Page 366 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

344 11 Air Dispersion

Consider an instantaneous short-term release of air pollutant from a stack, where
the mass of air pollutant released is mðkgÞ. Integrating Eq. (11.57) with the
boundary conditions

C ! 0ast !1; x; y; z 0
C ! 0ast ! 0; x; y; z [ 0
Z 1 1 Z 1
Cdxdydz ¼ m ðconservation of massÞ
Z
0 1 1
leads to

" !#
m 1 x 2 y 2 z 2
Cx; y; z; tÞ ¼ exp þ þ ð11:58Þ
ð
3 1 4t D D D
2
ð 4ptÞ D x D y D z 2 x y z
Similar to Eq. (11.31), we define
2
r ¼ 2D i t i ¼ x; y; z ð11:59Þ
i
and Eq. (11.58) can be rewritten in another form as
" # " 2 #

m x 2 y 2 ð z HÞ

C ¼ exp exp exp : ð11:60Þ
3=2 2r 2 2r 2 2r 2
ð 2pÞ r x r y r z x y z
When not available, the x-direction dispersion coefficient can be approximate
using r x r y because they both are for horizontal directions.
The Gaussian puff model is useful in safety analysis of accidental release of air
pollutants and other chemicals rather than a continuous release of air pollutants.
Readers are referred to the literature for in-depth understanding of these topics.
Corresponding computer programs have been developed for different models
and they are widely available at government agencies and consulting firms, case by
case. However, users of any air dispersion models must be advised that they are for
estimates with differences from actual observations as a result of inversion aloft,
short-term fluctuations, inversion breakup fumigation, etc. Advanced dispersion
models aiming at these additional topics are available in literature and readers are
suggested to explore them as needed.

11.5 Practice Problems

1. An air parcel temperature is 300 K and the surrounding atmosphere temperature
is 280 K, what is the acceleration of this air parcel at this location? Assume air
pressure p = 1 atm.