Comprehensive Energy Systems, vol.1a - Energy Fundamentals

520 Pages·2018·24.694 MB·English

by  Canan Acar, Martin Agelin-Chaab, Christos Agrafiotis, Pouria Ahmadi, Haider Ali, Amine Allouhi, Ali Almansoori, Fethi Aloui, Şengül Alpay-Karaoğlu, Abdullah Al-Sharafi, Abdullah A AlZahrani, Maan Al-Zareer, Imran Amin, Rasa Apanaviciene, Selin Aradag, Alessia Arteconi, Fabrizio Ascione, Ahmet K Avci, Nezihe Ayas, Ece Aylı, Christopher Baldwin, Sassi Ben Nasrallah, Fatih Ş Beriş, Alberto Betancourt-Torcat, Prabal P S Bhadauria, Nicola Bianco, Yusuf Bicer, Ling Bing Kong, Ali Boharb, Sinem Bozar, Kenneth Bruninx, Reiner Buck, Francesco Calise, Ahmet Cansiz, Jale Çatak, Carlos A M T Cavalcante, Wilco Chan, Liang Chang, Jennifer Charry-Sanchez, Jianyong Chen, Can O Colpan, Brock Conley, Pedro Costa, Cynthia A Cruickshank, Tugba Davran-Candan, Murat E Demir, Yaşar Demirel, Shiming Deng, Ibrahim Dincer, İlker Dinçer, Eric J Dufek, Animesh Dutta, Yalçın Elerman, Mustafa Ercelik, Ilknur Erucar, Muhammad F Ezzat, Claudia Fabiani, Murat Farsak, Adonias M S Ferreira, Paris A Fokaides

1.1 Energy Units, Conversions, and Dimensional Analysis
İlhamiYıldız andYuLiu, Dalhousie University, Halifax, NS,Canada
r2018ElsevierInc.Allrightsreserved.
1.1.1 Introduction 2
1.1.2 Quantities 2
1.1.2.1 Relationship BetweenQuantities 3
1.1.2.2 Base Quantities 3
1.1.2.3 Derived Quantities 3
1.1.2.4 Multiples andSubmultiples ofQuantities 3
1.1.2.5 Typesof Quantity Equations 4
1.1.3 Dimensional Analysis 4
1.1.4 UnitsandConversions 4
1.1.4.1 Useful Units inElectricity 6
1.1.4.1.1 Coulomb 6
1.1.4.1.2 Volt 6
1.1.4.1.3 Watt 6
1.1.4.1.4 Ohm 6
1.1.5 Rulesfor UsingSI Units 6
1.1.5.1 Capitalization 6
1.1.5.2 Use ofPlurals 6
1.1.5.3 Use ofHyphenation andSpace 9
1.1.5.4 Use ofNumerals andPeriods 9
1.1.5.5 Use ofSymbols for Mathematical Operations 9
1.1.6 OverallExamples 10
1.1.7 ConcludingRemarks 22
References 22
RelevantWebsites 23
Nomenclature J Unitofenergyandwork,joule
a Atto k Kilo
a Index;acceleration,ms(cid:1)2;constant,2897mmK k Dimensionlesscoefficient,thermal
A Unitofelectriccurrent,ampere;area,m2 conductivity,Wm(cid:1)1K(cid:1)1orBtuh(cid:1)1ft(cid:1)11F(cid:1)1
b Index kg Unitofmass,kg
Btu Britishthermalunit kWh Unitofenergy,kilowatt-hour(¼3.6MJ)
c Centi K Unitofthermodynamictemperature
c Index;speedoflight,3(cid:3)108ms(cid:1)1 l Length,morft
C Unitofelectriccharge,coulomb;Celsius L Length
C Specificheat,Jkg(cid:1)1K(cid:1)1orBtulb (cid:1)11F(cid:1)1 m Milli
m
cd Luminousintensityunit m Unitoflength,m;mass,kgorlb
m
d Deci m_ Massflowrate,kgs(cid:1)1
da Deka M Mega;mass
E Exa mol Unitofamountofsubstance,mol
E Energy,JorBtuh(cid:1)1 n Nano
f Femto N Unitofforce,newton
F Fahrenheit p Pico
F Force,Norlb p Pressure,Paorlb
f f
g Gravitationalacceleration,ms(cid:1)2 P Peta
G Giga P Power,WorBtuh(cid:1)1
h Hecto Pa Unitofpressure,pascal
h Height,m;pumphead,m;enthalpy,Jkg(cid:1)1, r Radius,m
heattransfercoefficient,Wm(cid:1)2K(cid:1)1orBtuh(cid:1)1 R Thermalresistance,m2KW(cid:1)1orhft21FBtu(cid:1)1
ft(cid:1)21F(cid:1)1;Planck’sconstant,6.626(cid:3)10(cid:1)34Js rad Unitofplaneangle,radian
hp UnitofpowerinI–P,horsepower s Entropy,Jg(cid:1)1orBtulb (cid:1)1
m
I Radiantfluxdensity,Wm(cid:1)2orBtuh(cid:1)1ft(cid:1)2 sr Unitofsolidangle,steradian
ComprehensiveEnergySystems,Volume1 doi:10.1016/B978-0-12-809597-3.00101-2 1
2 EnergyUnits, Conversions, andDimensional Analysis
T Tera;time,s;temperature,1C,1F,K,orR w Width
therm Unitofheatenergy,105.5MJor100,000Btu W Unitofpower,watt
ton Refrigerationton,12,000Btuh(cid:1)1or3.52kW W Work
U Thermaltransmittance,Wm(cid:1)2K(cid:1)1orBtuh(cid:1)1 x Distance,morft
ft(cid:1)21F(cid:1)1 y Yocto
V Unitofelectricpotential,potentialdifference, Y Yotta
andelectromotiveforce,volt z Zepto
V Volume,m3orft3 Z Zetta
Greekletters n Kinematicviscosity,m2s(cid:1)1;specificvolume,
D Difference m3kg(cid:1)1orft3lb (cid:1)1;frequency,cycles
