6-1 CHAPTER 6 Fundamental Dimensions and Units © 2011 Cengage Learning Engineering. All Rights Reserved

6-1

CHAPTER 6Fundamental Dimensions and Units

© 2011 Cengage Learning Engineering. All Rights Reserved.© 2011 Cengage Learning Engineering. All Rights Reserved.

6-2

Engineering Fundamentals – Concepts Every Engineer Should Know

• Fundamental dimensions and units

• Length and length-related parameters

• Time and time-related parameters

• Mass and mass-related parameters

• Force and force-related parameters

• Temperature and temperature-related parameters

• Electric current and related parameters

• Energy and power


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Outline

In this chapter we will

• Explain fundamental dimensions and units

• Explain the steps necessary to convert information from one system of units to another

• Explain what is meant by an engineering components and systems


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Outline (continued)

In this chapter we will

• Emphasize the importance of showing appropriate units with all calculations

• Discuss how you can learn the engineering fundamental concepts using fundamental dimensions


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Objectives

The objectives of this chapter are to

• Introduce the fundamental dimensions and units that every engineer should know

• Show how these fundamental quantities are related to design


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Fundamental Dimensions

• Length

• Mass

• Time

• Electric current

• Temperature

• Amount of substance

• Luminous intensity

The physical quantities used to fully describe natural events and our surroundings are:


6-7

Units

• Used to measure physical dimensions

• Appropriate divisions of physical dimensions to keep numbers manageable

19 years old instead of 612,000,000 seconds old

• Common systems of units International System (SI) of Units British Gravitational (BG) System of Units U.S. Customary Units


6-8

Units – SI

• Most common system of units used in the world

• Examples of SI units are: kg, N, m, cm,

• Approved by the General Conference on Weights and Measures (CGPM)

• Series of prefixes & symbols of decimal multiples (adapted by CGPM, 1960)


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Fundamental Unit of Length

meter (m) – length of the path traveled by light in a vacuum during a time interval of 1/299,792,458 of a second


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kilogram (kg) – a unit of mass; it is equal to the mass of the international prototype of the kilogram

Fundamental Unit of Mass


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Fundamental Unit of Time

second (s) – duration of 9,192,631,770 periods of the radiation corresponding to the transition between the 2 hyperfine levels of the ground state of cesium 133 atom


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ampere (A) – constant current which, if maintained in 2 straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 meter apart in a vacuum, would produce between these conductors a force equal to 2x10-7N/m length

Fundamental Unit of Electric Current


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kelvin (K) – unit of thermodynamic temperature, is the fraction 1/273.16 of thermodynamic temperature of the triple point of water

Fundamental Unit of Temperature


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mole (mol) – the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12

Fundamental Unit of Amount of Substance


6-15

Fundamental Unit of Luminous Intensity

candela (cd) – in a given direction, of a source that emits monochromatic radiation of frequency 540x1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian


6-16

SI – Prefix & Symbol

Adopted by CGPM in 1960


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Examples of Derived Units in Engineering

More in chapters

7-13


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• Primary units are foot (ft) for length (1 ft = 0.3048 m) second for time pound (lb) for force (1 lb = 4.448 N) Fahrenheit (oF) for temperature

• Slug is unit of mass which is derived from Newton’s second law

1 lb = (1 slug)(1 ft/s2)

British Gravitation (BG) System

KTRTCTFT5

9 32

5

9

More on temperature in chapter 11


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U.S. Customary System of Units

• Primary units are Foot (ft) for length (1 ft = 0.3048 m) second for time pound mass (lbm) for mass (1 lbm = 0.453592

kg, 1slug = 32.2 lbm)

• Pound force (lbf) is defined as the weight of an object having a mass of 1 lbm at sea level and at a latitude of 45o, where acceleration due to gravity is 32.2 ft/s2 (1lbf = 4.448 N)

More on derived units in chapters

7-13


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Examples of SI Units in Everyday Use


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Examples of U.S. Customary Units in Everyday Use


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Systems of Units and Conversion Factors


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Unit Conversion

• In engineering analysis and design, there may be a need to convert from one system of units to another

• When communicate with engineers outside of U.S.

