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336 11 Air Dispersion

where the subscript s stands for stack, q and q are the densities of the stack
a
s
2
emission gas and the surrounding air, respectively. g ¼ 9:81 m/s is the gravita-
tional acceleration; v s is the vertical discharge speed of the emission gas from the
stack (m/s), which is assumed along þz direction. d s is the inner diameter of the
2
4
4
3
stack (m). The units of F B and F M are m =s and m =s , respectively.
A practical parameter is the flue gas temperature instead of the air density. Both
the stack emission gas and the surrounding air can be considered as ideal gases, and
both are under atmospheric pressure. From the relationship between density and
temperature described in Eq. (11.6), we have
q
s M s T a T a
q a ¼ M a T s T s ð11:37Þ
Despite the difference in molar weights of stack emission gas and the sur-
rounding air in the atmosphere, the difference of molar weights is much less than
that of temperature. Therefore, we can simplify the density ratio by ignoring the
molar weight ratio. In such a case, Eqs. (11.35) and (11.36) become

T a d s
2
F B ¼ 1 gv s ð11:38Þ
T s 4
2
T a d s 2
F M ¼ v s ð11:39Þ
T s 4
When both buoyancy and momentum determine the plume rise, the transitional
plume rise is described as

1=3
25 F M 25 F B 2
Dh ¼ x þ x ð11:40Þ
3 u 2 6 u 3
where u is the average wind speed at the stack height (m/s), x is the downwind
distance away from the stack (m).
When one is dominating over another, the equation can be further simplified.
When the plume temperature is much greater than that of the surrounding atmo-
sphere temperature, the plume is mostly buoyancy-dominant, especially those from
a power plant because the emission stream is hotter than the ambient air (T s [ T a ).
For a buoyancy dominating plume, the transitional plume rise is
1=3
2
25 F B x
Dh ¼ ð11:41Þ
6 u 3