# Psychrometric Programming Functions

Library of psychrometric functions to calculate thermodynamic properties of air for Python, C, C#, Fortran, JavaScript and VBA/Excel

## Overview

Psychrometrics are the study of physical and thermodynamic properties of moist air. These properties include, for example, the air’s dew point temperature, its wet bulb temperature, relative humidity, humidity ratio, enthalpy.

The estimation of these properties is critical in several engineering and scientific applications such as heating, ventilation, and air conditioning (HVAC) and meteorology. Although formulae to calculate the psychrometric properties of air are widely available in the literature (@Stull2011@Wexler1983@Stoecker1982@Dilley1968@Humphreys1920), their implementation in computer programs or spreadsheets can be challenging and time consuming.

PsychroLib is a library of functions to enable calculating psychrometric properties of moist and dry air. The library is available for Python, C, C#, Fortran, JavaScript, Microsoft Excel Visual Basic for Applications (VBA). It works in both metric (SI) and imperial (IP) systems of units. The functions are based of formulae from the 2017 ASHRAE Handbook — Fundamentals, Chapter 1, SI and IP editions. Functions can be grouped into two categories:

1. Functions for the calculation of dew point temperature, wet-bulb temperature, partial vapour pressure of water, humidity ratio or relative humidity, knowing any other of these and dry bulb temperature and atmospheric pressure.
2. Functions for the calculation of other moist air properties. All these use the humidity ratio as input.

## Python

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1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 # PsychroLib (version 2.3.0) (https://github.com/psychrometrics/psychrolib) # Copyright (c) 2018 D. Thevenard and D. Meyer for the current library implementation # Copyright (c) 2017 ASHRAE Handbook — Fundamentals for ASHRAE equations and coefficients # Licensed under the MIT License. """ psychrolib.py Contains functions for calculating thermodynamic properties of gas-vapor mixtures and standard atmosphere suitable for most engineering, physical and meteorological applications. Most of the functions are an implementation of the formulae found in the 2017 ASHRAE Handbook - Fundamentals, in both International System (SI), and Imperial (IP) units. Please refer to the information included in each function for their respective reference. Example >>> import psychrolib >>> # Set the unit system, for example to SI (can be either psychrolib.SI or psychrolib.IP) >>> psychrolib.SetUnitSystem(psychrolib.SI) >>> # Calculate the dew point temperature for a dry bulb temperature of 25 C and a relative humidity of 80% >>> TDewPoint = psychrolib.GetTDewPointFromRelHum(25.0, 0.80) >>> print(TDewPoint) 21.309397163661785 Copyright - For the current library implementation Copyright (c) 2018 D. Thevenard and D. Meyer. - For equations and coefficients published ASHRAE Handbook — Fundamentals, Chapter 1 Copyright (c) 2017 ASHRAE Handbook — Fundamentals (https://www.ashrae.org) License MIT (https://github.com/psychrometrics/psychrolib/LICENSE.txt) Note from the Authors We have made every effort to ensure that the code is adequate, however, we make no representation with respect to its accuracy. Use at your own risk. Should you notice an error, or if you have a suggestion, please notify us through GitHub at https://github.com/psychrometrics/psychrolib/issues. """ import math from enum import Enum, auto from typing import Optional ####################################################################################################### # Global constants ####################################################################################################### ZERO_FAHRENHEIT_AS_RANKINE = 459.67 """float: Zero degree Fahrenheit (°F) expressed as degree Rankine (°R) Units: °R Reference: ASHRAE Handbook - Fundamentals (2017) ch. 39 """ ZERO_CELSIUS_AS_KELVIN = 273.15 """float: Zero degree Celsius (°C) expressed as Kelvin (K) Units: K Reference: ASHRAE Handbook - Fundamentals (2017) ch. 39 """ R_DA_IP = 53.350 """float: Universal gas constant for dry air (IP version) Units: ft lb_Force lb_DryAir⁻¹ R⁻¹ Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 """ R_DA_SI = 287.042 """float: Universal gas constant for dry air (SI version) Units: J kg_DryAir⁻¹ K⁻¹ Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 """ MAX_ITER_COUNT = 100 """int: Maximum number of iterations before exiting while loops. """ MIN_HUM_RATIO = 1e-7 """float: Minimum acceptable humidity ratio used/returned by any functions. Any value above 0 or below the MIN_HUM_RATIO will be reset to this value. """ FREEZING_POINT_WATER_IP = 32.0 """float: Freezing point of water in Fahrenheit. """ FREEZING_POINT_WATER_SI = 0.0 """float: Freezing point of water in Celsius. """ TRIPLE_POINT_WATER_IP = 32.018 """float: Triple point of water in Fahrenheit. """ TRIPLE_POINT_WATER_SI = 0.01 """float: Triple point of water in Celsius. """ ####################################################################################################### # Helper functions ####################################################################################################### # Unit system to use. class UnitSystem(Enum): """ Private class not exposed used to set automatic enumeration values. """ IP = auto() SI = auto() IP = UnitSystem.IP SI = UnitSystem.SI PSYCHROLIB_UNITS = None PSYCHROLIB_TOLERANCE = 1.0 # Tolerance of temperature calculations def SetUnitSystem(Units: UnitSystem) -> None: """ Set the system of units to use (SI or IP). Args: Units: string indicating the system of units chosen (SI or IP) Notes: This function *HAS TO BE CALLED* before the library can be used """ global PSYCHROLIB_UNITS global PSYCHROLIB_TOLERANCE if not isinstance(Units, UnitSystem): raise ValueError("The system of units has to be either SI or IP.") PSYCHROLIB_UNITS = Units # Define tolerance on temperature calculations # The tolerance is the same in IP and SI if Units == IP: PSYCHROLIB_TOLERANCE = 0.001 * 9. / 5. else: PSYCHROLIB_TOLERANCE = 0.001 def GetUnitSystem() -> Optional[UnitSystem]: """ Return system of units in use. """ return PSYCHROLIB_UNITS def isIP() -> bool: """ Check whether the system in use is IP or SI. """ if PSYCHROLIB_UNITS == IP: return True elif PSYCHROLIB_UNITS == SI: return False else: raise ValueError('The system of units has not been defined.') ####################################################################################################### # Conversion between temperature units ####################################################################################################### def GetTRankineFromTFahrenheit(TFahrenheit: float) -> float: """ Utility function to convert temperature to degree Rankine (°R) given temperature in degree Fahrenheit (°F). Args: TRankine: Temperature in degree Fahrenheit (°F) Returns: Temperature in degree Rankine (°R) Reference: Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 section 3 Notes: Exact conversion. """ TRankine = TFahrenheit + ZERO_FAHRENHEIT_AS_RANKINE return TRankine def GetTFahrenheitFromTRankine(TRankine: float) -> float: """ Utility function to convert temperature to degree Fahrenheit (°F) given temperature in degree Rankine (°R). Args: TRankine: Temperature in degree Rankine (°R) Returns: Temperature in degree Fahrenheit (°F) Reference: Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 section 3 Notes: Exact conversion. """ return TRankine - ZERO_FAHRENHEIT_AS_RANKINE def GetTKelvinFromTCelsius(TCelsius: float) -> float: """ Utility function to convert temperature to Kelvin (K) given temperature in degree Celsius (°C). Args: TCelsius: Temperature in degree Celsius (°C) Returns: Temperature in Kelvin (K) Reference: Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 section 3 Notes: Exact conversion. """ TKelvin = TCelsius + ZERO_CELSIUS_AS_KELVIN return TKelvin def GetTCelsiusFromTKelvin(TKelvin: float) -> float: """ Utility function to convert temperature to degree Celsius (°C) given temperature in Kelvin (K). Args: TKelvin: Temperature in Kelvin (K) Returns: Temperature in degree Celsius (°C) Reference: Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 section 3 Notes: Exact conversion. """ return TKelvin - ZERO_CELSIUS_AS_KELVIN ####################################################################################################### # Conversions between dew point, wet bulb, and relative humidity ####################################################################################################### def GetTWetBulbFromTDewPoint(TDryBulb: float, TDewPoint: float, Pressure: float) -> float: """ Return wet-bulb temperature given dry-bulb temperature, dew-point temperature, and pressure. Args: TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] TDewPoint : Dew-point temperature in °F [IP] or °C [SI] Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] Returns: Wet-bulb temperature in °F [IP] or °C [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 """ if TDewPoint > TDryBulb: raise ValueError("Dew point temperature is above dry bulb temperature") HumRatio = GetHumRatioFromTDewPoint(TDewPoint, Pressure) TWetBulb = GetTWetBulbFromHumRatio(TDryBulb, HumRatio, Pressure) return TWetBulb def GetTWetBulbFromRelHum(TDryBulb: float, RelHum: float, Pressure: float) -> float: """ Return wet-bulb temperature given dry-bulb temperature, relative humidity, and pressure. Args: TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] RelHum : Relative humidity in range [0, 1] Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] Returns: Wet-bulb temperature in °F [IP] or °C [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 """ if RelHum < 0 or RelHum > 1: raise ValueError("Relative humidity is outside range [0, 1]") HumRatio = GetHumRatioFromRelHum(TDryBulb, RelHum, Pressure) TWetBulb = GetTWetBulbFromHumRatio(TDryBulb, HumRatio, Pressure) return TWetBulb def GetRelHumFromTDewPoint(TDryBulb: float, TDewPoint: float) -> float: """ Return relative humidity given dry-bulb temperature and dew-point temperature. Args: TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] TDewPoint : Dew-point temperature in °F [IP] or °C [SI] Returns: Relative humidity in range [0, 1] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 22 """ if TDewPoint > TDryBulb: raise ValueError("Dew point temperature is above dry bulb temperature") VapPres = GetSatVapPres(TDewPoint) SatVapPres = GetSatVapPres(TDryBulb) RelHum = VapPres / SatVapPres return RelHum def GetRelHumFromTWetBulb(TDryBulb: float, TWetBulb: float, Pressure: float) -> float: """ Return relative humidity given dry-bulb temperature, wet bulb temperature and pressure. Args: TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] TWetBulb : Wet-bulb temperature in °F [IP] or °C [SI] Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] Returns: Relative humidity in range [0, 1] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 """ if TWetBulb > TDryBulb: raise ValueError("Wet bulb temperature is above dry bulb temperature") HumRatio = GetHumRatioFromTWetBulb(TDryBulb, TWetBulb, Pressure) RelHum = GetRelHumFromHumRatio(TDryBulb, HumRatio, Pressure) return RelHum def GetTDewPointFromRelHum(TDryBulb: float, RelHum: float) -> float: """ Return dew-point temperature given dry-bulb temperature and relative humidity. Args: TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] RelHum: Relative humidity in range [0, 1] Returns: Dew-point temperature in °F [IP] or °C [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 """ if RelHum < 0 or RelHum > 1: raise ValueError("Relative humidity is outside range [0, 1]") VapPres = GetVapPresFromRelHum(TDryBulb, RelHum) TDewPoint = GetTDewPointFromVapPres(TDryBulb, VapPres) return TDewPoint def GetTDewPointFromTWetBulb(TDryBulb: float, TWetBulb: float, Pressure: float) -> float: """ Return dew-point temperature given dry-bulb temperature, wet-bulb temperature, and pressure. Args: TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] TWetBulb : Wet-bulb temperature in °F [IP] or °C [SI] Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] Returns: Dew-point temperature in °F [IP] or °C [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 """ if TWetBulb > TDryBulb: raise ValueError("Wet bulb temperature is above dry bulb temperature") HumRatio = GetHumRatioFromTWetBulb(TDryBulb, TWetBulb, Pressure) TDewPoint = GetTDewPointFromHumRatio(TDryBulb, HumRatio, Pressure) return TDewPoint ####################################################################################################### # Conversions between dew point, or relative humidity and vapor pressure ####################################################################################################### def GetVapPresFromRelHum(TDryBulb: float, RelHum: float) -> float: """ Return partial pressure of water vapor as a function of relative humidity and temperature. Args: TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] RelHum : Relative humidity in range [0, 1] Returns: Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 12, 22 """ if RelHum < 0 or RelHum > 1: raise ValueError("Relative humidity is outside range [0, 1]") VapPres = RelHum * GetSatVapPres(TDryBulb) return VapPres def GetRelHumFromVapPres(TDryBulb: float, VapPres: float) -> float: """ Return relative humidity given dry-bulb temperature and vapor pressure. Args: TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] VapPres: Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] Returns: Relative humidity in range [0, 1] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 12, 22 """ if VapPres < 0: raise ValueError("Partial pressure of water vapor in moist air cannot be negative") RelHum = VapPres / GetSatVapPres(TDryBulb) return RelHum def dLnPws_(TDryBulb: float) -> float: """ Helper function returning the derivative of the natural log of the saturation vapor pressure as a function of dry-bulb temperature. Args: TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] Returns: Derivative of natural log of vapor pressure of saturated air in Psi [IP] or Pa [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 5 & 6 """ if isIP(): T = GetTRankineFromTFahrenheit(TDryBulb) if TDryBulb <= TRIPLE_POINT_WATER_IP: dLnPws = 1.0214165E+04 / math.pow(T, 2) - 5.3765794E-03 + 2 * 1.9202377E-07 * T \ + 3 * 3.5575832E-10 * math.pow(T, 2) - 4 * 9.0344688E-14 * math.pow(T, 3) + 4.1635019 / T else: dLnPws = 1.0440397E+04 / math.pow(T, 2) - 2.7022355E-02 + 2 * 1.2890360E-05 * T \ - 3 * 2.4780681E-09 * math.pow(T, 2) + 6.5459673 / T else: T = GetTKelvinFromTCelsius(TDryBulb) if TDryBulb <= TRIPLE_POINT_WATER_SI: dLnPws = 5.6745359E+03 / math.pow(T, 2) - 9.677843E-03 + 2 * 6.2215701E-07 * T \ + 3 * 2.0747825E-09 * math.pow(T, 2) - 4 * 9.484024E-13 * math.pow(T, 3) + 4.1635019 / T else: dLnPws = 5.8002206E+03 / math.pow(T, 2) - 4.8640239E-02 + 2 * 4.1764768E-05 * T \ - 3 * 1.4452093E-08 * math.pow(T, 2) + 6.5459673 / T return dLnPws def GetTDewPointFromVapPres(TDryBulb: float, VapPres: float) -> float: """ Return dew-point temperature given dry-bulb temperature and vapor pressure. Args: TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] VapPres: Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] Returns: Dew-point temperature in °F [IP] or °C [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn. 5 and 6 Notes: The dew point temperature is solved by inverting the equation giving water vapor pressure at saturation from temperature rather than using the regressions provided by ASHRAE (eqn. 37 and 38) which are much less accurate and have a narrower range of validity. The Newton-Raphson (NR) method is used on the logarithm of water vapour pressure as a function of temperature, which is a very smooth function Convergence is usually achieved in 3 to 5 iterations. TDryBulb is not really needed here, just used for convenience. """ if isIP(): BOUNDS = [-148, 392] else: BOUNDS = [-100, 200] # Validity check -- bounds outside which a solution cannot be found if VapPres < GetSatVapPres(BOUNDS[0]) or VapPres > GetSatVapPres(BOUNDS[1]): raise ValueError("Partial pressure of water vapor is outside range of validity of equations") # We use NR to approximate the solution. # First guess TDewPoint = TDryBulb # Calculated value of dew point temperatures, solved for iteratively lnVP = math.log(VapPres) # Partial pressure of water vapor in moist air index = 1 while True: TDewPoint_iter = TDewPoint # TDewPoint used in NR calculation lnVP_iter = math.log(GetSatVapPres(TDewPoint_iter)) # Derivative of function, calculated analytically d_lnVP = dLnPws_(TDewPoint_iter) # New estimate, bounded by the search domain defined above TDewPoint = TDewPoint_iter - (lnVP_iter - lnVP) / d_lnVP TDewPoint = max(TDewPoint, BOUNDS[0]) TDewPoint = min(TDewPoint, BOUNDS[1]) if ((math.fabs(TDewPoint - TDewPoint_iter) <= PSYCHROLIB_TOLERANCE)): break if (index > MAX_ITER_COUNT): raise ValueError("Convergence not reached in GetTDewPointFromVapPres. Stopping.") index = index + 1 TDewPoint = min(TDewPoint, TDryBulb) return TDewPoint def GetVapPresFromTDewPoint(TDewPoint: float) -> float: """ Return vapor pressure given dew point temperature. Args: TDewPoint : Dew-point temperature in °F [IP] or °C [SI] Returns: Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 36 """ VapPres = GetSatVapPres(TDewPoint) return VapPres ####################################################################################################### # Conversions from wet-bulb temperature, dew-point temperature, or relative humidity to humidity ratio ####################################################################################################### def GetTWetBulbFromHumRatio(TDryBulb: float, HumRatio: float, Pressure: float) -> float: """ Return wet-bulb temperature given dry-bulb temperature, humidity ratio, and pressure. Args: TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] HumRatio : Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] Returns: Wet-bulb temperature in °F [IP] or °C [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 33 and 35 solved for Tstar """ if HumRatio < 0: raise ValueError("Humidity ratio cannot be negative") BoundedHumRatio = max(HumRatio, MIN_HUM_RATIO) TDewPoint = GetTDewPointFromHumRatio(TDryBulb, BoundedHumRatio, Pressure) # Initial guesses TWetBulbSup = TDryBulb TWetBulbInf = TDewPoint TWetBulb = (TWetBulbInf + TWetBulbSup) / 2 index = 1 # Bisection loop while ((TWetBulbSup - TWetBulbInf) > PSYCHROLIB_TOLERANCE): # Compute humidity ratio at temperature Tstar Wstar = GetHumRatioFromTWetBulb(TDryBulb, TWetBulb, Pressure) # Get new bounds if Wstar > BoundedHumRatio: TWetBulbSup = TWetBulb else: TWetBulbInf = TWetBulb # New guess of wet bulb temperature TWetBulb = (TWetBulbSup + TWetBulbInf) / 2 if (index >= MAX_ITER_COUNT): raise ValueError("Convergence not reached in GetTWetBulbFromHumRatio. Stopping.") index = index + 1 return TWetBulb def GetHumRatioFromTWetBulb(TDryBulb: float, TWetBulb: float, Pressure: float) -> float: """ Return humidity ratio given dry-bulb temperature, wet-bulb temperature, and pressure. Args: TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] TWetBulb : Wet-bulb temperature in °F [IP] or °C [SI] Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] Returns: Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 33 and 35 """ if TWetBulb > TDryBulb: raise ValueError("Wet bulb temperature is above dry bulb temperature") Wsstar = GetSatHumRatio(TWetBulb, Pressure) if isIP(): if TWetBulb >= FREEZING_POINT_WATER_IP: HumRatio = ((1093 - 0.556 * TWetBulb) * Wsstar - 0.240 * (TDryBulb - TWetBulb)) \ / (1093 + 0.444 * TDryBulb - TWetBulb) else: HumRatio = ((1220 - 0.04 * TWetBulb) * Wsstar - 0.240 * (TDryBulb - TWetBulb)) \ / (1220 + 0.444 * TDryBulb - 0.48*TWetBulb) else: if TWetBulb >= FREEZING_POINT_WATER_SI: HumRatio = ((2501. - 2.326 * TWetBulb) * Wsstar - 1.006 * (TDryBulb - TWetBulb)) \ / (2501. + 1.86 * TDryBulb - 4.186 * TWetBulb) else: HumRatio = ((2830. - 0.24 * TWetBulb) * Wsstar - 1.006 * (TDryBulb - TWetBulb)) \ / (2830. + 1.86 * TDryBulb - 2.1 * TWetBulb) # Validity check. return max(HumRatio, MIN_HUM_RATIO) def GetHumRatioFromRelHum(TDryBulb: float, RelHum: float, Pressure: float) -> float: """ Return humidity ratio given dry-bulb temperature, relative humidity, and pressure. Args: TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] RelHum : Relative humidity in range [0, 1] Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] Returns: Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 """ if RelHum < 0 or RelHum > 1: raise ValueError("Relative humidity is outside range [0, 1]") VapPres = GetVapPresFromRelHum(TDryBulb, RelHum) HumRatio = GetHumRatioFromVapPres(VapPres, Pressure) return HumRatio def GetRelHumFromHumRatio(TDryBulb: float, HumRatio: float, Pressure: float) -> float: """ Return relative humidity given dry-bulb temperature, humidity ratio, and pressure. Args: TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] HumRatio : Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] Returns: Relative humidity in range [0, 1] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 """ if HumRatio < 0: raise ValueError("Humidity ratio cannot be negative") VapPres = GetVapPresFromHumRatio(HumRatio, Pressure) RelHum = GetRelHumFromVapPres(TDryBulb, VapPres) return RelHum def GetHumRatioFromTDewPoint(TDewPoint: float, Pressure: float) -> float: """ Return humidity ratio given dew-point temperature and pressure. Args: TDewPoint : Dew-point temperature in °F [IP] or °C [SI] Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] Returns: Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 13 """ VapPres = GetSatVapPres(TDewPoint) HumRatio = GetHumRatioFromVapPres(VapPres, Pressure) return HumRatio def GetTDewPointFromHumRatio(TDryBulb: float, HumRatio: float, Pressure: float) -> float: """ Return dew-point temperature given dry-bulb temperature, humidity ratio, and pressure. Args: TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] HumRatio : Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] Returns: