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where
u = Settling velocity of particles (m/s, ft/s).
g = Gravitational acceleration (m/s 2 , ft/s 2 ).
p p = Density of particles (kg/m 3 , lb/ft 3 ).
p = Density of water (kg/m 3 , lb/ft 3 ).
d = Diameter of particles (m, ft).
C D = Coefficient of drag.
The terminal settling velocity is derived by equating the drag, buoyant, and gravitational forces act-
ing on the particle. At low settling velocities, the equation is not dependent on the shape of the par-
ticle and most sedimentation processes are designed so as to remove small particles, ranging from
1.0 to 0.5 µm, which settle slowly. Larger particles settle at higher velocity and will be removed
whether or not they follow Newton's law or Stokes' law—the governing equation when the drag
coefficient is sufficiently small (0.5 or less) as is the case for colloidal products (McGhee, 1991).
Typically, a large range of particle sizes will exist in the raw water supply. There are four types
of sedimentation (Gregory and Zabel, 1990):
Type 1 —Discrete particle settling (particles of various sizes, in a dilute suspension, which
settle without flocculating).
Type 2 —Flocculant settling (heavier particles coalesced with smaller and lighter particles).
Type 3 —Hindered settling (high densities of particles in suspension resulting in an interaction
of pa r ticles).
Type 4 — Compression settling.
The values of the drag coefficient depend on the density of water ( p ), relative velocity ( u ), particle
diameter ( d ), and viscosity of water (µ), which gives the Reynolds number, Re, as
Re = ××
pud
µ
(23.60)
As the Reynolds number increases, the value of C D increases. For Re less than 2, C D is related to Re
by the linear expression as follows:
C D = 24
Re
(23.61)
At low levels of Re, the Stokes equation for laminar low conditions is used (Equations 23.60 and
23.61 substituted into Equation 23.59):
(
) 2
Gp
pd
p
u
=
18µ
In the region of higher Reynolds numbers (2 < Re < 500-1000), C D becomes (Fair et al. 1968)
24
3
C D =+ +
034
.
(23.62)
Re
Re
Note: In the region of turbulent flow (500-1000 < Re < 200,000), C D remains approximately con-
stant at 0.44.
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