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Calculate the total filtering cloth area (
A
c
) from the acfm and filtering velocity determined above:
A
c
=
Q
a
/
v
f
= 13,654/2.5 = 5461.6 ft
2
Calculate the filtering area per bag. Bags are assumed to be cylindrical; the bag area is
A
= π ×
D
×
h
, where
D
= bag diameter and
h
= bag length.
For bag A,
A
= π ×
D
×
h
= π × (8/12) × 16 = 33.5 ft
2
For bag B,
A
= π ×
D
×
h
= π × (10/12) × 16 = 41.9 ft
2
Determine the number of bags required (
N
):
N
= (Filtering cloth area of each bag,
A
c
)/(Bag area,
A
)
For bag A,
N
= 5461.6/33.5 = 163
For bag B,
N
= 5461.6/41.9 = 130
Determine the total cost for each bag:
Total cost =
N
× Cost per bag
For bag A, total cost = 163 × 26.00 = $4238
For bag B, total cost = 130 × 38.00 = $4940
Select the most appropriate filter bag considering the performance and cost. Because the total cost
for bag A is less than bag B, select bag A.
■
EXAMPLE 17.13
Problem:
Determine the number of filtering bags required and cleaning frequency for a plant equipped
with a fabric filter system. Operating and design data are given below (USEPA, 1984b, p. 86).
Given:
Volumetric flow rate of the gas stream = 50,000 acfm
Dust concentration = 5.0 grains/ft
3
Efficiency of the fabric filter system = 98.0%
Filtration velocity = 10 ft/min
Diameter of filtering bag = 1.0 ft
Length of filtering bag = 15 ft
The system is designed to begin cleaning when the pressure drop reaches 8.9 inches of water. The
pressure drop is given by
∆
p
= 0.2
v
f
+ 5
c
(
v
f
)
2
t
where
∆
p
= Pressure drop (in. H
2
O).
v
f
= Filtration velocity (ft/min).
c
= Dust concentration (lb/ft
3
).
t
= Time since the bags were cleaned (min).
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