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Psychrometric constant

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

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

Although <math> \left( c_p \right)_{H_2 O} </math> is constant, varied air composition results in varied <math> \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>e_s = e \left[ T_{wet}\right]</math>
Actual vapor pressure, <math>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.

See also

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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. 
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