Dimensional Analysis Chapter 2

Systems of Units Section 2.3 Physical Quantity Unit Abbreviation Mass Kilogram Gram (CGS) kg Length Meter Centimeter (CGS) m Time Second s Temperature Kelvin K Amount of substance Mole mol Electric Current Ampere A Luminous intensity Candela cd

Derived Units Quantity Unit Symbol Equivalent in Terms of Base Units Volume liter L 0.001 m3 1000 cm3 Force newton (SI) dyne (CGS) N 1 kg ∙ m/s2 1 g ∙ cm/s2 Pressure pascal (SI) Pa 1 N/m2 Energy, work joule (SI) erg (CGS) gram-calorie J cal 1 N ∙ m = 1 kg ∙ m2/s2 1 dyne∙cm = 1 g∙cm2/s2 4.184 J = 4.184 kg ∙ m2/s2 Power watt W 1 J/s = 1 kg ∙ m2/s2

Section 2.2 Dimensional Analysis Utilizes conversion factors in order to convert between units of one thing to units of something else Examples of conversion factors: 1 foot = 12 inches 2.54 cm = 1 inch

Example How many centimeters are in 1.39 feet? Hint: 1 in = 2.54 cm See Sample Exercise 1.9 (Pg. 25) 42.4 cm

Conversions Involving More than One Unit The speed of sound in air at sea level is 340 m/s. Express this speed in miles per hour. Hint: 1 mile = 1.6093 km See Sample Exercise 1.10 (Pg. 26) and Useful Conversion Factors and Relationships (Inside back cover) 760 mile/hr

Conversions Involving Cubed Units Express a density of 8.4 g/cm3 in terms of SI base units (kg/m3). See Sample Exercise 1.11 (pg. 27-28) 8400 kg/m3 OR 8.4 x 103 kg/m3

Combination Carry out the following conversion: 0.04 g/min ∙ m3 to lbm/hr ∙ ft3 1.5 x 10-4 lbm/hr ∙ ft3

For Super Duper Fun In 1916 Nusselt derived a theoretical relation for predicting the coefficient of heat transfer between a pure saturated vapor and a colder surface: where h = mean heat transfer coefficient, Btu/(hr)(ft2)(ºF) k = thermal conductivity, Btu/(hr)(ft)(ºF)  = density, lb/ft3 g = acceleration of gravity, 4.17 x 108 ft/(hr)2  = enthalpy change, Btu/lb L = length of tube, ft  = viscosity, lbm/(hr)(ft) T= temperature difference, ºF What are the units of the constant, 0.943?

Assignments Complete the following questions at the end of Chapter 2: 2.1, 2.2, 2.6, 2.8, 2.11