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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