Page 181 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

156 6 Separation of Particles from a Gas

Fig. 6.3 A turbulent flow y
model of gravity settling L
chamber

Q
H
C x C x+dx

δ x x+dx x

During an infinitesimal period of time dt, the particles at the bottom of the chamber
within a distance δ = v TS dt above the lower collecting plate are considered col-
lected since only these particles can reach the surface (shaded area in the Fig. 6.3).
Then the amount of particles entering the element defined by dx equals to the
total depositing on the bottom surface and that penetrating through the element, i.e.,

C x UWH ¼ Cv TS W dxðÞ þ C xþdx UWH ð6:17Þ

The ratio of the amount of settled particles to the total amount of particles that
enter the element defined by dx equals to the shaded area over the total elemental
area, which gives

dC v TS
¼ dt ð6:18Þ
C H
The negative sign indicates the decreasing particle number concentration along
x-direction.
Substitute the elemental residence time, dt ¼ dx=U, into the above equation, and
we have,

dC v TS
¼ dx ð6:19Þ
C HU

Integration of both sides leads to
C Z o dC Z v TS
L
¼ dx ð6:20Þ
C HU
C i 0
We can get the penetration efficiency of the particles through the chamber

v TS L
P ¼ exp ð6:21Þ
HU