m
F Pumppower,Worhp s(cid:1)1¼hertz¼Hz
Z Conversionefficiency,% y Pumppower,Worhp
l Wavelength,mm r Density,kgm(cid:1)3orlb ft(cid:1)3
m
m Micro O Unitofelectricresistance,ohm
m Dynamicviscosity,Pas
Subscripts max Maximum
bk Breakpower p Pump;constantpressure
fl Fluidpower pe Potentialenergy
ke Kineticenergy v Constantvolume
Superscripts 0 Minute(angle)
1 Degree 00 Second(angle)
1.1.1 Introduction
When dealing with engineering and scientific relationships, in order to appreciate the magnitudes of physical quantities, it is
essential to have a solid grasp of units, and recognize two types of equations, namely, quantity equations and numerical
equations.Bothtypesarefoundintextsandreferencebooks,andtheconceptofunitsandquantitiesisusefulinunderstanding
theirrespectivefeatures.Inthischapter,wecoverthemainfeaturesofquantitiesandquantityequations,andprovidethemost
importantunitsandconversionsrelatingtoenergy.Quantityequationsarealsocalledequationsbetweenquantities,orphysical
equations.And,numericalequationsarealternativelycalledmeasureequations.Wealsointroducethetechniqueofdimensional
analysis,whichisusedtoderivebasicphysicalrelationshipswithoutperformingafullanalysisofasystem.
1.1.2 Quantities
In1954,the10thgeneralconferenceonweightsandmeasures(CGPM)decidedthataninternationalsystemshouldbederived
from six base units to provide for the measurement of temperature and optical radiation in addition to mechanical and elec-
tromagneticquantities.Sixbaseunitsrecommendedatthisconferencewerethemeter,kilogram,second,ampere,degreeKelvin
(laterrenamedkelvin),andcandela.In1960,the11thCGPMnamedthesystemtheInternationalSystemofUnits,SIfromthe
Frenchname,LeSystèmeInternationald'Unités[1].Later,theseventhbaseunit,themole,wasaddedin1971bythe14thCGPM
[2].SIisthemodernformofthemetricsystem,andtodayisthemostwidelyusedmeasurementsystem.
Therefore, the International System of Quantities (ISQ) is now a system based on seven base quantities: length, mass, time,
thermodynamictemperature,electriccurrent,luminousintensity,andamountofsubstance.Otherquantities,suchasarea,pressure,
and electrical resistance are all derived fromthese basequantities. The ISQ defines quantityasany physical propertythatcan be
measuredwiththeSIunits[3].Aquantitymayalsobeaphysicalconstant,suchasthegasconstant,orthePlanck’sconstant.Several
hundredquantitiesareemployedtodescribeandmeasurethephysicalworld,andafewofthesequantitiesarelistedbelow[4]:
Length Viscosity Area Electromotiveforce
Time Energy Luminance Entropy
Mass Speed Angle Pressure
Force Power Temperature Momentum
Energy Units, Conversions, andDimensional Analysis 3
1.1.2.1 RelationshipBetweenQuantities
Thestudyofphysicstoagreatextentcanbedefinedasthestudyofmathematicalrelationshipsamongvariousphysicalproperties.
Physicalquantitiesaredefined,asabove,whenthesepropertiesallowareasonablemathematicaldescription.Therelationshipof
allotherquantitiescanbeestablished interms ofafewbasequantities selectedproperly,eitherbydefinition,bygeometry,by
physicallaw,orbyacombinationofthebasequantities.
Forinstance,pressureisaquantitythatisrelated,bydefinition,toaquantityforcedividedbyaquantityarea.Area,onthe
otherhand,isaquantityrelated,bygeometry,totheproductoftwoquantitiesoflength.Moreover,forceisaquantityrelated(by
Newton’ssecondlaw)tothequantitymasstimesthequantityacceleration.
Therelationshipsbetweenquantitiesareexpressedintheformofquantityequations.Wecanrelateevenanisolatedquantity,
suchastemperaturetothequantitiespressure,volume,andmass.Wecanfurtherrelatethequantitieslengthandtimebyusingthe
universalconstantandthespeedoflight.Therefore,ifwedefineourconceptscorrectly,wecanrelateanyquantitytoanyother
quantity. Thus the equation area¼length(cid:3)width is a quantity equation, which states that the quantity (area of a rectangle) is
equaltothequantity(length)timesthequantity(width).
