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

Problems 455

of 15 m/s V35 m/s, and change the air density

range of 1.11 kg /m

3

r1.29 kg /m

3

. The given
air density range corresponds to 0to 45C. You may
use the ideal gas law to relate the density of the air to
its temperature. Present your findings in both kilo-
watts and horsepower as shown in the accompany-
ing spreadsheet. Discuss your findings in terms of
power consumption as a function of speed and air
temperature.
14.12. The cantilevered beam shown in the accompanying
figure is used to support a load acting on a balcony.
The deflection of the centerline of the beam is given
by the following equation:

where

y deflection at a givenxlocation ( m)

wdistributed load (N/m)

Emodulus of elasticity (N/m

2

)

I second moment of area ( m

4

)

x distance from the support as shown (x)

Llength of the beam ( m)

y

wx

2

24 EI

1 x

2

 4 Lx 6 L

2

2

Common examples include a motorcycle or lawn

mower engine head, extended surfaces used in elec-

tronic equipment, and finned tube heat exchangers in

room heating and cooling applications. Consider a

rectangular profile of aluminum fins shown in the

accompanying figure, which are used to remove heat

from a surface whose temperature is 100C (Tbase

100 C). The temperature of the ambient air is 20C.

We are interested in determining how the temperature

of the fin varies along its length and plotting this

temperature variation. For long fins, the temperature

distribution along the fin is given by

where

hthe heat transfer coefficient (W/m

2

K)

pperimeter of the fin 2*(ab), ( m)

Across-sectional area of the fin (a*b), ( m

2

)

kthermal conductivity of the fin material

(W/m K)

Plot the temperature distribution along the fin using

the following data: k168 W/m K, h

12 W/m

2

K,a0.05 m,b0.01 m. Varyxfrom

0 to 0.1 m in increments of 0.01 m.

m

B

hp

kA

TTambient 1 TbaseTambient 2 e

mx

L

w

x

Problem 14.12

14.14. A person by the name of Huebscher developed a rela-

tionship between the equivalent size of round ducts

and rectangular ducts according to

D1.3

1 ab 2

0.625

1 ab 2

0.25

Using Excel, plot the deflection of a beam whose

length is 5 m with the modulus of elasticity ofE

200 GPa andI99.1   10

6

mm

4

. The beam is
designed to carry a load of 10,000 N/m. What is the
maximum deflection of the beam?
14.13. Fins, or extended surfaces, are commonly used in a
variety of engineering applications to enhance cooling.

x

a

b

Base

Problem 14.13

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