Applications of Chemical Kinetics in Environmental Systems - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 320

consider the ideal case where a parcel of dry air is allowed to rise adiabatically through
the atmosphere. The air parcel experiences a decrease in temperature as it expands in
response to decreasing temperature with increasing elevation. This is called the adia-
baticlapserate , d T/ d z) ,andisastandardvalueof1 ◦ C/100 mfordryair,aswe

saw in Chapter 2. For saturated air this value is slightly smaller (0.6 ◦ C/100 m). If the
prevailing atmosphere has an environmental lapse rate ,

Γ adia ( =

Γ adia , the atmosphere
is considered unstable and rapid mixing occurs, thereby diluting the air pollutant. If
Γ env <

Γ env >

Γ adia , the atmosphere is stable and little or mixing occurs.
The second important parameter is the wind velocity. In general, the velocity of
wind above the surface follows a profile given by Deacon's power law,

z
z 1

p

U z
U z 1 =

,

where U z is the wind velocity at height z , U z 1 is the wind velocity at height z 1 , and
p is a positive exponent (varies between 0 and 1 in accordance with the atmospheric
stability).
The above effects of temperature and wind velocity are introduced in the disper-
sion models through the Pasquill stability criteria. However, we are still left with one
additional issue, that of the terrain itself. Obviously, the wind velocity near a sur-
face is strongly influenced by the type of terrain. Rough surfaces or irregular terrain
(buildings or other structures) will give rise to varying wind directions and velocities
near the surface. Open wide terrains do not provide that much wind resistance.
The dispersion of gases and vapors in the atmosphere is influenced by the degree
of atmospheric stability, which in turn in determined by the temperature profile in the
atmosphere, the wind direction, wind velocity, and surface roughness. These factors
are considered in arriving at equations to determine the dispersion of pollutants in a
prevailing atmosphere. Let us consider the emission of a plume of air pollutant from
a tall chimney as shown in Figure 6.30. The emission occurs from a point source and
is continuous in time. The process is at steady state. The air leaving the chimney is
often at a higher temperature than the ambient air. The buoyancy of the plume causes
a rise in the air parcel before it takes a more or less horizontal travel path. We apply
the convective-dispersion equation that was derived in Section 6.1.3, extended to all
three Cartesian co-ordinates.We consider here a nonreactive (conservative) pollutant.
Hence, we have the following equation:

∂ 2 ∂ 2 ∂ 2

U ∂

]
∂x =

[ A [ A ] [ A ] [ A ]

D x + D y + D z . (6.142)

∂x 2 ∂y 2 ∂z 2

For stack diffusion problems, from experience the following observations can be
made:

(i) In the x -direction, the mass transfer due to bulk motion, U∂ [ A ] /∂x ,far

/∂x 2 .
(ii) The wind speed on the average remains constant, that is, U is constant.

exceeds the dispersion, D x ∂ 2

[ A ]