Page 180 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

6.2 Gravity Settling Chambers 155

collected on the surface of the lower plate. This height H c can be referred to as the
critical height. Then the fractional efficiency of the chamber for this group of
particles (d p )is

H c

g d p ¼ ð6:10Þ
H
The time for a particle entering the chamber at the critical height, H c , falls down
through a vertical distance H c while traveling a horizontal distance L,is

L H c
t ¼ ¼ ð6:11Þ
U v TS
It leads to

v TS L
H c ¼ ð6:12Þ
U
Substitute Eq. (6.12) into the efficiency Eq. (6.10) above, and we have

v TS L

g d p ¼ ð6:13Þ
UH
where the gas incoming speed can be determined from the flow rate of the air
passing through the chamber,
Q
U ¼ ð6:14Þ
WH
where W is the width of the chamber. The terminal settling speed of a spherical
particle falling in a gravitational field is

2
q d gC c
p p
v TS ¼ ð6:15Þ
18 l
Therefore, the fractional particle separation efficiency can be described as
2
q gd C c LW
p p
g d p ¼ ð6:16Þ
18 l Q
6.2.2 Turbulent Flow Model

For turbulent flow model, we assume that the particles and the air are completely
mixed at any cross section that is normal to the direction of airflow. Consider an
element with an infinitesimal length dx. The concentration of particles within which
is assumed to be uniform and the particles settle down at a terminal velocity of v TS .