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

6.4 Dimensional Homogeneity 141

Density of air, r

Example 6.2 For the following problems, use the conversion factors given on the front and back end covers

of this book.

a) Convert the given value of area,A, from cm

2

to m

2

.

b) Convert the given value of volume,V, from mm

3

to m

3

.

c) Convert the given value of atmospheric pressure,P, from N/m

2

to lbf/in

2

.

d) Convert the given value of the density of water, r, from kg /m

3

to lbm/ft

3

.

6 6..4 4 DDiimmeennssiioonnaall HHoommooggeenneeiittyy

Another important concept that you need to understand completely is that all formulas used

in engineering analysis must be dimensionally homogeneous. What do we mean by “dimen-

sionally homogeneous?” Can you, say, add someone’s height who is 6 feet tall to his weight of

185 lbfand his body temperature of 98F? Of course not! What would be the result of such a

calculation? Therefore, if we were to use the formulaLabc, in which the variableL

on the left-hand side of the equation has a dimension of length, then the variablesa,b,andc

on the right-hand side of equation should also have dimensions of length. Otherwise, if vari-

ablesa,b,andchad dimensions such as length, weight, and temperature, respectively, the given

ra 1000

kg

m

3 ba

1 lbm

0.4536 kg

ba

1 m

3.28 ft

b

3

62.5 lbm/ft

3

r1000 kg/m

3

Pa 10

5

N

m

2 ba

1 lbf

4.448 N

ba

0.0254 m

1 in.

b

2

14.5 lbf/in

2

P 10

5

N/m

2

V 1 1000 mm

3

2a

1 m

1000 mm

b

3

 10

 6

m

3

V1000 mm

3

A 1 100 cm

2

2a

1 m

100 cm

b

2

0.01 m

2

A100 cm

2

ra0.0735

lbm

ft

3 ba

0.453 kg

1 lbm

ba

1 ft

0.3048 m

b

3

1.176 kg/m

3

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