1.1.2.2 BaseQuantities
In order to reduce a set of quantity equations, we have to first establish a number of so-called base quantities. Hence, base
quantitiesarecalledthebuildingblocksuponwhichwedeveloptheentirestructureandrelationshipsofthephysicalworld.As
mentionedearlier,theinternationalsystemofunits,orSI,makesuseofsevenbasequantities:mass(kg),length(m),time(s),
temperature(K),electriccurrent(A),luminousintensity(cd),andamountofsubstance(mol).Thenumberofbasequantities,as
wellastheirchoice,isquiteanarbitrarychoice;but,generally,weselectquantitiesthatareeasytounderstandandfrequentlyused,
andforwhichaccurateandmeasurablestandardscanbeestablished.
1.1.2.3 Derived Quantities
As mentioned in the relationship section earlier, using the selected base quantities as building blocks, derived quantities are
expressedasthosethatcanbedeductedbydefinition,geometry,orphysicallaw.Somederivedquantityexamplesarearea(equals
theproductsoftwolengths),velocity(equalslength/time),andforce(equalsmass(cid:3)acceleration),pressure,power,etc.Wealso
havewhatarecalledsupplementaryunits(asaclassofderivedunits),namely,theplaneangle(radian¼rad¼mm(cid:1)1)andsolid
angle(steradian¼sr¼m2m(cid:1)2).
1.1.2.4 Multiples andSubmultiples of Quantities
Notethat themagnitude ofaquantity canhave anextremely largerange.Inaneffort tohandlesuchalarge range,theSIunit
systemgenerated20prefixesshowninTable1.
Table1 MultiplesandsubmultiplesinSIunitsystem
Prefix Symbol Multiplier Example
Yotta Y 1024 5Ym¼5yottameters¼5(cid:3)1024m
Zetta Z 1021 2Zm¼2zettameters¼2(cid:3)1021m
Exa E 1018 7Em¼7exameters¼7(cid:3)1018m
Peta P 1015 6PJ¼6petajoules¼6(cid:3)1015J
Tera T 1012 5TW¼5terawatts¼5(cid:3)1012W
Giga G 109 8GJ¼8gigajoules¼8(cid:3)109J
Mega M 106 2MW¼2megawatts¼2(cid:3)106W
Kilo k 103 3km¼3kilometers¼3(cid:3)103m
Hecto h 100 6hL¼6hectoliters¼600L
Deka da 10 2dam¼2decameters¼20m
Deci d 10(cid:1)1 3dL¼3deciliters¼0.3L
Centi c 10(cid:1)2 5cm¼5centimeters¼0.05m
Milli m 10(cid:1)3 9mV¼9millivolts¼9(cid:3)10(cid:1)3V
Micro m 10(cid:1)6 5mm¼5micrometers¼5(cid:3)10(cid:1)6m
Nano n 10(cid:1)9 2ns¼2nanoseconds¼2(cid:3)10(cid:1)9s
Pico p 10(cid:1)12 3pJ¼3picojoules¼3(cid:3)10(cid:1)12J
Femto f 10(cid:1)15 6fm¼6femtometers¼6(cid:3)10(cid:1)15m
Atto a 10(cid:1)18 5aJ¼5attojoules¼5(cid:3)10(cid:1)18J
zepto z 10(cid:1)21 6zJ¼6zeptojoules¼6(cid:3)10(cid:1)21J
yocto y 10(cid:1)24 8yJ¼8yoctojoules¼8(cid:3)10(cid:1)24J
4 EnergyUnits, Conversions, andDimensional Analysis
1.1.2.5 Typesof Quantity Equations
Theenergyofwind,thepressureatthebottomofanairorwatercolumn,theweightofanobject,andtheviscosityofaliquidare
allphysicalquantitiesofnature.And,whethertheyaremeasuredornot,thesequantitiesarealwaysthereinteractingwitheach
other according to fundamental laws. Physicists often express these laws in terms of quantity equations because quantities
conformtotheselaws.Quantityequationspossesstwoimportantfeatures:first,theyshowtherelationshipbetweenquantities,
andsecond,theycanbeusedwithanysystemofunits.
Therearethreebasictypesofquantityequations:
1. Quantityequationsdevelopedfromthelawsofnature;forinstance,Newton’ssecondlawofmotion
F¼ma
whereFisthemagnitudeoftheforce,misthemagnitudeofthemass,andaisthemagnitudeoftheacceleration.
2. Quantityequationsdevelopedfromgeometry;forinstance,areaofacircle
A¼pr2
whereAisthemagnitudeofthearea,pisthecoefficientbasedonthegeometryofacircle,andristhemagnitudeoftheradius.
3. Quantityequationsdevelopedfromadefinition;forinstance,definitionofpressure
p¼F=A
wherepisthemagnitudeofthepressure,Fisthemagnitudeoftheforce,andAisthemagnitudeofthearea.
