Engineering Fundamentals and Problem Solving, 6e

Chapter 7Dimensions, Units and Conversions

Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup MickelsonCopyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

Chapter Objectives•Identify physical quantities in terms of

dimensions and units

•Differentiate between fundamental and derived dimensions

•Understand the use of non-SI dimensional systems (gravitational and absolute)

•Recognize base, supplementary, and derived SI units

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Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup MickelsonCopyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

Chapter Objectives – cont’d•Apply the appropriate SI symbols and

prefixes

•Describe the relationship between U.S. Customary, Engineering System, and SI

•Systematically convert units from one system to another

•Use knowledge of dimensions and units, along with conversion rules, in the solution of engineering problems.

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Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup MickelsonCopyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

Progress towards Metrification

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Engineers in the U.S. must be prepared whatever system of units they encounter.

With a large French Canadian population, Canada has adopted the metric system.

Canadian highway signs

Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup MickelsonCopyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

Dimensions

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• Independent of units• Fundamental or derived• Absolute system is based on mass (no gravity)• Gravitational system is based on force

Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup MickelsonCopyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

SI Units and Symbols

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SI Units fall into 3 categories1. Base Units2. Supplementary Units3. Derived Units

Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup MickelsonCopyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

SI Base Units

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• 7 Base Units• Can be reproduced anywhere in the

world (except kg)

Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup MickelsonCopyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

SI Supplementary Units

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• May be considered base or derived units• Radian is commonly used. Steradian less so.• Radians are dimensionless

1 Radian: Angle when arc length =

radius

radius

arc length = radius

Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup MickelsonCopyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

SI derived units with names

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Formed by combining •Base•Supplementary or•Other derived units

Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup MickelsonCopyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

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SI derived units without names

Some derived units have no special SI unit names or symbols

Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup MickelsonCopyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

Non-SI units accepted for use in U.S.

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Certain units outside SI are accepted for use with SI in the U.S. even though they diminish the system’s

coherence.

Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup MickelsonCopyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

Unit Prefixes

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Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup MickelsonCopyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

Significant Figures

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Distance Precision # of significant figures

10.000 km 9 999.5 to 10 000.5 m 5

10.00 km 9 995 to 10 005 m 4

10.0 km 9 950 to 10 050 m 3

10 km 5 000 to 15 000 m 1

SI prefix notations can be used to denote intended significance

Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup MickelsonCopyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

Significant Figures

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Distance Precision # of significant figures

1.000 0 x 104 m 9 999.5 to 10 000.5 m 5

1.000 x 104 m 9 995 to 10 005 m 4

1.00 x 104 m 9 950 to 10 050 m 3

1.0 x 104 m 9 500 to 10 500 m 2

1 x 104 m 5 000 to 15 000 m 1

Scientific notation can be used to denote intended significance

Engineering: Fundamentals and Problem Solving, 6e Eide Jenison Northup MickelsonCopyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

Greek Alphabet

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