv : specific enthalpy of vapor kJ/kg da
x: moisture content kg w /kgda
hg :specific enthalpy of saturated vaporat the temperature of the mixture kJ/kg wh: specific enthalpy of mixture kJ/kg da
16.- Wet bulb temperature twb = f(tdb, f, H)
Input data Saturation pressure of water at wet bulb temperaturetdb = 37.8 °C Input
f = 31.5 % Initially assumed and solution of the wet bulb temperatureH = 3.4 m 23.89 °C
Input data Absolute humidity tdb = 37.8 °C x = ((2501-2.381*twb)*xsat_twb - (tdb-twb)) / (2501+1.805*tdb-4.186*twb)twb = 23.9 °C tdb = 37.8 °CH = 3.4 m twb = 23.9 °C
0.01876 kg/kgAtmospheric pressure [1], Eq. (3) x = 0.01294 kg/kg
1.01325 * (1 - 0.0000225577 * H) ^ 5.25588 H = 3.4 m Using the function 21
1.013 bar x = Sicro_Absolute_Humidity_tdb_twb_Htdb = 37.8 °C
Saturation pressure of water at wet bulb temperature twb = 23.9 °C [2] H = 3.4 m
twb = 23.9 °C x = #VALUE! kg/kgPsat =(1/100)* Exp(ca / tK + cb + cc * tK + cd * tK ^ 2 + ce * tK ^ 3 + cf * Ln(tK)) [bar]
tK = t + 273.15 °C Water vapor partial pressure. tK = 297.0388889 K Pvap = x * Patm / ( 0.62198 + x )ca = -5800.22006 x = 0.01294 kg/lgcb = -5.516256 Patm = 1.013 barcc = -0.04864024 Pvap = 0.02065 barcd = 4.17648E-05 Pvap = 2065 Pace = -1.4452E-08cf = 6.5459673 Dew point temperature
0.0297 bar tdp = -35.97 - 1.8726 * Ln(Pvap) + 1.1689 * (Ln((PvaP) )^2Pvap = 2065 Pa
Using function 1 [2] tdp = 17.84 °CSicro_Saturated_vapor_pressure_t
twb = 23.9 °C Using function 24#VALUE! bar tdp = Sicro_Dew_Point_tdb_twb_H(tdb, twb, H)
tdb = 37.8 °CAbsolute humidity at saturation and at twb [1], Eq. (8) twb = 23.9 °C
Saturation pressure of water at wet bulb temperature [2]Input
twb = 23.9 °C x =Psat =(1/100)*Exp(ca tK+cb+cc * tK + cd * tK ^ 2 + ce * tK ^ 3 + cf * Ln(tK)) [bar] tdb =
twb =tK = t + 273.15 °CtK = 297.0388889 K x =
ca = -5800.22006 Using the function 21cb = -5.516256 x =cc = -0.04864024 tdb =cd = 4.17648E-05 twb =ce = -1.4452E-08 H =cf = 6.5459673 x =
0.0297 bar Enthalpyh =
tdb =[2], Eq. (30), page 6.9 x =
h =
h = t + x * (2501 + 1.805 * t) Using the function 25h: specific enthalpy [kJ/kg da] ent = t: dry bulb temperature [°C] tdb =x: absolute humidity [kg/lg] twb =
x * Patm / ( 0.62198 + x ) [1], Eq. (8a) Some properties do not require the input of three variables.x = 0.01294 kg/lg The VBA functions in many cases use other functions for the
1.013 bar calculation and these functions may depend on the complete set.0.02065 bar For this reason all VBA functions will require the input of a set
2065 Pa of three variables.
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Patm =
Pvap =
Patm =Pvap =Pvap =
Pvap=x⋅Patm
0. 62198+x [1 ] , Eq .(8a )
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34.- Dew point temperature tdp = f(tdb, x, H)
Dew point temperature Eq. (35), [2], page 6.9tdp = -35.97 - 1.8726 * Ln(Pvap) + 1.1689 * (Ln((PvaP) )^2
2065 Pa tdp = 17.84 °C (approx. Equation)
Using the function 34tdp = Sicro_Dew_Point_x_H(tdb, x, H)tdb = 37.8 ºCx = 0.01294 °CH = 3.4 m
tdp = #VALUE! °C
Some properties do not require the input of three variables.The VBA functions in many cases use other functions for thecalculation and these functions may depend on the complete set.For this reason all VBA functions will require the input of a setof three variables.
