Chapter 1 (Part 1) Introduction to Engineering Calculations

8/15/2019 Chapter 1 (Part 1) Introduction to Engineering Calculations

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CHAPTER 1

Basic Concepts

emical Engineering Process Princip


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In designing a new process or analyzing anexisting one, calculation of amounts andproperties of raw materials and products iscrucial.

This chapter presents the calculationtechniques of expressing the values of

process variables.


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Topic Outcomes

At the end of Chapter , you should!

• Convert one set of units in a function orequation into another equivalent set formass, length, area, volume, time, energy and

force using conversion factor tables.

• Identify the units commonly used to expressboth mass and weight.

• Identify the number of signicant gures in a

given value and state the precision withwhich the value is known.


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Introduction to

Engineering

Calculations

Units andDimensions

Conversion ofUnits

Systems ofUnits

What are in this chapter?


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dded !xample" #.$%kg

&'.%(kg )yes* +ubtracted !xample" %m 'm

)yes*-hr #min )no*

ultiplied/ivided!xample " 0m x 'm 1

2# m#

Units

Units


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"# mg g $ %.%"# g

%%% mg

Conversion of Units

& 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 valuesof a quantity expressed in different units.

& (et say to convert "# mg to gram.

Conversionfactor


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Dimensional Equation

& Convert cm)s

*

to +m)yr

*

. rite the given quantity and units on left.

*. rite the units of conversion factors that cancel the old unit andreplace them with the desired unit.

". -ill the value of the conversion factors

cm s* h* day* m +m

s* h* day* yr* cm m

cm "#%%* s* ** h* "#/* day* m +m

s* * h* * day* * yr* %% cm %%% m

"#%%* x ** x "#/* +m$ 0.0/ x %0 +m) yr *

%% x %%% yr*


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1

Systems of Units


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Base Units

Base Units

2uantity 3I 3ymbol American 3ymbol C43 3ymbol

(ength meter m foot ft centimeter cm

5ass +ilogram +gpoundmass lbm gram g

5olesgram6mole mole pound mole lbmole gram6mole mole

Time second s second s second s

Temperature 7elvin 7 8an+ine 8 7elvin 7


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Multiple Units%

● Fractions of base unit

-Example : Years Days

Hours

Minutes

● Multiple Unit prefixes

-Example :

3econds

5ultiple 9nit :references

tera ;T< $ % * centi ;c< $ % 6*

giga ;4< $ % 0 milli ;m< $ % 6"

mega ;5< $ % # micro ;μ) = % 6#

+ilo ;+< $ %*

nano ;n< $ %60


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Derivatives SI Units

Derive SI Units

!uantity Unit Sym"ol Equivalent to the Base Unit

=olume (iter ( %.%%m" $ %%% cm"

-orce >ewton

;3I<?yne

;C43<

> +g.m)s*

g.cm)s*

:ressure :ascal :a >)m*

@nergy)

or+

oule

Calorie

cal

>.m $ +g.m* )s*

.1 $.1 +g.m*

)s*

:ower att )s $ +g.m* )s"


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Systems of Units

• 3 systems of unit:

a) ! system

b) "merican en#ineerin# system

c) $% system


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Chec# $our Unerstanin%

Derived unit for &elocity in t'e ! ystem( 'e $%ystem( 'e "merican En#ineerin# ystem(


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EXERCISE& Convert miles per hour to meter per

second

Length1 m = 100 cm = 1000 mm

=106 microns = 1010angstrom = 39.37 in = 3.2808 ft = 1.0936 y =0.000621! mile1 ft = 12 in = 1"3 y =0.30!8 m

= 30.!8 cm

sm447.0

shr

36001

milem

0006214.01

hr mile1

hr mi 1 =××=


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/

EXERCISE& Convert *" Ibm.ft)min* to its equivalent

+g.cm)s*

#ass1 $g = 1000 g = 0.001

metric tonne= 2.20!62 %&m =

3'.2739 o(

1 %&m = 16 o( = ' ) 10*! ton

= !'3.'93 g =0.!'3'93 $g

22

2

2

2

22 s

kg.cm088.0

s

min

60

1

2808.3

cm100

Ibm1

kg0.453593

min

ftIbm. 23

min

ftIbm. 23 =×××=

ft

Length1 m = 100 cm = 1000 mm

=106

microns = 1010angstrom = 39.37 in = 3.2808 ft = 1.0936 y =0.000621! mile

1 ft = 12 in = 1"3 y =0.30!8 m = 30.!8 cm


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#


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&orce ' Wei%ht

• Force is proportional to pro*uct of mass an* acceleration+

• Usually *efine* usin# *eri&e* units ,

.e/ton 0.) 1 2#+ms4

*yne 1 #+cms4

!bf 1 34+56 !bm+fts4

• 7ei#'t of an ob8ect is force exerte* on t'e ob8ect by#ra&itational attraction of t'e eart' i+e+ force of #ra&ity9 #+

