to the dew point temperature at point Q and the line XP, corresponds to the
saturation temperature at point P.
The XY line in Fig. A2.10, represents the adiabatic evaporation curve,
corresponding to the temperature and vapor pressure changes of a given air
sample under adiabatic conditions, i.e. without any heat exchanges with the outside
environment.
The equation relating the temperature of a given air sample at a lower vapor
pressure than the saturation pressure with the equivalent temperature T s in line
segment XZ, is expressed by:
T e ¼ T þ ðe=cÞ
ð A2:62Þ
The corresponding equation, relating a point of the saturation curve with the
corresponding equivalent temperature in line segment YZ is expressed by:
T e ¼ T wet þ e s T wet
ð
Þ=y
ðA2:63Þ
A2.5.2 Empirical Approach
An alternative approach to calculating the relative humidity of air from dry and wet
temperatures using the aspiration psychrometer is based on the application of
successive empirical polynomial equations.
The saturation water vapor pressure in the air, at wet temperature, can be
calculated using the Eq. (A2.64) below:
e s T wet
ð
Þ ¼ 6:209 Ã 10
À5
À
Á
T
3
wet þ 2:188 Ã 10
À4
À
Á
T
2
wet þ 6:319 Ã 10
À2
À
Á
T wet þ 0:524
ðA2:64Þ
As for the relationship between the absolute humidity of the air v, for the wet
T wet and dry T dry temperatures, we have:
v dry ¼ v sTwet À qc p
a
D if
2
3
T dry À T wet
À
Á
L
ðA2:65Þ
where D if is the air mass diffusivity, a the thermal diffusivity, and v sTwet is the
absolute saturation humidity, at the wet temperature.
The v sTwet can be obtained from the following expression:
v STwet ¼ 3:688 Ã 10
À7
À
Á
T
3
wet þ 3:779 Ã 10
À6
À
Á
T
2
wet þ 4:221 Ã 10
À4
À
Á
T wet þ 4:42 Ã 10
À3
À
Á
ðA2:66Þ
All other air properties can be obtained from the average temperature T wet and
T dry (equals to (T wet + T dry )/2) using the Eqs. (A2.67)–(A2.71), described below.
Annex A2: Basic Topics on Laws of Motion and Evaporation
363