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where
Tt
is the acoustic virtual temperature of dry air and
v
M
the molar mass of water vapour,
and
d
M
describes the molar mass of dry air. The ratios
d
v
M
M
with the value 0.621978 and
d
v
γ
γ
with
the value 0.95108 can be included in the equation as fixed constants. [3]
The ratio
p
e
describes the water vapour pressure divided by the air pressure. , corrected by the
effect of the water vapour pressure on the air pressure..
The vapour pressure
e
can be calculated according to the relationship
s
e
RH
e
•
=
100
where
RH
stands for relative humidity and
s
e
for saturation vapour pressure.
The saturation vapour pressure is a function of temperature and can be calculated according to the
Magnus formula with coefficient according to Sonntag
( )
T
K
T
s
e
hPa
T
e
+
•
•
=
12
.
243
62
.
17
112
.
6
[4]
with the temperature of interest where T must be specified in °C.
The following simplified expression with T as the temperature in Kelvin results for calculation of the
acoustic virtual temperature measured with humid air:
[
]
•
−
•
+
•
=
e
p
e
Tt
Tv
378022
,
0
329102
,
0
1
The correcting effect of the water vapour pressure on the air pressure is relatively low, and is, for
ex., approx. 2,8 % with + 40 °C and 100 % relative humidity.
The water vapour pressures to be expected in the nature are clearly below. The error with the
simplification of the formalism can consequently almost be neglected.
Simplified formula:
•
+
•
=
p
e
Tt
Tv
329
,
0
1
Example:
With an air temperature of +20°C, relative humidity of 100% and an air pressure of 1000hPa an
acoustic virtual temperature of 22.25°C is calculated fro m the sound velocity.
The acoustic virtual temperature is therefore 2.25°C ab ove the actual air temperature and can be
corrected accordingly using the above equation if the humidity level of the air is known, e.g. relative
humidity and the air pressure.
Calibrated measurements performed in the climatic exposure test cabinet with different
temperatures as parameters and relative humidity levels between 10% and 90% have shown that
the factor in the above equation should be nearer 0.30.
•
+
•
=
p
e
Tt
Tv
30
.
0
1
If required to improve accuracy of the calculated real air temperature, one or more iteration steps
could be performed to determine the accurate saturation vapour pressure when using the
measured relative humidity and the measured acoustic temperature as corrective variables as the
real air temperature (corrected acoustic virtual-temperature) is necessary for the calculation of the
saturation vapour pressure.