Dew-point temperature in °F [IP] or °C [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 """ if HumRatio < 0: raise ValueError("Humidity ratio cannot be negative") VapPres = GetVapPresFromHumRatio(HumRatio, Pressure) TDewPoint = GetTDewPointFromVapPres(TDryBulb, VapPres) return TDewPoint ####################################################################################################### # Conversions between humidity ratio and vapor pressure ####################################################################################################### def GetHumRatioFromVapPres(VapPres: float, Pressure: float) -> float: """ Return humidity ratio given water vapor pressure and atmospheric pressure. Args: VapPres : Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] Returns: Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 20 """ if VapPres < 0: raise ValueError("Partial pressure of water vapor in moist air cannot be negative") HumRatio = 0.621945 * VapPres / (Pressure - VapPres) # Validity check. return max(HumRatio, MIN_HUM_RATIO) def GetVapPresFromHumRatio(HumRatio: float, Pressure: float) -> float: """ Return vapor pressure given humidity ratio and pressure. Args: HumRatio : Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] Returns: Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 20 solved for pw """ if HumRatio < 0: raise ValueError("Humidity ratio is negative") BoundedHumRatio = max(HumRatio, MIN_HUM_RATIO) VapPres = Pressure * BoundedHumRatio / (0.621945 + BoundedHumRatio) return VapPres ####################################################################################################### # Conversions between humidity ratio and specific humidity ####################################################################################################### def GetSpecificHumFromHumRatio(HumRatio: float) -> float: """ Return the specific humidity from humidity ratio (aka mixing ratio). Args: HumRatio : Humidity ratio in lb_H₂O lb_Dry_Air⁻¹ [IP] or kg_H₂O kg_Dry_Air⁻¹ [SI] Returns: Specific humidity in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 9b """ if HumRatio < 0: raise ValueError("Humidity ratio cannot be negative") BoundedHumRatio = max(HumRatio, MIN_HUM_RATIO) SpecificHum = BoundedHumRatio / (1.0 + BoundedHumRatio) return SpecificHum def GetHumRatioFromSpecificHum(SpecificHum: float) -> float: """ Return the humidity ratio (aka mixing ratio) from specific humidity. Args: SpecificHum : Specific humidity in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] Returns: Humidity ratio in lb_H₂O lb_Dry_Air⁻¹ [IP] or kg_H₂O kg_Dry_Air⁻¹ [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 9b (solved for humidity ratio) """ if SpecificHum < 0.0 or SpecificHum >= 1.0: raise ValueError("Specific humidity is outside range [0, 1[") HumRatio = SpecificHum / (1.0 - SpecificHum) # Validity check. return max(HumRatio, MIN_HUM_RATIO) ####################################################################################################### # Dry Air Calculations ####################################################################################################### def GetDryAirEnthalpy(TDryBulb: float) -> float: """ Return dry-air enthalpy given dry-bulb temperature. Args: TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] Returns: Dry air enthalpy in Btu lb⁻¹ [IP] or J kg⁻¹ [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 28 """ if isIP(): DryAirEnthalpy = 0.240 * TDryBulb else: DryAirEnthalpy = 1006 * TDryBulb return DryAirEnthalpy def GetDryAirDensity(TDryBulb: float, Pressure: float) -> float: """ Return dry-air density given dry-bulb temperature and pressure. Args: TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] Returns: Dry air density in lb ft⁻³ [IP] or kg m⁻³ [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 Notes: Eqn 14 for the perfect gas relationship for dry air. Eqn 1 for the universal gas constant. The factor 144 in IP is for the conversion of Psi = lb in⁻² to lb ft⁻². """ if isIP(): DryAirDensity = (144 * Pressure) / R_DA_IP / GetTRankineFromTFahrenheit(TDryBulb) else: DryAirDensity = Pressure / R_DA_SI / GetTKelvinFromTCelsius(TDryBulb) return DryAirDensity def GetDryAirVolume(TDryBulb: float, Pressure: float) -> float: """ Return dry-air volume given dry-bulb temperature and pressure. Args: TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] Returns: Dry air volume in ft³ lb⁻¹ [IP] or in m³ kg⁻¹ [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 Notes: Eqn 14 for the perfect gas relationship for dry air. Eqn 1 for the universal gas constant. The factor 144 in IP is for the conversion of Psi = lb in⁻² to lb ft⁻². """ if isIP(): DryAirVolume = R_DA_IP * GetTRankineFromTFahrenheit(TDryBulb) / (144 * Pressure) else: DryAirVolume = R_DA_SI * GetTKelvinFromTCelsius(TDryBulb) / Pressure return DryAirVolume def GetTDryBulbFromEnthalpyAndHumRatio(MoistAirEnthalpy: float, HumRatio: float) -> float: """ Return dry bulb temperature from enthalpy and humidity ratio. Args: MoistAirEnthalpy : Moist air enthalpy in Btu lb⁻¹ [IP] or J kg⁻¹ HumRatio : Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] Returns: Dry-bulb temperature in °F [IP] or °C [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 30 Notes: Based on the GetMoistAirEnthalpy function, rearranged for temperature. """ if HumRatio < 0: raise ValueError("Humidity ratio is negative") BoundedHumRatio = max(HumRatio, MIN_HUM_RATIO) if isIP(): TDryBulb = (MoistAirEnthalpy - 1061.0 * BoundedHumRatio) / (0.240 + 0.444 * BoundedHumRatio) else: TDryBulb = (MoistAirEnthalpy / 1000.0 - 2501.0 * BoundedHumRatio) / (1.006 + 1.86 * BoundedHumRatio) return TDryBulb def GetHumRatioFromEnthalpyAndTDryBulb(MoistAirEnthalpy: float, TDryBulb: float) -> float: """ Return humidity ratio from enthalpy and dry-bulb temperature. Args: MoistAirEnthalpy : Moist air enthalpy in Btu lb⁻¹ [IP] or J kg⁻¹ TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] Returns: Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 30. Notes: Based on the GetMoistAirEnthalpy function, rearranged for humidity ratio. """ if isIP(): HumRatio = (MoistAirEnthalpy - 0.240 * TDryBulb) / (1061.0 + 0.444 * TDryBulb) else: HumRatio = (MoistAirEnthalpy / 1000.0 - 1.006 * TDryBulb) / (2501.0 + 1.86 * TDryBulb) # Validity check. return max(HumRatio, MIN_HUM_RATIO) ####################################################################################################### # Saturated Air Calculations ####################################################################################################### def GetSatVapPres(TDryBulb: float) -> float: """ Return saturation vapor pressure given dry-bulb temperature. Args: TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] Returns: Vapor pressure of saturated air in Psi [IP] or Pa [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 5 & 6 Important note: the ASHRAE formulae are defined above and below the freezing point but have a discontinuity at the freezing point. This is a small inaccuracy on ASHRAE's part: the formulae should be defined above and below the triple point of water (not the feezing point) in which case the discontinuity vanishes. It is essential to use the triple point of water otherwise function GetTDewPointFromVapPres, which inverts the present function, does not converge properly around the freezing point. """ if isIP(): if (TDryBulb < -148 or TDryBulb > 392): raise ValueError("Dry bulb temperature must be in range [-148, 392]°F") T = GetTRankineFromTFahrenheit(TDryBulb) if (TDryBulb <= TRIPLE_POINT_WATER_IP): LnPws = (-1.0214165E+04 / T - 4.8932428 - 5.3765794E-03 * T + 1.9202377E-07 * T**2 \ + 3.5575832E-10 * math.pow(T, 3) - 9.0344688E-14 * math.pow(T, 4) + 4.1635019 * math.log(T)) else: LnPws = -1.0440397E+04 / T - 1.1294650E+01 - 2.7022355E-02* T + 1.2890360E-05 * T**2 \ - 2.4780681E-09 * math.pow(T, 3) + 6.5459673 * math.log(T) else: if (TDryBulb < -100 or TDryBulb > 200): raise ValueError("Dry bulb temperature must be in range [-100, 200]°C") T = GetTKelvinFromTCelsius(TDryBulb) if (TDryBulb <= TRIPLE_POINT_WATER_SI): LnPws = -5.6745359E+03 / T + 6.3925247 - 9.677843E-03 * T + 6.2215701E-07 * T**2 \ + 2.0747825E-09 * math.pow(T, 3) - 9.484024E-13 * math.pow(T, 4) + 4.1635019 * math.log(T) else: LnPws = -5.8002206E+03 / T + 1.3914993 - 4.8640239E-02 * T + 4.1764768E-05 * T**2 \ - 1.4452093E-08 * math.pow(T, 3) + 6.5459673 * math.log(T) SatVapPres = math.exp(LnPws) return SatVapPres def GetSatHumRatio(TDryBulb: float, Pressure: float) -> float: """ Return humidity ratio of saturated air given dry-bulb temperature and pressure. Args: TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] Returns: Humidity ratio of saturated air in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 36, solved for W """ SatVaporPres = GetSatVapPres(TDryBulb) SatHumRatio = 0.621945 * SatVaporPres / (Pressure - SatVaporPres) # Validity check. return max(SatHumRatio, MIN_HUM_RATIO) def GetSatAirEnthalpy(TDryBulb: float, Pressure: float) -> float: """ Return saturated air enthalpy given dry-bulb temperature and pressure. Args: TDryBulb: Dry-bulb temperature in °F [IP] or °C [SI] Pressure: Atmospheric pressure in Psi [IP] or Pa [SI] Returns: Saturated air enthalpy in Btu lb⁻¹ [IP] or J kg⁻¹ [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 """ SatHumRatio = GetSatHumRatio(TDryBulb, Pressure) SatAirEnthalpy = GetMoistAirEnthalpy(TDryBulb, SatHumRatio) return SatAirEnthalpy ####################################################################################################### # Moist Air Calculations ####################################################################################################### def GetVaporPressureDeficit(TDryBulb: float, HumRatio: float, Pressure: float) -> float: """ Return Vapor pressure deficit given dry-bulb temperature, humidity ratio, and pressure. Args: TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] HumRatio : Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] Returns: Vapor pressure deficit in Psi [IP] or Pa [SI] Reference: Oke (1987) eqn 2.13a """ if HumRatio < 0: raise ValueError("Humidity ratio is negative") RelHum = GetRelHumFromHumRatio(TDryBulb, HumRatio, Pressure) VaporPressureDeficit = GetSatVapPres(TDryBulb) * (1 - RelHum) return VaporPressureDeficit def GetDegreeOfSaturation(TDryBulb: float, HumRatio: float, Pressure: float) -> float: """ Return the degree of saturation (i.e humidity ratio of the air / humidity ratio of the air at saturation at the same temperature and pressure) given dry-bulb temperature, humidity ratio, and atmospheric pressure. Args: TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] HumRatio : Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] Returns: Degree of saturation in arbitrary unit Reference: ASHRAE Handbook - Fundamentals (2009) ch. 1 eqn 12 Notes: This definition is absent from the 2017 Handbook. Using 2009 version instead. """ if HumRatio < 0: raise ValueError("Humidity ratio is negative") BoundedHumRatio = max(HumRatio, MIN_HUM_RATIO) SatHumRatio = GetSatHumRatio(TDryBulb, Pressure) DegreeOfSaturation = BoundedHumRatio / SatHumRatio return DegreeOfSaturation def GetMoistAirEnthalpy(TDryBulb: float, HumRatio: float) -> float: """ Return moist air enthalpy given dry-bulb temperature and humidity ratio. Args: TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] HumRatio : Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] Returns: Moist air enthalpy in Btu lb⁻¹ [IP] or J kg⁻¹ Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 30 """ if HumRatio < 0: raise ValueError("Humidity ratio is negative") BoundedHumRatio = max(HumRatio, MIN_HUM_RATIO) if isIP(): MoistAirEnthalpy = 0.240 * TDryBulb + BoundedHumRatio * (1061 + 0.444 * TDryBulb) else: MoistAirEnthalpy = (1.006 * TDryBulb + BoundedHumRatio * (2501. + 1.86 * TDryBulb)) * 1000 return MoistAirEnthalpy def GetMoistAirVolume(TDryBulb: float, HumRatio: float, Pressure: float) -> float: """ Return moist air specific volume given dry-bulb temperature, humidity ratio, and pressure. Args: TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] HumRatio : Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] Returns: Specific volume of moist air in ft³ lb⁻¹ of dry air [IP] or in m³ kg⁻¹ of dry air [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 26 Notes: In IP units, R_DA_IP / 144 equals 0.370486 which is the coefficient appearing in eqn 26 The factor 144 is for the conversion of Psi = lb in⁻² to lb ft⁻². """ if HumRatio < 0: raise ValueError("Humidity ratio is negative") BoundedHumRatio = max(HumRatio, MIN_HUM_RATIO) if isIP(): MoistAirVolume = R_DA_IP * GetTRankineFromTFahrenheit(TDryBulb) * (1 + 1.607858 * BoundedHumRatio) / (144 * Pressure) else: MoistAirVolume = R_DA_SI * GetTKelvinFromTCelsius(TDryBulb) * (1 + 1.607858 * BoundedHumRatio) / Pressure return MoistAirVolume def GetTDryBulbFromMoistAirVolumeAndHumRatio(MoistAirVolume: float, HumRatio: float, Pressure: float) -> float: """ Return dry-bulb temperature given moist air specific volume, humidity ratio, and pressure. Args: MoistAirVolume: Specific volume of moist air in ft³ lb⁻¹ of dry air [IP] or in m³ kg⁻¹ of dry air [SI] HumRatio : Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] Returns: TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 26 Notes: In IP units, R_DA_IP / 144 equals 0.370486 which is the coefficient appearing in eqn 26 The factor 144 is for the conversion of Psi = lb in⁻² to lb ft⁻². Based on the GetMoistAirVolume function, rearranged for dry-bulb temperature. """ if HumRatio < 0: raise ValueError("Humidity ratio is negative") BoundedHumRatio = max(HumRatio, MIN_HUM_RATIO) if isIP(): TDryBulb = GetTFahrenheitFromTRankine(MoistAirVolume * (144 * Pressure) / (R_DA_IP * (1 + 1.607858 * BoundedHumRatio))) else: TDryBulb = GetTCelsiusFromTKelvin(MoistAirVolume * Pressure / (R_DA_SI * (1 + 1.607858 * BoundedHumRatio))) return TDryBulb def GetMoistAirDensity(TDryBulb: float, HumRatio: float, Pressure:float) -> float: """ Return moist air density given humidity ratio, dry bulb temperature, and pressure. Args: TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] HumRatio : Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] Returns: MoistAirDensity: Moist air density in lb ft⁻³ [IP] or kg m⁻³ [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 11 """ if HumRatio < 0: raise ValueError("Humidity ratio is negative") BoundedHumRatio = max(HumRatio, MIN_HUM_RATIO) MoistAirVolume = GetMoistAirVolume(TDryBulb, BoundedHumRatio, Pressure) MoistAirDensity = (1 + BoundedHumRatio) / MoistAirVolume return MoistAirDensity ####################################################################################################### # Standard atmosphere ####################################################################################################### def GetStandardAtmPressure(Altitude: float) -> float: """ Return standard atmosphere barometric pressure, given the elevation (altitude). Args: Altitude: Altitude in ft [IP] or m [SI] Returns: Standard atmosphere barometric pressure in Psi [IP] or Pa [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 3 """ if isIP(): StandardAtmPressure = 14.696 * math.pow(1 - 6.8754e-06 * Altitude, 5.2559) else: StandardAtmPressure = 101325 * math.pow(1 - 2.25577e-05 * Altitude, 5.2559) return StandardAtmPressure def GetStandardAtmTemperature(Altitude: float) -> float: """ Return standard atmosphere temperature, given the elevation (altitude). Args: Altitude: Altitude in ft [IP] or m [SI] Returns: Standard atmosphere dry-bulb temperature in °F [IP] or °C [SI] Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 4 """ if isIP(): StandardAtmTemperature = 59 - 0.00356620 * Altitude else: StandardAtmTemperature = 15 - 0.0065 * Altitude return StandardAtmTemperature def GetSeaLevelPressure(StationPressure: float, Altitude: float, TDryBulb: float) -> float: """ Return sea level pressure given dry-bulb temperature, altitude above sea level and pressure. Args: StationPressure : Observed station pressure in Psi [IP] or Pa [SI] Altitude: Altitude in ft [IP] or m [SI] TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] Returns: Sea level barometric pressure in Psi [IP] or Pa [SI] Reference: Hess SL, Introduction to theoretical meteorology, Holt Rinehart and Winston, NY 1959, ch. 6.5; Stull RB, Meteorology for scientists and engineers, 2nd edition, Brooks/Cole 2000, ch. 1. Notes: The standard procedure for the US is to use for TDryBulb the average of the current station temperature and the station temperature from 12 hours ago. """ if isIP(): # Calculate average temperature in column of air, assuming a lapse rate # of 3.6 °F/1000ft TColumn = TDryBulb + 0.0036 * Altitude / 2 # Determine the scale height H = 53.351 * GetTRankineFromTFahrenheit(TColumn) else: # Calculate average temperature in column of air, assuming a lapse rate # of 6.5 °C/km TColumn = TDryBulb + 0.0065 * Altitude / 2 # Determine the scale height H = 287.055 * GetTKelvinFromTCelsius(TColumn) / 9.807 # Calculate the sea level pressure SeaLevelPressure = StationPressure * math.exp(Altitude / H) return SeaLevelPressure def GetStationPressure(SeaLevelPressure: float, Altitude: float, TDryBulb: float) -> float: """ Return station pressure from sea level pressure. Args: SeaLevelPressure : Sea level barometric pressure in Psi [IP] or Pa [SI] Altitude: Altitude in ft [IP] or m [SI] TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] Returns: Station pressure in Psi [IP] or Pa [SI] Reference: See 'GetSeaLevelPressure' Notes: This function is just the inverse of 'GetSeaLevelPressure'. """ StationPressure = SeaLevelPressure / GetSeaLevelPressure(1, Altitude, TDryBulb) return StationPressure ###################################################################################################### # Functions to set all psychrometric values ####################################################################################################### def CalcPsychrometricsFromTWetBulb(TDryBulb: float, TWetBulb: float, Pressure: float) -> tuple: """ Utility function to calculate humidity ratio, dew-point temperature, relative humidity, vapour pressure, moist air enthalpy, moist air volume, and degree of saturation of air given dry-bulb temperature, wet-bulb temperature, and pressure. Args: TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] TWetBulb : Wet-bulb temperature in °F [IP] or °C [SI] Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] Returns: Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] Dew-point temperature in °F [IP] or °C [SI] Relative humidity in range [0, 1] Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] Moist air enthalpy in Btu lb⁻¹ [IP] or J kg⁻¹ [SI] Specific volume of moist air in ft³ lb⁻¹ [IP] or in m³ kg⁻¹ [SI] Degree of saturation [unitless] """ HumRatio = GetHumRatioFromTWetBulb(TDryBulb, TWetBulb, Pressure) TDewPoint = GetTDewPointFromHumRatio(TDryBulb, HumRatio, Pressure) RelHum = GetRelHumFromHumRatio(TDryBulb, HumRatio, Pressure) VapPres = GetVapPresFromHumRatio(HumRatio, Pressure) MoistAirEnthalpy = GetMoistAirEnthalpy(TDryBulb, HumRatio) MoistAirVolume = GetMoistAirVolume(TDryBulb, HumRatio, Pressure) DegreeOfSaturation = GetDegreeOfSaturation(TDryBulb, HumRatio, Pressure) return HumRatio, TDewPoint, RelHum, VapPres, MoistAirEnthalpy, MoistAirVolume, DegreeOfSaturation def CalcPsychrometricsFromTDewPoint(TDryBulb: float, TDewPoint: float, Pressure: float) -> tuple: """ Utility function to calculate humidity ratio, wet-bulb temperature, relative humidity, vapour pressure, moist air enthalpy, moist air volume, and degree of saturation of air given dry-bulb temperature, dew-point temperature, and pressure. Args: TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] TDewPoint : Dew-point temperature in °F [IP] or °C [SI] Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] Returns: Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] Wet-bulb temperature in °F [IP] or °C [SI] Relative humidity in range [0, 1] Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] Moist air enthalpy in Btu lb⁻¹ [IP] or J kg⁻¹ [SI] Specific volume of moist air in ft³ lb⁻¹ [IP] or in m³ kg⁻¹ [SI] Degree of saturation [unitless] """ HumRatio = GetHumRatioFromTDewPoint(TDewPoint, Pressure) TWetBulb = GetTWetBulbFromHumRatio(TDryBulb, HumRatio, Pressure) RelHum = GetRelHumFromHumRatio(TDryBulb, HumRatio, Pressure) VapPres = GetVapPresFromHumRatio(HumRatio, Pressure) MoistAirEnthalpy = GetMoistAirEnthalpy(TDryBulb, HumRatio) MoistAirVolume = GetMoistAirVolume(TDryBulb, HumRatio, Pressure) DegreeOfSaturation = GetDegreeOfSaturation(TDryBulb, HumRatio, Pressure) return HumRatio, TWetBulb, RelHum, VapPres, MoistAirEnthalpy, MoistAirVolume, DegreeOfSaturation def CalcPsychrometricsFromRelHum(TDryBulb: float, RelHum: float, Pressure: float) -> tuple: """ Utility function to calculate humidity ratio, wet-bulb temperature, dew-point temperature, vapour pressure, moist air enthalpy, moist air volume, and degree of saturation of air given dry-bulb temperature, relative humidity and pressure. Args: TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] RelHum : Relative humidity in range [0, 1] Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] Returns: Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] Wet-bulb temperature in °F [IP] or °C [SI] Dew-point temperature in °F [IP] or °C [SI]. Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] Moist air enthalpy in Btu lb⁻¹ [IP] or J kg⁻¹ [SI] Specific volume of moist air in ft³ lb⁻¹ [IP] or in m³ kg⁻¹ [SI] Degree of saturation [unitless] """ HumRatio = GetHumRatioFromRelHum(TDryBulb, RelHum, Pressure) TWetBulb = GetTWetBulbFromHumRatio(TDryBulb, HumRatio, Pressure) TDewPoint = GetTDewPointFromHumRatio(TDryBulb, HumRatio, Pressure) VapPres = GetVapPresFromHumRatio(HumRatio, Pressure) MoistAirEnthalpy = GetMoistAirEnthalpy(TDryBulb, HumRatio) MoistAirVolume = GetMoistAirVolume(TDryBulb, HumRatio, Pressure) DegreeOfSaturation = GetDegreeOfSaturation(TDryBulb, HumRatio, Pressure) return HumRatio, TWetBulb, TDewPoint, VapPres, MoistAirEnthalpy, MoistAirVolume, DegreeOfSaturation 

