Science of Water : Concepts and Applications

56 The Science of Water: Concepts and Applications
Solution:
Flow (cfs) 6ft 3ft 4ft/s 72cfs
Discharge or fl ow can be recorded as gallons per day (gpd), gallons per minute (gpm), or cubic
feet per second. Flows treated by many waterworks plants are large and often referred to in million
gallons per day (MGD). The discharge or fl ow rate can be converted from cfs to other units such as
gallons per minute or million gallons per day by using appropriate conversion factors.
Example 3.11
Problem:
A pipe, 12 in. in diameter, has water fl owing through it at 10 ft/s. What is the discharge in (a) cubic feet
per second; (b) gallons per minute; and (c) million gallons per day?
Solution:
Before we can use the basic formula (3.13), we must determine the area A of the pipe. The formula for
the area of a circle is
2
D
A
r
4
2
(3.13)
where π is the constant, of value 3.14159 or, simply, 3.14 and D is the diameter of the circle in feet
and r the radius of the circle in feet.
Therefore, the area of the pipe is
2
2
D (1 ft)
A314
. 0.785ft
4 4
Now, we can determine the discharge in cfs for part (a)
2 3
QVA10ft/s0.785ft 7.85ft
/s or cfs
For part (b), we need to know that 1 cfs is 449 gpm, so 7.85 cfs × 449 gpm/cfs = 3525 gpm
(rounded).
Finally, for part (c), 1 million gal per day is 1.55 cfs, so
7.85cfs
1.55cfs MGD
506 .
MGD
√ Important Point: Flow may be laminar (streamline—see Figure 3.6) or turbulent (see Figure
3.7). Laminar fl ow occurs at extremely low velocities. The water moves in straight parallel
lines, called streamlines, or laminae, which slide upon each other as they travel, rather than
mixing up. Normal pipe fl ow is turbulent fl ow, which occurs because of friction encountered on
the inside of the pipe. The outside layers of the fl ow are thrown into the inner layers; the result
is that all the layers mix and move in different directions at different velocities. However, the
direction of the fl ow is forward.
2