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

Problems 499

Emodulus of elasticity (N/m

2

)

Isecond moment of area ( m

4

)

xdistance from the support as shown ( m)

Llength of the beam ( m)

Using MATLAB, plot the deflection of a beam

whose length is 5 m with the modulus of elasticity of

E200 GPa andI99.1  10

6

mm

4

. The beam is
designed to carry a load of 10000 N/m. What is the
maximum deflection of the beam?
15.12.Fins, or extended surfaces, commonly are used in a va-
riety of engineering applications to enhance cooling.
Common examples include a motorcycle engine head,
a lawn mower engine head, extended surfaces used in
electronic equipment, and finned tube heat exchang-
ers in room heating and cooling applications. Con-
sider aluminum fins of a rectangular profile shown in
Problem 14.13, which are used to remove heat from a
surface whose temperature is 100°C. The temperature
of the ambient air is 20°C. We are interested in deter-
mining 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

and

hthe heat transfer coefficient (W/m

2

K)

pperimeter 2*(ab) of the fin ( 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, andb0.01 m. Varyx

from 0 to 0.1 m in increments of 0.01 m.

15.13. A person by the name ofHuebscherdeveloped a rela-

tionship between the equivalent size of round ducts

and rectangular ducts according to

where

Ddiameter of equivalent circular duct ( mm)

adimension of one side of the rectangular

duct ( mm)

bdimension of the other side of the rectangu-

lar duct ( mm)

Using MATLAB, create a table that shows the rela-

tionship between the circular and the rectangular duct,

similar to the one shown in the accompanying table.

15.14. A Pitot tube is a device commonly used in a wind

tunnel to measure the speed of the air flowing over a

model. The air speed is measured from the following

equation:

where

Vair speed ( m/s)

Pddynamic pressure (Pa)

rdensity of air (1.23 kg /m

3

)

V

B

2 Pd

r

D1.3

1 ab 2

0.625

1 ab 2

0.25

m

B

hp

kA

TTambient 1 TbaseTambient 2 e

mx

Problem 15.11

Length of One Side of

Rectangular Duct (length a), mm

Length b 100 125 150 175 200

400

450

500

550

600

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