Manyquantityequationscanbedevelopedasacombinationofthebasicquantityequationsgivenabove,andinallcases,we
canuseanyunitswewanttodescribethemagnitudesoftherelevantphysicalquantities.
1.1.3 Dimensional Analysis
Dimensionalanalysisisquiteausefulmethodforderivinganalgebraicrelationshipbetweendifferentphysicalquantities,which
reliesongoodphysicalintuitioninchoosingthedifferentappropriatephysicalvariables.Theideabehindthisanalysisisthateach
variableisexpressedintermsofitsfundamentalunitsofmassM,lengthL,andtimeT,etc.,raisedtosomearbitraryindexa,b,c,
etc.Theseunknownindicesarethendeterminedbyequatingtheindicesoflikeunits[5].Onemightalsochooseforce,length,and
massasthebasedimensions,withassociateddimensionsF,L,M,whichcorrespondstoadifferentbasis.Itmaysometimesbe
usefultochooseoneoranotherextendedsetofdimensionalsymbols.Inelectromagnetism,forinstance,itmaybeadvantageous
tousedimensionsofM,L,T,andQ,whereQisusedtorepresentthedimensionofelectriccharge.Anotherexampleisthat,for
instance,inthermodynamics,thebasesetofdimensionsisoftenextendedtoincludeadimensionfortemperature,Y.
Let’snowperformasimpledimensionalanalysistofindanexpressionforthehydrostaticpressureinafluid.Thehydrostatic
pressureisdependentonthedensityr,thegravitationalaccelerationg,anddepthh.Now,let’sassumeageneralalgebraicequation
intheformof
r¼kragbhc
wherekisacoefficient(dimensionless),anda,b,andcaretheindices(numbers)tobedetermined.Now,wecanreplaceeach
symbolbyitsfundamentalphysicalunit,andhave
(cid:1) (cid:3) (cid:1) (cid:3)
M1L(cid:1)1T(cid:1)2¼ ML(cid:1)3 a LT(cid:1)2 bðLÞc
or
M1L(cid:1)1T(cid:1)2¼MaL(cid:1)3aþbþcT(cid:1)2b
M,L,andTareallindependentquantities;therefore,wecanequatetheindicesonbothsides,andhavethefollowingequations
1¼a; (cid:1)1¼ (cid:1)3aþbþc; (cid:1)2¼ (cid:1)2b
Then we can solve for and find that a¼b¼c¼1; consequently, the expression for hydrostatic pressure can be found
asp¼krgh,wherethecoefficientkcannotbedeterminedfromdimensionalanalysisbecauseitisdimensionless.
Moredimensionalanalysisexamplesareprovidedintheexamplessectionlater.
1.1.4 Units and Conversions
Thissection,asmodifiedafterASHRAE[6,7],referencestheStandardforMetricPractice,ASTMStandardE380-84[8],asoneof
the basic standards for SI usage [9–13]. Table 2 provides conversion factors rounded to three or four significant figures for
conversionbetweenSIandI–P.AndTable3providesconversionfactorsfordifferentphysicalquantitiesrelatedtoenergyfurther.
Energy Units, Conversions, andDimensional Analysis 5
Table2 SIenergyrelatedunitsandconversions
Divide By Toobtain Divide By Toobtain
ha 0.405 acre J 1.36 ft(cid:4)lb (work)
f
kPa 100 bar Jkg(cid:1)1 2.99 ft(cid:4)lb lb(cid:1)1(specificenergy)
f
L 159 barrel(42USgal,petroleum) W 0.0226 ft(cid:4)lb min(cid:1)1(power)
f
m3 0.159 L 3.79 gallon(US,231in3)
kJ 1.055 Btu,IT m3 0.00379 gallon
kJm(cid:1)3;JL(cid:1)1 37.3 Btuft(cid:1)3 mLs(cid:1)1 1.05 gph
kJL(cid:1)1 0.279 Btugal(cid:1)1 Ls(cid:1)1 0.0631 gpm
W(mK)(cid:1)1 1.731 Btufth(cid:1)1ft31F mLJ(cid:1)1 0.0179 gpmton(cid:1)1refrigeration
Btuin(hft31F)(cid:1)1 g 0.0648 grain(1/7000lb)
W(mK)(cid:1)1 0.144 (thermalconductivity,k) mgL(cid:1)1 17.1 grgal(cid:1)1
W(m1C)(cid:1)1 gkg(cid:1)1 0.143 grlb(cid:1)1
W 0.293 Btuh(cid:1)1 kW 9.81 horsepower(boiler)
