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

628 Chapter 18 Mathematics in Engineering

where

Fdmeasured drag force (N or lb)

Cddrag coefficient (unitless)

rair density (kg /m

3

or slugs /ft

3

)

Vair speed inside the wind tunnel ( m/s or

ft /s)

Afrontal area of the car ( m

2

or ft

2

)

The power requirement to overcome the air resistance

is computed by

Plot the power requirement (in hp) to overcome the

air resistance for a car with a frontal area of 2800 in

2

,

a drag coefficient of 0.4, and for an air density of

0.00238 slugs /ft

3

. Vary the speed from zero to 110 ft /s
(75 mph). Also, plot the rate of change of power
requirement as a function of speed.
18.7. The cooling rate for three different materials is shown
in the accompanying figure. The mathematical equa-
tion describing the cooling rate for each material is of
the exponential formT(t) Tinitiale
at
. In this rela-
tionship,T(t) is the temperature of material at timet
and the coefficientarepresents the thermal capacity
and resistance of the material. Determine the initial
temperature and theacoefficient for each material.
Which material cools the fastest, and what is the cor-
respondingavalue?

PFdV

18.5. The deflection of a cantilevered beam supporting the

weight of an advertising sign is given by

where

ydeflection at a givenxlocation ( m)

Wweight of the sign (N)

Emodulus of elasticity (N/m

2

)

Isecond moment of area ( m

4

)

xdistance from the support as shown ( m)

Llength of the beam ( m)

y

Wx

2

6 EI

13 Lx 2

L

x

Sign

Problem 18.5

Plot the deflection of a beam with a length of 3 m,

the modulus of elasticity ofE200 GPa, andI

1.2  10

6

mm

4

and for a sign weighing 1500 N.

What is the slope of the deflection of the beam at the

wall (x0) and at the end of the beam where it sup-

ports the sign (xL).

18.6. As we explained in earlier chapters, the drag force

acting on a car is determined experimentally by placing

the car in a wind tunnel. The drag force acting on the

car is determined from

Fd

1

2

C (^) d rV
2
A
Temperature (°C )
80
70
60
50
40
30
20
10
0
0246810
Time (min)
Material A
Material C
Material B
Problem 18.7
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