Engineering

Fundamentals and Problem Solving, 6e Chapter 7 Dimensions, Units and Conversions

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

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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.

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

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Progress towards Metrification

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  Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

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Dimensions

• • • • 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  Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

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SI Units and Symbols

SI Units fall into 3 categories 1. Base Units 2. Supplementary Units 3. Derived Units Engineering: Fundamentals and Problem Solving, 6e Eide  Jenison  Northup  Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

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SI Base Units

• • 7 Base Units Can be reproduced anywhere in the world (except kg) Engineering: Fundamentals and Problem Solving, 6e Eide  Jenison  Northup  Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

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• • •

SI Supplementary Units

May be considered base or derived units Radian is commonly used. Steradian less so.

Radians are dimensionless radius arc length = radius 1 Radian: Angle when arc length = radius Engineering: Fundamentals and Problem Solving, 6e Eide  Jenison  Northup  Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

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SI derived units with names

• • • Formed by combining Base Supplementary or Other derived units Engineering: Fundamentals and Problem Solving, 6e Eide  Jenison  Northup  Mickelson Copyright © 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  Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

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

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  Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

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Unit Prefixes

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

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Significant Figures

SI prefix notations can be used to denote intended significance

Distance

10.000 km 10.00 km 10.0 km 10 km

Precision

9 999.5 to 10 000.5 m 9 995 to 10 005 m 9 950 to 10 050 m 5 000 to 15 000 m

# of significant figures

5 4 3 1 Engineering: Fundamentals and Problem Solving, 6e Eide  Jenison  Northup  Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

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Significant Figures

Scientific notation can be used to denote intended significance

Distance Precision

1.000 0 x 10 4 m 9 999.5 to 10 000.5 m 1.000 x 10 4 m 1.00 x 10 4 m 9 995 to 10 005 m 9 950 to 10 050 m 1.0 x 10 1 x 10 4 4 m m 9 500 to 10 500 m 5 000 to 15 000 m

# of significant figures

5 4 3 2 1 Engineering: Fundamentals and Problem Solving, 6e Eide  Jenison  Northup  Mickelson Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

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Greek Alphabet

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

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