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

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.

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

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

SI Units and Symbols SI Units fall into 3 categories Base Units Supplementary Units Derived Units

SI Base Units 7 Base Units Can be reproduced anywhere in the world (except kg)

SI Supplementary Units May be considered base or derived units Radian is commonly used. Steradian less so. Radians are dimensionless arc length = radius 1 Radian: Angle when arc length = radius radius

SI derived units with names Formed by combining Base Supplementary or Other derived units

SI derived units without names Some derived units have no special SI unit names or symbols

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.

Unit Prefixes

Significant Figures SI prefix notations can be used to denote intended significance 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

Significant Figures Scientific notation can be used to denote intended significance 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

Greek Alphabet