## C_sharp

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1221 1222 1223 1224 1225 1226 1227 /* * PsychroLib (version 2.3.0) (https://github.com/psychrometrics/psychrolib) * Copyright (c) 2018 D. Thevenard and D. Meyer, D. Gosnell for the current library implementation * Copyright (c) 2017 ASHRAE Handbook — Fundamentals for ASHRAE equations and coefficients * Ported to C# by https://github.com/DJGosnell * Licensed under the MIT License. */ using System; namespace PsychroLib { /// /// Class of functions to enable the calculation of psychrometric properties of moist and dry air. /// public class Psychrometrics { /****************************************************************************************************** * Global constants *****************************************************************************************************/ /// /// Zero degree Fahrenheit (°F) expressed as degree Rankine (°R). /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 39. /// private const double ZERO_FAHRENHEIT_AS_RANKINE = 459.67; /// /// Zero degree Celsius (°C) expressed as Kelvin (K). /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 39. /// private const double ZERO_CELSIUS_AS_KELVIN = 273.15; /// /// Universal gas constant for dry air (IP version) in ft lb_Force lb_DryAir⁻¹ R⁻¹. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1. /// private const double R_DA_IP = 53.350; /// /// Universal gas constant for dry air (SI version) in J kg_DryAir⁻¹ K⁻¹. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1. /// private const double R_DA_SI = 287.042; /// /// Invalid value (dimensionless). /// private const double INVALID = -99999; /// /// Maximum number of iterations before exiting while loops. /// private const double MAX_ITER_COUNT = 100; /// /// Minimum acceptable humidity ratio used/returned by any functions. /// Any value above 0 or below the MIN_HUM_RATIO will be reset to this value. /// private const double MIN_HUM_RATIO = 1e-7; /// /// Freezing point of water in Fahrenheit. /// private const double FREEZING_POINT_WATER_IP = 32.0; /// /// Freezing point of water in Celsius. /// private const double FREEZING_POINT_WATER_SI = 0.0; /// /// Triple point of water in Fahrenheit. /// private const double TRIPLE_POINT_WATER_IP = 32.018; /// /// Triple point of water in Celsius. /// private const double TRIPLE_POINT_WATER_SI = 0.01; /// /// Gets or Sets the current system of units for the calculations. /// public UnitSystem UnitSystem { get => _unitSystem; set { _unitSystem = value; if (value == UnitSystem.IP) PSYCHROLIB_TOLERANCE = 0.001 * 9.0 / 5.0; else PSYCHROLIB_TOLERANCE = 0.001; } } private double PSYCHROLIB_TOLERANCE; private UnitSystem _unitSystem; /// /// Constructor to create instance with the specified unit system. /// /// System of units to utilize for calculations. public Psychrometrics(UnitSystem unitSystem) { UnitSystem = unitSystem; } /****************************************************************************************************** * Conversion between temperature units *****************************************************************************************************/ /// /// Utility function to convert temperature to degree Rankine (°R) /// given temperature in degree Fahrenheit (°F). /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 section 3 /// /// Temperature in Fahrenheit (°F) /// Rankine (°R) public double GetTRankineFromTFahrenheit(double tF) { return tF + ZERO_FAHRENHEIT_AS_RANKINE; /* exact */ } /// /// Utility function to convert temperature to degree Fahrenheit (°F) /// given temperature in degree Rankine (°R). /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 section 3 /// /// Temperature in Rankine (°R) /// Fahrenheit (°F) public double GetTFahrenheitFromTRankine(double tR) { return tR - ZERO_FAHRENHEIT_AS_RANKINE; /* exact */ } /// /// Utility function to convert temperature to Kelvin (K) /// given temperature in degree Celsius (°C). /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 section 3 /// /// Temperature in Celsius (°C) /// Rankine (°R) public double GetTKelvinFromTCelsius(double tC) { return tC + ZERO_CELSIUS_AS_KELVIN; /* exact */ } /// /// Utility function to convert temperature to degree Celsius (°C) /// given temperature in Kelvin (K). /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 section 3 /// /// Temperature in Rankine (°R) /// Celsius (°C) public double GetTCelsiusFromTKelvin(double tK) { return tK - ZERO_CELSIUS_AS_KELVIN; /* exact */ } /****************************************************************************************************** * Conversions between dew point, wet bulb, and relative humidity *****************************************************************************************************/ /// /// Return wet-bulb temperature given dry-bulb temperature, dew-point temperature, and pressure. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 /// /// Dry bulb temperature in °F [IP] or °C [SI] /// Dew point temperature in °F [IP] or °C [SI] /// Atmospheric pressure in Psi [IP] or Pa [SI] /// Wet bulb temperature in °F [IP] or °C [SI] public double GetTWetBulbFromTDewPoint(double tDryBulb, double tDewPoint, double pressure) { if (!(tDewPoint <= tDryBulb)) throw new InvalidOperationException("Dew point temperature is above dry bulb temperature"); var humRatio = GetHumRatioFromTDewPoint(tDewPoint, pressure); return GetTWetBulbFromHumRatio(tDryBulb, humRatio, pressure); } /// /// Return wet-bulb temperature given dry-bulb temperature, relative humidity, and pressure. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 /// /// Dry bulb temperature in °F [IP] or °C [SI] /// Relative humidity [0-1] /// Atmospheric pressure in Psi [IP] or Pa [SI] /// Wet bulb temperature in °F [IP] or °C [SI] public double GetTWetBulbFromRelHum(double tDryBulb, double relHum, double pressure) { if (!(relHum >= 0.0 && relHum <= 1.0)) throw new InvalidOperationException("Relative humidity is outside range [0,1]"); var humRatio = GetHumRatioFromRelHum(tDryBulb, relHum, pressure); return GetTWetBulbFromHumRatio(tDryBulb, humRatio, pressure); } /// /// Return relative humidity given dry-bulb temperature and dew-point temperature. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 22 /// /// Dry bulb temperature in °F [IP] or °C [SI] /// Dew point temperature in °F [IP] or °C [SI] /// Relative humidity [0-1] public double GetRelHumFromTDewPoint(double tDryBulb, double tDewPoint) { if (!(tDewPoint <= tDryBulb)) throw new InvalidOperationException("Dew point temperature is above dry bulb temperature"); var vapPres = GetSatVapPres(tDewPoint); var satVapPres = GetSatVapPres(tDryBulb); return vapPres / satVapPres; } /// /// Return relative humidity given dry-bulb temperature, wet bulb temperature and pressure. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 /// /// Dry bulb temperature in °F [IP] or °C [SI] /// Wet bulb temperature in °F [IP] or °C [SI] /// Atmospheric pressure in Psi [IP] or Pa [SI] /// Relative humidity [0-1] public double GetRelHumFromTWetBulb(double tDryBulb, double tWetBulb, double pressure) { if (!(tWetBulb <= tDryBulb)) throw new InvalidOperationException("Wet bulb temperature is above dry bulb temperature"); var humRatio = GetHumRatioFromTWetBulb(tDryBulb, tWetBulb, pressure); return GetRelHumFromHumRatio(tDryBulb, humRatio, pressure); } /// /// Return dew-point temperature given dry-bulb temperature and relative humidity. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 /// /// Dry bulb temperature in °F [IP] or °C [SI] /// Relative humidity [0-1] /// Dew Point temperature in °F [IP] or °C [SI] public double GetTDewPointFromRelHum(double tDryBulb, double relHum) { if (!(relHum >= 0.0 && relHum <= 1.0)) throw new InvalidOperationException("Relative humidity is outside range [0,1]"); var vapPres = GetVapPresFromRelHum(tDryBulb, relHum); return GetTDewPointFromVapPres(tDryBulb, vapPres); } /// /// Return dew-point temperature given dry-bulb temperature, wet-bulb temperature, and pressure. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 /// /// Dry bulb temperature in °F [IP] or °C [SI] /// Wet bulb temperature in °F [IP] or °C [SI] /// Atmospheric pressure in Psi [IP] or Pa [SI] /// Dew Point temperature in °F [IP] or °C [SI] public double GetTDewPointFromTWetBulb(double tDryBulb, double tWetBulb, double pressure) { if (!(tWetBulb <= tDryBulb)) throw new InvalidOperationException("Wet bulb temperature is above dry bulb temperature"); var humRatio = GetHumRatioFromTWetBulb(tDryBulb, tWetBulb, pressure); return GetTDewPointFromHumRatio(tDryBulb, humRatio, pressure); } /****************************************************************************************************** * Conversions between dew point, or relative humidity and vapor pressure *****************************************************************************************************/ /// /// Return partial pressure of water vapor as a function of relative humidity and temperature. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 12, 22 /// /// Dry bulb temperature in °F [IP] or °C [SI] /// Relative humidity [0-1] /// Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] public double GetVapPresFromRelHum(double tDryBulb, double relHum) { if (!(relHum >= 0.0 && relHum <= 1.0)) throw new InvalidOperationException("Relative humidity is outside range [0,1]"); return relHum * GetSatVapPres(tDryBulb); } /// /// Return relative humidity given dry-bulb temperature and vapor pressure. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 12, 22 /// /// Dry bulb temperature in °F [IP] or °C [SI] /// Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] /// Relative humidity [0-1] public double GetRelHumFromVapPres(double tDryBulb, double vapPres) { if (!(vapPres >= 0.0)) throw new InvalidOperationException("Partial pressure of water vapor in moist air is negative"); return vapPres / GetSatVapPres(tDryBulb); } /// /// Helper function returning the derivative of the natural log of the saturation vapor pressure /// as a function of dry-bulb temperature. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn. 5 & 6 /// /// Dry bulb temperature in °F [IP] or °C [SI] /// Derivative of natural log of vapor pressure of saturated air in Psi [IP] or Pa [SI] private double dLnPws_(double tDryBulb) { double dLnPws, T; if (UnitSystem == UnitSystem.IP) { T = GetTRankineFromTFahrenheit(tDryBulb); if (tDryBulb <= TRIPLE_POINT_WATER_IP) dLnPws = 1.0214165E+04 / Math.Pow(T, 2) - 5.3765794E-03 + 2 * 1.9202377E-07 * T + 3 * 3.5575832E-10 * Math.Pow(T, 2) - 4 * 9.0344688E-14 * Math.Pow(T, 3) + 4.1635019 / T; else dLnPws = 1.0440397E+04 / Math.Pow(T, 2) - 2.7022355E-02 + 2 * 1.2890360E-05 * T - 3 * 2.4780681E-09 * Math.Pow(T, 2) + 6.5459673 / T; } else { T = GetTKelvinFromTCelsius(tDryBulb); if (tDryBulb <= TRIPLE_POINT_WATER_SI) dLnPws = 5.6745359E+03 / Math.Pow(T, 2) - 9.677843E-03 + 2 * 6.2215701E-07 * T + 3 * 2.0747825E-09 * Math.Pow(T, 2) - 4 * 9.484024E-13 * Math.Pow(T, 3) + 4.1635019 / T; else dLnPws = 5.8002206E+03 / Math.Pow(T, 2) - 4.8640239E-02 + 2 * 4.1764768E-05 * T - 3 * 1.4452093E-08 * Math.Pow(T, 2) + 6.5459673 / T; } return dLnPws; } /// /// Return dew-point temperature given dry-bulb temperature and vapor pressure. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn. 5 and 6 /// Notes: the dew point temperature is solved by inverting the equation giving water vapor pressure /// at saturation from temperature rather than using the regressions provided /// by ASHRAE (eqn. 37 and 38) which are much less accurate and have a /// narrower range of validity. /// The Newton-Raphson (NR) method is used on the logarithm of water vapour /// pressure as a function of temperature, which is a very smooth function /// Convergence is usually achieved in 3 to 5 iterations. /// tDryBulb is not really needed here, just used for convenience. /// /// Dry bulb temperature in °F [IP] or °C [SI] /// Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] /// (o) Dew Point temperature in °F [IP] or °C [SI] public double GetTDewPointFromVapPres(double tDryBulb, double vapPres) { // Bounds function of the system of units var bounds = UnitSystem == UnitSystem.IP ? new[] {-148.0, 392.0} : new[] {-100.0, 200.0}; // Bounds outside which a solution cannot be found if (vapPres < GetSatVapPres(bounds[0]) || vapPres > GetSatVapPres(bounds[1])) throw new InvalidOperationException( "Partial pressure of water vapor is outside range of validity of equations"); // We use NR to approximate the solution. // First guess var tDewPoint = tDryBulb; // Calculated value of dew point temperatures, solved for iteratively in °F [IP] or °C [SI] var lnVP = Math.Log(vapPres); // Natural logarithm of partial pressure of water vapor pressure in moist air double tDewPoint_iter; // Value of tDewPoint used in NR calculation double lnVP_iter; // Value of log of vapor water pressure used in NR calculation var index = 1; do { // Current point tDewPoint_iter = tDewPoint; lnVP_iter = Math.Log(GetSatVapPres(tDewPoint_iter)); // Derivative of function, calculated analytically var d_lnVP = dLnPws_(tDewPoint_iter); // New estimate, bounded by domain of validity of eqn. 5 and 6 tDewPoint = tDewPoint_iter - (lnVP_iter - lnVP) / d_lnVP; tDewPoint = Math.Max(tDewPoint, bounds[0]); tDewPoint = Math.Min(tDewPoint, bounds[1]); if (index > MAX_ITER_COUNT) throw new InvalidOperationException( "Convergence not reached in GetTDewPointFromVapPres. Stopping."); index++; } while (Math.Abs(tDewPoint - tDewPoint_iter) > PSYCHROLIB_TOLERANCE); return Math.Min(tDewPoint, tDryBulb); } /// /// Return vapor pressure given dew point temperature. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn. 36 /// /// Dew point temperature in °F [IP] or °C [SI] /// Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] public double GetVapPresFromTDewPoint(double tDewPoint) { return GetSatVapPres(tDewPoint); } /****************************************************************************************************** * Conversions from wet-bulb temperature, dew-point temperature, or relative humidity to humidity ratio *****************************************************************************************************/ /// /// Return wet-bulb temperature given dry-bulb temperature, humidity ratio, and pressure. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 33 and 35 solved for Tstar /// /// Dry bulb temperature in °F [IP] or °C [SI] /// Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] /// Atmospheric pressure in Psi [IP] or Pa [SI] /// Wet bulb temperature in °F [IP] or °C [SI] public double GetTWetBulbFromHumRatio(double tDryBulb, double humRatio, double pressure) { // Declarations double Wstar; double tDewPoint, tWetBulb, tWetBulbSup, tWetBulbInf, boundedHumRatio; var index = 1; if (!(humRatio >= 0.0)) throw new InvalidOperationException("Humidity ratio is negative"); boundedHumRatio = Math.Max(humRatio, MIN_HUM_RATIO); tDewPoint = GetTDewPointFromHumRatio(tDryBulb, boundedHumRatio, pressure); // Initial guesses tWetBulbSup = tDryBulb; tWetBulbInf = tDewPoint; tWetBulb = (tWetBulbInf + tWetBulbSup) / 2.0; // Bisection loop while ((tWetBulbSup - tWetBulbInf) > PSYCHROLIB_TOLERANCE) { // Compute humidity ratio at temperature Tstar Wstar = GetHumRatioFromTWetBulb(tDryBulb, tWetBulb, pressure); // Get new bounds if (Wstar > boundedHumRatio) tWetBulbSup = tWetBulb; else tWetBulbInf = tWetBulb; // New guess of wet bulb temperature tWetBulb = (tWetBulbSup + tWetBulbInf) / 2.0; if (index > MAX_ITER_COUNT) throw new InvalidOperationException( "Convergence not reached in GetTWetBulbFromHumRatio. Stopping."); index++; } return tWetBulb; } /// /// Return humidity ratio given dry-bulb temperature, wet-bulb temperature, and pressure. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 33 and 35 /// /// Dry bulb temperature in °F [IP] or °C [SI] /// Wet bulb temperature in °F [IP] or °C [SI] /// Atmospheric pressure in Psi [IP] or Pa [SI] /// Humidity Ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] public double GetHumRatioFromTWetBulb(double tDryBulb, double tWetBulb, double pressure) { double wsstar; double humRatio = INVALID; if (!(tWetBulb <= tDryBulb)) throw new InvalidOperationException("Wet bulb temperature is above dry bulb temperature"); wsstar = GetSatHumRatio(tWetBulb, pressure); if (UnitSystem == UnitSystem.IP) { if (tWetBulb >= FREEZING_POINT_WATER_IP) humRatio = ((1093.0 - 0.556 * tWetBulb) * wsstar - 0.240 * (tDryBulb - tWetBulb)) / (1093.0 + 0.444 * tDryBulb - tWetBulb); else humRatio = ((1220.0 - 0.04 * tWetBulb) * wsstar - 0.240 * (tDryBulb - tWetBulb)) / (1220.0 + 0.444 * tDryBulb - 0.48 * tWetBulb); } else { if (tWetBulb >= FREEZING_POINT_WATER_SI) humRatio = ((2501.0 - 2.326 * tWetBulb) * wsstar - 1.006 * (tDryBulb - tWetBulb)) / (2501.0 + 1.86 * tDryBulb - 4.186 * tWetBulb); else humRatio = ((2830.0 - 0.24 * tWetBulb) * wsstar - 1.006 * (tDryBulb - tWetBulb)) / (2830.0 + 1.86 * tDryBulb - 2.1 * tWetBulb); } // Validity check. return Math.Max(humRatio, MIN_HUM_RATIO); } /// /// Return humidity ratio given dry-bulb temperature, relative humidity, and pressure. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 /// /// Dry bulb temperature in °F [IP] or °C [SI] /// Relative humidity [0-1] /// Atmospheric pressure in Psi [IP] or Pa [SI] /// Humidity Ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] public double GetHumRatioFromRelHum(double tDryBulb, double relHum, double pressure) { if (!(relHum >= 0.0 && relHum <= 1.0)) throw new InvalidOperationException("Relative humidity is outside range [0,1]"); var vapPres = GetVapPresFromRelHum(tDryBulb, relHum); return GetHumRatioFromVapPres(vapPres, pressure); } /// /// Return relative humidity given dry-bulb temperature, humidity ratio, and pressure. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 /// /// Dry bulb temperature in °F [IP] or °C [SI] /// Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] /// Atmospheric pressure in Psi [IP] or Pa [SI] /// Relative humidity [0-1] public double GetRelHumFromHumRatio(double tDryBulb, double humRatio, double pressure) { if (!(humRatio >= 0.0)) throw new InvalidOperationException("Humidity ratio is negative"); var vapPres = GetVapPresFromHumRatio(humRatio, pressure); return GetRelHumFromVapPres(tDryBulb, vapPres); } /// /// Return humidity ratio given dew-point temperature and pressure. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 /// /// Dew point temperature in °F [IP] or °C [SI] /// Atmospheric pressure in Psi [IP] or Pa [SI] /// Humidity Ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] public double GetHumRatioFromTDewPoint(double tDewPoint, double pressure) { var vapPres = GetSatVapPres(tDewPoint); return GetHumRatioFromVapPres(vapPres, pressure); } /// /// Return dew-point temperature given dry-bulb temperature, humidity ratio, and pressure. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 /// /// Dry bulb temperature in °F [IP] or °C [SI] /// Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] /// Atmospheric pressure in Psi [IP] or Pa [SI] /// Dew Point temperature in °F [IP] or °C [SI] public double GetTDewPointFromHumRatio(double tDryBulb, double humRatio, double pressure) { if (!(humRatio >= 0.0)) throw new InvalidOperationException("Humidity ratio is negative"); var vapPres = GetVapPresFromHumRatio(humRatio, pressure); return GetTDewPointFromVapPres(tDryBulb, vapPres); } /****************************************************************************************************** * Conversions between humidity ratio and vapor pressure *****************************************************************************************************/ /// /// Return humidity ratio given water vapor pressure and atmospheric pressure. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 20 /// /// Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] /// Atmospheric pressure in Psi [IP] or Pa [SI] /// Humidity Ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] public double GetHumRatioFromVapPres(double vapPres, double pressure) { if (!(vapPres >= 0.0)) throw new InvalidOperationException("Partial pressure of water vapor in moist air is negative"); var humRatio = 0.621945 * vapPres / (pressure - vapPres); // Validity check. return Math.Max(humRatio, MIN_HUM_RATIO); } /// /// Return vapor pressure given humidity ratio and pressure. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 20 solved for pw /// /// Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] /// Atmospheric pressure in Psi [IP] or Pa [SI] /// Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] public double GetVapPresFromHumRatio(double humRatio, double pressure) { if (!(humRatio >= 0.0)) throw new InvalidOperationException("Humidity ratio is negative"); var boundedHumRatio = Math.Max(humRatio, MIN_HUM_RATIO); var vapPres = pressure * boundedHumRatio / (0.621945 + boundedHumRatio); return vapPres; } /****************************************************************************************************** * Conversions between humidity ratio and specific humidity *****************************************************************************************************/ /// /// Return the specific humidity from humidity ratio (aka mixing ratio) /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 9b /// /// Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] /// Specific humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] public double GetSpecificHumFromHumRatio(double humRatio) { if (!