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

7.6 Area 173

This mental exercise gives you a good idea why, given the same amount of ice, the crushed

ice cools a drink faster than ice cubes do. You may not know it, but you already own the best

heat and mass exchanger in the world. Your lungs! Human lungs are the best heat and mass

exchangers that we know of, with an approximate area density (surface area of heat exchange

per unit volume) of 20,000 m

2

/m

3

.

Area plays an important role in aerodynamics as well. Air resistance to the motion of a

vehicle is something that all of you are familiar with. As you may also know, the drag force act-

ing on a vehicle is determined experimentally by placing it in a wind tunnel. The airspeed inside

the tunnel is changed, and the drag force acting on the vehicle is measured. Engineers have

learned that when designing new vehicles, the total exposed surface area and the frontal area are

important factors in reducing air resistance. The experimental data is normally given by a single

coefficient, which is called thedrag coefficient. It is defined by the following relationship:

The frontal area represents the frontal projection of the vehicle’s area and could be approximated

simply by calculating 0.85 times the width and the height of a rectangle that outlines the front of

the vehicle. This is the area that you see when you view the car or truck from a direction normal

to the front grill. Later in your engineering education, some of you may take a class in the physics

of flight, fluid mechanics, or aerodynamics, where you will learn that the lift force acting on the

wings of a plane is proportional to the planform area of the wing. The planform area is the area

that you would see if you were to look from above at the wing from a direction normal to the wing.

Cross-sectional area also plays an important role in distributing a force over an area. Foun-

dations of buildings, hydraulic systems, and cutting tools (see Figure 7.9) are examples of objects

for which the role of area is important. For example, have you ever thought about why the edge

of a sharp knife cuts well? What do we mean by a “sharp” knife? A good sharp knife is one that

has a cross-sectional area as small as possible along its cutting edge. The pressure along the cut-

ting edge of a knife is simply determined by

pressure at the cutting surface (7.3)

force

cross-sectional area at the cutting edge

drag coefficient

drag force

1

2

1 air density 21 air speed 2

2

1 frontal area 2

1 m

1 m

0.5 m

0.5 m 0.5 m

1 m

■Figure 7.8

The relationship between the area

and volume of a cube.

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