Science of Water : Concepts and Applications

Water Treatment Calculations 349
In regard to paddle fl occulator design and operation, environmental engineers are mainly interested
in determining the velocity of a paddle at a set distance, the drag force of the paddle on the
water, and the power input imparted to the water by the paddle.
Because of slip, factor k, the velocity of the water, will be less than the velocity of the paddle.
If baffl es are placed along the walls in a direction perpendicular to the water movement, the value
of k decreases because the baffl es obstruct the movement of the water (Droste, 1997). The frictional
dissipation of energy depends on the relative velocity, v. The relative velocity can be determined
using Equation 10.42:
vvpvtvpkvpvp(1 k)
(10.42)
where v t is the water velocity and v p is the paddle velocity.
To determine the velocity of the paddle at a distance r from the shaft, we use Equation 10.43:
v
p
2 N
r
60
where N is the rate of revolution of the shaft (rpm).
To determine the drag force of the paddle on the water, we use Equation 10.44:
where
A = area of the paddle
F D = drag force
C D = drag coeffi cient
1
FDpCDAv 2
(10.43)
2 (10.44)
To determine the power input imparted to the water by an elemental area of the paddle, we usually
use Equation 10.45:
SEDIMENTATION CALCULATIONS
dP dFDV pCDvdA 3 1
2
(10.45)
Sedimentation, the solid–liquid separation by gravity, is one of the most basic processes of water
and wastewater treatment. In water treatment, plain sedimentation, such as the use of a presedimentation
basin for grit removal and sedimentation basin following coagulation–fl occulation, is the
most commonly used.
TANK VOLUME CALCULATIONS
The two common shapes of sedimentation tanks are rectangular and cylindrical. The equations for
calculating the volume for each type tank are shown below.
CALCULATING TANK VOLUME
For rectangular sedimentation basins, we use Equation 10.46:
Volume, gal (length, ft)(width, ft)(depth, ft)(7.48 gal ft 3
) (10.46)