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8/13/2019 Chapter 1 Introduction to Engineering Calculations
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Introduction to EngineeringCalculations
Chapter 1
Material and Energy Balances
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In designing a new process or analyzing anexisting one, calculation of amounts and
properties of raw materials and products iscrucial.
This chapter presents the calculationtechniques of expressing the values ofprocess variables.
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Introduction toEngineering
Calculations
Units andDimensions
Conversion ofUnits
Systems ofUnits
What are in this chapter?
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Units and Dimensions #imensions are!
$roperties that can be measured such as length,time, mass, temperature.
$roperties that can calculated by multiplying ordividing other dimensions , such as velocity%length&time', volume, density.
(nits are used for expressing the dimensions suchas feet %ft' or meter %m' for length, hours&seconds%hr&s' for time.
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)* mg g + . )* g
mg
Conversion of Units
A measured quantity can be expressed in terms of anyunits having the appropriate dimension.
To convert a quantity expressed in terms of one unit toequivalent in terms of another unit , multiply the givenquantity by the conversion factor .
Conversion factor - a ratio of equivalent values of aquantity expressed in different units.
et say to convert )* mg to gram
Conversionfactor
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Dimensional Equation
To convert a quantity with a unit to its equivalent interm of other units, set up a dimensional equation !
/rite the given quantity and units on left /rite the units of conversion factors that cancel
the old unit and replace them with the desiredunit
0ill the value of the conversion factors Carry out the arithmetic value
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Dimensional Equation
Convert cm&s 1 to "m&yr 1
cm s 1 h 1 day 1 m "m
s 1 h 1 day 1 yr 1 cm m
cm )* 1 s 1 12 1 h 1 )*3 1 day 1
m "m
s 1 1 h 1 1 day 1 1 yr 1 cm m
)* 1 x 12 1 x )*3 1 "m+ 4.43 x 4 "m& yr 1
x yr 1
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Convert 2 "g&m ) to lb m &ft)
Dimensional Equation
2 "g . 15) 6 ) m ) lb mm ) ft ) .23)34) "g
2 "g m ) lb mm ) ft ) "g
2 x . 15) 6 ) x lb m+ 1. 1 x 72 lb m &ft)
x .23)34) ft )
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Systems of Units Components of a system of units!
8ase units 7 units for the dimensions of mass, length, time,temperature, electrical current, and light intensity .
9ultiple units7 multiple or fractions of base unit. :.g.! fortime can be hours, millisecond, year, etc.
#erived units 7 units that are obtained in one or two ways;a' 8y multiplying and dividing base units; also referred to as
compound units. :g.! ft&min %velocity', cm 1%area', "g.m&s 1 %force'
b' As defined equivalent of compound unit. %
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Systems of Units= ) systems of unit!
a' >I system
b' American engineering system
c' C?> system
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Base Units
Base Units
@uantity >I >ymbol American >ymbol C?> >ymbol
ength meter m foot ft centimeter cm
9ass "ilogram "gpoundmass lbm gram g
9olesgram7mole mole pound mole lbmole gram7mole mole
Time second s second s second s
Temperature elvin Ban"ine B elvin
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ultiple S! Units
9ultiple (nit $references
tera %T' + 1 centi %c' + 71
giga %?' + 4 milli %m' + 7)
mega %9' + * micro % ) = 7*
"ilo %"' + 1 nano %n' + 74
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Derivatives S! Units
Derived S! Units
"uantity Unit Sym#ol Equivalent to the Base Unit
olume iter . m ) + cm )
0orce I'#yne%C?>'
< "g.m&s 1
g.cm&s1
$ressure $ascal $a
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$orce % Wei&ht
= g c is used to denote the conversion factor from anatural force unit to a derived force unit.
g c + "g.m&s 1 + )1. 62 lb m .ft&s 1
< lb f
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Wei&ht % ass>ee this example!
?iven the density of 1 ft ) water is *1.2 lbm&ft ). At the sea level,the gravitational acceleration is )1. 62 ft&s 1.
The mass of water is
The weight of water is
( ) mm lb ft ft lb
M 8.12424.62 33 =
=
( )( ) f m
f m lb s ft lb
lb s ft ft
ft lb
W 8.124/174.32
1/174.3224.62
2
23
3 =
=
& Conversion factor
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Si&nificant $i&ures and'recision
Convenient way to represent very large and very smallnumbers is to use scientific notation . :g.
1), , + .1) x 5 . 15 + 1.5 x 72
>ignificant figures are the digits from the first nonzero digiton the left to!a' the last digit on the right %zero or nonzero' if there is a
decimal point.b' the last nonzero digit if there is no decimal point.
:g. 1.) x )
%1 significant figures', 1.) x )
%3significant figures', 1.) 2 x 2 %2 significant figures', ).3 x71 %1 significant figures', ).3 x 71 %2 significant figures'
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Try This(
$b 1.1 (se the table of conversion factor to converta' 6* miles&hr to m&s c' 3.)6 x ) "D&min to hpb' 41 "g&m ) to lb m &ft)
$b. 1.5 Calculate!a' The weight in lbf of 13. 7lbm obEect.b' The mass in "g of an obEect that weighs 13 newtons.c' The weight in dynes of a 7ton obEect.
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