kJm(cid:1)3 11.4 Btuft(cid:1)2 kW 0.746 horsepower(550ft-lb s(cid:1)1)
f
GJ(ym2)(cid:1)1 0.0000114 Btu(yft2)(cid:1)1 mm 25.4a inch
Toobtain by Multiply Toobtain by Multiply
Wm(cid:1)2 3.15 Btu(hft2)(cid:1)1 kPa 3.38 inofmercury(60(cid:5)F)
W(m2K)(cid:1)1 5.68 (overallheattransfercoef.,U) Pa 249 inofwater(60(cid:5)F)
(thermalconductance,C) mmm(cid:1)1 0.833 in/100ft,thermalexpansion
kJkg(cid:1)1 2.33 Btulb(cid:1)1 mNm 113 in(cid:4)lb (torqueormoment)
f
kJ(kgK)(cid:1)1 4.19 Btu(lb1F)(cid:1)1(specificheat,C) mm2 645 in2
kJ(kg1C)(cid:1)1 mL 16.4 in3(volume)
m3 0.0352 bushel mLs(cid:1)1 0.273 in3min(cid:1)1(SCIM)
J 4.19 calorie,gram mm3 16,400 in3(sectionmodulus)
kJ 4.19 calorie,kilogram;kilocalorie mm4 416,000 in4(sectionmoment)
mPa(cid:4)s 1.00a centipoise,viscosity,m ms(cid:1)1 0.278 kmh(cid:1)1
(absolute,dynamic) MJ 3.60a kWh
mm2s(cid:1)1 1.00a centistokes,kinematicviscosity,n GJ(y(cid:4)m2)(cid:1)1 0.0388 kWh(yft2)
Pa 0.100a dynecm(cid:1)2 JL(cid:1)1 2.12 kWh/100cfm
W 44.0 EDRhotwater(150Btuh(cid:1)1) N 9.81 kilopond(kgforce)
W 70.3 EDRstream(240Btuh(cid:1)1) kN 4.45 kip(1000lb)
f
COP 0.293 EER MPa 6.89 kipin(cid:1)2(ksi)
m 0.3048a ft m3 0.001a liter
mm 304.8a ft mPa 133 micronofmercury(60oF)
ms(cid:1)1 0.00508 ftmin(cid:1)1,fpm km 1.61 mile
ms(cid:1)1 0.3048a fts(cid:1)1,fps km 1.85 mile/nautical
kPa 2.99 ftofwater kmh(cid:1)1 1.61 mph
kPam(cid:1)1 0.0981 ftofwaterper100ftpipe ms(cid:1)1 0.44 mph
m2 0.0929 ft2 kPa 0.100a millibar
m2KW(cid:1)1 kPa 0.133 mmofmercury(601F)
m21CW(cid:1)1 0.176 ft2h1FBtu(cid:1)1 Pa 9.80 mmofwater(601F)
(thermalresistance,R) kPa 9.80 meterofwater
mm2s(cid:1)1 92900 ft2s(cid:1)1,kinematicviscosity,n g 28.3 ounce(mass,avoirdupois)
L 28.3 ft3 N 0.278 ounce(forceorthrust)
m3 0.0283 ft3 mL 29.6 ounce(liquid,US)
mLS(cid:1)1 7.78 ft3h(cid:1)1,cfh mN(cid:4)m 7.06 ounceinch(torqueormoment)
1. Ls(cid:1)1 0.472 ft3min(cid:1)1,cfm gL(cid:1)1 7.49 ounce(avoirdupois)pergallon
Ls(cid:1)1 28.3 ft3s(cid:1)1,cfs ng(s(cid:4)m2(cid:4)Pa)(cid:1)1 57.4 perm(permeance)
N(cid:4)m 1.36 ft(cid:4)lb (torqueormoment) ng(s(cid:4)m(cid:4)Pa)(cid:1)1 1.46 perminch(permeability)
f
mL 473 pint(liquid,US) kgm(cid:1)3 16.0 lbft(cid:1)3(density,r)
pound kgm(cid:1)3 120 lbgallon(cid:1)1
kg 0.454 lb(mass) mgkg(cid:1)1 1.00a ppm(bymass)
g 454 lb(mass) kPa 6.89 psi
N 4.45 lb (forceorthrust) EJ 1.055 quad
f
kgm(cid:1)1 1.49 lbft(cid:1)1(uniformload) L 0.946 quart(liquidUS)
mPas 0.413 lb (ft(cid:4)h)(cid:1)1viscosity m2 9.29 square(100sqft)
m
(absolute,dynamic,m) mL 15 tablespoon(approximately)
mPas 1490 lb (ft(cid:4)s)(cid:1)1viscosity mL 5 teaspoon(approximately)
f
(absolute,dynamic,m) MJ 105.5 therm(US)
gs(cid:1)1 0.126 lbh(cid:1)1 t(tonne);Mg 1.016 ton,long(2240lb)
kgs(cid:1)1 0.00756 lbmin(cid:1)1 t(tonne);Mg 0.907 ton,short(2000lb)
(Continued)
6 EnergyUnits, Conversions, andDimensional Analysis
Table2 Continued
Divide By Toobtain Divide By Toobtain
kW 0.284 lbofsteamperhour@2121F kW 3.52 ton,refrigeration(12,000Btuh(cid:1)1)
(1001C) Pa 133 torr(1mmHg@01C)
Pa 47.9 lb ft(cid:1)2 Wm(cid:1)2 10.8 wattpersquarefoot
f
mPas 47900 lb(cid:4)sft(cid:1)2viscosity m 0.9144a yd
f
(absolute,dynamic,m) m2 0.836 yd2
kgm(cid:1)2 4.88 lbft(cid:1)2 m3 0.765 yd3
Toobtain by Multiply Toobtain by Multiply
aConversionfactorisexact.