• Important to learn to convert information from one system of units to another correctly

• Always show the appropriate units that go with your calculations

• See the conversion tables given in the book


6-24

Example 6.1 – Unit Conversion

Given: a person who is 6’-1” tall and weighs 185 pound force (lbf)

Find: height and weight in SI units

Solution:

N 88.822lb 1

N 448.4lb 185

weight,sPerson'

m 854.1ft 1

m 3048.0

in 12

ft 1in 1ft 6

height, sPerson'

ff

W

W

H

H


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Example 6.1 – Unit Conversion (continued)

Given: a person is driving a car at a speed of 65 miles per hour (mph) over a distance of 25 miles

Find: speed and distance in SI units

Solution:

km 233.40m 1000

km 1

ft 1

m 0.3048

mile 1

ft 5280miles 25

traveled,Distance

m/s 057.29s 3600

h 1

h

m 607,104 or

km/h 104.607 m/h 607,104ft 1

m 0.3048

mile 1

ft 5280

h

miles65

car, of Speed

D

D

S

S

S


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Given: outside temperature is 80oF and has a density of 0.0735 pound mass per cubic foot (lbm/ft3)

Find: temperature and density in SI units

Solution:

33

m3m kg/m 176.1

m 0.3048

ft 1

lb 1

kg 453.0

ft

lb0735.0

air, ofDensity

C7.2632809

532F

9

5C

air, of eTemperatur

TT

T


6-27

Example 6.2 – Unit Conversion

Given: area A = 100 cm2

Find: A in m2

Solution:

22

2 m 01.0cm 100

m 1cm 100

A


6-28


Given: volume V = 1000 mm3

Find: V in m3

Solution:

363

3 m 10mm 1000

m 1mm 1000

V


6-29


Given: atmosphere pressure P = 105 N/m2

Find: P in lb/in2

Solution:

22

25 lb/in 5.14

in 1

m 0.0254

N 4.448

lb 1

m

N 10

P


6-30


Given: density of water = 1000 kg/m3

Find: density in lbm/ft3

Solution:

3m

3

m3

/ftlb 5.62ft 3.28

m 1

kg 0.4536

lb 1

m

kg 1000


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Examples of Unit Conversion


6-32

Dimension Homogeneity

• Given: L = a + b + c

• Left hand side of equation should have the same dimension as right hand side of equation

• If L represents dimension length, then a, b, and c must also have the dimension of length – this is called dimensionally homogeneous


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Example 6.3 – Dimension Homogeneity

Given: whered = end deflection, in mP = applied load, in NL = length of bar, in mA = cross-sectional area of bar, in m2 E: modulus of elasticity

Find: units for E

AE

PLd


6-34

Example 6.3 – Dimension Homogeneity (continued)

Solution:

22

2

m

N

mm

mN E

m

mN m

AE

PLd

E


6-35


Given:

Whereq = heat transfer ratek = thermal conductivity of the solid material in W/m●°CA = area in m2

T1 – T2 = temperature difference, °CL = thickness of the material, m

Find: units for q

L

TTkAq 21


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Solution:

Wm

Cm

Cm

W 221

L

TTkAq


6-37

Example 6.5 – Numerical Versus Symbolic Solutions

Given: hydraulic system shown

Find: m2

Numerical solution:

kg 900 N8829m/s 81.9

N 8829N 981m 05.0

m 15.0

N 981m/s 81.9kg 100

22

22

2

2

11

22

211

mmF

FA

AF

gmF


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Example 6.5 – Numerical Versus Symbolic Solutions (continued)

Given: hydraulic system shown

Find: m2

Symbolic solution:

kg 900kg 100m 05.0

m 15.0

2

2

121

22

2

121

22

211

22

mR

Rm

gmR

RgmF

A

AF


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Significant Digits (Figures)

• Engineers make measurements and carry out calculations

• Engineers record the results of measurements and calculations using numbers.

• Significant digits (figures) represent (convey) the extend to which recorded or computed data is dependable.


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Significant Digits – How to Record a Measurement

Least count – one half of the smallest scale division

What should we record for this temperature measurement?

71 ± 1oF


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What should we record for the length?

3.35 ± 0.05 in.


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What should we record for this pressure?

