Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

270 Chapter 10 Force and Force-Related Parameters

In Chapter 7, when we were discussing the importance of area and its role in engineering

applications, we briefly mentioned the importance of understanding pressure in situations

such as foundations of buildings, hydraulic systems, and cutting tools. We also said that in

order to design a sharp knife, one must design the cutting tool such that it creates large pres-

sures along the cutting edge. This is achieved by reducing the contact surface area along the cut-

ting edge. Understanding fluid pressure distributions is very important in engineering problems

in hydrostatics, hydrodynamics, and aerodynamics.Hydrostaticrefers to water at rest and its

study; however, the understanding of other fluids is also considered in hydrostatics. A good

example of a hydrostatic problem is calculating the water pressure acting on the surface of a dam

and how it varies along the height of the dam. Understanding pressure is also important in

hydrodynamics studies, which deal with understanding the motion of water and other fluids

such as those encountered in the flow of oil or water in pipelines or the flow of water around

the hull of a ship or a submarine. Air pressure distributions play important roles in the analy-

sis of air resistance to the movement of vehicles or in creating lift forces over the wings of an

airplane. Aerodynamics deals with understanding the motion of air around and over surfaces.

Common Units of Pressure

In the International System of units, pressure units are expressed in pascal. One pascal is the

pressure created by one newton force acting over a surface area of 1 m

2

:

(10.13)

In U.S. Customary units, pressure is commonly expressed in pounds per square inch or

pounds per square foot; one lb/in

2

(1 psi) represents the pressure created by a 1-pound force

over an area of 1 in

2

, and 1 lb/ft

2

represents the pressure created by a 1-pound force over an area

of 1 ft

2

. To convert the pressure from lb/ft
2
to lb/in
2
, we take the following step:

(10.14)

Note that 1 lb/in

2

is usually referred to as 1 psi, which reads one pound per square inch. Many

other units are also commonly used for pressure. For example, the atmospheric pressure

is generally given in inches of mercury (inHg) or millimeters of mercury ( mmHg). In air-

conditioning applications, often inches of water are used to express the magnitude of air

pressure. These units and their relationships with Pa and psi will be explained further in

Example 10.9, after we explain how the pressure of a fluid at rest changes with its depth.

For fluids at rest, there are two basic laws: (1) Pascal’s law, which explains that the pressure

of a fluid at a point is the same in all directions, and (2) the pressure of fluid increases with its

depth. Even though these laws are simple, they are very powerful tools for analyzing various

engineering problems.

Pascal’s Law

Pascal’s law states that for a fluid at rest,pressure at a pointis the same in all directions. Note care-

fully that we are discussing pressure at a point. To demonstrate this law, consider the vessel

shown in Figure 10.20; the pressure at pointAis the same in all directions.

P a

lb

in

2 bP^ a

lb

ft

2 ba

1 ft

2

144 in

2 b

1 Pa

1 N

m

2

A

■Figure 10.20

In a static fluid, pressure

at a pointis the same in all

directions.

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