Fundamental Chemistry and Hydraulics - Mathematics and Statistics for the Environment - page 370

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

Q = A × V (14.17)

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

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

■ EXAMPLE 14.29
Problem: A pipe 12 in. in diameter 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 is

2

D
=×

A π (14.18)

4

where
π = Constant value 3.14159.
D = Diameter of the circle in feet.

Thus, the area of the pipe is

2 2

D
=× =

1ft

2

A π 3 14159 . × = 0.785 ft

4 4

Now, we can determine the discharge in cubic feet per second for part (a):

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

For part (b), we need to know that 1 cfs is equal to 449 gpm, so 7.85 cfs × 449 gpm/cfs = 3525 gpm.
Finally, for part (c), 1 MGD is equal to 1.55 cfs, so

7.85 cfs
1.55 cfs/MGD

= 5.06 MGD

14.2.1.8 Law of Continuity
The law of continuity states that the discharge at each point in a pipe or channel is the same as the
discharge at any other point (if water does not leave or enter the pipe or channel). That is, under the
assumption of steady-state flow, the flow that enters the pipe or channel is the same flow that exits
the pipe or channel. In equation form, this becomes

Q 1 = Q 2 or A 1 V 1 = A 2 V 2 (14.19)