#!/usr/bin/env python3 # Desc: Humidity conversion functions from EVA-2020-02-2 # Ref/Attrib: https://gitlab.com/baltakatei/ninfacyzga-01 def rel_to_abs(T,P,RH): """Returns absolute humidity given relative humidity. Inputs: -------- T : float Absolute temperature in units Kelvin (K). P : float Total pressure in units Pascals (Pa). RH : float Relative humidity in units percent (%). Output: -------- absolute_humidity : float Absolute humidity in units [kg water vapor / kg dry air]. References: -------- 1. Sonntag, D. "Advancements in the field of hygrometry". 1994. https://doi.org/10.1127/metz/3/1994/51 2. Green, D. "Perry's Chemical Engineers' Handbook" (8th Edition). Page "12-4". McGraw-Hill Professional Publishing. 2007. Version: 0.0.1 Author: Steven Baltakatei Sandoval License: GPLv3+ """ import math; # Check input types T = float(T); P = float(P); RH = float(RH); #debug # print('DEBUG:Input Temperature (K) :' + str(T)); # print('DEBUG:Input Pressure (Pa) :' + str(P)); # print('DEBUG:Input Rel. Humidity (%) :' + str(RH)); # Set constants and initial conversions epsilon = 0.62198 # (molar mass of water vapor) / (molar mass of dry air) t = T - 273.15; # Celsius from Kelvin P_hpa = P / 100; # hectoPascals (hPa) from Pascals (Pa) # Calculate e_w(T), saturation vapor pressure of water in a pure phase, in Pascals ln_e_w = -6096*T**-1 + 21.2409642 - 2.711193*10**-2*T + 1.673952*10**-5*T**2 + 2.433502*math.log(T); # Sonntag-1994 eq 7; e_w in Pascals e_w = math.exp(ln_e_w); e_w_hpa = e_w / 100; # also save e_w in hectoPascals (hPa) # print('DEBUG:ln_e_w:' + str(ln_e_w)); # debug # print('DEBUG:e_w:' + str(e_w)); # debug # Calculate f_w(P,T), enhancement factor for water f_w = 1 + (10**-4*e_w_hpa)/(273 + t)*(((38 + 173*math.exp(-t/43))*(1 - (e_w_hpa / P_hpa))) + ((6.39 + 4.28*math.exp(-t / 107))*((P_hpa / e_w_hpa) - 1))); # Sonntag-1994 eq 22. # print('DEBUG:f_w:' + str(f_w)); # debug # Calculate e_prime_w(P,T), saturation vapor pressure of water in air-water mixture, in Pascals e_prime_w = f_w * e_w; # Sonntag-1994 eq 18 # print('DEBUG:e_prime_w:' + str(e_prime_w)); # debug # Calculate e_prime, vapor pressure of water in air, in Pascals e_prime = (RH / 100) * e_prime_w; # print('DEBUG:e_prime:' + str(e_prime)); # debug # Calculate r, the absolute humidity, in [kg water vapor / kg dry air] r = (epsilon * e_prime) / (P - e_prime); # print('DEBUG:r:' + str(r)); # debug return float(r); def rel_to_dpt(T,P,RH): """Returns dew point temperature given relative humidity. Inputs: -------- T : float Absolute temperature in units Kelvin (K). P : float Total pressure in units Pascals (Pa). RH : float Relative humidity in units percent (%). Output: -------- T_d : float Dew point temperature in units Kelvin (K). References: -------- 1. Sonntag, D. "Advancements in the field of hygrometry". 1994. https://doi.org/10.1127/metz/3/1994/51 2. Green, D. "Perry's Chemical Engineers' Handbook" (8th Edition). Page "12-4". McGraw-Hill Professional Publishing. 