Water Hydraulics - Mathematics and Statistics for the Environment - page 591

62.4 lb
of water

1 ft

1 ft

1 ft

FIGURE 22.1 One cubic foot of water weights 62.4 lb. (From Spellman, F.R. and Drinan, J., Water
Hydraulics , Technomic, Lancaster, PA, 2001.)

22.2.3 F orCe and p ressure
Water exerts force and pressure against the walls of its container, whether it is stored in a tank or
flowing in a pipeline. Force and pressure are different, although they are closely related. Force is the
push or pull influence that causes motion. In the English system, force and weight are often used in
the same way. The weight of 1 ft 3 of water is 62.4 lb. The force exerted on the bottom of a 1-ft cube
is 62.4 lb (Figure 22.1). If we stack two 1-ft cubes on top of one another, the force on the bottom
will be 124.8 lb. Pressure is the force per unit of area. In equation form, this can be expressed as

F
A

P = (22.4)

where
P = Pressure.
F = Force.
A = Area over which the force is distributed.

Pounds per square inch (lb/in. 2 or psi) or pounds per square foot (lb/ft 2 ) are common expressions
of pressure. The pressure on the bottom of the cube is 62.4 lb/ft 2 (see Figure 22.1). It is normal to
express pressure in pounds per square inch. This is easily accomplished by determining the weight
of 1 in. 2 of a 1-ft cube. If we have a cube that is 12 in. on each side, the number of square inches on
the bottom surface of the cube is 12 × 12 = 144 in 2 . Dividing the weight by the number of square
inches determines the weight on each square inch:

62.4 lb/ft
144 in.

psi = = 0.433 psi/ft

2

This is the weight of a column of water 1 in. square and 1 ft tall. If the column of water was 2 ft tall,
the pressure would be 2 ft × 0.433 psi/ft = 0.866. With the above information, feet of head can be
converted to psi by multiplying the feet of head by 0.433 psi/ft.

■ EXAMPLE 22.5
Problem: A tank is mounted at a height of 90 ft. Find the pressure at the bottom of the tank.

Solution:

90 ft × 0.433 psi/ft = 39 psi (rounded)

If we wanted to make the conversion of psi to feet, we would divide the psi by 0.433 psi/ft.