(humRatio >= 0.0)) throw new InvalidOperationException("Humidity ratio is negative"); var boundedHumRatio = Math.Max(humRatio, MIN_HUM_RATIO); return boundedHumRatio / (1.0 + boundedHumRatio); } /// /// Return the humidity ratio (aka mixing ratio) from specific humidity /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 9b (solved for humidity ratio) /// /// /// Humidity ratio in lb_H₂O lb_Dry_Air⁻¹ [IP] or kg_H₂O kg_Dry_Air⁻¹ [SI] public double GetHumRatioFromSpecificHum(double specificHum) { if (!(specificHum >= 0.0 && specificHum < 1.0)) throw new InvalidOperationException("Specific humidity is outside range [0, 1]"); var humRatio = specificHum / (1.0 - specificHum); // Validity check return Math.Max(humRatio, MIN_HUM_RATIO); } /****************************************************************************************************** * Dry Air Calculations *****************************************************************************************************/ /// /// Return dry-air enthalpy given dry-bulb temperature. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn. 28 /// /// Dry bulb temperature in °F [IP] or °C [SI] /// Dry air enthalpy in Btu lb⁻¹ [IP] or J kg⁻¹ [SI] public double GetDryAirEnthalpy(double tDryBulb) { if (UnitSystem == UnitSystem.IP) return 0.240 * tDryBulb; return 1006.0 * tDryBulb; } /// /// Return dry-air density given dry-bulb temperature and pressure. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 /// Notes: eqn 14 for the perfect gas relationship for dry air. /// Eqn 1 for the universal gas constant. /// The factor 144 in IP is for the conversion of Psi = lb in⁻² to lb ft⁻². /// /// Dry bulb temperature in °F [IP] or °C [SI] /// Atmospheric pressure in Psi [IP] or Pa [SI] /// Dry air density in lb ft⁻³ [IP] or kg m⁻³ [SI] public double GetDryAirDensity(double tDryBulb, double pressure) { if (UnitSystem == UnitSystem.IP) return (144.0 * pressure) / R_DA_IP / GetTRankineFromTFahrenheit(tDryBulb); return pressure / R_DA_SI / GetTKelvinFromTCelsius(tDryBulb); } /// /// Return dry-air volume given dry-bulb temperature and pressure. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1. /// Notes: eqn 14 for the perfect gas relationship for dry air. /// Eqn 1 for the universal gas constant. /// The factor 144 in IP is for the conversion of Psi = lb in⁻² to lb ft⁻². /// /// Dry bulb temperature in °F [IP] or °C [SI] /// Atmospheric pressure in Psi [IP] or Pa [SI] /// Dry air volume ft³ lb⁻¹ [IP] or in m³ kg⁻¹ [SI] public double GetDryAirVolume(double tDryBulb, double pressure) { if (UnitSystem == UnitSystem.IP) return R_DA_IP * GetTRankineFromTFahrenheit(tDryBulb) / (144.0 * pressure); return R_DA_SI * GetTKelvinFromTCelsius(tDryBulb) / pressure; } /// /// Return dry bulb temperature from enthalpy and humidity ratio. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 30. /// Notes: based on the GetMoistAirEnthalpy function, rearranged for temperature. /// /// Moist air enthalpy in Btu lb⁻¹ [IP] or J kg⁻¹ /// Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] /// Dry-bulb temperature in °F [IP] or °C [SI] public double GetTDryBulbFromEnthalpyAndHumRatio(double moistAirEnthalpy, double humRatio) { if (!(humRatio >= 0.0)) throw new InvalidOperationException("Humidity ratio is negative"); var boundedHumRatio = Math.Max(humRatio, MIN_HUM_RATIO); if (UnitSystem == UnitSystem.IP) return (moistAirEnthalpy - 1061.0 * boundedHumRatio) / (0.240 + 0.444 * boundedHumRatio); return (moistAirEnthalpy / 1000.0 - 2501.0 * boundedHumRatio) / (1.006 + 1.86 * boundedHumRatio); } /// /// Return humidity ratio from enthalpy and dry-bulb temperature. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 30. /// Notes: based on the GetMoistAirEnthalpy function, rearranged for humidity ratio. /// /// Moist air enthalpy in Btu lb⁻¹ [IP] or J kg⁻¹ /// Dry bulb temperature in °F [IP] or °C [SI] /// Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻ public double GetHumRatioFromEnthalpyAndTDryBulb(double moistAirEnthalpy, double tDryBulb) { { double humRatio; if (UnitSystem == UnitSystem.IP) humRatio = (moistAirEnthalpy - 0.240 * tDryBulb) / (1061.0 + 0.444 * tDryBulb); else humRatio = (moistAirEnthalpy / 1000.0 - 1.006 * tDryBulb) / (2501.0 + 1.86 * tDryBulb); // Validity check. return Math.Max(humRatio, MIN_HUM_RATIO); } } /****************************************************************************************************** * Saturated Air Calculations *****************************************************************************************************/ /// /// Return saturation vapor pressure given dry-bulb temperature. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn. 5 & 6 /// Important note: the ASHRAE formulae are defined above and below the freezing point but have /// a discontinuity at the freezing point. This is a small inaccuracy on ASHRAE's part: the formulae /// should be defined above and below the triple point of water (not the feezing point) in which case /// the discontinuity vanishes. It is essential to use the triple point of water otherwise function /// GetTDewPointFromVapPres, which inverts the present function, does not converge properly around /// the freezing point. /// /// Dry bulb temperature in °F [IP] or °C [SI] /// Vapor pressure of saturated air in Psi [IP] or Pa [SI] public double GetSatVapPres(double tDryBulb) { double lnPws; if (UnitSystem == UnitSystem.IP) { if (!(tDryBulb >= -148.0 && tDryBulb <= 392.0)) throw new InvalidOperationException("Dry bulb temperature is outside range [-148, 392]"); var T = GetTRankineFromTFahrenheit(tDryBulb); if (tDryBulb <= TRIPLE_POINT_WATER_IP) lnPws = (-1.0214165E+04 / T - 4.8932428 - 5.3765794E-03 * T + 1.9202377E-07 * T * T + 3.5575832E-10 * Math.Pow(T, 3) - 9.0344688E-14 * Math.Pow(T, 4) + 4.1635019 * Math.Log(T)); else lnPws = -1.0440397E+04 / T - 1.1294650E+01 - 2.7022355E-02 * T + 1.2890360E-05 * T * T - 2.4780681E-09 * Math.Pow(T, 3) + 6.5459673 * Math.Log(T); } else { if (!(tDryBulb >= -100.0 && tDryBulb <= 200.0)) throw new InvalidOperationException("Dry bulb temperature is outside range [-100, 200]"); var T = GetTKelvinFromTCelsius(tDryBulb); if (tDryBulb <= TRIPLE_POINT_WATER_SI) lnPws = -5.6745359E+03 / T + 6.3925247 - 9.677843E-03 * T + 6.2215701E-07 * T * T + 2.0747825E-09 * Math.Pow(T, 3) - 9.484024E-13 * Math.Pow(T, 4) + 4.1635019 * Math.Log(T); else lnPws = -5.8002206E+03 / T + 1.3914993 - 4.8640239E-02 * T + 4.1764768E-05 * T * T - 1.4452093E-08 * Math.Pow(T, 3) + 6.5459673 * Math.Log(T); } return Math.Exp(lnPws); } /// /// Return humidity ratio of saturated air given dry-bulb temperature and pressure. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 36, solved for W /// /// Dry bulb temperature in °F [IP] or °C [SI] /// Atmospheric pressure in Psi [IP] or Pa [SI] /// Humidity ratio of saturated air in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] public double GetSatHumRatio(double tDryBulb, double pressure) { var satVaporPres = GetSatVapPres(tDryBulb); var satHumRatio = 0.621945 * satVaporPres / (pressure - satVaporPres); // Validity check. return Math.Max(satHumRatio, MIN_HUM_RATIO); } /// /// Return saturated air enthalpy given dry-bulb temperature and pressure. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 /// /// Dry bulb temperature in °F [IP] or °C [SI] /// Atmospheric pressure in Psi [IP] or Pa [SI] /// Saturated air enthalpy in Btu lb⁻¹ [IP] or J kg⁻¹ [SI] public double GetSatAirEnthalpy(double tDryBulb, double pressure) { return GetMoistAirEnthalpy(tDryBulb, GetSatHumRatio(tDryBulb, pressure)); } /****************************************************************************************************** * Moist Air Calculations *****************************************************************************************************/ /// /// Return Vapor pressure deficit given dry-bulb temperature, humidity ratio, and pressure. /// Reference: see Oke (1987) eqn. 2.13a /// /// Dry bulb temperature in °F [IP] or °C [SI] /// Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] /// Atmospheric pressure in Psi [IP] or Pa [SI] /// Vapor pressure deficit in Psi [IP] or Pa [SI] public double GetVaporPressureDeficit(double tDryBulb, double humRatio, double pressure) { if (!(humRatio >= 0.0)) throw new InvalidOperationException("Humidity ratio is negative"); var relHum = GetRelHumFromHumRatio(tDryBulb, humRatio, pressure); return GetSatVapPres(tDryBulb) * (1.0 - relHum); } /// /// Return the degree of saturation (i.e humidity ratio of the air / humidity ratio of the air at saturation /// at the same temperature and pressure) given dry-bulb temperature, humidity ratio, and atmospheric pressure. /// Reference: ASHRAE Handbook - Fundamentals (2009) ch. 1 eqn. 12 /// Notes: the definition is absent from the 2017 Handbook /// /// Dry bulb temperature in °F [IP] or °C [SI] /// Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] /// Atmospheric pressure in Psi [IP] or Pa [SI] /// Degree of saturation (unitless) public double GetDegreeOfSaturation(double tDryBulb, double humRatio, double pressure) { if (!(humRatio >= 0.0)) throw new InvalidOperationException("Humidity ratio is negative"); var boundedHumRatio = Math.Max(humRatio, MIN_HUM_RATIO); return boundedHumRatio / GetSatHumRatio(tDryBulb, pressure); } /// /// Return moist air enthalpy given dry-bulb temperature and humidity ratio. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn. 30 /// /// Dry bulb temperature in °F [IP] or °C [SI] /// Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] /// Moist Air Enthalpy in Btu lb⁻¹ [IP] or J kg⁻¹ [SI] public double GetMoistAirEnthalpy(double tDryBulb, double humRatio) { if (!(humRatio >= 0.0)) throw new InvalidOperationException("Humidity ratio is negative"); var boundedHumRatio = Math.Max(humRatio, MIN_HUM_RATIO); if (UnitSystem == UnitSystem.IP) return 0.240 * tDryBulb + boundedHumRatio * (1061.0 + 0.444 * tDryBulb); return (1.006 * tDryBulb + boundedHumRatio * (2501.0 + 1.86 * tDryBulb)) * 1000.0; } /// /// Return moist air specific volume given dry-bulb temperature, humidity ratio, and pressure. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn. 26 /// Notes: in IP units, R_DA_IP / 144 equals 0.370486 which is the coefficient appearing in eqn 26. /// The factor 144 is for the conversion of Psi = lb in⁻² to lb ft⁻². /// /// Dry bulb temperature in °F [IP] or °C [SI] /// Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] /// Atmospheric pressure in Psi [IP] or Pa [SI] /// Specific Volume ft³ lb⁻¹ [IP] or in m³ kg⁻¹ [SI] public double GetMoistAirVolume(double tDryBulb, double humRatio, double pressure) { if (!(humRatio >= 0.0)) throw new InvalidOperationException("Humidity ratio is negative"); var boundedHumRatio = Math.Max(humRatio, MIN_HUM_RATIO); if (UnitSystem == UnitSystem.IP) return R_DA_IP * GetTRankineFromTFahrenheit(tDryBulb) * (1.0 + 1.607858 * boundedHumRatio) / (144.0 * pressure); return R_DA_SI * GetTKelvinFromTCelsius(tDryBulb) * (1.0 + 1.607858 * boundedHumRatio) / pressure; } /// /// Return dry-bulb temperature given moist air specific volume, humidity ratio, and pressure. /// Reference: /// ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 26 /// Notes: /// In IP units, R_DA_IP / 144 equals 0.370486 which is the coefficient appearing in eqn 26 /// The factor 144 is for the conversion of Psi = lb in⁻² to lb ft⁻². /// Based on the GetMoistAirVolume function, rearranged for dry-bulb temperature. /// /// Specific volume of moist air in ft³ lb⁻¹ of dry air [IP] or in m³ kg⁻¹ of dry air [SI] /// Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] /// Atmospheric pressure in Psi [IP] or Pa [SI] /// Dry-bulb temperature in °F [IP] or °C [SI] public double GetTDryBulbFromMoistAirVolumeAndHumRatio(double MoistAirVolume, double humRatio, double pressure) { if (!(humRatio >= 0.0)) throw new InvalidOperationException("Humidity ratio is negative"); var boundedHumRatio = Math.Max(humRatio, MIN_HUM_RATIO); if (UnitSystem == UnitSystem.IP) return GetTFahrenheitFromTRankine(MoistAirVolume * (144 * pressure) / (R_DA_IP * (1 + 1.607858 * boundedHumRatio))); return GetTCelsiusFromTKelvin(MoistAirVolume * pressure / (R_DA_SI * (1 + 1.607858 * boundedHumRatio))); } /// /// Return moist air density given humidity ratio, dry bulb temperature, and pressure. /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn. 11 /// /// Dry bulb temperature in °F [IP] or °C [SI] /// Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] /// Atmospheric pressure in Psi [IP] or Pa [SI] /// Moist air density in lb ft⁻³ [IP] or kg m⁻³ [SI] public double GetMoistAirDensity(double tDryBulb, double humRatio, double pressure) { if (!(humRatio >= 0.0)) throw new InvalidOperationException("Humidity ratio is negative"); var boundedHumRatio = Math.Max(humRatio, MIN_HUM_RATIO); return (1.0 + boundedHumRatio) / GetMoistAirVolume(tDryBulb, boundedHumRatio, pressure); } /****************************************************************************************************** * Standard atmosphere *****************************************************************************************************/ /// /// Return standard atmosphere barometric pressure, given the elevation (altitude). /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 3 /// /// altitude in ft [IP] or m [SI] /// Standard atmosphere barometric pressure in Psi [IP] or Pa [SI] public double GetStandardAtmPressure(double altitude) { if (UnitSystem == UnitSystem.IP) return 14.696 * Math.Pow(1.0 - 6.8754e-06 * altitude, 5.2559); return 101325.0 * Math.Pow(1.0 - 2.25577e-05 * altitude, 5.2559); } /// /// Return standard atmosphere temperature, given the elevation (altitude). /// Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 4 /// /// altitude in ft [IP] or m [SI] /// Standard atmosphere dry bulb temperature in °F [IP] or °C [SI] public double GetStandardAtmTemperature(double altitude) { if (UnitSystem == UnitSystem.IP) return 59.0 - 0.00356620 * altitude; return 15.0 - 0.0065 * altitude; } /// /// Return sea level pressure given dry-bulb temperature, altitude above sea level and pressure. /// Reference: Hess SL, Introduction to theoretical meteorology, Holt Rinehart and Winston, NY 1959, /// ch. 6.5; Stull RB, Meteorology for scientists and engineers, 2nd edition, /// Brooks/Cole 2000, ch. 1. /// Notes: the standard procedure for the US is to use for tDryBulb the average /// of the current station temperature and the station temperature from 12 hours ago. /// /// Observed station pressure in Psi [IP] or Pa [SI] /// Altitude above sea level in ft [IP] or m [SI] /// Dry bulb temperature in °F [IP] or °C [SI] /// Sea level barometric pressure in Psi [IP] or Pa [SI] public double GetSeaLevelPressure(double stnPressure, double altitude, double tDryBulb) { double h; if (UnitSystem == UnitSystem.IP) { // Calculate average temperature in column of air, assuming a lapse rate // of 3.6 °F/1000ft var tColumn = tDryBulb + 0.0036 * altitude / 2.0; // Determine the scale height h = 53.351 * GetTRankineFromTFahrenheit(tColumn); } else { // Calculate average temperature in column of air, assuming a lapse rate // of 6.5 °C/km var tColumn = tDryBulb + 0.0065 * altitude / 2.0; // Determine the scale height h = 287.055 * GetTKelvinFromTCelsius(tColumn) / 9.807; } // Calculate the sea level pressure var seaLevelPressure = stnPressure * Math.Exp(altitude / h); return seaLevelPressure; } /// /// Return station pressure from sea level pressure /// Reference: see 'GetSeaLevelPressure' /// Notes: this function is just the inverse of 'GetSeaLevelPressure'. /// /// Sea level barometric pressure in Psi [IP] or Pa [SI] /// Altitude above sea level in ft [IP] or m [SI] /// Dry bulb temperature in °F [IP] or °C [SI] /// Station pressure in Psi [IP] or Pa [SI] public double GetStationPressure(double seaLevelPressure, double altitude, double tDryBulb) { return seaLevelPressure / GetSeaLevelPressure(1.0, altitude, tDryBulb); } /****************************************************************************************************** * Functions to set all psychrometric values *****************************************************************************************************/ /// /// Utility function to calculate humidity ratio, dew-point temperature, relative humidity, /// vapour pressure, moist air enthalpy, moist air volume, and degree of saturation of air given /// dry-bulb temperature, wet-bulb temperature, and pressure. /// /// Dry bulb temperature in °F [IP] or °C [SI] /// Wet bulb temperature in °F [IP] or °C [SI] /// Atmospheric pressure in Psi [IP] or Pa [SI] /// Calculated values. public PsychrometricValue CalcPsychrometricsFromTWetBulb(double tDryBulb, double tWetBulb, double pressure) { var value = new PsychrometricValue { TDryBulb = tDryBulb, TWetBulb = tWetBulb, Pressure = pressure }; value.HumRatio = GetHumRatioFromTWetBulb(tDryBulb, tWetBulb, pressure); value.TDewPoint = GetTDewPointFromHumRatio(tDryBulb, value.HumRatio, pressure); value.RelHum = GetRelHumFromHumRatio(tDryBulb, value.HumRatio, pressure); value.VapPres = GetVapPresFromHumRatio(value.HumRatio, pressure); value.MoistAirEnthalpy = GetMoistAirEnthalpy(tDryBulb, value.HumRatio); value.MoistAirVolume = GetMoistAirVolume(tDryBulb, value.HumRatio, pressure); value.DegreeOfSaturation = GetDegreeOfSaturation(tDryBulb, value.HumRatio, pressure); return value; } /// /// Utility function to calculate humidity ratio, wet-bulb temperature, relative humidity, /// vapour pressure, moist air enthalpy, moist air volume, and degree of saturation of air given /// dry-bulb temperature, dew-point temperature, and pressure. /// /// Dry bulb temperature in °F [IP] or °C [SI] /// Dew point temperature in °F [IP] or °C [SI] /// Atmospheric pressure in Psi [IP] or Pa [SI] /// Calculated values. public PsychrometricValue CalcPsychrometricsFromTDewPoint(double tDryBulb, double tDewPoint, double pressure) { var value = new PsychrometricValue { TDryBulb = tDryBulb, TDewPoint = tDewPoint, Pressure = pressure }; value.HumRatio = GetHumRatioFromTDewPoint(tDewPoint, pressure); value.TWetBulb = GetTWetBulbFromHumRatio(tDryBulb, value.HumRatio, pressure); value.RelHum = GetRelHumFromHumRatio(tDryBulb, value.HumRatio, pressure); value.VapPres = GetVapPresFromHumRatio(value.HumRatio, pressure); value.MoistAirEnthalpy = GetMoistAirEnthalpy(tDryBulb, value.HumRatio); value.MoistAirVolume = GetMoistAirVolume(tDryBulb, value.HumRatio, pressure); value.DegreeOfSaturation = GetDegreeOfSaturation(tDryBulb, value.HumRatio, pressure); return value; } /// /// Utility function to calculate humidity ratio, wet-bulb temperature, dew-point temperature, /// vapour pressure, moist air enthalpy, moist air volume, and degree of saturation of air given /// dry-bulb temperature, relative humidity and pressure. /// /// Dry bulb temperature in °F [IP] or °C [SI] /// Relative humidity [0-1] /// Atmospheric pressure in Psi [IP] or Pa [SI] /// Calculated values. public PsychrometricValue CalcPsychrometricsFromRelHum(double tDryBulb, double relHum, double pressure) { var value = new PsychrometricValue { TDryBulb = tDryBulb, RelHum = relHum, Pressure = pressure }; value.HumRatio = GetHumRatioFromRelHum(tDryBulb, relHum, pressure); value.TWetBulb = GetTWetBulbFromHumRatio(tDryBulb, value.HumRatio, pressure); value.TDewPoint = GetTDewPointFromHumRatio(tDryBulb, value.HumRatio, pressure); value.VapPres = GetVapPresFromHumRatio(value.HumRatio, pressure); value.MoistAirEnthalpy = GetMoistAirEnthalpy(tDryBulb, value.HumRatio); value.MoistAirVolume = GetMoistAirVolume(tDryBulb, value.HumRatio, pressure); value.DegreeOfSaturation = GetDegreeOfSaturation(tDryBulb, value.HumRatio, pressure); return value; } } /// /// Contains output results of a Psychrometric calculation. /// public class PsychrometricValue { /// /// Dry bulb temperature in °F [IP] or °C [SI] /// public double TDryBulb { get; set; } /// /// Wet bulb temperature in °F [IP] or °C [SI] /// public double TWetBulb { get; set; } /// /// Atmospheric pressure in Psi [IP] or Pa [SI] /// public double Pressure { get; set; } /// /// Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] /// public double HumRatio { get; set; } /// /// Dew point temperature in °F [IP] or °C [SI] /// public double TDewPoint { get; set; } /// /// Relative humidity [0-1] /// public double RelHum { get; set; } /// /// Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] /// public double VapPres { get; set; } /// /// Moist air enthalpy in Btu lb⁻¹ [IP] or J kg⁻¹ [SI] /// public double MoistAirEnthalpy { get; set; } /// /// Specific volume ft³ lb⁻¹ [IP] or in m³ kg⁻¹ [SI] /// public double MoistAirVolume { get; set; } /// /// Degree of saturation [unitless] /// public double DegreeOfSaturation { get; set; } } /// /// Standard unit systems /// public enum UnitSystem { /// /// Imperial Units /// IP = 1, /// /// Metric System Units /// SI = 2 } } 

