Fundamental Engineering Concepts - Mathematics and Statistics for the Environment - page 244

11.5.2 s peCiFiC g ravity
Specific gravity is the ratio of the weight of a liquid or solid substance to the weight of an equal vol-
ume of water, a number that can be determined by dividing the weight of a body by the weight of an
equal volume of water. Because the weight of any body per unit of volume is its density, then

Density of body
Densityof

Specificgravity = (11.6)

water

■ EXAMPLE 11.9
Problem: The density of a particular material is 0.24 lb/in. 3 , and the density of water is 0.0361 lb/
in. 3 . What is the specific gravity?

Solution:

Density of body
Densityof

024
0 0361

.

Specificgravity = = = 66 .

water .

The material is 6.6 times as heavy as water. This ratio does not change, regardless of the units that
may be used, which is an advantage for two reasons: (1) the ratio will always be the same for the
same material, and (2) specific gravity is less confusing than the concept of density, which changes
as the units change.

11.5.3 F orCe , m ass , and a CCeleration
Let's review what we learned earlier about force, mass, and acceleration. According to Newton's
second law of motion:

The acceleration produced by unbalanced force acting on a mass is directly proportional to the unbal-
anced force, in the direction of the unbalanced force, and inversely proportional to the total mass being
accelerated by the unbalanced force.

If we express Newton's second law mathematically, it is greatly simplified and becomes

F = ma (11.7)

where F is force, m is mass, and a is acceleration; 1 Newton = 1 kg × m/s 2 . This equation is
extremely important in physics and engineering. It simply relates acceleration to force and mass.
Acceleration is defined as the change in velocity divided by the time taken. This definition tells us
how to measure acceleration. F = ma tells us what causes the acceleration—an unbalanced force.
Mass may be defined as the quotient obtained by dividing the weight of a body by the acceleration
caused by gravity. Because gravity is always present, we can, for practical purposes, think of mass
in terms of weight, making the necessary allowance for gravitational acceleration.

11.5.4 C entriFugal and C entripetal F orCes
Two terms with which the environmental professional should be familiar are centrifugal force and
centripetal force . Centrifugal force is a concept based on an apparent (but not real) force. It may
be regarded as a force that acts radially outward from a spinning or orbiting object (a ball tied to a
string whirling about), thus balancing a real force, the centripetal force (the force that acts radially
inwards). This concept is important in environmental engineering, because many of the machines