7.5 ± 0.5 in.



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Significant Digits

• 175, 25.5, 1.85, and 0.00125 each has three significant digits.

• The number of significant digits for the number 1500 is not clear.

It could be 2, 3, or 4 If recorded as 1.5 x 103 or 15 x 102, then

2 significant digits


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Significant Digits – Addition And Subtraction Rules

When adding or subtracting numbers, the result of the calculation should be recorded with the last significant digit in the result determined by the position of the last column of digits common to all of the numbers being added or subtracted.

For example,

152.47 or 132. 853

+ 3.9 - 5

156.37 127.853 (your calculator will display)

156.3 127 (however, the result should be recorded this way)


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When multiplying or dividing numbers, the result of the calculation should be recorded with the least number of significant digits given by any of the numbers used in the calculation.

For example,

152.47 or 152.47

× 3.9 ÷ 3.9

594.633 39.0948717949 (your calculator will display)

5.9 x 102 39 (however, the result should be recorded this way)

Significant Digits – Multiplication and Division Rules


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Significant Digits – Examples

276.34 + 12.782

289.12

2955 x 326

9.63 x 105


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Rounding Numbers

In many engineering calculations, it may be sufficient to record the results of a calculation to a fewer number of significant digits than obtained from the rules we just explained

56.341 to 56.34

12852 to 1.285 x 104


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Engineering Components & Systems

Every engineered product is made of components

sleeve component

chest component

other components


6-49

Engineering Components & Systems (continued)

Components:Cooling systemEngineWiper motor systemExhaust systemDrive trainBrake system

System:vehicle


6-50

Physical Laws and Observations in Engineering

• Engineers apply physical and chemical laws and principles along with mathematics to design, develop, test, and produce products and services that we use in our everyday lives

• Universe was created in a certain way

• We have learned through observation that things work a certain way in nature

For example, if we let go something, it will drop


6-51

Physical Laws and Observations in Engineering (continued)

• We use mathematics and basic physical quantities to express our observations in the form of a law

• For example, second law of thermodynamics Heat flows from higher temperature to

lower temperature region When a hot object is placed next to a cold

object, the hot object gets cooler and the cold object gets warmer; cold object does not get colder

More in thermodynamics

course


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• Engineers are good bookkeepers For example, conservation of mass

the rate by which mass enters a system minus the rate by which it leaves the system should equal to the rate of increase or decrease of mass within the system

Conservation of energy Keep track of various forms of energy and

how they may change from one form to another


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Newton’s second law of motion – there is a direct relationship between the push, mass being pushed, and acceleration of mass

More in chapter 10,

physics, and dynamics


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• Physical laws are based on observations

• Some physical laws may not fully describe all possible situations

• Some laws are stated in a particular way to keep the mathematical expression simple

• Engineering correlations are based on experimental results and have limited applications


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Learning Engineering Fundamental Concepts and Design Variables from Fundamental Dimensions

• In Chapters 7 to 12, we will focus on teaching you some of the engineering fundamentals that you will see over and over in some form or other during your college years.

• You should try to study these concepts, that every engineer should know, carefully and understand them completely.

• We will focus on an innovative way to teach some of the engineering fundamental concepts using fundamental dimensions.


6-56

Learning Engineering Fundamental Concepts and Design Variables from Fundamental Dimensions (continued)

• We only need a few physical quantities (fundamental dimensions) to describe events and our surroundings.

• With the help of these fundamental dimensions, we can define or derive engineering variables that are commonly used in analysis and design.


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Learning Engineering Fundamental Concepts and Design Variables from Fundamental Dimensions (continued)

Fundamental dimensions and how they are used in defining variables that are used in engineering analysis and design


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Summary

• You should understand the importance of fundamental dimensions in engineering analysis

• You should understand what is meant by an engineering system and an engineering component

• You should know the most common systems of units

• You should know how to convert values from one system of units to another


6-59

Summary (continued)

• You should understand the difference between numerical and symbolic solutions

• You should know how to present the result of your calculation or measurement using correct number of significant digits


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6-1 CHAPTER 6 Fundamental Dimensions and Units © 2011 Cengage Learning Engineering. All Rights Reserved