• alue of #ra&itational acceleration:

# 1 ;+> ms4 1 ;> cms4

1 34+56 fts4


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&orce ' Wei%ht

• #c is use* to *enote t'e con&ersion factor from a natural

force unit to a *eri&e* force unit+

gc $ +g.m)s* $ "*.B lbm.ft)s

*

> lbf


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Dimensions


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*

+,antity -%

nit

/imension

#ass ilogra

m

#

Length #eter L

emperat,re

ime s

B(SE U)ITS DIME)SIO)S


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**


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*"

-paghetti ecipe

%ngreients4

20 ml of coo$ing oil100 gram of mince meat1' cm spaghetti stic$s

5al,e nit /imension

20 milliliter LE

L:

100 gram #;--

#:

1' centimeter

LE

L:

E*(M+,E


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*

Dimensional Homogeneity

• ?uantities can be a**e*subtracte* if @.AY t'eir unitsare same+

• Unit same9 t'e D!ME.!@. of eac' term must be t'esame+

E#+ : EA@$!Y 1 AE.%H !ME0A) 0) 0A) 0)

0ms) 0ms)


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*/

• E


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*#

Examples:• F 1 ma /'ere F 1 Force 0. 1 2#+ms4)

m 1 mass 02#) 1 0 M )

a 1 acceleration 0ms4)1 0 A) 0 )4

2#+ms4 1 02# )0ms4)

; 5 < ; ( < $ ; 5 < x ; ( < ; T


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*B

Dimensional Analysis

• 'is is a &ery important tool to c'ec2 your /or2 E#+ : Doin# a problem you #et t'e ans/er *istance

* 1 & t4 0&elocity x time4)

Units on left si*e 1 0 A )

Units on ri#'t si*e 1 ( A )0 ) x 0 )4 1 0 A ) +0 )

• Aeft units an* ri#'t units *onBt matc'9 soans/er must be /ron#CC


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*1

Check your understanding…& The period P of a swinging pendulum depends only

on the length of the pendulum d and theacceleration of gravity g.

' hich of the following formulas for P could becorrect D

g

d P π 2=

(a)(a)

(b)(b)

(c(c)) g

d P π 2=

4iven ! d $ units of length ; (


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*0

• Identify unit of P. P has units of time (TT )

• Make sure Left Ri!ht unit dimensiona""y

homo!eneous (#onsistent)$

(a)(a)

(a)(a)

L L

T

L

T T ⋅

= ≠

2

2 4

4

( )P dg = 2 2 π

ot

ot

ight !!

ight !!

P d

g = 2 π

L

L

T

T T

2

2 = ≠

ot

ot

ight !!

ight !!

T T

T

L

L 2

2

==

P d

g = 2 π

CorrectCorrect units!!

(a)(a) (b)(b) (c)(c)


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-ree Template from www.brainybetty.com "%

• If an equation is dimensionallyhomogeneous but its additive terms haveinconsistent unit, the terms may be madeconsistent by applying conversion factors

!xample"

V (m/s) = Vo (m/s) + g (m/s2 ) t(min>

" Apply the con#ersion $actor

V (m/s) = Vo (m/s) + g (m/s2 ) t(min>(60s/min)V = Vo + 60 g t V = Vo + 60 g t


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-ree Template from www.brainybetty.com "

"n euation is only %ALID /'en it is *imensionally

Homo#eneous

& #onsistent in 'IT***


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"*

Dimensionless %uantities

• $an be a pure number E#+ : 49 +3 94

• a multiplicati&e combination of &ariables /it' no net*imensions

E#+ :

µ

ρ ud =Re

+ & (!,#m-) . u & (#m,s).d & (#m). / & (!,#m$s)

/%#E-%?LE--


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Chapter 1 (Part 1) Introduction to Engineering Calculations

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