Abbreviation:COP,coefficientofperformance;EDR,equivalentdirectradiation;EER,energyefficiencyratio;SCIM,standardcubicinchesperminute.
1.1.4.1 UsefulUnitsin Electricity
1.1.4.1.1 Coulomb
Inanelectriccircuit,theunitofelectricchargeinSIisthecoulomb,andhasthesymbolC.Anampere,whichhasthesymbolofA,
isdefinedastheamountofchargetransportedthroughanycross-sectionofaconductorinonesecondbyaconstantcurrentofone
ampere,andisequivalenttotheamountofchargeonabout6,241,510,000,000,000,000electrons.
1.1.4.1.2 Volt
Inanelectriccircuit,theunitofelectricpotential,potentialdifference,andelectromotiveforceinSIisthevoltandhasthesymbol
V.Ifandwhenweconsiderourhousewiringasplumbing,voltscanthenbeconsideredasameasureofthewaterpressure.One
volt is the potential difference between two points on a conductor when the current flowing is one ampere and the power
dissipatedbetweenthepointsisonewatt.
Thevoltisaderivedunit,andintermsofbaseunitsitcanbeexpressedasfollows:
(cid:1) (cid:3) (cid:1) (cid:3)
Volt¼watt=ampere¼ m2kg = s3A
1.1.4.1.3 Watt
Inanelectriccircuit,onewatt(joulespersecond)isacurrentofoneampereatapressureofonevolt.Intermsofbaseunits,
(cid:1) (cid:3)
Watt¼Js(cid:1)1¼ m2kg s(cid:1)3
1.1.4.1.4 Ohm
Inanelectriccircuit,theunitofelectricalresistance(aderivedunit)inSIiscalledanohmandhasthesymbolofO.Oneohmis
definedastheelectricalresistancebetweentwopointsonaconductorwhenaconstantpotentialdifferenceofonevolt,appliedto
these points, produces in the conductor a current of one ampere. Ohm is a derived unit, and in terms of base units it can be
expressedasfollows:
(cid:1) (cid:3) (cid:1) (cid:3)
OhmðOÞ¼volt=ampere¼ m2kg = s3A2
1.1.5 Rules for Using SI Units
1.1.5.1 Capitalization
Thenamesofunitsstartwithalowercaseletterwhenwritingtheunitsoutexceptforinatitleorthebeginningofasentence.The
only exception is “degree Celsius.”Unless they come from an individual's name (in which case the first letter of the symbol is
capitalized), lowercase is used in writing symbols for units. The only exception is L for liter. Symbols for numerical prefixes
(multiplesandsubmultiples)arealsolowercase,exceptforthoserepresentingmultipliersof106ormore,forinstance,mega(M),
giga(G),tera(T),peta(P),exa(E),zetta(Z),andyotta(Y).Itmeansthatallprefixesarewritteninlowercasewhenspelledout.
Lowercaseunits:m,kg,s,mol,etc.Uppercaseunits:A,K,Hz,Pa,C,etc.
Symbolsratherthanself-styledabbreviationsshouldalwaysbeusedtorepresentunits.
Correctusage:A,s.Incorrectusage:ampsec
1.1.5.2 Use ofPlurals
Remember that symbolsare neverexpressed asplural. That is,an “s” is neveradded tothesymbol todenote plural. However,
whenthenamesofunitsarespelledout,theyaremadepluralifthenumbertowhichtheyreferisgreaterthan1.Fractions,onthe
otherhand,arealwayswrittenassingular.Pluralsareusedasrequiredwhenwritingunitnames.Forexample,henriesispluralfor
henry.Thefollowingexceptionsarenoted:
Table3 Conversionfactors
Pressure
pascal dynecm(cid:1)2 kgcm(cid:1)2 bar mmHg atm inHg psi
1 10 1.0192(cid:3)10(cid:1)5 10(cid:1)5 0.00750 9.8692(cid:3)10(cid:1)6 2.953(cid:3)10(cid:1)4 1.45038(cid:3)10(cid:1)4
0.100 1 1.01972(cid:3)10(cid:1)6 10(cid:1)6 0.000750 9.8692(cid:3)10(cid:1)7 2.953(cid:3)10(cid:1)5 1.45038(cid:3)10(cid:1)5
98,066 980,665 1 0.98066 735.559 0.96784 28.959 14.223
105 106 1.01972 1 750.062 0.98692 29.530 14.5038
