Science of Water : Concepts and Applications

50 The Science of Water: Concepts and Applications
Example 3.4
Problem:
There are 1455 gal of a certain liquid in a basin. If the specifi c gravity of the liquid is 0.94, how many
pounds of liquid are in the basin?
Solution:
Normally, for a conversion from gallons to pounds, we would use the factor 8.34 lb/gal (the density
of water) if the substance’s specifi c gravity was between 0.98 and 1.02. However, in this instance, the
substance has a specifi c gravity outside this range, so the 8.34 factor must be adjusted.
Step 1: Multiply 8.34 lb/gal by the specifi c gravity to obtain the adjusted factor:
834 . lb/gal094 . 784
. lb/gal ( rounded)
Step 2: Then convert 1455 gal into pounds using the corrected factor:
FORCE AND PRESSURE
( 1455 gal)( 7. 84 lb/gal) 11,
407 lb ( rounded)
Water exerts force and pressure against the walls of its container, whether it is stored in a tank or
fl owing in a pipeline. There is a difference between force and pressure, though they are closely
related. Force and pressure are defi ned below.
Force is the push or pull infl uence 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 (see Figure 3.1). If we stack two cubes on top of each other, the force
on the bottom will be 124.8 lb.
Pressure is a force per unit of area. In equation form, this can be expressed as:
where
P = pressure
F = force
A = area over which the force is distributed
P F
A
As mentioned, pounds per square inch or pounds per square foot are common expressions of
pressure. The pressure on the bottom of the cube is 62.4 lb/ft 2 (see Figure 3.1). It is common to
express pressure in pounds per square inch. This is easily accomplished by determining the weight
of 1 in. 2 of a cube 1 ft high. 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
psi 0.433
psi/ft
2
144 in.
This is the weight of a 1-in. 2 and 1-ft-tall column of water. If the column of water were 2 ft tall, the
pressure would be 2 ft × 0.433 psi/ft = 0.866.
(3.4)