chapter 1 introduction to engineering calculations

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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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)


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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What have you learned?

chapter 1 introduction to engineering calculations

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