## Fortran

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PsychroLib (version 2.3.0) (https://github.com/psychrometrics/psychrolib) ! Copyright (c) 2018 D. Thevenard and D. Meyer for the current library implementation ! Copyright (c) 2017 ASHRAE Handbook — Fundamentals for ASHRAE equations and coefficients ! Licensed under the MIT License. module psychrolib !+ Module overview !+ Contains functions for calculating thermodynamic properties of gas-vapor mixtures !+ and standard atmosphere suitable for most engineering, physical, and meteorological !+ applications. !+ !+ Most of the functions are an implementation of the formulae found in the !+ 2017 ASHRAE Handbook - Fundamentals, in both International System (SI), !+ and Imperial (IP) units. Please refer to the information included in !+ each function for their respective reference. !+ !+ Example !+ use psychrolib, only: GetTDewPointFromRelHum, SetUnitSystem, SI !+ ! Set the unit system, for example to SI (can be either 'SI' or 'IP') !+ call SetUnitSystem(SI) !+ ! Calculate the dew point temperature for a dry bulb temperature of 25 C and a relative humidity of 80% !+ print *, GetTDewPointFromRelHum(25.0, 0.80) !+ 21.3094 !+ !+ Copyright !+ - For the current library implementation !+ Copyright (c) 2018 D. Thevenard and D. Meyer. !+ - For equations and coefficients published ASHRAE Handbook — Fundamentals, Chapter 1 !+ Copyright (c) 2017 ASHRAE Handbook — Fundamentals (https://www.ashrae.org) !+ !+ License !+ MIT (https://github.com/psychrometrics/psychrolib/LICENSE.txt) !+ !+ Note from the Authors !+ We have made every effort to ensure that the code is adequate, however, we make no !+ representation with respect to its accuracy. Use at your own risk. Should you notice !+ an error, or if you have a suggestion, please notify us through GitHub at !+ https://github.com/psychrometrics/psychrolib/issues. implicit none private public :: IP public :: SI public :: SetUnitSystem public :: GetUnitSystem public :: isIP public :: GetTRankineFromTFahrenheit public :: GetTFahrenheitFromTRankine public :: GetTKelvinFromTCelsius public :: GetTCelsiusFromTKelvin public :: GetTWetBulbFromTDewPoint public :: GetTWetBulbFromRelHum public :: GetRelHumFromTDewPoint public :: GetRelHumFromTWetBulb public :: GetTDewPointFromRelHum public :: GetTDewPointFromTWetBulb public :: GetVapPresFromRelHum public :: GetRelHumFromVapPres public :: GetTDewPointFromVapPres public :: GetVapPresFromTDewPoint public :: GetTWetBulbFromHumRatio public :: GetHumRatioFromTWetBulb public :: GetHumRatioFromRelHum public :: GetRelHumFromHumRatio public :: GetHumRatioFromTDewPoint public :: GetTDewPointFromHumRatio public :: GetHumRatioFromVapPres public :: GetVapPresFromHumRatio public :: GetDryAirEnthalpy public :: GetDryAirDensity public :: GetDryAirVolume public :: GetTDryBulbFromEnthalpyAndHumRatio public :: GetHumRatioFromEnthalpyAndTDryBulb public :: GetSatVapPres public :: GetSatHumRatio public :: GetSatAirEnthalpy public :: GetVaporPressureDeficit public :: GetDegreeOfSaturation public :: GetMoistAirEnthalpy public :: GetMoistAirVolume public :: GetTDryBulbFromMoistAirVolumeAndHumRatio public :: GetMoistAirDensity public :: GetStandardAtmPressure public :: GetStandardAtmTemperature public :: GetSeaLevelPressure public :: GetStationPressure public :: GetSpecificHumFromHumRatio public :: GetHumRatioFromSpecificHum public :: CalcPsychrometricsFromTWetBulb public :: CalcPsychrometricsFromTDewPoint public :: CalcPsychrometricsFromRelHum public :: dLnPws_ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! Global constants !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! real, parameter :: ZERO_FAHRENHEIT_AS_RANKINE = 459.67 !+ Zero degree Fahrenheit (°F) expressed as degree Rankine (°R). !+ Reference: !+ ASHRAE Handbook - Fundamentals (2017) ch. 39. real, parameter :: ZERO_CELSIUS_AS_KELVIN = 273.15 !+ Zero degree Celsius (°C) expressed as Kelvin (K). !+ Reference: !+ ASHRAE Handbook - Fundamentals (2017) ch. 39. real, parameter :: R_DA_IP = 53.350 !+ Universal gas constant for dry air (IP version) in ft lb_Force lb_DryAir⁻¹ R⁻¹. !+ Reference: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1. real, parameter :: R_DA_SI = 287.042 !+ Universal gas constant for dry air (SI version) in J kg_DryAir⁻¹ K⁻¹. !+ Reference: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1. integer, parameter :: IP = 1 integer, parameter :: SI = 2 integer :: PSYCHROLIB_UNITS = 0 ! 0 = undefined. !+ Unit system to use. real :: PSYCHROLIB_TOLERANCE = 1.0 !+ Tolerance of temperature calculations. integer, parameter :: MAX_ITER_COUNT = 100 !+ Maximum number of iterations before exiting while loops. real, parameter :: MIN_HUM_RATIO = 1e-7 !+ Minimum acceptable humidity ratio used/returned by any functions. !+ Any value above 0 or below the MIN_HUM_RATIO will be reset to this value. real, parameter :: FREEZING_POINT_WATER_IP = 32.0 !+ float: Freezing point of water in Fahrenheit. real, parameter :: FREEZING_POINT_WATER_SI = 0.0 !+ float: Freezing point of water in Celsius. real, parameter :: TRIPLE_POINT_WATER_IP = 32.018 !+ float: Triple point of water in Fahrenheit. real, parameter :: TRIPLE_POINT_WATER_SI = 0.01 !+ float: Triple point of water in Celsius. contains !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! Helper functions !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! subroutine SetUnitSystem(UnitSystem) !+ Set the system of units to use (SI or IP). !+ Notes: this function *HAS TO BE CALLED* before the library can be used integer, intent(in) :: UnitSystem !+ Units: string indicating the system of units chosen (SI or IP) if (.not. (UnitSystem == SI .or. UnitSystem == IP)) then error stop "The system of units has to be either SI or IP." end if PSYCHROLIB_UNITS = UnitSystem ! Define tolerance on temperature calculations ! The tolerance is the same in IP and SI if (UnitSystem == IP) then PSYCHROLIB_TOLERANCE = 0.001 * 9.0 / 5.0 else PSYCHROLIB_TOLERANCE = 0.001 end if end subroutine SetUnitSystem function GetUnitSystem() result(UnitSystem) !+ Return the system of units in use. integer :: UnitSystem UnitSystem = PSYCHROLIB_UNITS end function GetUnitSystem function isIP() !+ Check whether the system in use is IP or SI logical :: isIP if (PSYCHROLIB_UNITS == IP) then isIP = .true. else if (PSYCHROLIB_UNITS == SI) then isIP = .false. else error stop "The system of units has not been defined." end if end function isIP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! Conversion between temperature units !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! function GetTRankineFromTFahrenheit(TFahrenheit) result(TRankine) !+ Utility function to convert temperature to degree Rankine (°R) !+ given temperature in degree Fahrenheit (°F). !+ Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 section 3 real, intent(in) :: TFahrenheit !+ Temperature in degree Fahrenheit real :: TRankine !+ Temperature in degree Rankine TRankine = TFahrenheit + ZERO_FAHRENHEIT_AS_RANKINE end function GetTRankineFromTFahrenheit function GetTFahrenheitFromTRankine(TRankine) result(TFahrenheit) !+ Utility function to convert temperature to degree Fahrenheit (°F) !+ given temperature in degree Rankine (°R). !+ Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 section 3 real, intent(in) :: TRankine !+ Temperature in degree Rankine real :: TFahrenheit !+ Temperature in degree Fahrenheit TFahrenheit = TRankine - ZERO_FAHRENHEIT_AS_RANKINE end function GetTFahrenheitFromTRankine function GetTKelvinFromTCelsius(TCelsius) result(TKelvin) !+ Utility function to convert temperature to Kelvin (K) !+ given temperature in degree Celsius (°C). !+ Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 section 3 real, intent(in) :: TCelsius !+ Temperature in degree Celsius real :: TKelvin !+ Tempearatyre in Kelvin TKelvin = TCelsius + ZERO_CELSIUS_AS_KELVIN end function GetTKelvinFromTCelsius function GetTCelsiusFromTKelvin(TKelvin) result(TCelsius) !+ Utility function to convert temperature to degree Celsius (°C) !+ given temperature in Kelvin (K). !+ Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 section 3 real, intent(in) :: TKelvin !+ Tempearatyre in Kelvin real :: TCelsius !+ Temperature in degree Celsius TCelsius = TKelvin - ZERO_CELSIUS_AS_KELVIN end function GetTCelsiusFromTKelvin !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! Conversions between dew point, wet bulb, and relative humidity !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! function GetTWetBulbFromTDewPoint(TDryBulb, TDewPoint, Pressure) result(TWetBulb) !+ Return wet-bulb temperature given dry-bulb temperature, dew-point temperature, and pressure. !+ References: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: TDewPoint !+ Dew-point temperature in °F [IP] or °C [SI] real, intent(in) :: Pressure !+ Atmospheric pressure in Psi [IP] or Pa [SI] real :: TWetBulb !+ Wet-bulb temperature in °F [IP] or °C [SI] real :: HumRatio !+ Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] if (TDewPoint > TDryBulb) then error stop "Error: dew point temperature is above dry bulb temperature" end if HumRatio = GetHumRatioFromTDewPoint(TDewPoint, Pressure) TWetBulb = GetTWetBulbFromHumRatio(TDryBulb, HumRatio, Pressure) end function GetTWetBulbFromTDewPoint function GetTWetBulbFromRelHum(TDryBulb, RelHum, Pressure) result(TWetBulb) !+ Return wet-bulb temperature given dry-bulb temperature, relative humidity, and pressure. !+ References: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: RelHum !+ Relative humidity in range [0, 1] real, intent(in) :: Pressure !+ Atmospheric pressure in Psi [IP] or Pa [SI] real :: TWetBulb !+ Wet-bulb temperature in °F [IP] or °C [SI] real :: HumRatio !+ Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] if (RelHum < 0.0 .or. RelHum > 1.0) then error stop "Error: relative humidity is outside range [0,1]" end if HumRatio = GetHumRatioFromRelHum(TDryBulb, RelHum, Pressure) TWetBulb = GetTWetBulbFromHumRatio(TDryBulb, HumRatio, Pressure) end function GetTWetBulbFromRelHum function GetRelHumFromTDewPoint(TDryBulb, TDewPoint) result(RelHum) !+ Return relative humidity given dry-bulb temperature and dew-point temperature. !+ References: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 22 real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: TDewPoint !+ Dew-point temperature in °F [IP] or °C [SI] real :: RelHum !+ Relative humidity in range [0, 1] real :: VapPres !+ Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] real :: SatVapPres !+ Vapor pressure of saturated air in Psi [IP] or Pa [SI] if (TDewPoint > TDryBulb) then error stop "Error: dew point temperature is above dry bulb temperature" end if VapPres = GetSatVapPres(TDewPoint) SatVapPres = GetSatVapPres(TDryBulb) RelHum = VapPres / SatVapPres end function GetRelHumFromTDewPoint function GetRelHumFromTWetBulb(TDryBulb, TWetBulb, Pressure) result(RelHum) !+ Return relative humidity given dry-bulb temperature, wet bulb temperature and pressure. !+ References: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: TWetBulb !+ Wet-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: Pressure !+ Atmospheric pressure in Psi [IP] or Pa [SI] real :: RelHum !+ Relative humidity in range [0, 1] real :: HumRatio !+ Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] if (TWetBulb > TDryBulb) then error stop "Error: wet bulb temperature is above dry bulb temperature" end if HumRatio = GetHumRatioFromTWetBulb(TDryBulb, TWetBulb, Pressure) RelHum = GetRelHumFromHumRatio(TDryBulb, HumRatio, Pressure) end function GetRelHumFromTWetBulb function GetTDewPointFromRelHum(TDryBulb, RelHum) result(TDewPoint) !+ Return dew-point temperature given dry-bulb temperature and relative humidity. !+ References: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: RelHum !+ Relative humidity in range [0, 1] real :: TDewPoint !+ Dew-point temperature in °F [IP] or °C [SI] real :: VapPres !+ Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] if (RelHum < 0.0 .or. RelHum > 1.0) then error stop "Error: relative humidity is outside range [0,1]" end if VapPres = GetVapPresFromRelHum(TDryBulb, RelHum) TDewPoint = GetTDewPointFromVapPres(TDryBulb, VapPres) end function GetTDewPointFromRelHum function GetTDewPointFromTWetBulb(TDryBulb, TWetBulb, Pressure) result(TDewPoint) !+ Return dew-point temperature given dry-bulb temperature, wet-bulb temperature, and pressure. !+ References: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: TWetBulb !+ Wet-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: Pressure !+ Atmospheric pressure in Psi [IP] or Pa [SI] real :: TDewPoint !+ Dew-point temperature in °F [IP] or °C [SI] real :: HumRatio !+ Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] if (TWetBulb > TDryBulb) then error stop "Error: wet bulb temperature is above dry bulb temperature" end if HumRatio = GetHumRatioFromTWetBulb(TDryBulb, TWetBulb, Pressure) TDewPoint = GetTDewPointFromHumRatio(TDryBulb, HumRatio, Pressure) end function GetTDewPointFromTWetBulb !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! Conversions between dew point, or relative humidity and vapor pressure !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! function GetVapPresFromRelHum(TDryBulb, RelHum) result(VapPres) !+ Return partial pressure of water vapor as a function of relative humidity and temperature. !+ References: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 12, 22 real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: RelHum !+ Relative humidity in range [0, 1] real :: VapPres !+ Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] if (RelHum < 0.0 .or. RelHum > 1.0) then error stop "Error: relative humidity is outside range [0,1]" end if VapPres = RelHum * GetSatVapPres(TDryBulb) end function GetVapPresFromRelHum function GetRelHumFromVapPres(TDryBulb, VapPres) result(RelHum) !+ Return relative humidity given dry-bulb temperature and vapor pressure. !+ References: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 12, 22 real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: VapPres !+ Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] real :: RelHum !+ Relative humidity in range [0, 1] if (VapPres < 0.0) then error stop "Error: partial pressure of water vapor in moist air cannot be negative" end if RelHum = VapPres / GetSatVapPres(TDryBulb) end function GetRelHumFromVapPres function dLnPws_(TDryBulb) result(dLnPws) !+ Helper function returning the derivative of the natural log of the saturation vapor pressure !+ as a function of dry-bulb temperature. !+ Reference: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 5 real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real :: dLnPws !+ Derivative of natural log of vapor pressure of saturated air in Psi [IP] or Pa [SI] real :: T !+ Dry bulb temperature in R [IP] or K [SI] if (isIP()) then T = GetTRankineFromTFahrenheit(TDryBulb) if (TDryBulb <= TRIPLE_POINT_WATER_IP) then dLnPws = 1.0214165E+04 / T**2 - 5.3765794E-03 + 2 * 1.9202377E-07 * T & + 3 * 3.5575832E-10 * T**2 - 4 * 9.0344688E-14 * T**3 + 4.1635019 / T else dLnPws = 1.0440397E+04 / T**2 - 2.7022355E-02 + 2 * 1.2890360E-05 * T & - 3 * 2.4780681E-09 * T**2 + 6.5459673 / T end if else T = GetTKelvinFromTCelsius(TDryBulb) if (TDryBulb <= TRIPLE_POINT_WATER_SI) then dLnPws = 5.6745359E+03 / T**2 - 9.677843E-03 + 2 * 6.2215701E-07 * T & + 3 * 2.0747825E-09 * T**2 - 4 * 9.484024E-13 * T**3 + 4.1635019 / T else dLnPws = 5.8002206E+03 / T**2 - 4.8640239E-02 + 2 * 4.1764768E-05 * T & - 3 * 1.4452093E-08 * T**2 + 6.5459673 / T end if end if end function dLnPws_ function GetTDewPointFromVapPres(TDryBulb, VapPres) result(TDewPoint) !+ Return dew-point temperature given dry-bulb temperature and vapor pressure. !+ References: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn. 5 and 6 !+ Notes: !+ The dew point temperature is solved by inverting the equation giving water vapor pressure !+ at saturation from temperature rather than using the regressions provided !+ by ASHRAE (eqn. 37 and 38) which are much less accurate and have a !+ narrower range of validity. !+ The Newton-Raphson (NR) method is used on the logarithm of water vapour !+ pressure as a function of temperature, which is a very smooth function !+ Convergence is usually achieved in 3 to 5 iterations. !+ TDryBulb is not really needed here, just used for convenience. real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: VapPres !+ Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] real :: TDewPoint !+ Dew-point temperature in °F [IP] or °C [SI] real :: lnVP !+ Natural logarithm of partial pressure of water vapor pressure in moist air real :: d_lnVP !+ Derivative of function, calculated numerically real :: lnVP_iter !+ Value of log of vapor water pressure used in NR calculation real :: TDewPoint_iter !+ Value of TDewPoint used in NR calculation real, dimension(2) :: BOUNDS !+ Valid temperature range in °F [IP] or °C [SI] integer :: index !+ Index used in the calculation ! Bounds and step size as a function of the system of units if (isIP()) then BOUNDS(1) = -148.0 BOUNDS(2) = 392.0 else BOUNDS(1) = -100.0 BOUNDS(2) = 200.0 end if ! Validity check -- bounds outside which a solution cannot be found if (VapPres < GetSatVapPres(BOUNDS(1)) .or. VapPres > GetSatVapPres(BOUNDS(2))) then error stop "Error: partial pressure of water vapor is outside range of validity of equations" end if ! We use NR to approximate the solution. TDewPoint = TDryBulb lnVP = log(VapPres) index = 1 do while (.true.) TDewPoint_iter = TDewPoint ! TDewPoint_iter used in NR calculation lnVP_iter = log(GetSatVapPres(TDewPoint_iter)) ! Derivative of function, calculated analytically d_lnVP = dLnPws_(TDewPoint_iter) ! New estimate, bounded by the search domain defined above TDewPoint = TDewPoint_iter - (lnVP_iter - lnVP) / d_lnVP TDewPoint = max(TDewPoint, BOUNDS(1)) TDewPoint = min(TDewPoint, BOUNDS(2)) if (abs(TDewPoint - TDewPoint_iter) <= PSYCHROLIB_TOLERANCE) then exit end if if (index > MAX_ITER_COUNT) then error stop "Convergence not reached in GetTDewPointFromVapPres. Stopping." end if index = index + 1 end do TDewPoint = min(TDewPoint, TDryBulb) end function GetTDewPointFromVapPres function GetVapPresFromTDewPoint(TDewPoint) result(VapPres) !+ Return vapor pressure given dew point temperature. !+ References: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 36 real, intent(in) :: TDewPoint !+ Dew-point temperature in °F [IP] or °C [SI] real :: VapPres !+ Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] VapPres = GetSatVapPres(TDewPoint) end function GetVapPresFromTDewPoint !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! Conversions from wet-bulb temperature, dew-point temperature, or relative humidity to humidity ratio !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! function GetTWetBulbFromHumRatio(TDryBulb, HumRatio, Pressure) result(TWetBulb) !+ Return wet-bulb temperature given dry-bulb temperature, humidity ratio, and pressure. !+ References: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 33 and 35 solved for Tstar real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: HumRatio !+ Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] real, intent(in) :: Pressure !+ Atmospheric pressure in Psi [IP] or Pa [SI] real :: TWetBulb !+ Wet-bulb temperature in °F [IP] or °C [SI] real :: TDewPoint !+ TDewPoint : Dew-point temperature in °F [IP] or °C [SI] real :: TWetBulbSup !+ Upper value of wet bulb temperature in bissection method (initial guess is from dry bulb temperature) in °F [IP] or °C [SI] real :: TWetBulbInf !+ Lower value of wet bulb temperature in bissection method (initial guess is from dew point temperature) in °F [IP] or °C [SI] real :: Wstar !+ Humidity ratio at temperature Tstar in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] real :: BoundedHumRatio !+ Humidity ratio bounded to MIN_HUM_RATIO integer :: index !+ index used in iteration if (HumRatio < 0.0) then error stop "Error: humidity ratio cannot be negative" end if BoundedHumRatio = max(HumRatio, MIN_HUM_RATIO) TDewPoint = GetTDewPointFromHumRatio(TDryBulb, BoundedHumRatio, Pressure) ! Initial guesses TWetBulbSup = TDryBulb TWetBulbInf = TDewPoint TWetBulb = (TWetBulbInf + TWetBulbSup) / 2.0 index = 1 ! Bisection loop do while ((TWetBulbSup - TWetBulbInf) > PSYCHROLIB_TOLERANCE) ! Compute humidity ratio at temperature Tstar Wstar = GetHumRatioFromTWetBulb(TDryBulb, TWetBulb, Pressure) ! Get new bounds if (Wstar > BoundedHumRatio) then TWetBulbSup = TWetBulb else TWetBulbInf = TWetBulb end if ! New guess of wet bulb temperature TWetBulb = (TWetBulbSup + TWetBulbInf) / 2.0 if (index > MAX_ITER_COUNT) then error stop "Convergence not reached in GetTWetBulbFromHumRatio. Stopping." end if index = index + 1 end do end function GetTWetBulbFromHumRatio function GetHumRatioFromTWetBulb(TDryBulb, TWetBulb, Pressure) result(HumRatio) !+ Return humidity ratio given dry-bulb temperature, wet-bulb temperature, and pressure. !+ References: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 33 and 35 real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: TWetBulb !+ Wet-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: Pressure !+ Atmospheric pressure in Psi [IP] or Pa [SI] real :: HumRatio !+ Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] real :: Wsstar !+ Humidity ratio at temperature Tstar in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] if (TWetBulb > TDryBulb) then error stop "Error: wet bulb temperature is above dry bulb temperature" end if Wsstar = GetSatHumRatio(TWetBulb, Pressure) if (isIP()) then if (TWetBulb >= FREEZING_POINT_WATER_IP) then HumRatio = ((1093.0 - 0.556 * TWetBulb) * Wsstar - 0.240 * (TDryBulb - TWetBulb)) & / (1093.0 + 0.444 * TDryBulb - TWetBulb) else HumRatio = ((1220.0 - 0.04 * TWetBulb) * Wsstar - 0.240 * (TDryBulb - TWetBulb)) & / (1220.0 + 0.444 * TDryBulb - 0.48 * TWetBulb) end if else if (TWetBulb >= FREEZING_POINT_WATER_SI) then HumRatio = ((2501.0 - 2.326 * TWetBulb) * Wsstar - 1.006 * (TDryBulb - TWetBulb)) & / (2501.0 + 1.86 * TDryBulb - 4.186 * TWetBulb) else HumRatio = ((2830.0 - 0.24 * TWetBulb) * Wsstar - 1.006 * (TDryBulb - TWetBulb)) & / (2830.0 + 1.86 * TDryBulb - 2.1 * TWetBulb) end if end if ! Validity check. HumRatio = max(HumRatio, MIN_HUM_RATIO) end function GetHumRatioFromTWetBulb function GetHumRatioFromRelHum(TDryBulb, RelHum, Pressure) result(HumRatio) !+ Return humidity ratio given dry-bulb temperature, relative humidity, and pressure. !+ Reference: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: RelHum !+ Relative humidity in range [0, 1] real, intent(in) :: Pressure !+ Atmospheric pressure in Psi [IP] or Pa [SI] real :: HumRatio !+ Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] real :: VapPres !+ Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] if (RelHum < 0.0 .or. RelHum > 1.0) then error stop "Error: relative humidity is outside range [0,1]" end if VapPres = GetVapPresFromRelHum(TDryBulb, RelHum) HumRatio = GetHumRatioFromVapPres(VapPres, Pressure) end function GetHumRatioFromRelHum function GetRelHumFromHumRatio(TDryBulb, HumRatio, Pressure) result(RelHum) !+ Return relative humidity given dry-bulb temperature, humidity ratio, and pressure. !+ Reference: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: HumRatio !+ Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] real, intent(in) :: Pressure !+ Atmospheric pressure in Psi [IP] or Pa [SI] real :: RelHum !+ Relative humidity in range [0, 1] real :: VapPres !+ Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] if (HumRatio < 0.0) then error stop "Error: humidity ratio cannot be negative" end if VapPres = GetVapPresFromHumRatio(HumRatio, Pressure) RelHum = GetRelHumFromVapPres(TDryBulb, VapPres) end function GetRelHumFromHumRatio function GetHumRatioFromTDewPoint(TDewPoint, Pressure) result(HumRatio) !+ Return humidity ratio given dew-point temperature and pressure. !+ Reference: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 real, intent(in) :: TDewPoint !+ Dew-point temperature in °F [IP] or °C [SI] real, intent(in) :: Pressure !+ Atmospheric pressure in Psi [IP] or Pa [SI] real :: HumRatio !+ Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] real :: VapPres !+ Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] VapPres = GetSatVapPres(TDewPoint) HumRatio = GetHumRatioFromVapPres(VapPres, Pressure) end function GetHumRatioFromTDewPoint function GetTDewPointFromHumRatio(TDryBulb, HumRatio, Pressure) result(TDewPoint) !+ Return dew-point temperature given dry-bulb temperature, humidity ratio, and pressure. !+ Reference: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: HumRatio !+ Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] real, intent(in) :: Pressure !+ Atmospheric pressure in Psi [IP] or Pa [SI] real :: TDewPoint !+ Dew-point temperature in °F [IP] or °C [SI] real :: VapPres !+ Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] if (HumRatio < 0.0) then error stop "Error: humidity ratio cannot be negative" end if VapPres = GetVapPresFromHumRatio(HumRatio, Pressure) TDewPoint = GetTDewPointFromVapPres(TDryBulb, VapPres) end function GetTDewPointFromHumRatio !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! Conversions between humidity ratio and vapor pressure !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! function GetHumRatioFromVapPres(VapPres, Pressure) result(HumRatio) !