Related Resources: fluid flow

### Wet Bulb Temperature Equation

Fluids Engineering

Wet Bulb Temperature Equation

The wet-bulb temperature, Twet, is a common humidity variable (e.g., Schwerdtfeger 1976, p 50ff.). A wetted thermometer will read lower than the ambient air temperature because of evaporation (but higher with condensation), and that rate of evaporation depends on the mixing ratio. At equilibrium, a wellventilated wet-bulb thermometer obeys (Andreas 1995; Bohren and Albrecht 1998, p. 218ff).

(Eq 1)

where:

cp = specific heat of dry air at temperature Ta
Lv = latent heat of vaporization at Ta
r = ambient mixing ratio
rsat = saturation mixing ratio at the wet-bulb temperature.

Rearranging (Eq. 1) shows that the wet-bulb temperature predicts the mixing ratio,

(Eq 2)

And

(Eq 3)

Where:

e = Water vapor pressure
esat = Saturation pressure of water vapor
P = Barometric pressure
Ma = Molecular weight of air (= 28.9644 × 10-3 kg mol-1)
mw = Mass of pure water in a salt or fresh water sample
Ta = Air temperature

which is approximately

(Eq. 4)

That is, the wet-bulb temperature also predicts the vapor pressure. Table 1 shows the vapor pressure computed from (EQ. 4) for a range of Ta and Ta − Twet values.

Equations (Eq 2) and (Eq 4) apply to perfect wet-bulb thermometers. Schwerdtfeger (1976, p. 51f.) and Brock and Richardson (2001, p. 94) describe some second-order corrections that may be necessary to account for ventilation rate, radiative effects, and the size of the wet bulb.

Vapor pressure (e, in mb) from (Eq 4) as a function of the air temperature (Ta) and the wet-bulb depression for wet-bulb temperatures above freezing. The column with Ta − Twet = 0 is also the saturation vapor pressure (esat) at the indicated air temperature; consequently, the ratio of e at Ta − Twet > 0 to esat is the fractional relative humidity (f) at Ta − Twet. The barometric pressure P is assumed to be 1000 mb.

Wet-Bulb Depression, Ta − Twet (°C)
Table 1

 - - - - - - - Wet-Bulb Depression, Ta − Twet (°C) 0.0 0.2 0.4 0.6 0.8 1.0 1.5 2.0 3.0 4.0 5.0 6.0 8.0 10.0 Ta (°C) 0 6.1 - - - - - - - - - - - - - 2 7.1 6.9 6.6 6.4 6.2 6.0 5.4 4.8 - - 4 8.2 7.9 7.7 7.4 7.2 7.0 6.4 5.8 4.7 3.5 - - 6 9.4 9.1 8.9 8.6 8.4 8.1 7.5 6.9 5.7 4.5 3.3 2.2 - 8 10.8 10.5 10.2 9.9 9.7 9.4 8.7 8.1 6.8 5.6 4.4 3.2 0.9 - 10 12.3 12.0 11.7 11.4 11.2 10.9 10.2 9.5 8.1 6.8 5.5 4.3 1.9 - 12 14.1 13.8 13.5 13.1 12.8 12.5 11.8 11.0 9.6 8.2 6.8 5.5 2.9 0.5 14 16.0 15.7 15.4 15.0 14.7 14.4 13.6 12.8 11.2 9.7 8.2 6.8 4.1 1.6 16 18.3 17.9 17.5 17.2 16.8 16.5 15.6 14.7 13.1 11.5 9.9 8.4 5.5 2.8 18 20.7 20.3 19.9 19.6 19.2 18.8 17.9 16.9 15.1 13.4 11.7 10.1 7.1 4.2 20 23.5 23.0 22.6 22.2 21.8 21.4 20.4 19.4 17.5 15.6 13.8 12.1 8.8 5.7 22 26.5 26.1 25.6 25.2 24.7 24.3 23.2 22.1 20.1 18.1 16.1 14.3 10.8 7.5 24 30.0 29.5 29.0 28.5 28.0 27.5 26.4 25.2 23.0 20.8 18.7 16.7 13.0 9.4 26 33.7 33.2 32.7 32.2 31.7 31.1 29.9 28.6 26.2 23.9 21.6 19.5 15.4 11.6 28 38.0 37.4 36.8 36.2 35.7 35.1 33.8 32.4 29.8 27.3 24.9 22.6 18.2 14.1 30 42.6 42.0 41.4 40.8 40.2 39.6 38.1 36.6 33.8 31.1 28.5 26.0 21.2 16.8 32 47.8 47.1 46.4 45.8 45.1 44.5 42.9 41.3 38.2 35.3 32.5 29.7 24.6 19.9 34 53.4 52.7 52.0 51.3 50.6 49.9 48.1 46.4 43.1 39.9 36.9 33.9 28.4 23.3 36 59.7 58.9 58.1 57.4 56.6 55.8 53.9 52.1 48.5 45.1 41.8 38.6 32.6 27.1 38 66.6 65.7 64.9 64.0 63.2 62.4 60.4 58.4 54.5 50.8 47.2 43.7 37.2 31.2 40 74.1 73.2 72.3 71.4 70.5 69.6 67.4 65.2 61.0 57.0 53.1 49.4 42.4 35.9