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

formula would be inhomogeneous, which would be like adding someone’s height to his weight

and body temperature! Example 6.3 shows how to check for homogeneity of dimensions in an

engineering formula.

Example 6.3 (a) When a constant load is applied to a bar of constant cross section, as shown in Figure 6.2,

the amount by which the end of the bar will deflect can be determined from the following

relationship:

(6.1)

where

dend deflection of the bar in meter ( m)

Papplied load in newton (N)

Llength of the bar in meter ( m)

Across-sectional area of the bar in m

2

Emodulus of elasticity of the material

What are the units for modulus of elasticity?

For Equation (6.1) to be dimensionally homogeneous, the units on the left-hand side of

the equation must equal the units on the right-hand side. This equality requires the modulus

of elasticity to have the units of N/m

2

, as follows:

Solving for the units ofEleads to N/m

2

, newton per squared meter, or force per unit area.

(b) The heat transfer rate through a solid material is governed by Fourier’s law:

(6.2)

where

qheat transfer rate

kthermal conductivity of the solid material in watts per meter degree Celsius,

W/mC

Aarea in m

2

T 1 T 2 temperature difference, C

Lthickness of the material, m

What is the appropriate unit for the heat transfer rateq?

Substituting for the units ofk,A,T 1 ,T 2 ,andL, we have

From this you can see that the appropriate SI unit for the heat transfer rate is the watt.

qkA

T 1 T 2

L

a

W

m#°C

b1m

2

2a

°C

m

bW

qkA

T 1 T 2

L

d

PL

AE

1 m

1 N 21 m 2

m

2

E

d

PL

AE

142 Chapter 6 Fundamental Dimensions and Units

L

d

A

P

(a)

■Figure 6.2

(a) The bar in Example 6.3

and (b) heat transfer

through a solid material.

(b)

T 1

T 2

L

A

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