+ Return humidity ratio given water vapor pressure and atmospheric pressure. !+ Reference: !+ ASHRAE Fundamentals (2005) ch. 6 eqn. 22; !+ ASHRAE Fundamentals (2009) ch. 1 eqn. 22. real, intent(in) :: VapPres !+ Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] real, intent(in) :: Pressure !+ Atmospheric pressure in Psi [IP] or Pa [SI] real :: HumRatio !+ Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] if (VapPres < 0.0) then error stop "Error: partial pressure of water vapor in moist air cannot be negative" end if HumRatio = 0.621945 * VapPres / (Pressure-VapPres) ! Validity check. HumRatio = max(HumRatio, MIN_HUM_RATIO) end function GetHumRatioFromVapPres function GetVapPresFromHumRatio(HumRatio, Pressure) result(VapPres) !+ Return vapor pressure given humidity ratio and pressure. !+ Reference: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 20 solved for pw real, intent(in) :: HumRatio !+ Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] real, intent(in) :: Pressure !+ Atmospheric pressure in Psi [IP] or Pa [SI] real :: VapPres !+ Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] real :: BoundedHumRatio !+ Humidity ratio bounded to MIN_HUM_RATIO if (HumRatio < 0.0) then error stop "Error: humidity ratio is negative" end if BoundedHumRatio = max(HumRatio, MIN_HUM_RATIO) VapPres = Pressure * BoundedHumRatio / (0.621945 + BoundedHumRatio) end function GetVapPresFromHumRatio !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! Conversions between humidity ratio and specific humidity !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! function GetSpecificHumFromHumRatio(HumRatio) result(SpecificHum) !+ Return the specific humidity from humidity ratio (aka mixing ratio). !+ Reference: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 9b real, intent(in) :: HumRatio !+ Humidity ratio in lb_H₂O lb_Dry_Air⁻¹ [IP] or kg_H₂O kg_Dry_Air⁻¹ [SI] real :: SpecificHum !+ Specific humidity in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] real :: BoundedHumRatio !+ Humidity ratio bounded to MIN_HUM_RATIO if (HumRatio < 0.0) then error stop "Error: humidity ratio cannot be negative" end if BoundedHumRatio = max(HumRatio, MIN_HUM_RATIO) SpecificHum = BoundedHumRatio / (1.0 + BoundedHumRatio) end function GetSpecificHumFromHumRatio function GetHumRatioFromSpecificHum(SpecificHum) result(HumRatio) !+ Return the humidity ratio (aka mixing ratio) from specific humidity. !+ Reference: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 9b (solved for humidity ratio) real, intent(in) :: SpecificHum !+ Specific humidity in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] real :: HumRatio !+ Humidity ratio in lb_H₂O lb_Dry_Air⁻¹ [IP] or kg_H₂O kg_Dry_Air⁻¹ [SI] if (SpecificHum < 0.0 .or. SpecificHum >= 1.0) then error stop "Error: specific humidity is outside range [0, 1[" end if HumRatio = SpecificHum / (1.0 - SpecificHum) ! Validity check. HumRatio = max(HumRatio, MIN_HUM_RATIO) end function GetHumRatioFromSpecificHum !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! Dry Air Calculations !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! function GetDryAirEnthalpy(TDryBulb) result(DryAirEnthalpy) !+ Return dry-air enthalpy given dry-bulb temperature. !+ Reference: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 28 real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real :: DryAirEnthalpy !+ Dry air enthalpy in Btu lb⁻¹ [IP] or J kg⁻¹ [SI] if (isIP()) then DryAirEnthalpy = 0.240 * TDryBulb else DryAirEnthalpy = 1006 * TDryBulb end if end function GetDryAirEnthalpy function GetDryAirDensity(TDryBulb, Pressure) result(DryAirDensity) !+ Return dry-air density given dry-bulb temperature and pressure. !+ Reference: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 !+ Notes: !+ Eqn 14 for the perfect gas relationship for dry air. !+ Eqn 1 for the universal gas constant. !+ The factor 144 in IP is for the conversion of Psi = lb in⁻² to lb ft⁻². real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: Pressure !+ Atmospheric pressure in Psi [IP] or Pa [SI] real :: DryAirDensity !+ Dry air density in lb ft⁻³ [IP] or kg m⁻³ [SI] if (isIP()) then DryAirDensity = (144 * Pressure) / R_DA_IP / GetTRankineFromTFahrenheit(TDryBulb) else DryAirDensity = Pressure / R_DA_SI / GetTKelvinFromTCelsius(TDryBulb) end if end function GetDryAirDensity function GetDryAirVolume(TDryBulb, Pressure) result(DryAirVolume) !+ Return dry-air volume given dry-bulb temperature and pressure. !+ Reference: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 !+ Notes: !+ Eqn 14 for the perfect gas relationship for dry air. !+ Eqn 1 for the universal gas constant. !+ The factor 144 in IP is for the conversion of Psi = lb in⁻² to lb ft⁻². real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: Pressure !+ Atmospheric pressure in Psi [IP] or Pa [SI] real :: DryAirVolume !+ Dry air volume in ft³ lb⁻¹ [IP] or in m³ kg⁻¹ [SI] if (isIP()) then DryAirVolume = GetTRankineFromTFahrenheit(TDryBulb) * R_DA_IP / (144 * Pressure) else DryAirVolume = GetTKelvinFromTCelsius(TDryBulb) * R_DA_SI / Pressure end if end function GetDryAirVolume function GetTDryBulbFromEnthalpyAndHumRatio(MoistAirEnthalpy, HumRatio) result(TDryBulb) !+ Return dry bulb temperature from enthalpy and humidity ratio. !+ Reference: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 30 !+ Notes: !+ Based on the GetMoistAirEnthalpy function, rearranged for temperature. real, intent(in) :: MoistAirEnthalpy !+ Moist air enthalpy in Btu lb⁻¹ [IP] or J kg⁻¹ real, intent(in) :: HumRatio !+ Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] real :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real :: BoundedHumRatio !+ Humidity ratio bounded to MIN_HUM_RATIO if (HumRatio < 0.0) then error stop "Error: humidity ratio is negative" end if BoundedHumRatio = max(HumRatio, MIN_HUM_RATIO) if (isIP()) then TDryBulb = (MoistAirEnthalpy - 1061.0 * BoundedHumRatio) / (0.240 + 0.444 * BoundedHumRatio) else TDryBulb = (MoistAirEnthalpy / 1000.0 - 2501.0 * BoundedHumRatio) / (1.006 + 1.86 * BoundedHumRatio) end if end function GetTDryBulbFromEnthalpyAndHumRatio function GetHumRatioFromEnthalpyAndTDryBulb(MoistAirEnthalpy, TDryBulb) result(HumRatio) !+ Return humidity ratio from enthalpy and dry-bulb temperature. !+ Reference: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 30 !+ Notes: !+ Based on the GetMoistAirEnthalpy function, rearranged for humidity ratio. real, intent(in) :: MoistAirEnthalpy !+ Moist air enthalpy in Btu lb⁻¹ [IP] or J kg⁻¹ real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real :: HumRatio !+ Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] if (isIP()) then HumRatio = (MoistAirEnthalpy - 0.240 * TDryBulb) / (1061.0 + 0.444 * TDryBulb) else HumRatio = (MoistAirEnthalpy / 1000.0 - 1.006 * TDryBulb) / (2501.0 + 1.86 * TDryBulb) end if ! Validity check. HumRatio = max(HumRatio, MIN_HUM_RATIO) end function GetHumRatioFromEnthalpyAndTDryBulb !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! Saturated Air Calculations !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! function GetSatVapPres(TDryBulb) result(SatVapPres) !+ Return saturation vapor pressure given dry-bulb temperature. !+ Reference: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 5 !+ Important note: the ASHRAE formulae are defined above and below the freezing point but have !+ a discontinuity at the freezing point. This is a small inaccuracy on ASHRAE's part: the formulae !+ should be defined above and below the triple point of water (not the feezing point) in which case !+ the discontinuity vanishes. It is essential to use the triple point of water otherwise function !+ GetTDewPointFromVapPres, which inverts the present function, does not converge properly around !+ the freezing point. real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real :: SatVapPres !+ Vapor pressure of saturated air in Psi [IP] or Pa [SI] real :: LnPws !+ Log of Vapor Pressure of saturated air (dimensionless) real :: T !+ Dry bulb temperature in R [IP] or K [SI] if (isIP()) then if (TDryBulb < -148.0 .or. TDryBulb > 392.0) then error stop "Error: dry bulb temperature must be in range [-148, 392]°F" end if T = GetTRankineFromTFahrenheit(TDryBulb) if (TDryBulb <= TRIPLE_POINT_WATER_IP) then LnPws = (-1.0214165E+04 / T - 4.8932428 - 5.3765794E-03 * T + 1.9202377E-07 * T**2 & + 3.5575832E-10 * T**3 - 9.0344688E-14 * T**4 + 4.1635019 * log(T)) else LnPws = -1.0440397E+04 / T - 1.1294650E+01 - 2.7022355E-02* T + 1.2890360E-05 * T**2 & - 2.4780681E-09 * T**3 + 6.5459673 * log(T) end if else if (TDryBulb < -100.0 .or. TDryBulb > 200.0) then error stop "Error: dry bulb temperature must be in range [-100, 200]°C" end if T = GetTKelvinFromTCelsius(TDryBulb) if (TDryBulb <= TRIPLE_POINT_WATER_SI) then LnPws = -5.6745359E+03 / T + 6.3925247 - 9.677843E-03 * T + 6.2215701E-07 * T**2 & + 2.0747825E-09 * T**3 - 9.484024E-13 * T**4 + 4.1635019 * log(T) else LnPws = -5.8002206E+03 / T + 1.3914993 - 4.8640239E-02 * T + 4.1764768E-05 * T**2 & - 1.4452093E-08 * T**3 + 6.5459673 * log(T) end if end if SatVapPres = exp(LnPws) end function GetSatVapPres function GetSatHumRatio(TDryBulb, Pressure) result(SatHumRatio) !+ Return humidity ratio of saturated air given dry-bulb temperature and pressure. !+ Reference: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 36, solved for W real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: Pressure !+ Atmospheric pressure in Psi [IP] or Pa [SI] real :: SatHumRatio !+ Humidity ratio of saturated air in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] real :: SatVaporPres !+ Vapor pressure of saturated air in in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] SatVaporPres = GetSatVapPres(TDryBulb) SatHumRatio = 0.621945 * SatVaporPres / (Pressure-SatVaporPres) ! Validity check. SatHumRatio = max(SatHumRatio, MIN_HUM_RATIO) end function GetSatHumRatio function GetSatAirEnthalpy(TDryBulb, Pressure) result(SatAirEnthalpy) !+ Return saturated air enthalpy given dry-bulb temperature and pressure. !+ Reference: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: Pressure !+ Atmospheric pressure in Psi [IP] or Pa [SI] real :: SatAirEnthalpy !+ Saturated air enthalpy in Btu lb⁻¹ [IP] or J kg⁻¹ [SI] SatAirEnthalpy = GetMoistAirEnthalpy(TDryBulb, GetSatHumRatio(TDryBulb, Pressure)) end function GetSatAirEnthalpy !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! Moist Air Calculations !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! function GetVaporPressureDeficit(TDryBulb, HumRatio, Pressure) result(VaporPressureDeficit) !+ Return Vapor pressure deficit given dry-bulb temperature, humidity ratio, and pressure. !+ Reference: !+ Oke (1987) eqn 2.13a real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: HumRatio !+ Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] real, intent(in) :: Pressure !+ Atmospheric pressure in Psi [IP] or Pa [SI] real :: VaporPressureDeficit !+ Vapor pressure deficit in Psi [IP] or Pa [SI] real :: RelHum !+ Relative humidity in range [0, 1] if (HumRatio < 0.0) then error stop "Error: humidity ratio is negative" end if RelHum = GetRelHumFromHumRatio(TDryBulb, HumRatio, Pressure) VaporPressureDeficit = GetSatVapPres(TDryBulb) * (1.0 - RelHum) end function GetVaporPressureDeficit function GetDegreeOfSaturation(TDryBulb, HumRatio, Pressure) result(DegreeOfSaturation) !+ Return the degree of saturation (i.e humidity ratio of the air / humidity ratio of the air at saturation !+ at the same temperature and pressure) given dry-bulb temperature, humidity ratio, and atmospheric pressure. !+ Reference: !+ ASHRAE Handbook - Fundamentals (2009) ch. 1 eqn 12 !+ Notes: !+ This definition is absent from the 2017 Handbook. Using 2009 version instead. real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: HumRatio !+ Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] real, intent(in) :: Pressure !+ Atmospheric pressure in Psi [IP] or Pa [SI] real :: DegreeOfSaturation !+ Degree of saturation in arbitrary unit real :: BoundedHumRatio !+ Humidity ratio bounded to MIN_HUM_RATIO if (HumRatio < 0.0) then error stop "Error: humidity ratio is negative" end if BoundedHumRatio = max(HumRatio, MIN_HUM_RATIO) DegreeOfSaturation = BoundedHumRatio / GetSatHumRatio(TDryBulb, Pressure) end function GetDegreeOfSaturation function GetMoistAirEnthalpy(TDryBulb, HumRatio) result(MoistAirEnthalpy) !+ Return moist air enthalpy given dry-bulb temperature and humidity ratio. !+ Reference: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 30 real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: HumRatio !+ Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] real :: MoistAirEnthalpy !+ Moist air enthalpy in Btu lb⁻¹ [IP] or J kg⁻¹ real :: BoundedHumRatio !+ Humidity ratio bounded to MIN_HUM_RATIO if (HumRatio < 0.0) then error stop "Error: humidity ratio is negative" end if BoundedHumRatio = max(HumRatio, MIN_HUM_RATIO) if (isIP()) then MoistAirEnthalpy = 0.240 * TDryBulb + BoundedHumRatio * (1061.0 + 0.444 * TDryBulb) else MoistAirEnthalpy = (1.006 * TDryBulb + BoundedHumRatio * (2501.0 + 1.86 * TDryBulb)) * 1000.0 end if end function GetMoistAirEnthalpy function GetMoistAirVolume(TDryBulb, HumRatio, Pressure) result(MoistAirVolume) !+ Return moist air specific volume given dry-bulb temperature, humidity ratio, and pressure. !+ Reference: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 26 !+ Notes: !+ In IP units, R_DA_IP / 144 equals 0.370486 which is the coefficient appearing in eqn 26 !+ The factor 144 is for the conversion of Psi = lb in⁻² to lb ft⁻². real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: HumRatio !+ Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] real, intent(in) :: Pressure !+ Atmospheric pressure in Psi [IP] or Pa [SI] real :: MoistAirVolume !+ Specific volume of moist air in ft³ lb⁻¹ of dry air [IP] or in m³ kg⁻¹ of dry air [SI] real :: BoundedHumRatio !+ Humidity ratio bounded to MIN_HUM_RATIO if (HumRatio < 0.0) then error stop "Error: humidity ratio is negative" end if BoundedHumRatio = max(HumRatio, MIN_HUM_RATIO) if (isIP()) then MoistAirVolume = R_DA_IP * GetTRankineFromTFahrenheit(TDryBulb) * (1.0 + 1.607858 * BoundedHumRatio) / (144.0 * Pressure) else MoistAirVolume = R_DA_SI * GetTKelvinFromTCelsius(TDryBulb) * (1.0 + 1.607858 * BoundedHumRatio) / Pressure end if end function GetMoistAirVolume function GetTDryBulbFromMoistAirVolumeAndHumRatio(MoistAirVolume, HumRatio, Pressure) result(TDryBulb) !+ Return dry-bulb temperature given moist air specific volume, humidity ratio, and pressure. !+ Reference: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 26 !+ Notes: !+ In IP units, R_DA_IP / 144 equals 0.370486 which is the coefficient appearing in eqn 26 !+ The factor 144 is for the conversion of Psi = lb in⁻² to lb ft⁻². !+ Based on the GetMoistAirVolume function, rearranged for dry-bulb temperature. real, intent(in) :: MoistAirVolume !+ Specific volume of moist air in ft³ lb⁻¹ of dry air [IP] or in m³ kg⁻¹ of dry air [SI] real, intent(in) :: HumRatio !+ Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] real, intent(in) :: Pressure !+ Atmospheric pressure in Psi [IP] or Pa [SI] real :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real :: BoundedHumRatio !+ Humidity ratio bounded to MIN_HUM_RATIO if (HumRatio < 0.0) then error stop "Error: humidity ratio is negative" end if BoundedHumRatio = max(HumRatio, MIN_HUM_RATIO) if (isIP()) then TDryBulb = GetTFahrenheitFromTRankine(MoistAirVolume * (144 * Pressure) & / (R_DA_IP * (1 + 1.607858 * BoundedHumRatio))) else TDryBulb = GetTCelsiusFromTKelvin(MoistAirVolume * Pressure & / (R_DA_SI * (1 + 1.607858 * BoundedHumRatio))) end if end function GetTDryBulbFromMoistAirVolumeAndHumRatio function GetMoistAirDensity(TDryBulb, HumRatio, Pressure) result(MoistAirDensity) !+ Return moist air density given humidity ratio, dry bulb temperature, and pressure. !+ Reference: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 11 real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: HumRatio !+ Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] real, intent(in) :: Pressure !+ Atmospheric pressure in Psi [IP] or Pa [SI] real :: MoistAirDensity !+ Moist air density in lb ft⁻³ [IP] or kg m⁻³ [SI] real :: BoundedHumRatio !+ Humidity ratio bounded to MIN_HUM_RATIO if (HumRatio < 0.0) then error stop "Error: humidity ratio is negative" end if BoundedHumRatio = max(HumRatio, MIN_HUM_RATIO) MoistAirDensity = (1.0 + BoundedHumRatio) / GetMoistAirVolume(TDryBulb, BoundedHumRatio, Pressure) end function GetMoistAirDensity !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! Standard atmosphere !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! function GetStandardAtmPressure(Altitude) result(StandardAtmPressure) !+ Return standard atmosphere barometric pressure, given the elevation (altitude). !+ Reference: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 3 real, intent(in) :: Altitude !+ Altitude in ft [IP] or m [SI] real :: StandardAtmPressure !+ Standard atmosphere barometric pressure in Psi [IP] or Pa [SI] if (isIP()) then StandardAtmPressure = 14.696 * (1.0 - 6.8754e-06 * Altitude)**5.2559 else StandardAtmPressure = 101325 * (1 - 2.25577e-05 * Altitude)**5.2559 end if end function GetStandardAtmPressure function GetStandardAtmTemperature(Altitude) result(StandardAtmTemperature) !+ Return standard atmosphere temperature, given the elevation (altitude). !+ Reference: !+ ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 4 real, intent(in) :: Altitude !+ Altitude in ft [IP] or m [SI] real :: StandardAtmTemperature !+ Standard atmosphere dry-bulb temperature in °F [IP] or °C [SI] if (isIP()) then StandardAtmTemperature = 59.0 - 0.00356620 * Altitude else StandardAtmTemperature = 15.0 - 0.0065 * Altitude end if end function GetStandardAtmTemperature function GetSeaLevelPressure(StnPressure, Altitude, TDryBulb) result(SeaLevelPressure) !+ Return sea level pressure given dry-bulb temperature, altitude above sea level and pressure. !+ Reference: !+ Hess SL, Introduction to theoretical meteorology, Holt Rinehart and Winston, NY 1959, !+ ch. 6.5; Stull RB, Meteorology for scientists and engineers, 2nd edition, !+ Brooks/Cole 2000, ch. 1. !+ Notes: !+ The standard procedure for the US is to use for TDryBulb the average !+ of the current station temperature and the station temperature from 12 hours ago. real, intent(in) :: StnPressure !+ Observed station pressure in Psi [IP] or Pa [SI] real, intent(in) :: Altitude !+ Altitude in ft [IP] or m [SI] real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real :: SeaLevelPressure !+ Sea level barometric pressure in Psi [IP] or Pa [SI] real :: TColumn !+ Average temperature in column of air in R [IP] or K [SI] real :: H !+ scale height (dimensionless) if (isIP()) then ! Calculate average temperature in column of air, assuming a lapse rate ! of 3.6 °F/1000ft TColumn = TDryBulb + 0.0036 * Altitude / 2.0 ! Determine the scale height H = 53.351 * GetTRankineFromTFahrenheit(TColumn) else ! Calculate average temperature in column of air, assuming a lapse rate ! of 6.5 °C/km TColumn = TDryBulb + 0.0065 * Altitude / 2.0 ! Determine the scale height H = 287.055 * GetTKelvinFromTCelsius(TColumn) / 9.807 end if ! Calculate the sea level pressure SeaLevelPressure = StnPressure * exp(Altitude / H) end function GetSeaLevelPressure function GetStationPressure(SeaLevelPressure, Altitude, TDryBulb) result(StationPressure) !+ Return station pressure from sea level pressure. !+ Reference: !+ See 'GetSeaLevelPressure' !+ Notes: !+ This function is just the inverse of 'GetSeaLevelPressure'. real, intent(in) :: SeaLevelPressure !+ Sea level barometric pressure in Psi [IP] or Pa [SI] real, intent(in) :: Altitude !+ Altitude in ft [IP] or m [SI] real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real :: StationPressure !+ Station pressure in Psi [IP] or Pa [SI] StationPressure = SeaLevelPressure / GetSeaLevelPressure(1.0, Altitude, TDryBulb) end function GetStationPressure !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! Functions to set all psychrometric values !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! subroutine CalcPsychrometricsFromTWetBulb(TDryBulb, & TWetBulb, & Pressure, & HumRatio, & TDewPoint, & RelHum, & VapPres, & MoistAirEnthalpy, & MoistAirVolume, & DegreeOfSaturation) !+ Utility function to calculate humidity ratio, dew-point temperature, relative humidity, !+ vapour pressure, moist air enthalpy, moist air volume, and degree of saturation of air given !+ dry-bulb temperature, wet-bulb temperature, and pressure. real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: TWetBulb !+ Wet-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: Pressure !+ Atmospheric pressure in Psi [IP] or Pa [SI] real, intent(out) :: HumRatio !+ Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] real, intent(out) :: TDewPoint !+ Dew-point temperature in °F [IP] or °C [SI] real, intent(out) :: RelHum !+ Relative humidity in range [0, 1] real, intent(out) :: VapPres !+ Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] real, intent(out) :: MoistAirEnthalpy !+ Moist air enthalpy in Btu lb⁻¹ [IP] or J kg⁻¹ [SI] real, intent(out) :: MoistAirVolume !+ Specific volume of moist air in ft³ lb⁻¹ [IP] or in m³ kg⁻¹ [SI] real, intent(out) :: DegreeOfSaturation !+ Degree of saturation [unitless] HumRatio = GetHumRatioFromTWetBulb(TDryBulb, TWetBulb, Pressure) TDewPoint = GetTDewPointFromHumRatio(TDryBulb, HumRatio, Pressure) RelHum = GetRelHumFromHumRatio(TDryBulb, HumRatio, Pressure) VapPres = GetVapPresFromHumRatio(HumRatio, Pressure) MoistAirEnthalpy = GetMoistAirEnthalpy(TDryBulb, HumRatio) MoistAirVolume = GetMoistAirVolume(TDryBulb, HumRatio, Pressure) DegreeOfSaturation = GetDegreeOfSaturation(TDryBulb, HumRatio, Pressure) end subroutine CalcPsychrometricsFromTWetBulb subroutine CalcPsychrometricsFromTDewPoint(TDryBulb, & TDewPoint, & Pressure, & HumRatio, & TWetBulb, & RelHum, & VapPres, & MoistAirEnthalpy, & MoistAirVolume, & DegreeOfSaturation) !+ Utility function to calculate humidity ratio, wet-bulb temperature, relative humidity, !+ vapour pressure, moist air enthalpy, moist air volume, and degree of saturation of air given !+ dry-bulb temperature, dew-point temperature, and pressure. real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: TDewPoint !+ Dew-point temperature in °F [IP] or °C [SI] real, intent(in) :: Pressure !+ Atmospheric pressure in Psi [IP] or Pa [SI] real, intent(out) :: HumRatio !+ Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] real, intent(out) :: TWetBulb !+ Wet-bulb temperature in °F [IP] or °C [SI] real, intent(out) :: RelHum !+ Relative humidity in range [0, 1] real, intent(out) :: VapPres !+ Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] real, intent(out) :: MoistAirEnthalpy !+ Moist air enthalpy in Btu lb⁻¹ [IP] or J kg⁻¹ [SI] real, intent(out) :: MoistAirVolume !+ Specific volume of moist air in ft³ lb⁻¹ [IP] or in m³ kg⁻¹ [SI] real, intent(out) :: DegreeOfSaturation !+ Degree of saturation [unitless] HumRatio = GetHumRatioFromTDewPoint(TDewPoint, Pressure) TWetBulb = GetTWetBulbFromHumRatio(TDryBulb, HumRatio, Pressure) RelHum = GetRelHumFromHumRatio(TDryBulb, HumRatio, Pressure) VapPres = GetVapPresFromHumRatio(HumRatio, Pressure) MoistAirEnthalpy = GetMoistAirEnthalpy(TDryBulb, HumRatio) MoistAirVolume = GetMoistAirVolume(TDryBulb, HumRatio, Pressure) DegreeOfSaturation = GetDegreeOfSaturation(TDryBulb, HumRatio, Pressure) end subroutine CalcPsychrometricsFromTDewPoint subroutine CalcPsychrometricsFromRelHum(TDryBulb, & RelHum, & Pressure, & HumRatio, & TWetBulb, & TDewPoint, & VapPres, & MoistAirEnthalpy, & MoistAirVolume, & DegreeOfSaturation) !+ Utility function to calculate humidity ratio, wet-bulb temperature, dew-point temperature, !+ vapour pressure, moist air enthalpy, moist air volume, and degree of saturation of air given !+ dry-bulb temperature, relative humidity and pressure. real, intent(in) :: TDryBulb !+ Dry-bulb temperature in °F [IP] or °C [SI] real, intent(in) :: RelHum !+ Relative humidity in range [0, 1] real, intent(in) :: Pressure !+ Atmospheric pressure in Psi [IP] or Pa [SI] real, intent(out) :: HumRatio !+ Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] real, intent(out) :: TWetBulb !+ Wet-bulb temperature in °F [IP] or °C [SI] real, intent(out) :: TDewPoint !+ Dew-point temperature in °F [IP] or °C [SI] real, intent(out) :: VapPres !+ Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] real, intent(out) :: MoistAirEnthalpy !+ Moist air enthalpy in Btu lb⁻¹ [IP] or J kg⁻¹ [SI] real, intent(out) :: MoistAirVolume !+ Specific volume of moist air in ft³ lb⁻¹ [IP] or in m³ kg⁻¹ [SI] real, intent(out) :: DegreeOfSaturation !+ Degree of saturation [unitless] HumRatio = GetHumRatioFromRelHum(TDryBulb, RelHum, Pressure) TWetBulb = GetTWetBulbFromHumRatio(TDryBulb, HumRatio, Pressure) TDewPoint = GetTDewPointFromHumRatio(TDryBulb, HumRatio, Pressure) VapPres = GetVapPresFromHumRatio(HumRatio, Pressure) MoistAirEnthalpy = GetMoistAirEnthalpy(TDryBulb, HumRatio) MoistAirVolume = GetMoistAirVolume(TDryBulb, HumRatio, Pressure) DegreeOfSaturation = GetDegreeOfSaturation(TDryBulb, HumRatio, Pressure) end subroutine CalcPsychrometricsFromRelHum end module psychrolib 

