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SEDIMENTATION 10-3

2
g acceleration due to gravity, m/s
3
V volume of particle, m
P

C D drag coefficient
2
A p cross-sectional area of particle, m
v velocity of particle, m/s
The driving force for acceleration of the particle is the difference between the gravitational and
buoyant forces:

F

G F B ( s g ) V p (10-4)
When the drag force is equal to the driving force, the particle velocity reaches a constant value
called the terminal settling velocity ( v s ).

F G F B F D (10-5)

2
v (10-6)

( s ) g V p CA ( )
Dp
2

For spherical particles with a diameter d,

V p 4 3 / ()( d 2 / ) 3 2 (10-7)
d
A ()( d 2 / ) 2 3

p
Using Equations 10-6 and 10 -7 to solve for the terminal settling velocity:

/
⎡ 4 g( s d ) ⎤ 12
v s ⎢ C D ⎥ (10-8)
⎣ 3 ⎦

F
D
F D

F G

FIGURE 10-1
Forces acting on a free-falling particle in a fluid ( F D drag force; F G gravitational
force; F B buoyancy force). ( Source: Davis and Cornwell, 2008.)
F B