Page 140 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

6 Sedimentation

3
3
Gravity settling, or ‘‘sedimentation,’’ is used at several points r s is the specific mass of particle (kg=m ) or (slugs=ft )
3
in both water and wastewater treatment trains. The difference r f is the specific mass of fluid medium (kg=m )or
3
in each application is the nature of the suspension to be (slugs=ft )
2
2
settled. Table 6.1 describes these suspensions, where they g is the acceleration of gravity (9.81 m=s ) or (32.2 ft=s )
occur in treatment, and the respective kinds of settling units.
Drag forces, F D , act on any object, e.g., a particle moving
through a fluid. In turbulent flow, drag forces are caused by
6.1 KEY NOTIONS IN DESIGN (1) boundary shear (skin friction) and (2) unequal pressure
Basic themes in the design of sedimentation basins are (1) the distribution around the object (form drag). In laminar flow,
suspension characteristics, and (2) basin hydraulics. These drag is due to the viscous shear forces distributed through the
two themes are the basis for theory and practice (Camp, fluid. The general expression for the drag force due to fluid
1946). motion is
The suspensions in Table 6.1 can be classified in settling as
discrete settling, flocculent settling, hindered settling, and v 2 s
F D ¼ C D rA (6:3)
compression settling. Each suspension has its own character- 2
istic settling behavior, described in Sections 6.2.3 and 6.4.
The second theme of the basin design is hydraulics. A where
settling particle is subject to the vagaries of water flow, i.e., F D is the drag force on particle (N) or (lb)
the patterns of current, the superimposed eddies, and the C D is the drag coefficient
microscale turbulence. Such effects are not predictable (except A is the projected area of particle normal to the direction of
2
2
by CFD computer technology as noted in Box 6.1) and so the flow (m ) or (ft ) 3 3
concept of the ideal basin (Section 6.3.3) has become the point r is the density of fluid (kg=m ) or (slugs=ft )
of departure in depicting basin hydraulics. v s is the velocity of particle (m=s) or (ft=s)

For dynamic equilibrium, per Figure 6.1, the drag force
6.2 PARTICLE SETTLING developed equals the propulsion force, i.e.,
The settling velocity of a single particle is the starting point of
settling theory, leading to the concept of the ideal settling F B ¼ F D (6:4)
basin. As stated previously, the notion of the ‘‘ideal’’ basin is
the reference for understanding the behavior of real systems. Substituting Equations 6.2 and 6.3 into Equation 6.4 gives

v 2
6.2.1 PARTICLE SETTLING PRINCIPLES s
V(r r )g ¼ C D Ar (6:5)
f
s
2
Figure 6.1 is a free body diagram for a falling particle in
dynamic equilibrium. Dynamic equilibrium means the drag
force, F D , equal the propulsion force, W B . The propulsion
force for a falling particle is its buoyant weight, i.e., 6.2.2 STOKES’ LAW
The drag coefficient of Equation 6.5, C D , is functionally
W B ¼ V(g g ) (6:1) related to Reynolds number, R. For the special case when
s
f
R 1, i.e., the laminar flow range, C D ¼ 24=R. Now, recall
¼ V(r r )g (6:2)
s f that R ¼ rv s d=m and substitute in Equation 6.5, to give,
where
24 v 2
W B is the buoyant weight of particle in fluid medium (N) Ar s (6:6)
s
f
V(r r )g ¼
or (lb) rvd=m 2
3
3
V is the volume of water displaced by particle (m ) or (ft )
3
3
g s is the specific weight of the particle (N=m ) or (lb=ft ) where
3
g f is the specific weight of fluid medium (N=m )or d is the diameter of particle (m) or (ft)
2
3
2
(lb=ft ) m is the dynamic viscosity of fluid (N s=m ) or (lb s=ft )
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