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'''
Created on 08/02/2016
@author: mmpe
'''
import numpy as np
def saturated_vapor_pressure(T):
"""Calculate pressure of saturated water vapor at specified temperature as described at
http://wahiduddin.net/calc/density_altitude.htm
Parameters
---------
t : float
Temperature [C]
Returns
-------
float
Pressure [mb]
"""
eso = 6.1078
c0 = 0.99999683
c1 = -0.90826951 * 10 ** -2
c2 = 0.78736169 * 10 ** -4
c3 = -0.61117958 * 10 ** -6
c4 = 0.43884187 * 10 ** -8
c5 = -0.29883885 * 10 ** -10
c6 = 0.21874425 * 10 ** -12
c7 = -0.17892321 * 10 ** -14
c8 = 0.11112018 * 10 ** -16
c9 = -0.30994571 * 10 ** -19
p = (c0 + T * (c1 + T * (c2 + T * (c3 + T * (c4 + T * (c5 + T * (c6 + T * (c7 + T * (c8 + T * (c9))))))))))
return eso / p ** 8
def saturated_vapor_pressure2(t):
"""Calculate pressure of saturated water vapor at specified temperature as described at
http://wahiduddin.net/calc/density_altitude.htm
Parameters
---------
t : float
Temperature [C]
Returns
-------
float
Pressure [mb]
"""
c0 = 6.1078
c1 = 7.5
c2 = 237.3
return c0 * 10 ** ((c1 * t) / (c2 + t))
def saturated_vapor_pressure3(t):
"""Calculate pressure of saturated water vapor at specified temperature according to
The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use
W. Wagner and A. Pruss
J. Phys. Chem. Ref. Data 31, 387 (2002); http://dx.doi.org/10.1063/1.1461829
Parameters
---------
t : float
Temperature [C]
Returns
-------
float
Pressure [mb]
"""
T = t + 273.15
Tc = 647.096
Pc = 220640
v = 1 - T / Tc
C1 = -7.85951783
C2 = 1.84408259
C3 = -11.7866497
C4 = 22.6807411
C5 = -15.9618719
C6 = 1.80122502
return Pc * np.exp(Tc / T * (C1 * v + C2 * v ** 1.5 + C3 * v ** 3 + C4 * v ** 3.5 + C5 * v ** 4 + C6 * v ** 7.5))
def saturated_vapor_pressure4(t):
"""Calculate the saturated vapor pressure as described in
http://www.vaisala.com/Vaisala%20Documents/Application%20notes/Humidity_Conversion_Formulas_B210973EN-F.pdf
Parameters
---------
t : float
Temperature [C]
Returns
-------
Saturated vapor pressure [mBar]
"""
A = 6.116441
m = 7.591386
Tn = 240.7263
return A * 10 ** ((m * t) / (t + Tn))
def saturated_vapor_pressure_IEC(t):
"""Calculate the saturated vapor pressure according to IEC 61400-12-1
Parameters
---------
t : float
Temperature [C]
Returns
-------
Saturated vapor pressure [mBar]
"""
T = t + 273.15
return 0.000000205 * np.exp(0.0631846 * T)
def drew_point(t, RH):
A = 6.116441
m = 7.591386
Tn = 240.7263
Pw = saturated_vapor_pressure4(t) * RH / 100
return Tn / (m / np.log10(Pw / A) - 1)
def air_density(P, t, rh=0, saturated_vapor_pressure_function=saturated_vapor_pressure):
"""Calculate the density of atmospheric air at specified pressure, temperature and humidity
source: http://wahiduddin.net/calc/density_altitude.htm
Equivalent to formulation in IEC61400-12-1 if used with the saturated_vapor_pressure_IEC function
Parameters
---------
P : float
Atmospheric pressure [mb]=[hPa]
t : float
Temperature [C]
rh : float
Relative humidity [%]
saturated_vapor_pressure_function : function
Function, f(t)->P, that takes the temperature in celcius as input and
returns the saturated vapor pressure in mbar
Returns
-------
float
Density of atmospheric air
"""
Pv = saturated_vapor_pressure_function(t) * rh / 100
Pd = P - Pv
Rv = 461.4964
Rd = 287.0531
Tk = t + 273.15
return (Pd * 100 / (Rd * Tk)) + (Pv * 100 / (Rv * Tk))
def R(rh=0, t=15, P=1014):
"""Specific gas constant ~287.058 J/(kg K) for dry air
Parameters
---------
rh : float
Relative humidity [%]
t : float
Temperature [C]
P : float
pressure [hPa]
Returns
-------
Specific gas constant
"""
#assert np.all((900<P)&(P<1100)), "Pressure outside range 900 to 1100"
#assert np.all((-50<t)&(t<100)), "Temperature outside range -50 to 100"
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Tk = t + 273.15
return P * 100 / (air_density(P, t, rh) * Tk)
if __name__ == "__main__":
pass
# #print (air_density(1013, 65, 50))
# #print (drew_point(40, 50))
# import matplotlib.pyplot as plt
# if 0:
# t = np.arange(-20, 50)
# plt.plot(t, saturated_vapor_pressure(t))
# plt.plot(t, saturated_vapor_pressure2(t), "--")
# plt.plot(t, saturated_vapor_pressure3(t), ":")
# plt.show()
#
# if 0:
# t = np.arange(5, 25)
# plt.xlabel("Temperature [C]")
# plt.ylabel("Density [kg/m3]")
# plt.plot(t, air_density(990, t, 50), label='P: 990 hPa')
# plt.plot(t, air_density(1018, t, 50), label='P: 1018 hPa')
# plt.legend()
# plt.show()
#
# p = 1013
# t = 20
# rh = 70
# print (R(p, t, rh) * (t + 273.15))
# print ((p * 100) / air_density(p, t, rh))
#
# print (R(p,10,80))
# print (R(p,100,80))
#
# if 0:
# rh = np.arange(0, 100)
# plt.xlabel("Rh [%]")
# plt.ylabel("R")
# plt.plot(rh, R(990, 20, rh), label='P: 990 hPa, 20 t')
#
# plt.legend()
# plt.show()