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Psychrometric constant

## Summary

The psychrometric constant ${\displaystyle \gamma }$ relates the partial pressure of water in air to the air temperature. This lets one interpolate actual vapor pressure from paired dry and wet thermometer bulb temperature readings.[1]

${\displaystyle \gamma ={\frac {\left(c_{p}\right)_{air}*P}{\lambda _{v}*MW_{ratio}}}}$
${\displaystyle \gamma =}$ psychrometric constant [kPa °C−1],
P = atmospheric pressure [kPa],
${\displaystyle \lambda _{v}=}$ latent heat of water vaporization, 2.26 [MJ kg−1],
${\displaystyle c_{p}=}$ specific heat of air at constant pressure, [MJ kg−1 °C−1],
${\displaystyle MW_{ratio}=}$ ratio molecular weight of water vapor/dry air = 0.622.

Both ${\displaystyle \lambda _{v}}$ and ${\displaystyle MW_{ratio}}$ are constants.
Since atmospheric pressure, P, depends upon altitude, so does ${\displaystyle \gamma }$.
At higher altitude water evaporates and boils at lower temperature.

Although ${\displaystyle \left(c_{p}\right)_{H_{2}O}}$ is constant, varied air composition results in varied ${\displaystyle \left(c_{p}\right)_{air}}$.

Thus on average, at a given location or altitude, the psychrometric constant is approximately constant. Still, it is worth remembering that weather impacts both atmospheric pressure and composition.

## Vapor Pressure Estimation

Saturated vapor pressure, ${\displaystyle e_{s}=e\left[T_{wet}\right]}$
Actual vapor pressure, ${\displaystyle e_{a}=e_{s}-\gamma *\left(T_{dry}-T_{wet}\right)}$

here e[T] is vapor pressure as a function of temperature, T.
Tdew = the dewpoint temperature at which water condenses.
Twet = the temperature of a wet thermometer bulb from which water can evaporate to air.
Tdry = the temperature of a dry thermometer bulb in air.

## References

1. ^ Allen, R.G.; Pereira, L.S.; Raes, D.; Smith, M. (1998). Crop Evapotranspiration—Guidelines for Computing Crop Water Requirements. FAO Irrigation and drainage paper 56. Rome, Italy: Food and Agriculture Organization of the United Nations. ISBN 92-5-104219-5. Retrieved 2007-10-08.