133.32 1333.2 0.0013595 0.0013332 1 0.00131579 0.03937 0.0193368
101,325 1,013,250 1.03323 1.01325 760.0 1 29.921 14.6960
3386.4 33,864 0.034532 0.33864 25.400 0.033421 1 0.491154
6894.8 68,948 0.07030696 0.068948 51.715 0.068046 2.0360 1
Mass kg lb
1¼ 2.20462
0.45359¼ 1
Volume metre3 liter gal ft3 in3
1 1000 264.173 35.315 61,023.74
0.001a 1 0.264173 0.035315 61.02374
0.0037854 3.7854 1 0.13368 231.0
0.028317 28.317 7.48055 1 1728a
1.63871(cid:3)10(cid:1)5 0.0163871 4.329(cid:3)10(cid:1)3 5.787(cid:3)10(cid:1)4 1
Energy Watt-sec joule calorie fllb Btu
E
n
1 1 0.2390 0.73756 9.4845(cid:3)104 erg
4.184a 4.184a 1 3.08596 3.9683(cid:3)103 y
1.3558 1.3558 0.32405 1 1.2859(cid:3)103 Un
1054.35 1054.35 251.9957 777.65 1 its
,
Density kgm(cid:1)3(gL(cid:1)1) gcm(cid:1)3 lbgal(cid:1)1 lbft(cid:1)3 C
o
n
v
1 0.001 0.008345 0.0624280 ers
1000 1 8.34538 62.4280 io
n
119.827 0.119827 1 7.48055 s
,
16.018463 0.016018 0.133680 1 a
n
Specificvolume m3kg(cid:1)1(Lg(cid:1)1) cm3g(cid:1)1 gallb(cid:1)1 ft3lb(cid:1)1 d
D
im
1 1000 119.827 16.018463 e
n
0.001 1 0.119827 0.016018 sio
0.008345 8.34538 1 0.133680 n
a
0.0624280 62.4280 7.48055 1 l
A
Specificheat J(gK)(cid:1)1 cal(gK)(cid:1)1 Btulb(cid:1)11F na
ly
s
orentropy 1 0.2390 0.2390 is
4.184a 1 1.0
4.184a 1 1 7
(Continued)
Table3 Continued 8
Pressure
pascal dynecm(cid:1)2 kgcm(cid:1)2 bar mmHg atm inHg psi En
e
rg
Entropy Jg(cid:1)1 calg(cid:1)1 Btulb(cid:1)1 yU
14.184a 01.2390 01..48a3021 nits,
2.3244 0.5556 1 Co
n
Thermal W(mK)(cid:1)1 W(cm1C)(cid:1)1 J(scm1C)(cid:1)1 cal(s(cid:4)cm1C)(cid:1)1 Btuh(cid:1)1ft1F ve
rs
conductivity 418.4a 1 1 0.2390 57.816 ion
418.4a 4.184a 4.184a 1 241.91 s,
1.7296 0.017296 0.017296 4.1338(cid:3)10(cid:1)3 1 an
d
Viscosity(1poise¼dyne-seccm(cid:1)2¼0.1newton-secm(cid:1)2) D
lbm(fts)(cid:1)1 Nsm(cid:1)2 kg(ms)(cid:1)1 lbfhrft(cid:1)2 lbfsft(cid:1)2 Poiseg(cms)(cid:1)1 ime
n
s
1 1.4882 1.4882 8.6336(cid:3)10(cid:1)6 3.1081(cid:3)10(cid:1)2 14.8819 ion
0.0671955 1 1 5.8014(cid:3)10(cid:1)6 0.020885 10 al
115,827 172,369 172,369 1 3600 1,723,689 An
32.17405 47.88026 47.88026 2.7778(cid:3)10(cid:1)4 1 478.8026 aly
6.71955(cid:3)10(cid:1)2 0.1 0.1 5.8014(cid:3)10(cid:1)7 2.0885(cid:3)10(cid:1)3 1 sis
Coefficientof W(m2K)(cid:1)1 kcal(hm21C)(cid:1)1 W(cm21C)(cid:1)1 cal(hcm21C)(cid:1)1 Btuh(cid:1)1ft21F
heattransfer 1 0.8598 1(cid:3)10(cid:1)4 2.388(cid:3)10(cid:1)5 0.1761
1.630 1 1.1630(cid:3)10(cid:1)4 2.778(cid:3)10(cid:1)5 0.2048
10,000 8598 1 0.2388 1761.1
41,869 36,000 4.1869 1 7373.5
5.6783 4.8823 5.6783(cid:3)10(cid:1)4 1.3562(cid:3)10(cid:1)4 1
aInternationalTableBtu,cal,andkcal.Lineartemperaturedifference:1For1R,1CorK.
Energy Units, Conversions, andDimensional Analysis 9
Singular:lux,hertz,siemensPlural:lux,hertz,Siemens
Example1: Correctandincorrectusages
Correctusage Incorrectusage
5kg 5kgs
5kilograms 5kilogram
5.57kg –
5.57kilograms 5.57kilogram
0.57kilogram 0.57kilograms
1.1.5.3 Use ofHyphenation andSpace
Also remember that a hyphen or a space is not used to separate a prefix from the name of the unit. A space, however, is left
betweenasymbolandthenumbertowhichitrefers,withtheexceptionofthesymbolsfordegree,minute,andsecondofangles,
andfordegreeCelsius.
Inthreecasesthefinalvowelintheprefixisomitted:megohm,kilohm,andhectare.