## Visual Basic, VBA

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1821 1822 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 ' PsychroLib (version 2.3.0) (https://github.com/psychrometrics/psychrolib) ' Copyright (c) 2018 D. Thevenard and D. Meyer for the current library implementation ' Copyright (c) 2017 ASHRAE Handbook — Fundamentals for ASHRAE equations and coefficients ' Licensed under the MIT License. ' ' psychrolib.vba ' ' Contains functions for calculating thermodynamic properties of gas-vapor mixtures ' and standard atmosphere suitable for most engineering, physical and meteorological ' applications. ' ' Most of the functions are an implementation of the formulae found in the ' 2017 ASHRAE Handbook - Fundamentals, in both International System (SI), ' and Imperial (IP) units. Please refer to the information included in ' each function for their respective reference. ' ' Example ' ' Set the unit system, for example to SI (can be either ' SI' or ' IP' ) ' ' by uncommenting the following line in the psychrolib module ' Const PSYCHROLIB_UNITS = UnitSystem.SI ' ' ' Calculate the dew point temperature for a dry bulb temperature of 25 C and a relative humidity of 80% ' TDewPoint = GetTDewPointFromRelHum(25.0, 0.80) ' Debug.Print(TDewPoint) ' 21.309397163661785 ' ' Copyright ' - For the current library implementation ' Copyright (c) 2018 D. Thevenard and D. Meyer. ' - For equations and coefficients published ASHRAE Handbook — Fundamentals, Chapter 1 ' Copyright (c) 2017 ASHRAE Handbook — Fundamentals (https://www.ashrae.org) ' ' License ' MIT (https://github.com/psychrometrics/psychrolib/LICENSE.txt) ' ' Note from the Authors ' We have made every effort to ensure that the code is adequate, however, we make no ' representation with respect to its accuracy. Use at your own risk. Should you notice ' an error, or if you have a suggestion, please notify us through GitHub at ' https://github.com/psychrometrics/psychrolib/issues. ' Option Explicit '****************************************************************************************************** ' IMPORTANT: Manually uncomment the system of units to use '****************************************************************************************************** 'Enumeration to define systems of units Enum UnitSystem IP = 1 SI = 2 End Enum ' Uncomment one of these two lines to define the system of units ("IP" or "SI") 'Const PSYCHROLIB_UNITS = UnitSystem.IP 'Const PSYCHROLIB_UNITS = UnitSystem.SI '****************************************************************************************************** ' Global constants '****************************************************************************************************** Private Const ZERO_FAHRENHEIT_AS_RANKINE = 459.67 ' Zero degree Fahrenheit (°F) expressed as degree Rankine (°R). 'Reference: ASHRAE Handbook - Fundamentals (2017) ch. 39. Private Const ZERO_CELSIUS_AS_KELVIN = 273.15 ' Zero degree Celsius (°C) expressed as Kelvin (K). ' Reference: ASHRAE Handbook - Fundamentals (2017) ch. 39. Private Const R_DA_IP = 53.35 ' Universal gas constant for dry air (IP version) in ft lbf/lb_DryAir/R. Private Const R_DA_SI = 287.042 ' Universal gas constant for dry air (SI version) in J/kg_DryAir/K. Private Const MAX_ITER_COUNT = 100 ' Maximum number of iterations before exiting while loops. Private Const MIN_HUM_RATIO = 1e-7 ' Minimum acceptable humidity ratio used/returned by any functions. ' Any value above 0 or below the MIN_HUM_RATIO will be reset to this value. Private Const FREEZING_POINT_WATER_IP = 32.0 ' Freezing point of water, in °F Private Const FREEZING_POINT_WATER_SI = 0.0 ' Freezing point of water, in °C Private Const TRIPLE_POINT_WATER_IP = 32.018 ' Triple point of water, in °F Private Const TRIPLE_POINT_WATER_SI = 0.01 ' Triple point of water, in °C '****************************************************************************************************** ' Helper functions '****************************************************************************************************** Function GetUnitSystem() As UnitSystem ' ' This function returns the system of units currently in use (SI or IP). ' ' Args: ' none ' ' Returns: ' The system of units currently in use ('SI' or 'IP') ' ' Note: ' ' If you get an error here, it's because you have not uncommented one of the two lines ' defining PSYCHROLIB_UNITS (see Global Constants section) ' GetUnitSystem = PSYCHROLIB_UNITS End Function Private Function isIP() As Variant ' ' This function checks whether the system of units currently in use is IP or SI. ' ' Args: ' none ' ' Returns: ' True if IP, False if SI, and raises error if undefined ' If (PSYCHROLIB_UNITS = UnitSystem.IP) Then isIP = True ElseIf (PSYCHROLIB_UNITS = UnitSystem.SI) Then isIP = False Else MsgBox ("The system of units has not been defined.") isIP = CVErr(xlErrNA) End If End Function Private Function GetTol() As Variant ' ' This function returns the tolerance on temperatures used for iterative solving. ' The value is physically the same in IP or SI. ' ' Args: ' none ' ' Returns: ' Tolerance on temperatures ' If (PSYCHROLIB_UNITS = UnitSystem.IP) Then GetTol = 0.001 * 9 / 5 Else GetTol = 0.001 End If End Function Private Sub MyMsgBox(ByVal ErrMsg As String) ' ' Error message output ' Override this function with your own if needed, or comment its code out if you don't want to see the messages ' ' Message disabled by default ' MsgBox (ErrMsg) End Sub Private Function Min(ByVal Num1 As Variant, ByVal Num2 As Variant) As Variant ' ' Min function to return minimum of two numbers ' If (Num1 <= Num2) Then Min = Num1 Else Min = Num2 End If End Function Private Function Max(ByVal Num1 As Variant, ByVal Num2 As Variant) As Variant ' ' Max function to return maximum of two numbers ' If (Num1 >= Num2) Then Max = Num1 Else Max = Num2 End If End Function '***************************************************************************** ' Conversions between temperature units '***************************************************************************** Function GetTRankineFromTFahrenheit(ByVal T_Fahrenheit As Variant) As Variant ' ' Utility function to convert temperature to degree Rankine (°R) ' given temperature in degree Fahrenheit (°F). ' 'Args: ' T_Fahrenheit: Temperature in degree Fahrenheit (°F) ' 'Returns: ' Temperature in degree Rankine (°R) ' 'Reference: ' Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 section 3 ' 'Notes: ' Exact conversion. ' On Error GoTo ErrHandler GetTRankineFromTFahrenheit = (T_Fahrenheit + ZERO_FAHRENHEIT_AS_RANKINE) Exit Function ErrHandler: GetTRankineFromTFahrenheit = CVErr(xlErrNA) End Function Function GetTFahrenheitFromTRankine(ByVal T_Rankine As Variant) As Variant ' ' Utility function to convert temperature to degree Fahrenheit (°F) ' given temperature in degree Rankine (°R). ' 'Args: ' TRankine: Temperature in degree Rankine (°R) ' 'Returns: ' Temperature in degree Fahrenheit (°F) ' 'Reference: ' Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 section 3 ' 'Notes: ' Exact conversion. ' On Error GoTo ErrHandler GetTFahrenheitFromTRankine = (T_Rankine - ZERO_FAHRENHEIT_AS_RANKINE) Exit Function ErrHandler: GetTFahrenheitFromTRankine = CVErr(xlErrNA) End Function Function GetTKelvinFromTCelsius(ByVal T_Celsius As Variant) As Variant ' ' Utility function to convert temperature to Kelvin (K) ' given temperature in degree Celsius (°C). ' 'Args: ' TCelsius: Temperature in degree Celsius (°C) ' 'Returns: ' Temperature in Kelvin (K) ' 'Reference: ' Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 section 3 ' 'Notes: ' Exact conversion. ' On Error GoTo ErrHandler GetTKelvinFromTCelsius = (T_Celsius + ZERO_CELSIUS_AS_KELVIN) Exit Function ErrHandler: GetTKelvinFromTCelsius = CVErr(xlErrNA) End Function Function GetTCelsiusFromTKelvin(ByVal T_Kelvin As Variant) As Variant ' ' Utility function to convert temperature to degree Celsius (°C) ' given temperature in Kelvin (K). ' 'Args: ' TKelvin: Temperature in Kelvin (K) ' 'Returns: ' Temperature in degree Celsius (°C) ' 'Reference: ' Reference: ASHRAE Handbook - Fundamentals (2017) ch. 1 section 3 ' 'Notes: ' Exact conversion. ' On Error GoTo ErrHandler GetTCelsiusFromTKelvin = (T_Kelvin - ZERO_CELSIUS_AS_KELVIN) Exit Function ErrHandler: GetTCelsiusFromTKelvin = CVErr(xlErrNA) End Function '****************************************************************************************************** ' Conversions between dew point, wet bulb, and relative humidity '****************************************************************************************************** Function GetTWetBulbFromTDewPoint(ByVal TDryBulb As Variant, ByVal TDewPoint As Variant, ByVal Pressure As Variant) As Variant ' ' Return wet-bulb temperature given dry-bulb temperature, dew-point temperature, and pressure. ' ' Args: ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' TDewPoint : Dew-point temperature in °F [IP] or °C [SI] ' Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] ' ' Returns: ' Wet-bulb temperature in °F [IP] or °C [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 ' Dim HumRatio As Variant On Error GoTo ErrHandler If TDewPoint > TDryBulb Then MyMsgBox ("Dew point temperature is above dry bulb temperature") GoTo ErrHandler End If HumRatio = GetHumRatioFromTDewPoint(TDewPoint, Pressure) GetTWetBulbFromTDewPoint = GetTWetBulbFromHumRatio(TDryBulb, HumRatio, Pressure) Exit Function ErrHandler: GetTWetBulbFromTDewPoint = CVErr(xlErrNA) End Function Function GetTWetBulbFromRelHum(ByVal TDryBulb As Variant, ByVal RelHum As Variant, ByVal Pressure As Variant) As Variant ' ' Return wet-bulb temperature given dry-bulb temperature, relative humidity, and pressure. ' ' Args: ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' RelHum : Relative humidity in range [0, 1] ' Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] ' ' Returns: ' Wet-bulb temperature in °F [IP] or °C [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 ' Dim HumRatio As Variant On Error GoTo ErrHandler If (RelHum < 0 Or RelHum > 1) Then MyMsgBox ("Relative humidity is outside range [0,1]") GoTo ErrHandler End If HumRatio = GetHumRatioFromRelHum(TDryBulb, RelHum, Pressure) GetTWetBulbFromRelHum = GetTWetBulbFromHumRatio(TDryBulb, HumRatio, Pressure) Exit Function ErrHandler: GetTWetBulbFromRelHum = CVErr(xlErrNA) End Function Function GetRelHumFromTDewPoint(ByVal TDryBulb As Variant, ByVal TDewPoint As Variant) As Variant ' ' Return relative humidity given dry-bulb temperature and dew-point temperature. ' ' Args: ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' TDewPoint : Dew-point temperature in °F [IP] or °C [SI] ' ' Returns: ' Relative humidity in range [0, 1] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 22 ' Dim VapPres As Variant Dim SatVapPres As Variant On Error GoTo ErrHandler If (TDewPoint > TDryBulb) Then MyMsgBox ("Dew point temperature is above dry bulb temperature") GoTo ErrHandler End If VapPres = GetSatVapPres(TDewPoint) SatVapPres = GetSatVapPres(TDryBulb) GetRelHumFromTDewPoint = VapPres / SatVapPres Exit Function ErrHandler: GetRelHumFromTDewPoint = CVErr(xlErrNA) End Function Function GetRelHumFromTWetBulb(ByVal TDryBulb As Variant, ByVal TWetBulb As Variant, ByVal Pressure As Variant) As Variant ' ' Return relative humidity given dry-bulb temperature, wet bulb temperature and pressure. ' ' Args: ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' TWetBulb : Wet-bulb temperature in °F [IP] or °C [SI] ' Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] ' ' Returns: ' Relative humidity in range [0, 1] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 ' Dim HumRatio As Variant On Error GoTo ErrHandler If TWetBulb > TDryBulb Then MyMsgBox ("Wet bulb temperature is above dry bulb temperature") GoTo ErrHandler End If HumRatio = GetHumRatioFromTWetBulb(TDryBulb, TWetBulb, Pressure) GetRelHumFromTWetBulb = GetRelHumFromHumRatio(TDryBulb, HumRatio, Pressure) Exit Function ErrHandler: GetRelHumFromTWetBulb = CVErr(xlErrNA) End Function Function GetTDewPointFromRelHum(ByVal TDryBulb As Variant, ByVal RelHum As Variant) As Variant ' ' Return dew-point temperature given dry-bulb temperature and relative humidity. ' ' Args: ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' RelHum: Relative humidity in range [0, 1] ' ' Returns: ' Dew-point temperature in °F [IP] or °C [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 ' Dim VapPres As Variant On Error GoTo ErrHandler If RelHum < 0 Or RelHum > 1 Then MyMsgBox ("Relative humidity is outside range [0, 1]") GoTo ErrHandler End If VapPres = GetVapPresFromRelHum(TDryBulb, RelHum) GetTDewPointFromRelHum = GetTDewPointFromVapPres(TDryBulb, VapPres) Exit Function ErrHandler: GetTDewPointFromRelHum = CVErr(xlErrNA) End Function Function GetTDewPointFromTWetBulb(ByVal TDryBulb As Variant, ByVal TWetBulb As Variant, ByVal Pressure As Variant) As Variant ' ' Return dew-point temperature given dry-bulb temperature, wet-bulb temperature, and pressure. ' ' Args: ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' TWetBulb : Wet-bulb temperature in °F [IP] or °C [SI] ' Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] ' ' Returns: ' Dew-point temperature in °F [IP] or °C [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 ' Dim HumRatio As Variant On Error GoTo ErrHandler If TWetBulb > TDryBulb Then MyMsgBox ("Wet bulb temperature is above dry bulb temperature") GoTo ErrHandler End If HumRatio = GetHumRatioFromTWetBulb(TDryBulb, TWetBulb, Pressure) GetTDewPointFromTWetBulb = GetTDewPointFromHumRatio(TDryBulb, HumRatio, Pressure) Exit Function ErrHandler: GetTDewPointFromTWetBulb = CVErr(xlErrNA) End Function '****************************************************************************************************** ' Conversions between dew point, or relative humidity and vapor pressure '****************************************************************************************************** Function GetVapPresFromRelHum(ByVal TDryBulb As Variant, ByVal RelHum As Variant) As Variant ' ' Return partial pressure of water vapor as a function of relative humidity and temperature. ' ' Args: ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' RelHum : Relative humidity in range [0, 1] ' ' Returns: ' Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 12, 22 ' On Error GoTo ErrHandler If RelHum < 0 Or RelHum > 1 Then MyMsgBox ("Relative humidity is outside range [0, 1]") GoTo ErrHandler End If GetVapPresFromRelHum = RelHum * GetSatVapPres(TDryBulb) Exit Function ErrHandler: GetVapPresFromRelHum = CVErr(xlErrNA) End Function Function GetRelHumFromVapPres(ByVal TDryBulb As Variant, ByVal VapPres As Variant) As Variant ' Return relative humidity given dry-bulb temperature and vapor pressure. ' ' Args: ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' VapPres: Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] ' ' Returns: ' Relative humidity in range [0, 1] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 12, 22 ' On Error GoTo ErrHandler If (VapPres < 0) Then MyMsgBox ("Partial pressure of water vapor in moist air is negative") GoTo ErrHandler End If GetRelHumFromVapPres = VapPres / GetSatVapPres(TDryBulb) Exit Function ErrHandler: GetRelHumFromVapPres = CVErr(xlErrNA) End Function Private Function dLnPws_(TDryBulb As Variant) As Variant ' ' Helper function returning the derivative of the natural log of the saturation vapor pressure ' as a function of dry-bulb temperature. ' ' Args: ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' ' Returns: ' Derivative of natural log of vapor pressure of saturated air in Psi [IP] or Pa [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 5 & 6 ' Dim T As Variant If (isIP()) Then T = GetTRankineFromTFahrenheit(TDryBulb) If (TDryBulb <= TRIPLE_POINT_WATER_IP) Then dLnPws_ = 10214.165 / T ^ 2 - 0.0053765794 + 2 * 0.00000019202377 * T _ + 3 * 3.5575832E-10 * T ^ 2 - 4 * 9.0344688E-14 * T ^ 3 + 4.1635019 / T Else dLnPws_ = 10440.397 / T ^ 2 - 0.027022355 + 2 * 0.00001289036 * T _ - 3 * 2.4780681E-09 * T ^ 2 + 6.5459673 / T End If Else T = GetTKelvinFromTCelsius(TDryBulb) If (TDryBulb <= TRIPLE_POINT_WATER_SI) Then dLnPws_ = 5674.5359 / T ^ 2 - 0.009677843 + 2 * 0.00000062215701 * T _ + 3 * 2.0747825E-09 * T ^ 2 - 4 * 9.484024E-13 * T ^ 3 + 4.1635019 / T Else dLnPws_ = 5800.2206 / T ^ 2 - 0.048640239 + 2 * 0.000041764768 * T _ - 3 * 0.000000014452093 * T ^ 2 + 6.5459673 / T End If End If End Function Function GetTDewPointFromVapPres(ByVal TDryBulb As Variant, ByVal VapPres As Variant) As Variant ' ' Return dew-point temperature given dry-bulb temperature and vapor pressure. ' ' Args: ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' VapPres: Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] ' ' Returns: ' Dew-point temperature in °F [IP] or °C [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn. 5 and 6 ' ' Notes: ' The dew point temperature is solved by inverting the equation giving water vapor pressure ' at saturation from temperature rather than using the regressions provided ' by ASHRAE (eqn. 37 and 38) which are much less accurate and have a ' narrower range of validity. ' The Newton-Raphson (NR) method is used on the logarithm of water vapour ' pressure as a function of temperature, which is a very smooth function ' Convergence is usually achieved in 3 to 5 iterations. ' TDryBulb is not really needed here, just used for convenience. ' Dim BOUNDS(2) As Variant Dim PSYCHROLIB_TOLERANCE As Variant If (isIP()) Then BOUNDS(1) = -148. BOUNDS(2) = 392. Else BOUNDS(1) = -100. BOUNDS(2) = 200. End If On Error GoTo ErrHandler If ((VapPres < GetSatVapPres(BOUNDS(1))) Or (VapPres > GetSatVapPres(BOUNDS(2)))) Then MyMsgBox ("Partial pressure of water vapor is outside range of validity of equations") GoTo ErrHandler End If PSYCHROLIB_TOLERANCE = GetTol() Dim TDewPoint As Variant Dim lnVP As Variant Dim d_lnVP As Variant Dim TDewPoint_iter As Variant Dim lnVP_iter Dim index As Variant index = 1 ' We use NR to approximate the solution. ' First guess TDewPoint = TDryBulb ' Calculated value of dew point temperatures, solved for iteratively lnVP = Log(VapPres) ' Partial pressure of water vapor in moist air ' Iteration Do TDewPoint_iter = TDewPoint ' Value of Tdp used in NR calculation lnVP_iter = Log(GetSatVapPres(TDewPoint_iter)) ' Derivative of function, calculated analytically d_lnVP = dLnPws_(TDewPoint_iter) ' New estimate, bounded by domain of validity of eqn. 5 and 6 and by the freezing point TDewPoint = TDewPoint_iter - (lnVP_iter - lnVP) / d_lnVP TDewPoint = Max(TDewPoint, BOUNDS(1)) TDewPoint = Min(TDewPoint, BOUNDS(2)) If (index > MAX_ITER_COUNT) Then GoTo ErrHandler End If index = index + 1 Loop While (Abs(TDewPoint - TDewPoint_iter) > PSYCHROLIB_TOLERANCE) TDewPoint = Min(TDewPoint, TDryBulb) GetTDewPointFromVapPres = TDewPoint Exit Function ErrHandler: GetTDewPointFromVapPres = CVErr(xlErrNA) End Function Function GetVapPresFromTDewPoint(ByVal TDewPoint As Variant) As Variant ' ' Return vapor pressure given dew point temperature. ' ' Args: ' TDewPoint : Dew-point temperature in °F [IP] or °C [SI] ' ' Returns: ' Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 36 ' On Error GoTo ErrHandler GetVapPresFromTDewPoint = GetSatVapPres(TDewPoint) Exit Function ErrHandler: GetVapPresFromTDewPoint = CVErr(xlErrNA) End Function '****************************************************************************************************** ' Conversions from wet-bulb temperature, dew-point temperature, or relative humidity to humidity ratio '****************************************************************************************************** Function GetTWetBulbFromHumRatio(ByVal TDryBulb As Variant, ByVal HumRatio As Variant, ByVal Pressure As Variant) As Variant ' ' Return wet-bulb temperature given dry-bulb temperature, humidity ratio, and pressure. ' ' Args: ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' HumRatio : Humidity ratio in lb_H2O/lb_Air [IP] or kg_H2O/kg_Air [SI] ' Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] ' ' Returns: ' Wet-bulb temperature in °F [IP] or °C [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 33 and 35 solved for Tstar ' ' Declarations Dim Wstar As Variant Dim TDewPoint As Variant, TWetBulb As Variant, TWetBulbSup As Variant, TWetBulbInf As Variant Dim Tol As Variant, BoundedHumRatio As Variant, index As Variant On Error GoTo ErrHandler If HumRatio < 0 Then MyMsgBox ("Humidity ratio cannot be negative") GoTo ErrHandler End If BoundedHumRatio = max(HumRatio, MIN_HUM_RATIO) TDewPoint = GetTDewPointFromHumRatio(TDryBulb, BoundedHumRatio, Pressure) ' Initial guesses TWetBulbSup = TDryBulb TWetBulbInf = TDewPoint TWetBulb = (TWetBulbInf + TWetBulbSup) / 2 ' Bisection loop Tol = GetTol() index = 0 While ((TWetBulbSup - TWetBulbInf) > Tol) ' Compute humidity ratio at temperature Tstar Wstar = GetHumRatioFromTWetBulb(TDryBulb, TWetBulb, Pressure) ' Get new bounds If (Wstar > BoundedHumRatio) Then TWetBulbSup = TWetBulb Else TWetBulbInf = TWetBulb End If ' New guess of wet bulb temperature TWetBulb = (TWetBulbSup + TWetBulbInf) / 2 If (index > MAX_ITER_COUNT) Then GoTo ErrHandler End If index = index + 1 Wend GetTWetBulbFromHumRatio = TWetBulb Exit Function ErrHandler: GetTWetBulbFromHumRatio = CVErr(xlErrNA) End Function Function GetHumRatioFromTWetBulb(ByVal TDryBulb As Variant, ByVal TWetBulb As Variant, ByVal Pressure As Variant) As Variant ' ' Return humidity ratio given dry-bulb temperature, wet-bulb temperature, and pressure. ' ' Args: ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' TWetBulb : Wet-bulb temperature in °F [IP] or °C [SI] ' Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] ' ' Returns: ' Humidity ratio in lb_H2O/lb_Air [IP] or kg_H2O/kg_Air [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 33 and 35 Dim Wsstar As Variant, HumRatio As Variant Wsstar = GetSatHumRatio(TWetBulb, Pressure) On Error GoTo ErrHandler If TWetBulb > TDryBulb Then MyMsgBox ("Wet bulb temperature is above dry bulb temperature") GoTo ErrHandler End If If isIP() Then If (TWetBulb >= FREEZING_POINT_WATER_IP) Then HumRatio = ((1093 - 0.556 * TWetBulb) * Wsstar - 0.24 * (TDryBulb - TWetBulb)) / (1093 + 0.444 * TDryBulb - TWetBulb) Else HumRatio = ((1220 - 0.04 * TWetBulb) * Wsstar - 0.24 * (TDryBulb - TWetBulb)) / (1220 + 0.444 * TDryBulb - 0.48 * TWetBulb) End If Else If (TWetBulb >= FREEZING_POINT_WATER_SI) Then HumRatio = ((2501 - 2.326 * TWetBulb) * Wsstar - 1.006 * (TDryBulb - TWetBulb)) / (2501 + 1.86 * TDryBulb - 4.186 * TWetBulb) Else HumRatio = ((2830 - 0.24 * TWetBulb) * Wsstar - 1.006 * (TDryBulb - TWetBulb)) / (2830 + 1.86 * TDryBulb - 2.1 * TWetBulb) End If End If ' Validity check. GetHumRatioFromTWetBulb = max(HumRatio, MIN_HUM_RATIO) Exit Function ErrHandler: GetHumRatioFromTWetBulb = CVErr(xlErrNA) End Function Function GetHumRatioFromRelHum(ByVal TDryBulb As Variant, ByVal RelHum As Variant, ByVal Pressure As Variant) As Variant ' ' Return humidity ratio given dry-bulb temperature, relative humidity, and pressure. ' ' Args: ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' RelHum : Relative humidity in range [0, 1] ' Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] ' ' Returns: ' Humidity ratio in lb_H2O/lb_Air [IP] or kg_H2O/kg_Air [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 ' Dim VapPres As Variant On Error GoTo ErrHandler If RelHum < 0 Or RelHum > 1 Then MyMsgBox ("Relative humidity is outside range [0, 1]") GoTo ErrHandler End If VapPres = GetVapPresFromRelHum(TDryBulb, RelHum) GetHumRatioFromRelHum = GetHumRatioFromVapPres(VapPres, Pressure) Exit Function ErrHandler: GetHumRatioFromRelHum = CVErr(xlErrNA) End Function Function GetRelHumFromHumRatio(ByVal TDryBulb As Variant, ByVal HumRatio As Variant, ByVal Pressure As Variant) As Variant ' ' Return relative humidity given dry-bulb temperature, humidity ratio, and pressure. ' ' Args: ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' HumRatio : Humidity ratio in lb_H2O/lb_Air [IP] or kg_H2O/kg_Air [SI] ' Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] ' ' Returns: ' Relative humidity in range [0, 1] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 ' Dim VapPres As Variant On Error GoTo ErrHandler If HumRatio < 0 Then MyMsgBox ("Humidity ratio is negative") GoTo ErrHandler End If VapPres = GetVapPresFromHumRatio(HumRatio, Pressure) GetRelHumFromHumRatio = GetRelHumFromVapPres(TDryBulb, VapPres) Exit Function ErrHandler: GetRelHumFromHumRatio = CVErr(xlErrNA) End Function Function GetHumRatioFromTDewPoint(ByVal TDewPoint As Variant, ByVal Pressure As Variant) As Variant ' ' Return humidity ratio given dew-point temperature and pressure. ' ' Args: ' TDewPoint : Dew-point temperature in °F [IP] or °C [SI] ' Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] ' ' Returns: ' Humidity ratio in lb_H2O/lb_Air [IP] or kg_H2O/kg_Air [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 13 ' Dim VapPres As Variant On Error GoTo ErrHandler VapPres = GetSatVapPres(TDewPoint) GetHumRatioFromTDewPoint = GetHumRatioFromVapPres(VapPres, Pressure) Exit Function ErrHandler: GetHumRatioFromTDewPoint = CVErr(xlErrNA) End Function Function GetTDewPointFromHumRatio(ByVal TDryBulb As Variant, ByVal HumRatio As Variant, ByVal Pressure As Variant) As Variant ' ' Return dew-point temperature given dry-bulb temperature, humidity ratio, and pressure. ' ' Args: ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' HumRatio : Humidity ratio in lb_H2O/lb_Air [IP] or kg_H2O/kg_Air [SI] ' Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] ' ' Returns: ' Dew-point temperature in °F [IP] or °C [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 ' Dim VapPres As Variant On Error GoTo ErrHandler If HumRatio < 0 Then MyMsgBox ("Humidity ratio is negative") GoTo ErrHandler End If VapPres = GetVapPresFromHumRatio(HumRatio, Pressure) GetTDewPointFromHumRatio = GetTDewPointFromVapPres(TDryBulb, VapPres) Exit Function ErrHandler: GetTDewPointFromHumRatio = CVErr(xlErrNA) End Function '****************************************************************************************************** ' Conversions between humidity ratio and vapor pressure '****************************************************************************************************** Function GetHumRatioFromVapPres(ByVal VapPres As Variant, ByVal Pressure