B-1
Appendix B. Sensible Heat Flux without
a FW05
B.1 Speed of Sound and Sonic Temperature
In the following section the speed of sound will be expressed as a sonically
measured temperature. The effects of humidity, on the speed of sound, will be
combined into this temperature.
This temperature,
T
s
, is defined as the sonic virtual temperature or simply the
sonic temperature and is related to the speed of sound by two well known
constants.
The speed of sound (c) is defined by:
c
P
2
=
γ
ρ
(B-1)
where
P
is atmospheric pressure,
ρ
is the density of moist air, and
γ =
C
C
p
v
is
the ratio of the specific heats of moist air. The specific heats of moist air can
be written as:
(
)
(
)
C
qC
q C
C
q
p
p
p
p
w
d
d
=
+ −
=
+
1
1 0 84
.
(B-2)
(
)
(
)
C
qC
q C
C
q
v
v
v
v
w
d
d
=
+ −
=
+
1
1 0 94
.
(B-3)
where
q
is the specific humidity of air, the subscript
p
means constant pressure,
v
means constant volume,
w
means water vapor, and
d
means dry air.
The ideal gas law can be written as:
(
)
P
R T
R T
q
d v
d
=
=
+
ρ
ρ
1 0 61
.
(B-4)
where
R
d
is the gas constant for dry air (287.04 J K
-1
kg
-1
),
T
v
is the virtual air
temperature in Kelvin, and
T
is the air temperature in Kelvin.
Substitute Equation (B-4) into Equation (B-1) to write the speed of sound as a
function of temperature and humidity.
(
)
c
C
C
R T
q
p
v
d
2
1 0 61
=
+
.
(B-5)
The term,
γ
, is a function of specific humidity. To move humidity into a single
term, substitute Equations (B-2) and (B-3) into (B-5).
