MSc in Water and Environmental Management
___________________________________________________________________
SETTLEMENT THEORY
A particle moves horizontally at a velocity of V m s-1
The particle moves at a velocity V and follows the inclined path as shown.
Q(m3 / s)
V the speed of horizontal flow =
db (m2 )
Time of horizontal flow =
Length
Speed of horizontal flow
=
L
ms-1
Q / db
=
Ldb
ms-1
Q
Time of vertical flow =
= ms-1
d(m)
Vs(m / s)
s-1
For particle to arrive at s, the time of vertical fall = time of horizontal flow.
Dr. Glynn Skerratt Document Control 06/02/16
Page
1
MSc in Water and Environmental Management
___________________________________________________________________
d
Vs
Q
Lbd
Vs
Vs
=
=
Lbd
Q
VS
d
Q
Lb
Q
=
A
=
where A = surface area
The quantity
Q
A
is known as the overflow rate or surface loading
Consequently it is surface area that is the important factor
The depth of tank and simple consideration of retention time are of little
significance.
An alternative way of considering it would be:
Qd = VsLdb
Q = VsLb
and since
then
Q = Vdb
Vd = VsL

V
=
Vs L
d
so v the velocity at which the device may be operated is:
and
to L
 to dl
By reducing the value of d, we can increase the efficiency of the clarifier. Small
plate spacing and large surface area improve the settlement characteristics
Inclined plates mean that d (the distance a particle must settle to remain within
the tank) will vary according to the angle of the plates. The actual distance for
settlement d*is related to d by the expression:
Dr. Glynn Skerratt Document Control 06/02/16
Page
2
MSc in Water and Environmental Management
___________________________________________________________________
d = d* cos

The settling distance d* is increased by the factor
when
1
 = 60o then cos  =
1
cos 
2
The lower the angle of inclination the smaller the settling distance. However the
angle of inclination must exceed the angle of repose of the solids to be separated
(to make it fall down the plate and separate)
So
v =
L Vs
=
L cos 
d* Vs
d*
cos 
 values of 45o are used and 60o (for heavy particles and lighter particles
respectively.)
Dr. Glynn Skerratt Document Control 06/02/16
Page
3