Science of Water : Concepts and Applications

374 The Science of Water: Concepts and Applications
REQUIRED DEPTH OF BACKWASH WATER TANK, ft
The required depth of water in the backwash water tank is determined from the volume of water
required for backwashing. To make this calculation, use Equation 10.75:
Example 10.87
2 3
Volume, gal (0.785)( D )(Depth, ft)(7.48 galft )
(10.75)
Problem:
The volume of water required for backwashing has been calculated to be 85,000 gal. What is the
required depth of water in the backwash water tank to provide this amount of water if the diameter of
the tank is 60 ft?
Solution:
Use the volume equation for a cylindrical tank, fi lling in known data; then solve for x:
2 3
Volume, gal (0.785)( D )(depth, ft)(7.48 galft )
3
85,000 gal (0.785)(60
ft)(60 ft)( x ft)(7.48 galft )
85,000
(0.785)(60)(60) (7.48)
x 4ft
Example 10.88
Problem:
A total of 66,000 gal of water will be required for backwashing a fi lter at a rate of 8000 gpm for a 9-min
period. What depth of water is required in the backwash tank that has a diameter of 50 ft?
Solution:
Use the volume equation for cylindrical tanks:
BACKWASH PUMPING RATE, gpm
2 3
Volume, gal (0.785)( D )(depth, ft)(7.48 galft )
3
66,000 gal ( 0.785)(50 ft)(50 ft)( x ft)(7.48 galft )
66,000
x
(0.785)(50)(50)(7.48)
x 4.5 ft
The desired backwash pumping rate, gpm, for a fi lter depends on the desired backwash rate in
gpm/ft 2 and the ft 2 area of the fi lter. The backwash pumping rate, gpm can be determined by using
Equation 10.76.
2
2
Backwash pumping rate, gpm (desired backwash rate, gpmft )(filter
area, ft )
(10.76)