2007. Version: 0.0.1 Author: Steven Baltakatei Sandoval License: GPLv3+ """ import math; # Check input types T = float(T); P = float(P); RH = float(RH); #debug # print('DEBUG:Input Temperature (K) :' + str(T)); # print('DEBUG:Input Pressure (Pa) :' + str(P)); # print('DEBUG:Input Rel. Humidity (%) :' + str(RH)); # Set constants and initial conversions epsilon = 0.62198 # (molar mass of water vapor) / (molar mass of dry air) t = T - 273.15; # Celsius from Kelvin P_hpa = P / 100; # hectoPascals (hPa) from Pascals (Pa) # Calculate e_w(T), saturation vapor pressure of water in a pure phase, in Pascals ln_e_w = -6096*T**-1 + 21.2409642 - 2.711193*10**-2*T + 1.673952*10**-5*T**2 + 2.433502*math.log(T); # Sonntag-1994 eq 7; e_w in Pascals e_w = math.exp(ln_e_w); e_w_hpa = e_w / 100; # also save e_w in hectoPascals (hPa) # print('DEBUG:ln_e_w:' + str(ln_e_w)); # debug # print('DEBUG:e_w:' + str(e_w)); # debug # Calculate f_w(P,T), enhancement factor for water f_w = 1 + (10**-4*e_w_hpa)/(273 + t)*(((38 + 173*math.exp(-t/43))*(1 - (e_w_hpa / P_hpa))) + ((6.39 + 4.28*math.exp(-t / 107))*((P_hpa / e_w_hpa) - 1))); # Sonntag-1994 eq 22. # print('DEBUG:f_w:' + str(f_w)); # debug # Calculate e_prime_w(P,T), saturation vapor pressure of water in air-water mixture, in Pascals e_prime_w = f_w * e_w; # Sonntag-1994 eq 18 # print('DEBUG:e_prime_w:' + str(e_prime_w)); # debug # Calculate e_prime, vapor pressure of water in air, in Pascals e_prime = (RH / 100) * e_prime_w; # print('DEBUG:e_prime:' + str(e_prime)); # debug n = 0; repeat_flag = True; while repeat_flag == True: # print('DEBUG:n:' + str(n)); # debug # Calculate f_w_td, the enhancement factor for water at dew point temperature. if n == 0: f = 1.0016 + 3.15*10**-6*P_hpa - (0.074 / P_hpa); # Sonntag-1994 eq 24 f_w_td = f; # initial approximation elif n > 0: t_d_prev = float(t_d); # save previous t_d value for later comparison f_w_td = 1 + (10**-4*e_w_hpa)/(273 + t_d)*(((38 + 173*math.exp(-t_d/43))*(1 - (e_w_hpa / P_hpa))) + ((6.39 + 4.28*math.exp(-t_d / 107))*((P_hpa / e_w_hpa) - 1))); # Sonntag-1994 eq 22. # print('DEBUG:f_w_td:' + str(f_w_td)); # debug # Calculate e, the vapor pressure of water in the pure phase, in Pascals e = (e_prime / f_w_td); # Sonntag-1994 eq 9 and 20 # print('DEBUG:e:' + str(e)); # debug # Calculate y, an intermediate dew point calculation variable y = math.log(e / 611.213); # print('DEBUG:y:' + str(y)); # debug # Calculate t_d, the dew point temperature in degrees Celsius t_d = 13.715*y + 8.4262*10**-1*y**2 + 1.9048*10**-2*y**3 + 7.8158*10**-3*y**4;# Sonntag-1994 eq 10 # print('DEBUG:t_d:' + str(t_d)); # debug if n == 0: # First run repeat_flag = True; else: # Test t_d accuracy t_d_diff = math.fabs(t_d - t_d_prev); # print('DEBUG:t_d :' + str(t_d)); # debug # print('DEBUG:t_d_prev:' + str(t_d_prev)); # debug # print('DEBUG:t_d_diff:' + str(t_d_diff)); # debug if t_d_diff < 0.01: repeat_flag = False; else: repeat_flag = True; # Calculate T_d, the dew point temperature in Kelvin T_d = 273.15 + t_d; # print('DEBUG:T_d:' + str(T_d)); # debug if n > 100: return T_d; # good enough # update loop counter n += 1; return T_d;