# LEC WEEK 1 - Feb 2020.ppt - Week 1 Introduction to...

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This preview shows page 1 out of 23 pages. Unformatted text preview: Week 1 Introduction to engineering calculations 1.1 Units and dimensions 1.2 Conversion of units 1.3 Systems of units 1.4 Force and weight 1.5 Numerical calculation and estimation 1.6 Dimensional homogeneity and dimensionless quantities (Chapter 2 of the Text Book) Week 1 : Part 1 1.1 Units and dimensions 1.2 Conversion of units 1.3 Systems of units 1.4 Force and weight 1.5 Numerical calculation and estimation (Chapter 2 of the Text Book) 1.1 Units and dimensions Dimension: properties that can be measured such as length, time, mass .… Unit: scale of dimension Example : 2 meters Dimension : length value : 2 unit : meter 1.2 Conversion factors Ratio of conversion from 1 unit to another unit of certain dimension. Example : conversion of 1 g to mg 1g 1 → the conversion factor is 1000mg 1000 Example : conversion from 1 cm/s2 to km/yr2 1cm s2 x 3600 2 s 2 12 h 2 x 24 2 h 2 12 day 2 x 365 2 day 2 12 yr 2 x 1m x 1 km 10 2 cm 10 3 m Ref : Factor for unit conversions in THE TABLE OF CONVERSTION OF UNITS =9.95 x10 9 km / yr 2 CONVERSION OF UNITS 1.3 SYSTEMS OF UNITS Base units – mass (kg), length (m), time(hr), temperature (oC) Multiple unit – multiple or fraction of base unit ( mega (M) = 106) Derived units – compound units (multiplying and dividing base) cm2, ft/min, kg.m/s2 System International (SI) system CGS system American engineering system Note: Refer Table 2.3-1 Table 2.3-1: SI and CGS Units Based Units Quantity Unit Symbol Length Meter(SI) Centimeter(CGS) Foot (U.S system) m cm ft Mass Kilogram (SI) Gram(CGS) Pound mass (U.S system) kg g Ibm Moles Gram-mole mol or gmol or Ibmol Time Second s Temperature Kelvin K Electric Current Ampere A Light Intensity Candela cd Multiple Units • Tera (T) = 1012 • Giga (G) = 109 • Mega (M) = 10 6 • Kilo (k) = 103 • Centi (c) = 10-2 • Milli (m) = 10-3 • Micro (μ) = 10-6 • Nano (n) =10-9 Derived Units Quantity Unit Symbol Base unit 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 4.184J = 4.184 kg.m2/s2 watt W 1 J/s = 1 kg.m2/s3 Power Note: Refer Table of Conversion units for US System CONVERSION OF UNITS Try Example 2.3-1 – conversion units 1.4 Force, weight and mass Force = mass × acceleration Weight = mass (m) x gravity force (g) = mg Units of force: newton (SI) ; dyne (CGS); pound-force (US) 1 N ≡ 1 kg.m/s2 1 dyne ≡ 1 g.cm/s2 1 lbf ≡ 32.174 lbm.ft/s2 g = acceleration due to gravity = 9.8066 m/s2 = 980.66 cm/s2 = 32.174 ft/s2 TRY Example 2.4-1 – weight & mass 1.5 Numerical calculation and estimation Scientific notation – 123,000,000 = 1.23 x 10 8 Significant figures – 2300 2.3 x 103 ( two significant figure) 2.300 x 103 ( four significant figure) rounded-off number 1.35 ~ 1.4 END OF WEEK 1: PART 1 Week 1 : Part 2 1.6 DIMENSIONAL HOMOGENEITY AND DIMENSIONLESS QUANTITIES Dimensional homogeneity For valid equation both sides of the equation have to be dimensionally homogeneous i.e. similar dimension u (m/s) = uo(m/s) + g (m/s2 )t(s) Dimension – length/time Dimensional homogeneity Dimensionless quantity Exponents (2 in x2) Transcendental functions (exp, log, sin, cos..) Argument of transcendental functions (x in sin x..) Dimensionless quantity mol 20,000 5 k 1 . 2 x 10 exp 3 cm . s 1.987T END OF WEEK 1: PART 2 ...
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