Hydropower - Environmental Impacts of Renewable Energy - page 115

Mass
Volume

Density = (4.2)

Perhaps the most common measures of density are pounds per cubic foot (lb/ft 3 )
and pounds per gallon (lb/gal):

• 1 ft 3 of water weighs 62.4 lb; density = 62.4 lb/ft 3 .

• 1 gal of water weighs 8.34 lb; density = 8.34 lb/gal.

The density of dry material, such as cereal, lime, soda, or sand, is usually expressed
in pounds per cubic foot. The density of a liquid, such as liquid alum, liquid chlorine,
or water, can be expressed either as pounds per cubic foot or as pounds per gallon.
The density of a gas, such as chlorine gas, methane, carbon dioxide, or air, is usually
expressed in pounds per cubic foot. As shown in Table 4.3, the density of a substance
such as water changes slightly as the temperature of the substance changes. This occurs
because substances usually increase in volume by expanding as they become warmer.
Because of this expansion with warming, the same weight is spread over a larger vol-
ume, so the density is lower when a substance is warm rather than when it is cold.

Note: What is specific gravity? Specific gravity is the weight (or density) of a sub-
stance compared to the weight (or density) of an equal volume of water. The spe-
cific gravity of water is 1.

This relationship is easily seen when a cubic foot of water, which weighs 62.4
lb, is compared to a cubic foot of aluminum, which weighs 178 lb. Aluminum is 2.7
times as heavy as water. It is not that difficult to find the specific gravity of a piece
of metal. All you have to do is weigh the metal in air, then weigh it under water. Its
loss of weight is the weight of an equal volume of water. To find the specific gravity,
divide the weight of the metal by its loss of weight in water:

Weight of substance
Weight

Specificgravity = (4.3)

of equal volumeofwater

■ Example 4.3
Problem: Suppose a piece of metal weighs 150 lb in air and 85 lb under water. What
is the specific gravity?

Solution:

150 lb - 85 lb = 65 lb loss of weight in water

Specific gravity = 150 ÷ 65 = 2.3

DID YOU KNOW?

In a calculation of specific gravity, it is essential that the densities be expressed
in the same units.