Environmental Engineering Reference
In-Depth Information
has a height h . Because the exhaust gas is usually warmer than the ambient air, it rises due to
buoyancy by an incremental height
h . This is the “plume rise,” which will be evaluated later. The
final plume centerline is at height H
=
h
+
h . The pollutant time-averaged mass concentration
at a downwind distance x from a source of pollutant emitted at a mass rate Q p gs 1 ,at
a height H m, in the presence of wind of speed u ms 1 , is given by the following equation, called
the Gaussian plume equation (GPE):
c
(
x
,
y
,
z
)
exp
y 2
σ
2
Q p
1
2
y + (
z
H
)
c
(
x
,
y
,
z
) =
(9.3)
2
πσ y σ z u
σ
z
The
σ
's are the standard deviations of the Gaussian profile. Their dimension is given in meters.
The
's are called dispersion coefficients, although they should not be confused with diffusion
coefficients, which have a dimension m 2
σ
s 1 . The
's are a function of the turbulent condition
of the atmosphere and the distance from the source. The dispersion coefficients
σ
σ y and
σ z as
a function of downwind distance x are presented in Figure 9.2. It is seen that the
's are not
necessarily equal in the y and z directions. The six curves correspond to the atmospheric stability
categories A through F. Because the
σ
's are largest for unstable conditions and are smallest for stable
conditions, stability category A leads to a rapid dispersion of the emitted pollutants and leads to
highest ground concentration near the source. Category F leads to a slow dispersion and leads
to highest ground concentration far from the source. Mostly, we are interested in concentration
of pollutants on the ground; that is, z
σ
0. For ground-level concentrations it is assumed that the
pollutant molecules are not absorbed at the ground, but reflected as if they were an optical ray
that grazes a mirror. With this assumption, the factor 2 disappears in the denominator of the GPE
[equation (9.3)], and ground-level concentrations are twice that without reflection.
=
10000
1000
1000
A
B
A
B
C
D E
D
C
100
E
F
100
F
10
10
0.1
1 10
Distance downwind (km)
100
0.1
1
10
100
Distance downwind (km)
Figure 9.2 Horizontal and vertical dispersion coefficients.
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