1. CHAPTER 6 Fundamental Dimensions and Units
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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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3. 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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4. 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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5. 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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6. Fundamental Dimensions
The physical quantities used to fully describe natural events and our surroundings are:
Temperature
Amount of substance
Luminous intensity
Length
Mass
Time
Electric current
© 2011 Cengage Learning Engineering. All Rights Reserved.
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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
© 2011 Cengage Learning Engineering. All Rights Reserved.
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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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9. 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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© 2011 Cengage Learning Engineering. All Rights Reserved.

10. Fundamental Unit of Mass
kilogram (kg) – a unit of mass; it is equal to the mass of the international prototype of the kilogram
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11. 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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12. Fundamental Unit of Electric Current
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
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13. Fundamental Unit of Temperature
kelvin (K) – unit of thermodynamic temperature, is the fraction 1/ of thermodynamic temperature of the triple point of water
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14. Fundamental Unit of Amount of Substance
mole (mol) – the amount of substance of a system that contains as many elementary entities as there are atoms in kilogram of carbon 12
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© 2011 Cengage Learning Engineering. All Rights Reserved.

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
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16. SI – Prefix & Symbol Adopted by CGPM in 1960
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17. Examples of Derived Units in Engineering
More in chapters 7-13
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18. British Gravitation (BG) System
More on temperature in chapter 11
Primary units are
foot (ft) for length (1 ft = m)
second for time
pound (lb) for force (1 lb = 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)
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© 2011 Cengage Learning Engineering. All Rights Reserved.

19. U.S. Customary System of Units
More on derived units in chapters 7-13
Primary units are
Foot (ft) for length (1 ft = m)
second for time
pound mass (lbm) for mass (1 lbm = 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 = N)
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20. Examples of SI Units in Everyday Use
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21. Examples of U.S. Customary Units in Everyday Use
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22. Systems of Units and Conversion Factors
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23. 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
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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:
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25. 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:
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26. Example 6.1 – Unit Conversion (continued)
Given: outside temperature is 80oF and has a density of pound mass per cubic foot (lbm/ft3)
Find: temperature and density in SI units
Solution:
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© 2011 Cengage Learning Engineering. All Rights Reserved.

27. Example 6.2 – Unit Conversion
Given: area A = 100 cm2
Find: A in m2
Solution:
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28. Example 6.2 – Unit Conversion (continued)
Given: volume V = 1000 mm3
Find: V in m3
Solution:
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29. Example 6.2 – Unit Conversion (continued)
Given: atmosphere pressure P = 105 N/m2
Find: P in lb/in2
Solution:
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© 2011 Cengage Learning Engineering. All Rights Reserved.

30. Example 6.2 – Unit Conversion (continued)
Given: density of water = 1000 kg/m3
Find: density in lbm/ft3
Solution:
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© 2011 Cengage Learning Engineering. All Rights Reserved.

31. Examples of Unit Conversion
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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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33. Example 6.3 – Dimension Homogeneity
Given:
where
d = end deflection, in m
P = applied load, in N
L = length of bar, in m
A = cross-sectional area of bar, in m2
E: modulus of elasticity
Find: units for E
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© 2011 Cengage Learning Engineering. All Rights Reserved.

34. Example 6.3 – Dimension Homogeneity (continued)
Solution:
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© 2011 Cengage Learning Engineering. All Rights Reserved.

35. Example 6.3 – Dimension Homogeneity (continued)
Given:
Where
q = heat transfer rate
k = thermal conductivity of the solid material in W/m●°C
A = area in m2
T1 – T2 = temperature difference, °C
L = thickness of the material, m
Find: units for q
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© 2011 Cengage Learning Engineering. All Rights Reserved.

36. Example 6.3 – Dimension Homogeneity (continued)
Solution:
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© 2011 Cengage Learning Engineering. All Rights Reserved.

37. Example 6.5 – Numerical Versus Symbolic Solutions
Given: hydraulic system shown
Find: m2
Numerical solution:
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38. Example 6.5 – Numerical Versus Symbolic Solutions (continued)
Given: hydraulic system shown
Find: m2
Symbolic solution:
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© 2011 Cengage Learning Engineering. All Rights Reserved.

39. 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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40. 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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© 2011 Cengage Learning Engineering. All Rights Reserved.

41. Significant Digits – How to Record a Measurement
What should we record for the length?
3.35 ± 0.05 in.
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© 2011 Cengage Learning Engineering. All Rights Reserved.

42. Significant Digits – How to Record a Measurement
What should we record for this pressure?
7.5 ± 0.5 in.
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© 2011 Cengage Learning Engineering. All Rights Reserved.

43. Significant Digits
175, 25.5, 1.85, and 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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© 2011 Cengage Learning Engineering. All Rights Reserved.

44. 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, or
(your calculator will display)
(however, the result should be recorded this way)
© 2011 Cengage Learning Engineering. All Rights Reserved.
© 2011 Cengage Learning Engineering. All Rights Reserved.

45. Significant Digits – Multiplication and Division Rules
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, or
× ÷
(your calculator will display)
5.9 x (however, the result should be recorded this way)
© 2011 Cengage Learning Engineering. All Rights Reserved.
© 2011 Cengage Learning Engineering. All Rights Reserved.

46. Significant Digits – Examples
276.34
289.12
2955
x 326
9.63 x 105
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47. 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 to
to x 104
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48. Engineering Components & Systems
Every engineered product is made of components
chest component
other components
sleeve component
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49. Engineering Components & Systems (continued)
Cooling system
Engine
Wiper motor system
Exhaust system
Drive train
Brake system
System:
vehicle
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© 2011 Cengage Learning Engineering. All Rights Reserved.

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

51. Physical Laws and Observations in Engineering (continued)
More in thermodynamics course
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
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© 2011 Cengage Learning Engineering. All Rights Reserved.

52. Physical Laws and Observations in Engineering (continued)
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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53. Physical Laws and Observations in Engineering (continued)
More in chapter 10, physics, and dynamics
Newton’s second law of motion – there is a direct relationship between the push, mass being pushed, and acceleration of mass
© 2011 Cengage Learning Engineering. All Rights Reserved.
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54. Physical Laws and Observations in Engineering (continued)
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
© 2011 Cengage Learning Engineering. All Rights Reserved.
© 2011 Cengage Learning Engineering. All Rights Reserved.

55. 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.
© 2011 Cengage Learning Engineering. All Rights Reserved.
© 2011 Cengage Learning Engineering. All Rights Reserved.

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

57. 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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© 2011 Cengage Learning Engineering. All Rights Reserved.

58. 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
© 2011 Cengage Learning Engineering. All Rights Reserved.
© 2011 Cengage Learning Engineering. All Rights Reserved.

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