Using the function 35 Some properties do not require the input of three variables.Sicro_Enthalpy_tdb_x_H The VBA functions in many cases use other functions for the
tdb = 37.778 °C calculation and these functions may depend on the complete set.x = 0.01294 kg/kg For this reason all VBA functions will require the input of a setH = 4000 m.a.s.l. of three variables.
ent = #VALUE! kJ/kg
[2], Eq. (30), page 6.9
h = t + x * (2501 + 1.805 * t)h: specific enthalpy [kJ/kg da]t: dry bulb temperature [°C]x: absolute humidity [kg/lg]
h=t+ x⋅(2501+1 . 805⋅t ) (30 )
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35.- Enthalpy ent = ent(tdb, x, H)
Some properties do not require the input of three variables.The VBA functions in many cases use other functions for thecalculation and these functions may depend on the complete set.For this reason all VBA functions will require the input of a setof three variables.
ent=1 .006⋅t db+x⋅(2501+1 .86⋅t db )x⋅(2501+1 .86⋅tdb )=ent−1 . 006⋅t db
x=ent−1 .006⋅tdb2501+1 . 86⋅tdb
[1 ] , (32b )x=
ent−1 .006⋅tdb2501+1 . 86⋅t db
[1 ] , (32b )
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42.- Specific volume v = v(ent, x, H) and 43.- density Rho = f(ent, x, H)
[1], Eq.(11)
m³/kg dakg/kgkg/m³
Sicro_Density_ent_x_H(ent, x, H)
kJ/kgkg/kgmkg/m³
Some properties do not require the input of three variables.The VBA functions in many cases use other functions for thecalculation and these functions may depend on the complete set.For this reason all VBA functions will require the input of a setof three variables.
x * Patm / ( 0.62198 + x ) [1], Eq. (8a) H =x = 0.01294 kg/lg tdp =
1.013 bar0.02065 bar
2065 Pa
Some properties do not require the input of three variables.The VBA functions in many cases use other functions for thecalculation and these functions may depend on the complete set.For this reason all VBA functions will require the input of a setof three variables.
Pvap =
Patm =
Pvap =
Patm =Pvap =Pvap =
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44.- Dew point temperature tdp = tdp(ent, x, H)
Dew point temperature Eq. (35), [2], page 6.9 -35.97 - 1.8726 * Ln(Pvap) + 1.1689 * (Ln((PvaP) )^2
2065 Pa 17.84 °C (Approx. Equation)
Using the function 44Sicro_Dew_Point_x_H(ent,x, H)
71 kJ/kg0.01294 °C
3.4 m#VALUE! °C
Some properties do not require the input of three variables.The VBA functions in many cases use other functions for thecalculation and these functions may depend on the complete set.For this reason all VBA functions will require the input of a setof three variables.
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46.- Wet bulb temperature twb = twb(ent, x, H)
Absolute humidity at saturation and at twb
Input dataent 71.0 kJ/kg #VALUE! bar
x 0.01294 kg/kg 0.0297 barH = 3.4 m.a.s.l. #VALUE! kg/kg
tK = t + 273.15 °CtK = 297.0388889 Kca = -5800.22006cb = -5.516256 Some properties do not require the input of three variables.cc = -0.04864024 The VBA functions in many cases use other functions for thecd = 4.17648E-05 calculation and these functions may depend on the complete set.ce = -1.4452E-08 For this reason all VBA functions will require the input of a setcf = 6.5459673 of three variables.
twb = (2501*xsat_twb -tdb - 2501*x - 1.805 * tdb * x ) / (2.381 * xsat_twb - 4.186 * x - 1 )tdb = 71.0 °C
0.019311 kg/kgx = #VALUE! kg/kg
twb = #VALUE!
