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Wet Bulb Temperature Equation

Fluids Engineering

Wet Bulb Temperature Equation

Wet Bulb

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).

Wet Bulb Temperature
(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,

wet-bulb temperature predicts the mixing ratio
(Eq 2)

And

Water vapor pressure
(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

Water vapor pressure
(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


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