As Variant) As Variant ' ' Return humidity ratio given water vapor pressure and atmospheric pressure. ' ' Args: ' VapPres : Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] ' Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] ' ' Returns: ' Humidity ratio in lb_H2O/lb_Air [IP] or kg_H2O/kg_Air [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 20 ' Dim HumRatio As Variant On Error GoTo ErrHandler If VapPres < 0 Then MyMsgBox ("Partial pressure of water vapor in moist air is negative") GoTo ErrHandler End If HumRatio = 0.621945 * VapPres / (Pressure - VapPres) ' Validity check. GetHumRatioFromVapPres = max(HumRatio, MIN_HUM_RATIO) Exit Function ErrHandler: GetHumRatioFromVapPres = CVErr(xlErrNA) End Function Function GetVapPresFromHumRatio(ByVal HumRatio As Variant, ByVal Pressure As Variant) As Variant ' ' Return vapor pressure given humidity ratio and pressure. ' ' Args: ' HumRatio : Humidity ratio in lb_H2O/lb_Air [IP] or kg_H2O/kg_Air [SI] ' Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] ' ' Returns: ' Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 20 solved for pw ' Dim VapPres As Variant, BoundedHumRatio As Variant On Error GoTo ErrHandler If HumRatio < 0 Then MyMsgBox ("Humidity ratio is negative") GoTo ErrHandler End If BoundedHumRatio = max(HumRatio, MIN_HUM_RATIO) VapPres = Pressure * BoundedHumRatio / (0.621945 + BoundedHumRatio) GetVapPresFromHumRatio = VapPres Exit Function ErrHandler: GetVapPresFromHumRatio = CVErr(xlErrNA) End Function '****************************************************************************************************** ' Conversions between humidity ratio and specific humidity '****************************************************************************************************** Function GetSpecificHumFromHumRatio(ByVal HumRatio As Variant) As Variant ' ' Return the specific humidity from humidity ratio (aka mixing ratio). ' ' Args: ' HumRatio : Humidity ratio in lb_H₂O lb_Dry_Air⁻¹ [IP] or kg_H₂O kg_Dry_Air⁻¹ [SI] ' ' Returns: ' Specific humidity in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 9b ' ' Dim SpecificHum As Variant On Error GoTo ErrHandler If (HumRatio < 0) Then MyMsgBox ("Humidity ratio is negative") GoTo ErrHandler End If SpecificHum = HumRatio / (1.0 + HumRatio) GetSpecificHumFromHumRatio = SpecificHum Exit Function ErrHandler: GetSpecificHumFromHumRatio = CVErr(xlErrNA) End Function Function GetHumRatioFromSpecificHum(ByVal SpecificHum As Variant) As Variant ' ' Return the humidity ratio (aka mixing ratio) from specific humidity. ' ' Args: ' SpecificHum : Specific Humidity in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] ' ' Returns: ' Humidity ratio in lb_H₂O lb_Dry_Air⁻¹ [IP] or kg_H₂O kg_Dry_Air⁻¹ [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 9b (solved for humidity ratio) ' ' Dim HumRatio as Variant On Error GoTo ErrHandler If (SpecificHum < 0 Or SpecificHum >= 1) Then MyMsgBox ("Specific humidity is outside range [0, 1[") GoTo ErrHandler End If HumRatio = SpecificHum / (1.0 - SpecificHum) GetHumRatioFromSpecificHum = max(HumRatio, MIN_HUM_RATIO) Exit Function ErrHandler: GetHumRatioFromSpecificHum = CVErr(xlErrNA) End Function '****************************************************************************************************** ' Dry Air Calculations '****************************************************************************************************** Function GetDryAirEnthalpy(ByVal TDryBulb As Variant) As Variant ' ' Return dry-air enthalpy given dry-bulb temperature. ' ' Args: ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' ' Returns: ' Dry air enthalpy in Btu/lb [IP] or J/kg [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 28 ' On Error GoTo ErrHandler If (isIP()) Then GetDryAirEnthalpy = 0.24 * TDryBulb Else GetDryAirEnthalpy = 1006 * TDryBulb End If Exit Function ErrHandler: GetDryAirEnthalpy = CVErr(xlErrNA) End Function Function GetDryAirDensity(ByVal TDryBulb As Variant, ByVal Pressure As Variant) As Variant ' ' Return dry-air density given dry-bulb temperature and pressure. ' ' Args: ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] ' ' Returns: ' Dry air density in lb/ft³ [IP] or kg/m³ [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 ' ' Notes: ' Eqn 14 for the perfect gas relationship for dry air. ' Eqn 1 for the universal gas constant. ' The factor 144 in IP is for the conversion of Psi = lb/in² to lb/ft². ' On Error GoTo ErrHandler If (isIP()) Then GetDryAirDensity = (144 * Pressure) / R_DA_IP / GetTRankineFromTFahrenheit(TDryBulb) Else GetDryAirDensity = Pressure / R_DA_SI / GetTKelvinFromTCelsius(TDryBulb) End If Exit Function ErrHandler: GetDryAirDensity = CVErr(xlErrNA) End Function Function GetDryAirVolume(ByVal TDryBulb As Variant, ByVal Pressure As Variant) As Variant ' ' Return dry-air volume given dry-bulb temperature and pressure. ' ' Args: ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] ' ' Returns: ' Dry air volume in ft³/lb [IP] or in m³/kg [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 ' ' Notes: ' Eqn 14 for the perfect gas relationship for dry air. ' Eqn 1 for the universal gas constant. ' The factor 144 in IP is for the conversion of Psi = lb/in² to lb/ft². ' On Error GoTo ErrHandler If (isIP()) Then GetDryAirVolume = GetTRankineFromTFahrenheit(TDryBulb) * R_DA_IP / (144 * Pressure) Else: GetDryAirVolume = GetTKelvinFromTCelsius(TDryBulb) * R_DA_SI / Pressure End If Exit Function ErrHandler: GetDryAirVolume = CVErr(xlErrNA) End Function Function GetTDryBulbFromEnthalpyAndHumRatio(ByVal MoistAirEnthalpy As Variant, ByVal HumRatio As Variant) As Variant ' ' Return dry bulb temperature from enthalpy and humidity ratio. ' ' ' Args: ' MoistAirEnthalpy : Moist air enthalpy in Btu lb⁻¹ [IP] or J kg⁻¹ ' HumRatio : Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] ' ' Returns: ' Dry-bulb temperature in °F [IP] or °C [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 30 ' ' Notes: ' Based on the GetMoistAirEnthalpy function, rearranged for temperature. ' On Error GoTo ErrHandler If HumRatio < 0 Then MyMsgBox ("Humidity ratio is negative") GoTo ErrHandler End If If (isIP()) Then GetTDryBulbFromEnthalpyAndHumRatio = (MoistAirEnthalpy - 1061.0 * HumRatio) / (0.24 + 0.444 * HumRatio) Else: GetTDryBulbFromEnthalpyAndHumRatio = (MoistAirEnthalpy / 1000.0 - 2501.0 * HumRatio) / (1.006 + 1.86 * HumRatio) End If Exit Function ErrHandler: GetTDryBulbFromEnthalpyAndHumRatio = CVErr(xlErrNA) End Function Function GetHumRatioFromEnthalpyAndTDryBulb(ByVal MoistAirEnthalpy As Variant, ByVal TDryBulb As Variant) As Variant ' ' Return humidity ratio from enthalpy and dry-bulb temperature. ' ' ' Args: ' MoistAirEnthalpy : Moist air enthalpy in Btu lb⁻¹ [IP] or J kg⁻¹ ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' ' Returns: ' Humidity ratio in lb_H₂O lb_Air⁻¹ [IP] or kg_H₂O kg_Air⁻¹ [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 30 ' ' Notes: ' Based on the GetMoistAirEnthalpy function, rearranged for humidity ratio. ' On Error GoTo ErrHandler If (isIP()) Then GetHumRatioFromEnthalpyAndTDryBulb = (MoistAirEnthalpy - 0.24 * TDryBulb) / (1061.0 + 0.444 * TDryBulb) Else: GetHumRatioFromEnthalpyAndTDryBulb = (MoistAirEnthalpy / 1000.0 - 1.006 * TDryBulb) / (2501.0 + 1.86 * TDryBulb) End If Exit Function ErrHandler: GetHumRatioFromEnthalpyAndTDryBulb = CVErr(xlErrNA) End Function '****************************************************************************************************** ' Saturated Air Calculations '****************************************************************************************************** Function GetSatVapPres(ByVal TDryBulb As Variant) As Variant ' ' Return saturation vapor pressure given dry-bulb temperature. ' ' Args: ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' ' Returns: ' Vapor pressure of saturated air in Psi [IP] or Pa [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 5 & 6 ' Important note: the ASHRAE formulae are defined above and below the freezing point but have ' a discontinuity at the freezing point. This is a small inaccuracy on ASHRAE's part: the formulae ' should be defined above and below the triple point of water (not the feezing point) in which case ' the discontinuity vanishes. It is essential to use the triple point of water otherwise function ' GetTDewPointFromVapPres, which inverts the present function, does not converge properly around ' the freezing point. ' Dim LnPws As Variant, T As Variant On Error GoTo ErrHandler If (isIP()) Then If (TDryBulb < -148 Or TDryBulb > 392) Then MyMsgBox ("Dry bulb temperature is outside range [-148, 392] °F") GoTo ErrHandler End If T = GetTRankineFromTFahrenheit(TDryBulb) If (TDryBulb <= TRIPLE_POINT_WATER_IP) Then LnPws = (-10214.165 / T - 4.8932428 - 0.0053765794 * T + 0.00000019202377 * T ^ 2 _ + 3.5575832E-10 * T ^ 3 - 9.0344688E-14 * T ^ 4 + 4.1635019 * Log(T)) Else LnPws = -10440.397 / T - 11.29465 - 0.027022355 * T + 0.00001289036 * T ^ 2 _ - 2.4780681E-09 * T ^ 3 + 6.5459673 * Log(T) End If Else If (TDryBulb < -100 Or TDryBulb > 200) Then MyMsgBox ("Dry bulb temperature is outside range [-100, 200] °C") GoTo ErrHandler End If T = GetTKelvinFromTCelsius(TDryBulb) If (TDryBulb <= TRIPLE_POINT_WATER_SI) Then LnPws = -5674.5359 / T + 6.3925247 - 0.009677843 * T + 0.00000062215701 * T ^ 2 _ + 2.0747825E-09 * T ^ 3 - 9.484024E-13 * T ^ 4 + 4.1635019 * Log(T) Else LnPws = -5800.2206 / T + 1.3914993 - 0.048640239 * T + 0.000041764768 * T ^ 2 _ - 0.000000014452093 * T ^ 3 + 6.5459673 * Log(T) End If End If GetSatVapPres = Exp(LnPws) Exit Function ErrHandler: GetSatVapPres = CVErr(xlErrNA) End Function Function GetSatHumRatio(ByVal TDryBulb As Variant, ByVal Pressure As Variant) As Variant ' ' Return humidity ratio of saturated air given dry-bulb temperature and pressure. ' ' Args: ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] ' ' Returns: ' Humidity ratio of saturated air in lb_H2O/lb_Air [IP] or kg_H2O/kg_Air [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 36, solved for W ' Dim SatVaporPres As Variant, SatHumRatio As Variant On Error GoTo ErrHandler SatVaporPres = GetSatVapPres(TDryBulb) SatHumRatio = 0.621945 * SatVaporPres / (Pressure - SatVaporPres) GetSatHumRatio = max(SatHumRatio, MIN_HUM_RATIO) Exit Function ErrHandler: GetSatHumRatio = CVErr(xlErrNA) End Function Function GetSatAirEnthalpy(ByVal TDryBulb As Variant, ByVal Pressure As Variant) As Variant ' ' Return saturated air enthalpy given dry-bulb temperature and pressure. ' ' Args: ' TDryBulb: Dry-bulb temperature in °F [IP] or °C [SI] ' Pressure: Atmospheric pressure in Psi [IP] or Pa [SI] ' ' Returns: ' Saturated air enthalpy in Btu/lb [IP] or J/kg [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 ' On Error GoTo ErrHandler GetSatAirEnthalpy = GetMoistAirEnthalpy(TDryBulb, GetSatHumRatio(TDryBulb, Pressure)) Exit Function ErrHandler: GetSatAirEnthalpy = CVErr(xlErrNA) End Function '****************************************************************************************************** ' Moist Air Calculations '****************************************************************************************************** Function GetVaporPressureDeficit(ByVal TDryBulb As Variant, ByVal HumRatio As Variant, ByVal Pressure As Variant) As Variant ' ' Return Vapor pressure deficit given dry-bulb temperature, humidity ratio, and pressure. ' ' Args: ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' HumRatio : Humidity ratio in lb_H2O/lb_Air [IP] or kg_H2O/kg_Air [SI] ' Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] ' ' Returns: ' Vapor pressure deficit in Psi [IP] or Pa [SI] ' ' Reference: ' Oke (1987) eqn 2.13a ' Dim RelHum As Variant On Error GoTo ErrHandler If HumRatio < 0 Then MyMsgBox ("Humidity ratio is negative") GoTo ErrHandler End If RelHum = GetRelHumFromHumRatio(TDryBulb, HumRatio, Pressure) GetVaporPressureDeficit = GetSatVapPres(TDryBulb) * (1 - RelHum) Exit Function ErrHandler: GetVaporPressureDeficit = CVErr(xlErrNA) End Function Function GetDegreeOfSaturation(ByVal TDryBulb As Variant, ByVal HumRatio As Variant, ByVal Pressure As Variant) As Variant ' ' Return the degree of saturation (i.e humidity ratio of the air / humidity ratio of the air at saturation ' at the same temperature and pressure) given dry-bulb temperature, humidity ratio, and atmospheric pressure. ' ' Args: ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' HumRatio : Humidity ratio in lb_H2O/lb_Air [IP] or kg_H2O/kg_Air [SI] ' Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] ' ' Returns: ' Degree of saturation in arbitrary unit ' ' Reference: ' ASHRAE Handbook - Fundamentals (2009) ch. 1 eqn 12 ' ' Notes: ' This definition is absent from the 2017 Handbook. Using 2009 version instead. ' Dim BoundedHumRatio As Variant On Error GoTo ErrHandler If HumRatio < 0 Then MyMsgBox ("Humidity ratio is negative") GoTo ErrHandler End If BoundedHumRatio = max(HumRatio, MIN_HUM_RATIO) GetDegreeOfSaturation = BoundedHumRatio / GetSatHumRatio(TDryBulb, Pressure) Exit Function ErrHandler: GetDegreeOfSaturation = CVErr(xlErrNA) End Function Function GetMoistAirEnthalpy(ByVal TDryBulb As Variant, ByVal HumRatio As Variant) As Variant ' ' Return moist air enthalpy given dry-bulb temperature and humidity ratio. ' ' Args: ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' HumRatio : Humidity ratio in lb_H2O/lb_Air [IP] or kg_H2O/kg_Air [SI] ' ' Returns: ' Moist air enthalpy in Btu/lb [IP] or J/kg ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 30 ' Dim BoundedHumRatio As Variant On Error GoTo ErrHandler If (HumRatio < 0) Then MyMsgBox ("Humidity ratio is negative") GoTo ErrHandler End If BoundedHumRatio = max(HumRatio, MIN_HUM_RATIO) If (isIP()) Then GetMoistAirEnthalpy = 0.24 * TDryBulb + BoundedHumRatio * (1061 + 0.444 * TDryBulb) Else GetMoistAirEnthalpy = (1.006 * TDryBulb + BoundedHumRatio * (2501 + 1.86 * TDryBulb)) * 1000 End If Exit Function ErrHandler: GetMoistAirEnthalpy = CVErr(xlErrNA) End Function Function GetMoistAirVolume(ByVal TDryBulb As Variant, ByVal HumRatio As Variant, ByVal Pressure As Variant) As Variant ' ' Return moist air specific volume given dry-bulb temperature, humidity ratio, and pressure. ' ' Args: ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' HumRatio : Humidity ratio in lb_H2O/lb_Air [IP] or kg_H2O/kg_Air [SI] ' Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] ' ' Returns: ' Specific volume of moist air in ft³/lb of dry air [IP] or in m³/kg of dry air [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 26 ' ' Notes: ' In IP units, R_DA_IP / 144 equals 0.370486 which is the coefficient appearing in eqn 26 ' The factor 144 is for the conversion of Psi = lb/in² to lb/ft². ' Dim BoundedHumRatio As Variant On Error GoTo ErrHandler If (HumRatio < 0) Then MyMsgBox ("Humidity ratio is negative") GoTo ErrHandler End If BoundedHumRatio = max(HumRatio, MIN_HUM_RATIO) If (isIP()) Then GetMoistAirVolume = R_DA_IP * GetTRankineFromTFahrenheit(TDryBulb) * (1 + 1.607858 * BoundedHumRatio) / (144 * Pressure) Else GetMoistAirVolume = R_DA_SI * GetTKelvinFromTCelsius(TDryBulb) * (1 + 1.607858 * BoundedHumRatio) / Pressure End If Exit Function ErrHandler: GetMoistAirVolume = CVErr(xlErrNA) End Function Function GetTDryBulbFromMoistAirVolumeAndHumRatio(ByVal MoistAirVolume As Variant, ByVal HumRatio As Variant, ByVal Pressure As Variant) As Variant ' ' Return dry-bulb temperature given moist air specific volume, humidity ratio, and pressure. ' ' Args: ' MoistAirVolume: Specific volume of moist air in ft³ lb⁻¹ of dry air [IP] or in m³ kg⁻¹ of dry air [SI] ' HumRatio : Humidity ratio in lb_H2O/lb_Air [IP] or kg_H2O/kg_Air [SI] ' Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] ' ' Returns: ' Specific volume of moist air in ft³/lb of dry air [IP] or in m³/kg of dry air [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 26 ' ' Notes: ' In IP units, R_DA_IP / 144 equals 0.370486 which is the coefficient appearing in eqn 26 ' The factor 144 is for the conversion of Psi = lb/in² to lb/ft². ' Based on the GetMoistAirVolume function, rearranged for dry-bulb temperature. ' Dim BoundedHumRatio As Variant On Error GoTo ErrHandler If (HumRatio < 0) Then MyMsgBox ("Humidity ratio is negative") GoTo ErrHandler End If BoundedHumRatio = max(HumRatio, MIN_HUM_RATIO) If (isIP()) Then GetTDryBulbFromMoistAirVolumeAndHumRatio = GetTFahrenheitFromTRankine(MoistAirVolume * (144 * Pressure) / (R_DA_IP * (1 + 1.607858 * BoundedHumRatio))) Else GetTDryBulbFromMoistAirVolumeAndHumRatio = GetTCelsiusFromTKelvin(MoistAirVolume * Pressure / (R_DA_SI * (1 + 1.607858 * BoundedHumRatio))) End If Exit Function ErrHandler: GetTDryBulbFromMoistAirVolumeAndHumRatio = CVErr(xlErrNA) End Function Function GetMoistAirDensity(ByVal TDryBulb As Variant, ByVal HumRatio As Variant, ByVal Pressure As Variant) As Variant ' ' Return moist air density given humidity ratio, dry bulb temperature, and pressure. ' ' Args: ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' HumRatio : Humidity ratio in lb_H2O/lb_Air [IP] or kg_H2O/kg_Air [SI] ' Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] ' ' Returns: ' MoistAirDensity: Moist air density in lb/ft³ [IP] or kg/m³ [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 11 ' Dim MoistAirVolume As Variant, BoundedHumRatio As Variant On Error GoTo ErrHandler If (HumRatio < 0) Then MyMsgBox ("Humidity ratio is negative") GoTo ErrHandler End If BoundedHumRatio = max(HumRatio, MIN_HUM_RATIO) MoistAirVolume = GetMoistAirVolume(TDryBulb, BoundedHumRatio, Pressure) GetMoistAirDensity = (1 + BoundedHumRatio) / MoistAirVolume Exit Function ErrHandler: GetMoistAirDensity = CVErr(xlErrNA) End Function '****************************************************************************************************** ' Standard atmosphere '****************************************************************************************************** Function GetStandardAtmPressure(ByVal Altitude As Variant) As Variant ' ' Return standard atmosphere barometric pressure, given the elevation (altitude). ' ' Args: ' Altitude: Altitude in ft [IP] or m [SI] ' ' Returns: ' Standard atmosphere barometric pressure in Psi [IP] or Pa [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 3 ' On Error GoTo ErrHandler If (isIP()) Then GetStandardAtmPressure = 14.696 * (1 - 0.0000068754 * Altitude) ^ 5.2559 Else GetStandardAtmPressure = 101325 * (1 - 0.0000225577 * Altitude) ^ 5.2559 End If Exit Function ErrHandler: GetStandardAtmPressure = CVErr(xlErrNA) End Function Function GetStandardAtmTemperature(ByVal Altitude As Variant) As Variant ' ' Return standard atmosphere temperature, given the elevation (altitude). ' ' Args: ' Altitude: Altitude in ft ' ' Returns: ' Standard atmosphere dry-bulb temperature in °F [IP] or °C [SI] ' ' Reference: ' ASHRAE Handbook - Fundamentals (2017) ch. 1 eqn 4 ' On Error GoTo ErrHandler If (isIP()) Then GetStandardAtmTemperature = 59 - 0.0035662 * Altitude Else GetStandardAtmTemperature = 15 - 0.0065 * Altitude End If Exit Function ErrHandler: GetStandardAtmTemperature = CVErr(xlErrNA) End Function Function GetSeaLevelPressure(ByVal StationPressure As Variant, ByVal Altitude As Variant, ByVal TDryBulb As Variant) As Variant ' ' Return sea level pressure given dry-bulb temperature, altitude above sea level and pressure. ' ' Args: ' StationPressure : Observed station pressure in Psi [IP] or Pa [SI] ' Altitude: Altitude in ft [IP] or m [SI] ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' ' Returns: ' Sea level barometric pressure in Psi [IP] or Pa [SI] ' ' Reference: ' Hess SL, Introduction to theoretical meteorology, Holt Rinehart and Winston, NY 1959, ' ch. 6.5; Stull RB, Meteorology for scientists and engineers, 2nd edition, ' Brooks/Cole 2000, ch. 1. ' ' Notes: ' The standard procedure for the US is to use for TDryBulb the average ' of the current station temperature and the station temperature from 12 hours ago. ' ' Calculate average temperature in column of air, assuming a lapse rate ' of 6.5 °C/km Dim TColumn As Variant Dim H As Variant On Error GoTo ErrHandler If (isIP()) Then ' Calculate average temperature in column of air, assuming a lapse rate ' of 3.6 °F/1000ft TColumn = TDryBulb + 0.0036 * Altitude / 2 ' Determine the scale height H = 53.351 * GetTRankineFromTFahrenheit(TColumn) Else ' Calculate average temperature in column of air, assuming a lapse rate ' of 6.5 °C/km TColumn = TDryBulb + 0.0065 * Altitude / 2 ' Determine the scale height H = 287.055 * GetTKelvinFromTCelsius(TColumn) / 9.807 End If ' Calculate the sea level pressure GetSeaLevelPressure = StationPressure * Exp(Altitude / H) Exit Function ErrHandler: GetSeaLevelPressure = CVErr(xlErrNA) End Function Function GetStationPressure(ByVal SeaLevelPressure As Variant, ByVal Altitude As Variant, ByVal TDryBulb As Variant) As Variant ' ' Args: ' SeaLevelPressure : Sea level barometric pressure in Psi [IP] or Pa [SI] ' Altitude: Altitude in ft [IP] or m [SI] ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' ' Returns: ' Station pressure in Psi [IP] or Pa [SI] ' ' Reference: ' See 'GetSeaLevelPressure' ' ' Notes: ' This function is just the inverse of 'GetSeaLevelPressure'. ' On Error GoTo ErrHandler GetStationPressure = SeaLevelPressure / GetSeaLevelPressure(1, Altitude, TDryBulb) Exit Function ErrHandler: GetStationPressure = CVErr(xlErrNA) End Function '****************************************************************************************************** ' Functions to set all psychrometric values '****************************************************************************************************** Sub CalcPsychrometricsFromTWetBulb(ByVal TDryBulb As Variant, ByVal TWetBulb As Variant, ByVal Pressure As Variant, _ ByRef HumRatio As Variant, ByRef TDewPoint As Variant, ByRef RelHum As Variant, ByRef VapPres As Variant, _ ByRef MoistAirEnthalpy As Variant, ByRef MoistAirVolume As Variant, ByRef DegreeOfSaturation As Variant) ' ' Utility function to calculate humidity ratio, dew-point temperature, relative humidity, ' vapour pressure, moist air enthalpy, moist air volume, and degree of saturation of air given ' dry-bulb temperature, wet-bulb temperature, and pressure. ' ' Args: ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' TWetBulb : Wet-bulb temperature in °F [IP] or °C [SI] ' Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] ' ' Returns: ' Humidity ratio in lb_H2O/lb_Air [IP] or kg_H2O/kg_Air [SI] ' Dew-point temperature in °F [IP] or °C [SI] ' Relative humidity in range [0, 1] ' Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] ' Moist air enthalpy in Btu/lb [IP] or J/kg [SI] ' Specific volume of moist air in ft³/lb [IP] or in m³/kg [SI] ' Degree of saturation [unitless] ' HumRatio = GetHumRatioFromTWetBulb(TDryBulb, TWetBulb, Pressure) TDewPoint = GetTDewPointFromHumRatio(TDryBulb, HumRatio, Pressure) RelHum = GetRelHumFromHumRatio(TDryBulb, HumRatio, Pressure) VapPres = GetVapPresFromHumRatio(HumRatio, Pressure) MoistAirEnthalpy = GetMoistAirEnthalpy(TDryBulb, HumRatio) MoistAirVolume = GetMoistAirVolume(TDryBulb, HumRatio, Pressure) DegreeOfSaturation = GetDegreeOfSaturation(TDryBulb, HumRatio, Pressure) End Sub Sub CalcPsychrometricsFromTDewPoint(ByVal TDryBulb As Variant, ByVal TDewPoint As Variant, ByVal Pressure As Variant, _ ByRef HumRatio As Variant, ByRef TWetBulb As Variant, ByRef RelHum As Variant, ByRef VapPres As Variant, _ ByRef MoistAirEnthalpy As Variant, ByRef MoistAirVolume As Variant, ByRef DegreeOfSaturation As Variant) ' ' Utility function to calculate humidity ratio, wet-bulb temperature, relative humidity, ' vapour pressure, moist air enthalpy, moist air volume, and degree of saturation of air given ' dry-bulb temperature, dew-point temperature, and pressure. ' ' Args: ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' TDewPoint : Dew-point temperature in °F [IP] or °C [SI] ' Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] ' ' Returns: ' Humidity ratio in lb_H2O/lb_Air [IP] or kg_H2O/kg_Air [SI] ' Wet-bulb temperature in °F [IP] or °C [SI] ' Relative humidity in range [0, 1] ' Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] ' Moist air enthalpy in Btu/lb [IP] or J/kg [SI] ' Specific volume of moist air in ft³/lb [IP] or in m³/kg [SI] ' Degree of saturation [unitless] ' HumRatio = GetHumRatioFromTDewPoint(TDewPoint, Pressure) TWetBulb = GetTWetBulbFromHumRatio(TDryBulb, HumRatio, Pressure) RelHum = GetRelHumFromHumRatio(TDryBulb, HumRatio, Pressure) VapPres = GetVapPresFromHumRatio(HumRatio, Pressure) MoistAirEnthalpy = GetMoistAirEnthalpy(TDryBulb, HumRatio) MoistAirVolume = GetMoistAirVolume(TDryBulb, HumRatio, Pressure) DegreeOfSaturation = GetDegreeOfSaturation(TDryBulb, HumRatio, Pressure) End Sub Sub CalcPsychrometricsFromRelHum(ByVal TDryBulb As Variant, ByVal RelHum As Variant, ByVal Pressure As Variant, _ ByRef HumRatio As Variant, ByRef TWetBulb As Variant, ByRef TDewPoint As Variant, ByRef VapPres As Variant, _ ByRef MoistAirEnthalpy As Variant, ByRef MoistAirVolume As Variant, ByRef DegreeOfSaturation As Variant) ' ' Utility function to calculate humidity ratio, wet-bulb temperature, dew-point temperature, ' vapour pressure, moist air enthalpy, moist air volume, and degree of saturation of air given ' dry-bulb temperature, relative humidity and pressure. ' ' Args: ' TDryBulb : Dry-bulb temperature in °F [IP] or °C [SI] ' RelHum : Relative humidity in range [0, 1] ' Pressure : Atmospheric pressure in Psi [IP] or Pa [SI] ' ' Returns: ' Humidity ratio in lb_H2O/lb_Air [IP] or kg_H2O/kg_Air [SI] ' Wet-bulb temperature in °F [IP] or °C [SI] ' Dew-point temperature in °F [IP] or °C [SI]. ' Partial pressure of water vapor in moist air in Psi [IP] or Pa [SI] ' Moist air enthalpy in Btu/lb [IP] or J/kg [SI] ' Specific volume of moist air in ft³/lb [IP] or in m³/kg [SI] ' Degree of saturation [unitless] ' HumRatio = GetHumRatioFromRelHum(TDryBulb, RelHum, Pressure) TWetBulb = GetTWetBulbFromHumRatio(TDryBulb, HumRatio, Pressure) TDewPoint = GetTDewPointFromHumRatio(TDryBulb, HumRatio, Pressure) VapPres = GetVapPresFromHumRatio(HumRatio, Pressure) MoistAirEnthalpy = GetMoistAirEnthalpy(TDryBulb, HumRatio) MoistAirVolume = GetMoistAirVolume(TDryBulb, HumRatio, Pressure) DegreeOfSaturation = GetDegreeOfSaturation(TDryBulb, HumRatio, Pressure) End Sub 

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