Example2: Correctandincorrectusages
Correctusage Incorrectusage
5kg 5kg
40(cid:5)450 3000 40(cid:5)450 3000
30(cid:5)C 30(cid:5)C
5km 5km
MJ mF
5s 5s
5milliseconds 5milli-seconds
1.1.5.4 Use ofNumerals andPeriods
Remember that scientific and technical writing is different from any other writings, such as newspaper, magazine, and other
writings. In scientific and technical writing, numerals are used for all numbers expressing physical quantities; however, it is a
common practice to write out the numbers from one to nine and use numerals for other numbers in newspapers. In ordinary
books and magazines, for instance, whole numbers from one through ninety-nine, and any of these followed by “hundred,”
“thousand,”“million,”“billion,”etc.,arespelledout.Also,keepinmindthattheassociatednumberiswrittenasnumeralswhen
theunitisrepresentedbyanabbreviationorsymbol.
PeriodsareneverusedafterSIsymbolsunlessthesymbolisattheendofasentence.
1.1.5.5 Use ofSymbolsfor Mathematical Operations
Unitsarerepresentedbysymbols,notbytheirspelled-outnames,whentheunits(SI)areusedwithsymbolsformathematical
operations.
Notestoremember
1. Whenwritingunitnamesasaproduct,alwaysuseaspace(preferred)orahyphen.
Correctusage:newtonmeterornewton-meter
2. When expressing a quotient using unit names, always use the word per and not a solidus (/). The solidus or slash mark is
reservedforusewithsymbols.
Correctusage:meterpersecond Incorrectusage:meter/second
3. Whenwriting aunitnamethatrequiresapower,useamodifier,suchassquared orcubed,aftertheunitname.Forareaor
volume,themodifiercanbeplacedbeforetheunitname.
Correctusage:millimetersquaredorsquaremillimeter
4. Whendenotingaquotientbyunitsymbols,anyofthefollowingareacceptedform:
Correctusage:m/sorms(cid:1)1
Inmorecomplicatedcases,considerusingnegativepowersorparentheses.Foracceleration,usem/s2orms(cid:1)2butnotm/s/s.
Forelectricalpotential,usekg.m2/(s3A)orkgm2s(cid:1)3A(cid:1)1butnotkgm2/s3/A.
10 EnergyUnits, Conversions,andDimensional Analysis
Example3: Correctandincorrectusages
Correctusage Incorrectusage
Jkg(cid:1)1
Jkg(cid:1)1 jouleskg(cid:1)1
joulesperkilogram joules/kilogram
N.m newton.meter
newtonmeter
newton-meter
1.1.6 Overall Examples
Example4: Area
Find:ShowtheunitofareainSI,andperformdimensionalanalysis.
Solution:
Areaequationisaquantityequationarisingfromgeometry;forexample,theareaequationforapipeisexpressedasfollows:
AreaðAÞ¼pr2¼pðmÞ2
AreaðAÞ¼m2
whereAisthemagnitudeofareainm2,themagnitudeofpis3.14(dimensionless),andristhemagnitudeofradiusinm.
Orinanotherexample,theareaforarectangleisexpressedasfollows:
AreaðAÞ¼w (cid:3) l¼m (cid:3) m
AreaðAÞ¼m2
whereAisthemagnitudeofareainm2,wisthemagnitudeofwidthinm,andlisthemagnitudeoflengthinm.
Let’snowperformasimpledimensionalanalysistofindanexpressionforthearea.Theareaisdependentonthedimensionless
numberpandtheradius.So,
A¼kra
wherekisadimensionlessnumber,andaisthenumbertobedetermined.Now,wecanreplaceeachsymbolbyitsfundamental
physicalunit,andhave
L2¼La
Lisanindependentquantity;thereforewecanequatetheindicesonbothsides,andhavethefollowingequation
a¼2
Consequently, the expression for the area can be found as A¼k ra, where the coefficient k cannot be determined from
dimensionalanalysisbecauseitisdimensionless;however,fromgeometry,weknowthatk¼p.
Example5: Volume
Find:ShowtheunitofvolumeinSIandperformdimensionalanalysis.
Solution:
Volumeequationisaquantityequationarisingfromgeometry;forexample,thevolumeequationforapipeisexpressedasfollows:
VolumeðVÞ ¼pr2L
(cid:1) (cid:3)
¼p m2 ðmÞ
VolumeðVÞ¼m3
whereVisthemagnitudeofvolumeinm3,themagnitudeofpis3.14(dimensionless),andristhemagnitudeofradiusinm.
Orinanotherexample,thevolumeforarectangularcross-sectionisexpressedasfollows:
VolumeðVÞ¼w(cid:3)l(cid:3)h¼m(cid:3)m(cid:3)m
VolumeðVÞ¼m3
whereVisthemagnitudeofvolumeinm3,wisthemagnitudeofcross-sectionalwidthinm,listhemagnitudeofcross-sectional
lengthinm,andhisthemagnitudeofheight.
Let’s now perform a dimensional analysis to find an expression for the volume having a tubular cross-sectional area. The
volumeisdependentonthedimensionlessnumberp,theradius,andlengthofthetube.So,
V¼kraLb