Force, Pressure, Head, and Velocity Calculations - Basic Mathematics for Water and Wastewater Operators - page 180

4. Because this is the weight of one column of water 1 foot tall, the true expres-
sion would be 0.433 pounds per square inch per foot of head, or 0.433 psi/ft.
Note: 1 ft of head = 0.433 psi.

In addition to remembering the important parameter 1 foot of head = 0.433 psi,
it is important to understand the relationship between pressure and feet of head—in
other words, how many feet of head 1 psi represents. This is determined by dividing
1 by 0.433:

Feet of head = 1 ft ÷ 0.433 psi = 2.31 ft/psi

If a pressure gauge reads 12 psi, the height of the water necessary to represent this
pressure would be 12 psi × 2.31 ft/psi = 27.7 feet.
Note: Both the above conversions are commonly used in water/wastewater treat-
ment calculations; however, the most accurate conversion is 1 ft = 0.433 psi. This
is the conversion we use throughout this text.

VELOCITY
The velocity of the water moving through a pipe can be determined if the flow in cubic
feet per second (cfs) and the diameter of the pipe (inches) are known. The area of the
pipe must be calculated in square feet (ft 2 ) and the flow is then divided by the area.

Flow (cfs)
Area (ft 2

Velocity (fps) = (12.11)

)

or

Distance
Time

Velocity (fps) = (12.12)

Velocity is expressed in units such as ft/sec, miles/hour, ft/min, etc. The time unit of
velocity can vary, as long as it is the same within each problem.

■ Example 12.8
Problem : A 24-in. pipe carries a flow of 12 cfs. What is the velocity in the pipe?

Solution : Change diameter in inches to feet:

24 in. ÷ 12 in./ft = 2 ft; radius = 1 ft

Find the area of the pipe in square feet:

Area = π × r 2 = 3.14 × (1 ft) 2 = 3.14 ft 2

Find the velocity in fps:

12 cfs ÷ 3.14 ft 2 = 3.8 fps