#!/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;