Environmental Engineering Reference
In-Depth Information
relative humidity and dry bulb temperature were known. The
results from this equation are comparable to those obtained
when using the equation proposed by Tetens (1930).
The August-Roche-Magnus equation can be rearranged
and solved for relative humidity when the dew-point tem-
perature is known. The August-Roche-Magnus equation is
considered valid under the following conditions:
35
100
30
75
25
20
50
15
0
◦
C
<T <
60
◦
C
10
25
1%
<h
r
<
100%
(6.12)
5
0
◦
C
<t
d
<
50
◦
C
0
0
0369
Time, days
noon
3
6
9
12
The August-Roche-Magnus equation for the calculation
of dew point is as follows:
Figure 6.19
Illustration of the typical inverse relationship
between temperature and relative humidity throughout a day.
b
aT
/ (b
ln
h
r
/
100
+
T )
+
t
d
=
−
aT
/ (b
ln
h
r
/
100
(6.13)
a
+
T )
+
changes in humidity influence the actual evaporation from
a soil surface. It has been suggested that the changes in
relative humidity throughout each day should be taken into
consideration when modeling actual evaporation (Wilson,
1990). Diurnal variations can be based on either assumed
daily variations or actual measured changes in relative
humidity and temperature throughout each day.
where:
h
r
=
relative humidity, %,
dry bulb temperature,
◦
C,
T
=
dew point temperature,
◦
C
t
d
=
a
=
17.271, and
237.7
◦
C.
b
=
6.3.6.4 Calculation of Relative Humidity
from Dew-Point Measurements
The relative humidity of an air-water mixture can be calcu-
lated if the air temperature
T
and the dew-point temperature
T
d
are known. There are a number of equations that have
been proposed for the calculation of relative humidity based
on the dew-point temperature. There is a simple approxi-
mation that allows the relative humidity
h
r
to be calculated
based on the dew-point temperature
t
d
and the dry bulb
temperature
T
. The equation is as follows:
Rearranging Eq. 6.13 and solving for relative humidity
h
r
gives
100 exp
ab
t
d
−
T
T
)
t
d
+
b
h
r
=
(6.14)
(
b
+
6.3.6.6 Bosen (1958) Calculation of Relative Humidity
The Bosen (1958) equation was developed for the approx-
imation of the dew-point temperature when the relative
humidity and dry bulb temperature were known. The Bosen
(1958) equation for the calculation of dew point
5
T
t
d
h
r
=
100
−
−
(6.11)
is as
where:
follows:
air temperature,
◦
C, and
T
=
0
.
9
T ) h
0
.
125
r
t
d
=
(a
+
−
a
+
0
.
1
T
(6.15)
dew-point temperature,
◦
C.
t
d
=
where:
The equation is quite accurate as long as the relative
humidity is above 50%. The equation states that the relative
humidity changes by 5% for every 1
◦
C difference in temper-
ature between the dew point and the dry bulb temperature
starting at 100% relative humidity.
constant equal to 112 when temperature is in
◦
C.
a
=
The Bosen (1958) equation can be rearranged such that the
relative humidity
h
r
can be computed when the dew-point
temperature and the dry bulb temperature are known:
6.3.6.5 August-Roche-Magnus Calculation
of Relative Humidity
The August-Roche-Magnus equation was developed for the
calculation of the dew-point temperature when a specific
100
t
d
−
8
0
.
1
T
+
112
h
r
=
(6.16)
112
+
0
.
9
T
Search WWH ::
Custom Search