156 Chapter 6 Fundamental Dimensions and Units
Those of you who will pursue aerospace, chemical,
mechanical, or materials engineering will learn about
the underlying concepts that lead to the solution in
your heat-transfer class. What is the appropriate unit
forhif the preceding equation is to be homogeneous in
units? Show all steps of your work.
6.24. The air resistance to the motion of a vehicle is some-
thing important that engineers investigate. As you may
also know, the drag force acting on a car is determined
experimentally by placing the car in a wind tunnel. For
a given car, the experimental data is generally repre-
sented by a single coefficient that is called the drag
coefficient. It is given by the following relationship:where
Cddrag coefficient
Fdmeasured drag force (lb)
rair density (slugs /ft
3
)Vair speed inside the wind tunnel (ft /s)
A frontal area of the car (ft
2
)What is the appropriate unit forCdif the preceding
equation is to be homogeneous in units? Show all steps
of your work.
6.25. Fins, or extended surfaces, commonly are used in a
variety of engineering applications to enhance cooling.
Common examples include a motorcycle engine head,
a lawn mower engine head, heat sinks used in elec-
tronic equipment, and finned tube heat exchangers in
room heating and cooling applications. For long fins,
the temperature distribution along the fin is given by
the exponential relationship:where
Ttemperature (K)
hthe heat transfer coefficient (W/m
2
K)pperimeter of the fin ( m)
m
Bhp
kA
TTambient 1 TbaseTambient 2 e
mxCd
Fd
1
2 rV^2
AAcross-sectional area of the fin ( m
2
)kthermal conductivity of the fin material
xdistance from the base of the fin ( m)
What is the appropriate unit forkif the preceding
equation is to be homogeneous in units? Show all steps
of your work.
6.26. A person who is 180 cm tall and weights 750 newtons
is driving a car at a speed of 90 kilometers per hour
over a distance of 80 kilometers. The outside air tem-
perature is 30°C and has a density of 1.2 (kg /m
3
) kilo-
grams per cubic meter. Convert all of the values given
in this example from SI units to U.S. Customary units.
6.27. Use the conversion factors given on the front and back
end covers of this text and convert the given values.
(a) Value of area A16 in
2
to ft
2
, (b) Value of volume
V64 in
3
to ft
3
, (c) Value of area moment of inertia
I21.3 in
4
to ft
4
.
6.28. The acceleration due to gravity gis 9.81 m/s
2. Express
the value gin U.S. Customary and B.G. units. Show all
conversion steps.
6.29. Sir Isaac Newton discovered that any 2 masses m 1 and
m 2 attract each other with a force that is equal in mag-
nitude and acts in the opposite direction, according to
the following relationship:
where
Fattractive force, N
GUniversal Gravitational Constant
m 1 mass of particle-1, kg
m 2 mass of particle-2, kg
rdistance between the center of each
particle, mWhat is the appropriate unit for G, if the above equa-
tion is to be homogeneous in units?
6.30. Convert the atmospheric pressure in the given units to
requested units. Show all the conversion steps. (a)
14.7 lbf/in
2
to lbf/ft
2
, (b) 14.7 lbf/in
2
to Pa, (c) 14.7
lbf/in
2
to kPa, (d) 14.7 lbf/in
2
to bar (1 bar 100 kPa).
6.31. For gases under certain conditions, there is a relation-
ship between the pressure of the gas, its volume, and itsF
Gm 1 m 2
r
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