Geoscience Reference
In-Depth Information
■
EX AMPLE 17. 3
Problem:
Determine the minimum distance downstream from a cement dust-emitting source that
will be free of cement deposit. The source is equipped with a cyclone (USEPA, 1984b, p. 59).
Given:
Particle size range of cement dust = 2.5 to 50.0 µm
Specific gravity of the cement dust = 1.96
Wind speed = 3.0 mph
The cyclone is located 150 ft above ground level. Assume ambient conditions are at 60°F and 1 atm
and disregard meteorological aspects:
µ = Air viscosity at 60°F = 1.22 × 10
-5
lb/ft-s
µm (1 micron = 10
-6
m) = 3.048 × 10
5
ft
Solution:
A particle diameter of 2.5 µm is used to calculate the minimum distance downstream free
of dust since the smallest particle will travel the greatest horizontal distance. Determine the value
of
K
for the appropriate size of the dust, and calculate the particle density (
p
p
) using the specific
gravity given.
p
p
= Specific gravity of fly ash × Density of water = 1.96 × 62.4 = 122.3 lb/ft
3
Calculate the air density (
P
) by using the modified ideal gas equation:
PV
=
nR
u
T
= (
m
/
M
)
R
u
T
P
= Mass × Volume =
PM
/
R
u
T
= (1 × 29)/[0.73 × (60 + 460)] = 0.0764 lb/ft
3
Determine flow regime
K
:
033
.
Kd
gp p
pa
=
p
µ
2
For
d
p
= 2.5 µm:
033
.
(
)
033
.
Kd
gp
−
pp
25
25 400
.
32 2
.
×
(
122 300764
.
−
.
)
×
0 0764
.
p
=
=
=
0 104
.
p
(
)
µ
2
2
,
×
12
−
5
12210
.
×
where 1 ft = 25,400 × 12 µm = 304,800 µm. Now determine which fluid-particle dynamic law
applies for the above value of
K
. Compare the
K
value of 0.104 with the following range:
•
K
< 3.3, Stokes' law range
• 3.3 <
K
< 43.6, intermediate law range
• 43.6 <
K
< 2360.0, Newton's law range
The flow is in the Stokes' law range; thus, it is laminar. Now calculate the terminal settling velocity
in ft/s. For Stokes' law range, the velocity is
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