Page 205 - Schaum's Outline of Theory and Problems of Applied Physics

CHAPTER 16

Fluids at Rest

DENSITY

The density d of a substance is its mass per unit volume. The SI unit of density is kilograms per cubic meter
3
3
(kg/m ); the density of aluminum, for instance, is 2700 kg/m . Another common unit of density is grams per
6
3
3
3
3
cubic centimeter (g/cm ). Since 1 kg = 1000 g and 1 m = (100 cm) = 10 cm ,
3
3
1 g/cm = 10 kg/m 3
3
Hence the density of aluminum can also be given as 2.7 g/cm .
In British units density is properly expressed in slugs per cubic foot. The density of aluminum in these units
3
is 5.3 slugs/ft . Because weight rather than mass is normally specified in this system, the quantity weight density
is customarily used. The weight density of a substance is its weight per unit volume. Thus the weight density of
3
aluminum is 170 lb/ft . There is no special symbol for weight density, and either w/V or dg can be used for it.
SPECIFIC GRAVITY
The specific gravity (or relative density) of a substance is its density relative to that of pure water, which is
3
3
d(water) = 1000 kg/m = 1.00 g/cm = 1.94 slugs/ft 3
The weight density of water is
dg(water) = 62 lb/ft 3
3
Since the density of water is 1 g/cm , the specific gravity of a substance is the same as the numerical value of its
density given in grams per cubic centimeter. Thus the specific gravity of aluminum is 2.7.

SOLVED PROBLEM 16.1
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The specific gravity of gold is 19. (a) What is the mass of 1 cm of gold? (b) What is the weight of 1 in. 3
of gold?
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3
3
(a) Since the density of water is 1 g/cm , the density of gold is 19 g/cm and1cm has a mass of 19 g.
3
3
3
(b) Since the weight density of water is 62 lb/ft , the weight density of gold is dg = (19)(62) lb/ft = 1200 lb/ft .
3
3
Because 1 ft = (12 in.)(12 in.)(12 in.) = 1728 in. , a cubic inch of gold weighs
lb 1ft
3
w = (dg)V = 1200 = 0.7lb
ft 3 1728 in 3
190