Chemistry:Psychrometric constant

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Short description: Relation of the partial pressure of water in air to temperature

The psychrometric constant [math]\displaystyle{ \gamma }[/math] 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]

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

Both [math]\displaystyle{ \lambda_v }[/math] and [math]\displaystyle{ MW_{ratio} }[/math] are constants.
Since atmospheric pressure, P, depends upon altitude, so does [math]\displaystyle{ \gamma }[/math].
At higher altitude water evaporates and boils at lower temperature.

Although [math]\displaystyle{ \left( c_p \right)_{H_2 O} }[/math] is constant, varied air composition results in varied [math]\displaystyle{ \left( c_p \right)_{air} }[/math].

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, [math]\displaystyle{ e_s = e \left[ T_{wet}\right] }[/math]
Actual vapor pressure, [math]\displaystyle{ e_a = e_s - \gamma * \left( T_{dry} - T_{wet} \right) }[/math]

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. http://www.fao.org/docrep/X0490E/x0490e00.HTM. Retrieved 2007-10-08.