Pumping Calculations - Basic Mathematics for Water and Wastewater Operators - page 196

W ater in M otion
The study of water in motion is much more complicated than that of water at rest. It
is important to have an understanding of these principles because the water/waste-
water in a treatment plant or distribution/collection system is nearly always in motion
(much of this motion is the result of pumping, of course).

Discharge
Discharge is the quantity of water passing a given point in a pipe or channel during a
given period of time. It can be calculated by the following formula:

Q = A × V (14.2)

where
Q = Flow, or discharge, in cubic feet per second (cfs).
A = Cross-sectional area of the pipe or channel in square feet (ft 2 ).
V = Water velocity in feet per second (fps or ft/sec).

Discharge can be converted from cfs to other units such as gallons per minute
(gpm) or million gallons per day (MGD) by using appropriate conversion factors.

■ Example 14.4
Problem: A 12-in.-diameter pipe has water flowing through it at 10 fps. What is the
discharge in (a) cfs, (b) gpm, and (c) MGD?

Solution: Before we can use the basic formula, we must determine the area ( A ) of the
pipe. The formula for the area of a circle is

2

D

2

Area =× =× π π r

4

where
π = Constant value 3.14159, or simply 3.14.
D = Diameter of the circle (ft).
r = Radius of the circle (ft).

Therefore, the area of the pipe is

D 2

2

() 1ft

0.785 ft 2

Area =× =× =×= π π 314 . 1/4ft

4 4

(a) Now we can determine the discharge in cfs:

Q = V × A = 10 ft/sec × 0.785 ft 2 = 7.85 ft 3 /sec (cfs)

(b) We know that 1 cfs is 449 gpm, so

7.85 cfs × 449 gpm/cfs = 3525 gpm