The psychrometric constant

Victor M. Ponce

11 March 2014



Abstract. The variation of psychrometric constant γ with temperature has been explained and clarified. This should result in increased accuracy in online evaporation calculations.


1.  Bowen ratio

The Bowen ratio is defined as follows (Ponce, 1989):

           Qh                   Ts  -  Ta             p
B  =   ______   =  γ   ____________   ________
           Qe                   es  -  ea          1000
(1)

in which B = Bowen ratio; Qh = sensible heat transfer from water body to the atmosphere by convection and conduction; Qe = energy expended in the evaporation process; Ts = water surface temperature, in °C; Ta = overlying air temperature, in °C; es = saturation vapor pressure at the water surface temperature, in millibars (mb); ea = vapor pressure of the overlying air, in mb; p = atmospheric pressure, in mb; γ = psychrometric constant, in mb °C-1 (Note that 1000 has the units of mb).


2.  The psychrometric constant γ

The psychrometric constant γ is expressed as follows:

            cp p
γ  =  __________ 
            λ rMW
(2)

in which cp = specific heat of air at constant pressure, in cal gr-1 °C-1; p = atmospheric pressure, in mb; λ = latent heat of water vaporization, in cal gr-1; and rMW = ratio of the molecular weight of water vapor to dry air: rMW = 0.622.

The specific heat of air between 0°C and 40°C is: cp = 1.005 J gr-1 °C-1 = 0.24017 cal gr-1 °C-1. The mean sea-level atmospheric pressure is p = 1013.25 mb. Therefore, at sea level, the psychrometric constant is:

              (0.24017) (1013.25)
γ  =  ___________________________
                      λ (0.622)
(3)

which reduces to:

            391.24
γ  =  ___________
                 λ
(4)

with λ in cal gr-1 and γ in mb °C-1.


3.  Variation of γ with temperature

Since λ varies with temperature, γ also varies with temperature. Table 1 shows the variation of the psychrometric constant γ with temperature, at standard sea-level atmospheric pressure (p = 1013.25 mb).

Table 1  Variation of psychrometric constant γ with temperature,
at standard atmospheric pressure.

T
(°C)
λ
(cal gr-1)
γ
(mb °C-1)
0 597.3 0.655
5 594.5 0.658
10 591.7 0.661
15 588.9 0.664
20 586.0 0.668
25 583.2 0.671
30 580.4 0.674
35 577.6 0.677
40 574.7 0.681


4.  Summary

The variation of psychrometric constant γ with temperature has been explained and clarified. This should result in increased accuracy in online evaporation calculations (http://onlinecalc.sdsu.edu)


References

Ponce, V. M. 1989. Engineering Hydrology: Principles and Practices. Prentice Hall, Englewood Cliffs, New Jersey.


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