Basic Math Operations - Mathematics and Statistics for the Environment - page 70

2.12.2.6 Head and Pressure
If the head is known, the equivalent pressure can be calculated by

Head (ft)
2.31 ft/psi

Pressure (psi) = (2.20)

■ EXAMPLE 2.56
Problem: A tank is 15 ft deep. What is the pressure in psi at the bottom of the tank when it is filled
with wastewater?

Solution:

15 ft
2.31 ft/psi

Pressure (psi) = = 6.49 psi

Before we look at a few example problems dealing with force, pressure, and head, it is important
to review the key points related to force, pressure, and head:

1. By definition, water weighs 62.4 lb/ft 3 .

2. The surface of any one side of a 1-ft 3 cube contains 144 in. 2 (12 in. × 12 in. = 144 in. 2 );
therefore, the cube contains 144 columns of water that are 1 ft tall and 1 inch square.

3. The weight of each of these pieces can be determined by dividing the weight of the water
in the cube by the number of square inches:

62.4 lb
144 in.

2

Weight = = 0.433 lb/in.or 0.4 33 psi

2

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

Note: 1 foot of head = 0.433 psi.

In addition to remembering the important parameter that 1 ft 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 ft by 0.433 psi:

1ft
0.433 psi

Feet of head = = 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.

Key Point: Both of the above conversions are commonly used in water/wastewater treatment cal-
culations; however, the most accurate conversion is 1 ft = 0.433 psi. This is the conversion we use
throughout this text.