Environmental Engineering FOURTH EDITION

176 ENVIRONMENTAL, ENGINEERING

as the solids are more dense than the liquid? Simple settling is, however, affected by
other forces in certain circumstances. Particles settle in one of three general ways:

Class I: Discrete particle settling occurs when particles settle unhindered by con-

tainer walls or neighboring particles.

0 Class 11: Flocculent setding occurs when neighboring particles come into contact

with each other, changing particle size and hindering settling.

0 Class 111: Thickening occurs when the entire mass of particles settle with the same

velocity, and there is no interparticle movement.

The simplest case is Class I, discrete particle settling. A single particle, having
attained terminal velocity, has no net force acting on it. The three forces acting on the
particle - drag, buoyancy, and gravity - balance as in

Fg = FD + FB, (9.1)

which becomes

where

Fg =

FD =

FB =

m=

g=

Ps =

P=

CD =

v=

A=

V=

force due to gravity = mg,

drag force = (C~pv~A)/2,

buoyancy = pVg,

mass of particle = psV9

gravitational acceleration,

particle density (in kg/m2),

density of the medium,

drag coefficient,

velocity of particle in (ds),

projected surface area of particle (in m2), and

volume of particle (in m3).

Solving for the velocity,

If we now assume that the particle is a sphere,

3Separation of less dense solids may be achieved by flotation, or allowing the solids to float to the top.

This method is used, for example, in ore separation, but is not applicable to solids separation in primary

clari6em.