Thinking Like an Engineer

Stephan, Bowman, Park, Sill, Ohland Copyright © 2013 Pearson Prentice-Hall, Inc.

Metric System & Other Units

Dimensions & Base Units Thinking Like an Engineer 2e 1 Dimensions versus Units

• Dimension: measurable property

• Unit: specific value used to count an amount of measurable property

Length

• For example: Meters miles – Dimension Inches Fathom Feet Light-Year – Units Yard

Dimensions & Base Units Thinking Like an Engineer 2e 2 SI Units

• Metric system or MKS system – Meter – Kilogram – Second

• Seven fundamental dimensions

• Seven base units Dimension SI Unit – All others derived Electric current I ampere A Light intensity i candela cd • SI system Amount N mole mol – Based on power of 10 Temperature kelvin K – Uses named prefixes Mass M kilogram kg • Notation Rules Length L meter m Time T second s

Dimensions & Base Units Thinking Like an Engineer 2e 3 SI Notation Rules

– Only Capitalize if unit is named after a person (e.g. N for Newton) – Symbols of units are not shown as plural (5 cm, not 5 cms) – No period unless it is the end of a sentence – Use upright Roman type (not italics) – Separate number and symbol with one space – * for multiply, / for divide in derived units – Do not combine prefixes (e.g. 5 nkg)

Dimensions & Base Units Thinking Like an Engineer 2e 4 Accepted Non-SI Units

Some units are accepted for common use with SI units: – electron volt – ångstrom – hour – astronomical unit – liter – atomic mass unit (or dalton) – minute – bar – year – day – degree

Dimensions & Base Units Thinking Like an Engineer 2e 5 Systems of Units

• MKS system (SI Units) – Meter – Kilogram – Second • AES (American Engineering System) – Feet – Pound-mass – Second • USCS (United States Customary Units) – "English" units – Feet – Slug – Second

Dimension SI (MKS) AES (American) USCS (English) Length meter [m] foot [ft] foot [ft]

Mass kilogram [kg] pound-mass [lbm] slug Time second [s] second [s] second [s] Relative Temperature Celsius [°C] Fahrenheit [°F] Fahrenheit [°F] Absolute Temperature kelvin [K] Rankine [°R] Rankine [°R]

Dimensions & Base Units Thinking Like an Engineer 2e 6 Pound-force vs. Pound-mass

1.We measure our weight in pounds of force

2.Weight is the force that gravity exerts on us

3.Gravity is a force of attraction between two masses

4.The larger the masses, the larger the force.

Dimensions & Base Units Thinking Like an Engineer 2e 7 Pound-force vs. Pound-mass

1. We measure our weight in pounds of force 2. Weight is the force that gravity exerts on us 3. Gravity is a force of attraction between two masses. 4. The larger the masses, the larger the force. 5.The mass of the earth and the mass of our bodies determines our weight. 6.Your weight is a measure of the gravitational force between you and the celestial body (planet) your standing on. Dimensions & Base Units Thinking Like an Engineer 2e 8 Pound-force vs. Pound-mass

1. Our weight is due to our mass because if the weight changes its because we changed, not the earth.

2 2 2. But since W = mg and g = 32.2 ft/s , m must = 1 ft/32.2 lbf s

3. For convenience, this last term is called 1 pound-mass. This is

2 the unit of mass in the AES. 1 lbm = 1 ft/32.2 lbf s

4. However, the USCS unit of mass is the Slug. One Slug = 32.2 lbm

5. Remember Mass stays the same, but weight varies in each gravitational system, Dimensions & Base Units Thinking Like an Engineer 2e 9 Conversion Procedure

Method Steps

(1) Term to be converted

(2) Conversion formula

(3) Make a fraction equal to one

(4) Multiply

(5) Cancel, calculate, reasonable

Conversion Procedures Thinking Like an Engineer 2e 10 Example Dimensions & Units e-2

• It is estimated that SI Prefixes the Great Pyramid 103 103 kilo-kilo- kk at Giza has a mass 106 mega- M 9 of 5.45 X 10 109 giga- G kilograms 10121012 teratera- - TT 1015 peta- P • Express this mass 1018 exa- E in teragrams. 1021 zeta- Z

Conversion Procedures Thinking Like an Engineer 2e 11 Example, continued Dimensions & Units e-2

Method Steps (1) Term to be converted 5.45 X 109 kilograms [Tg] 1 kg = 103 g (2) Conversion formulae 1 Tg = 1012 g

103 g 1 Tg

(3) Make fractions 1 kg 1012 g 5.45 X 109 kg 103 g 1 Tg (4) Multiply 1 kg 1012 g

(5) Cancel, calculate, reasonable 5.45 Tg

Conversion Procedures Thinking Like an Engineer 2e 12 Example Dimensions & Units e-4 Area • The Clemson 1 acre = 40472 m2 University 1 acre = 4047 m Botanical Length Gardens cover 1 m 1 =m 3.281 = 3.281 ft ft 270 acres. 1 km = 0.621mi 1 cm = 0.3937 in • Express this area in units of square 1 mi = 5280 ft feet. 1 yd = 3 ft

Conversion Procedures Thinking Like an Engineer 2e 13 Example, continued Dimensions & Units e-4

Method Steps

(1) Term to be converted 270 acres [ft2]

(2) Conversion formula 1 acre = 4047 m2 1 m = 3.281 ft

4047 m 2 3.281ft 1acre 1m (3) Make a fraction

2 270 acre 4047 m 2 3.281ft 1acre 1m

270 acre 4047 m 2 10.765 ft 2 2 (4) Multiply 1acre 1m

7 2 Conversion(5) Cancel, Procedures calculate, reasonable Thinking1.17 Like an Engineer x 10 2e ft 14 Unusual Units

• Traditional units in other cultures • Historical and obsolete units • New units created as need arises

Conversion Procedures Thinking Like an Engineer 2e 15 What is expected of you… • Convert from one unit to a different unit within a fundamental dimension, such as converting from miles to feet or hours to days, following the 5-step conversion procedure • Convert from one unit to a different unit when multiple steps are required

Conversion Procedures Thinking Like an Engineer 2e 16