Basic Math Operations - Mathematics and Statistics for the Environment - page 56

Because the dimensions of the answer are square feet, this math setup is correct; therefore, by
dividing the numbers as was done with units, the answer will also be correct.

3

70 ft /s
4.5 ft/s

2

=15 56 . ft

■ EXAMPLE 2.33
Problem: We are given two terms, 5 m/s and 7 m 2 , and the answer to be obtained should be in cubic
meters per second (m 3 /s). Is multiplying the two terms the correct math setup?

Solution:

m
s

2 2

( m/s ) × () m = × m

Multiply the numerators and denominator of the fraction:

2 3

mm
s

× m

s

= =

Because the dimensions of the answer are cubic meters per second (m 3 is the math setup is correct;
therefore, multiply the numbers to get the correct answer:

5 m/s × 7 m 2 = 35 m 3 /s

■ EXAMPLE 2.34
Problem: The flow rate in a water line is 2.3 ft 3 is What is the flow rate expressed as gallons per
m inute?

Solution: Set up the math problem and then use dimensional analysis to check the math setup:

(2.3 ft 3 /s) × (7.48 ga l /f t 3 ) × (60 s/min)

Dimensional analysis can be used to check the math setup:

3 3

× =××= ft
s

ft
s

gal
ft

s
min

gal
ft

s
min

gal
min

3 3

( ft /s) al/ft × ( )( s/min ) ××=

3 3

The math setup is correct as shown above; therefore, this problem can be multiplied out to get the
answer in correct units:

(2.3 ft 3 /s) × (7.48 ga l /f t 3 ) × (60 s/min) = 1032.24 gal/min

■ EXAMPLE 2.35
Problem: During an 8-hr period, a water treatment plant treated 3.2 million gallons of water. What
is the plant total volume treated per day, assuming the same treatment rate?

Solution:

3.2 milliongal
8hr

24 hr
day

3.2 × 24

× = MGD = 9.66MGD

8