Basic Units of Measurement and Conversions - Basic Mathematics for Water and Wastewater Operators - page 31

60 1440

cfs cfm cfd

7.48 7.48 7.48

60 1440

gps gpm gpd

8.34 8.34 8.34

60 1440

lb/sec lb/min lb/day

gps = gallons per second
gpm = gallons per minute
gpd = gallons per day
e factors shown in the diagram have the following units associated with them:
60 sec/min, 1440 min/day, 7.48 gal/ft 3 , and 8.34 lb/gal.

cfs = cubic feet per second (ft 3 /sec)
cfm = cubic feet per minute (ft 3 /min)
cfd = cubic feet per day (ft 3 /day)

FIGURE 2.1 Flow conversions using the box method. (Adapted from Price, J.K., Applied
Math for Wastewater Plant Operators , CRC Press, Boca Raton, FL, 1991, p. 32.)

Note: Flow is symbolized by the letter Q , and Q = Area × Velocity. Basically, flow
is a volume over time.

Key Factors in Calculating Flow Problem Solutions
• Be sure the diameter ( D ) is squared.

• Be sure inches are converted to feet.

• Look closely at the units you are asked to find.

• Flow formulas come out in ft 3 /sec but you may be asked to find gpm or MGD.

• Use the flow conversion box (see Figure 2.1) or dimensional analysis to

convert flows to the units desired.

Flow through a Channel

Q (cfs) = Width (ft) × Depth (ft) × Velocity (ft/sec) (2.4)

■ Example 2.63
Problem: What is the flow in cubic feet per second (cfs) for a channel that is 2 ft wide
and 3 ft deep with water moving at 1.2 ft/sec?

Solution:

Q = Width (ft) × Depth (ft) × Velocity (ft/sec) = 2 ft × 3 ft × 1.2 ft/sec = 7.2 cfs