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The specific heats for moist air at constant pressure and volume are given by:
Eq. 7
Eq. 8
where, at constant pressure and volume, respectively (Fleagle and Businger 1980):
C
p
and C
v
= specific heat of moist air
C
pw
and C
vw
= specific heat of water vapor
C
pd
and C
vd
= specific heat of dry air
Substitute
(p. 97) and
(p. 97) into
(p. 96) and ignore the higher order terms. This
yields
Eq. 9
where:
T
s
= sonic virtual temperature
g
d
= ratio of specific heat of dry air at constant pressure to that at constant volume (Fleagle and
Businger 1980; Kaimal and Gaynor 1991; Kaimal and Businger 1963; Schotanus, Nieuwstadt, and
de Bruin 1983)
With
(p. 97), the effect of humidity on the speed of sound is included in the sonic virtual
temperature.
The sonic virtual temperature, in degrees Celsius, is given by
(p. 97), where
g
d
= 1.4 and R
d
= 287.04 JK
-1
kg
-1
.
Eq. 10
B.2 References
Fleagle, R.G. and J.A. Businger. 1980.
An Introduction to Atmospheric Physics
. New York: Academic
Press, Inc.
CSAT3BH Three-Dimensional Heated Sonic Anemometer
97