Page 344 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

322 11 Air Dispersion

Fig. 11.4 Atmosphere z
T=constant
stability
Unstable
Inversion
Neutral

Stable

P Initial elevation
Adiabatic
line

T

11.2.5 Atmospheric Stability

Consider an air parcel moving slowly in the atmosphere. It is subjected to gravity,
friction, and buoyancy. We can ignore friction at low velocity, the total force
exerted on the air parcel and the motion of the parcel is described using Newton’s
second law, with positive direction upward, as

dv

F ¼ q q Vg ¼ q V ð11:12Þ
a p p
dt
where q and q are the densities of the air parcel and the surrounding air,
p a
respectively; V is the volume of the air parcel and dv=dtÞ is the acceleration of the
ð
air parcel. Simplification of Eq. (11.12) leads to
!
dv q a
¼ 1 g: ð11:13Þ
dt q p
Both the air parcel and the surrounding air can be assumed ideal gases, and the
densities can be described using Eq. (11.6); with same atmospheric pressure P,
same molar weight M and same ideal gas constant R, Eq. (11.13) becomes

dv T p
¼ 1 g ð11:14Þ
dt T a
This equation shows that, when T p [ T a , the acceleration of the air parcel is
positive, which means that it moves upward, and vice versa. When T p ¼ T a , the air
parcel acceleration will be zero. Depending on the change rate of the air parcel
temperature with respect to that of the surrounding air, the air parcel may sink,