Some properties do not require the input of three variables.The VBA functions in many cases use other functions for thecalculation and these functions may depend on the complete set.For this reason all VBA functions will require the input of a set
Some properties do not require the input of three variables.The VBA functions in many cases use other functions for thecalculation and these functions may depend on the complete set.For this reason all VBA functions will require the input of a setof three variables.
Return to index
47.- Relative humidity f = f(ent, x, H)
Psat =
f = (Patm/Psat) * (x /(0.62198 + x ) )Patm =Psat =
Using the function 48 [2], Eq. (30), page 6.9ent = Sicro_Dry_Bulb_Temperature_ent_x_Hh = 71.0316 kJ/kg h = t + x * (2501 + 1.805 * t)x = 0.0129 kg/kg h: specific enthalpy H = 3.3528 t: dry bulb temperature
tdb = #VALUE! m x: absolute humidity
Some properties do not require the input of three variables.The VBA functions in many cases use other functions for thecalculation and these functions may depend on the complete set.For this reason all VBA functions will require the input of a setof three variables.
Using function 51 The absolute humidity is independent of the height above sea level.x = Sicro_Absolute_Humidity_tdb_ent(tdb, ent,H) The VBA functions in many cases use other functions for the
tdb = 37.8 °C calculation and these functions may depend on the height "H".ent = 71.0 kJ/kg For this reason all VBA functions will require the input of a setH = 0.0 of three variables.x = #VALUE! kg/kg
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x=ent−1 .006⋅tdb2501+1 . 86⋅t db
[1 ] , (32b )
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51.- Absolute humidity x = x(tdb, ent)
The absolute humidity is independent of the height above sea level.The VBA functions in many cases use other functions for thecalculation and these functions may depend on the height "H".For this reason all VBA functions will require the input of a setof three variables.
x=ent−1 .006⋅tdb2501+1 . 86⋅t db
[1 ] , (32b )
Input data Relative humidity [1], Eq. (8b)tdb = 37.78 ºC f =ent = 71.03 kJ/kg 1.012847288 barH = 3.4 m #VALUE! bar
x = 0.01294 kg/kgAtmospheric pressure [1], Eq. (3) f = #VALUE! -Patm= 1.01325 * (1-0.0000225577 *H) ^ 5.25588 f = #VALUE! %
H = 3.4 m1.01285 bar 'Vapor presure
fi * PsatSaturation pressure at dry bulb temperature fi = #VALUE!
4.- Air and water properties at atmospheric pressure
Saturated water properties 0 ºC <= t <= 100 ºC
Input data: Temperature t = 12 ºC
Function ResultsSaturatedWaterConductivity_t k = #VALUE! W/(m*K)SaturatedWaterSpecificHeat_t Cp = #VALUE! kJ/(kg*K)SaturatedWaterPrandtl_t Pr = #VALUE! -SaturatedWaterDensity_t #VALUE!SaturatedWaterAbsoluteViscosity_t m = #VALUE! Pa*sSaturatedWaterKinematicViscosity_t n = #VALUE!SaturatedWaterThermalDiffusivity_t a = #VALUE!
r = kg/m3
m2/sm2/s
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4.- Air and water properties at atmospheric pressureRev. cjc. 13.07.2013
Dry air properties -73.15b ºC <= t <= 726.85 ºC
Input data: Temperature t = 34 ºC
Function ResultsAirConductivity_t k = #VALUE! W/(m*K)AirSpecificHeat_t Cp = #VALUE! kJ/(kg*K)AirPrandtl_t Pr = #VALUE! -AirDensity_t #VALUE!AirAbsoluteViscosity m = #VALUE! Pa*sAirKinematicViscosity_t n = #VALUE!AirThermalDiffusivity_t a = #VALUE!
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r = kg/m3
m2/sm2/s
[1]
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Atmospheric pressure as function of height above sea level H [m]
[3] A quick derivation relating altitude to air pressureVersion 1.03, 12/22/20042004 Portland State Aerospace Society <http://www.psas.pdx.edu>Redistribution allowed under the terms of the GNU General Public License version 2 or later.http://psas.pdx.edu/RocketScience/PressureAltitude_Derived.pdf
[4] Fundamentals of heat and mass transferFrank P. Incropera and David P. De WittSecond editionJohn Wiley & sons1985