Particulate Emission Control - Mathematics and Statistics for the Environment - page 505

TABLE 17.4
Particle Size Distribution Data

Average Particle Size in Range d p (µm) wt%

1 3

5 20

10 15

20 20

30 16

40 10

50 6

60 3

>60 7

■ EX AMPLE 17.6
Problem: Determine the cut size diameter and overall collection efficiency of a cyclone given the
particle size distribution of a dust from a cement kiln (USEPA, 1984b, p. 66).

Given:
Gas viscosity (µ) = 0.02 cp = 0.02(6.72 × 10 -4 ) lb/ft-s
Specific gravity of the particle = 2.9
Inlet gas velocity to cyclone = 50 ft/s
Effective number of turns within cyclone = 5
Cyclone diameter = 10 ft
Cyclone inlet width = 2.5 ft

Particle size distribution data is shown in Table 17.4.

Solution: Calculate the cut diameter, [ d p ] cut . The cut diameter is the particle collected at 50% effi-
ciency. For cyclones,

05 .

9 µ B

c

d =

( )

p

cut

2 π nv pp −

ti p g

where
µ = Gas viscosity (lb/ft-s)
B c = Cyclone inlet width (ft)
n t = Number of turns
v i = Inlet gas velocity (ft/s)
p p = Particle density (lb/ft 3 )
p g = Gas density (lb/ft 3 ).

Determine the value of p p - p g . Because the particle density is much greater than the gas density,
p p - p g can be assumed to be p p :

p p - p g = p p = 2.9 × 62.4 = 180.96 lb/ft 3

Calculate the cut diameter: