Geoscience Reference
In-Depth Information
• For a laminar regime (Stokes' law range), the terminal settling velocity is
=
(
2
18µ
gp
pp
v
(17.6)
• For a transition regime (intermediate law range), the terminal settling velocity is
()()
()
114
.
0 71
.
071
.
0 153
.
gd
p
p
p
v
=
(17.7)
029
.
043
.
()
µ
p
a
• For a turbulent regime (Newton's law range), the terminal settling velocity is
05
.
gd p
p
pp
a
v
=
174
.
(17.8)
When particles approach sizes comparable with the mean free path of the fluid molecules (also
known as the Knudsen number,
Kn
), the medium can no longer be regarded as continuous, because
particles can fall between the molecules at a faster rate than predicted by aerodynamic theory.
Cunningham's correction factor, which includes thermal and momentum accommodation factors
based on the Millikan oil-drop studies and is empirically adjusted to fit a wide range of
Kn
values,
is introduced into Stoke's law to allow for this slip (Hesketh, 1991; USEPA, 1984b, p. 58):
=
(
2
18µ
gp
dC
pp
f
v
(17.9)
where
C
f
= Cunningham correction factor = 1 + (2
Al
/
d
p
).
A
= 1.257 + 0.40e
-1.10
d
p
/2
l
.
l
= Free path of the fluid molecules (6.53 × 10
-6
cm for ambient air).
■
EX AMPLE 17.1
Problem:
Calculate the settling velocity of a particle moving in a gas stream. Assume the following
information (USEPA, 1984a, p. 3-11):
Given:
d
p
= Particle diameter = 45 µm
g
= Gravity forces = 980 cm/s
2
p
p
= Particle density = 0.899 g/cm
3
p
a
= Fluid (gas) density = 0.012 g/cm
3
µ = Fluid (gas) viscosity = 1.82 × 10
-4
g/cm-s
C
f
= 1.0 (if applicable)
Solution:
Use Equation 17.5 calculate the
K
parameter to determine the proper flow regime:
033
.
.
764
25
25 400
.
32 2
.
×
(
122 300764
.
−
.
)
×
00
K
=
=
0 104
.
(
)
2
,
×
12
−
5
12210
.
×
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