mechanicalengineeringAnintroductionto1Lecturer:LiuJu-rongCHAPTER2Problem-SolvingSkillsOVERVIEW1UNITSYSTEMSANDCONVERSIONS23DIMENSIONALCONSISTENCY

2SIGNIFICANTDIGITS4ANERROROFUNITSONTHEWAYTOMAR5APPROXIMATIONINENGINEERING6PROBLEM-SOLVINGMETHODOLOGY7Vocabulary3Torque扭矩thermalconductivity熱導率shearstress剪應力fluidviscosity流體的粘度elasticmodulus彈性模量kineticenergy動能Reynoldsnumber雷諾數1OVERVIEW----theimportantofunit4Howimportantaunitis?Eachquantityinmechanicalengineeringhastwocomponents:anumericalvalueandaunit.Oneissimplymeaninglesswithouttheother,andpracticingengineerspayascloseandcarefulattentiontotheunitsinacalculationastheydotothenumbers.1OVERVIEW---Theabilitytobeavailableinthischapter5Afterstudy,whatshouldyoubeabletohave?Reportbothanumericalvalueanditsunitineachcalculationthatyouperform.ListthebaseunitsintheUnitedStatesCustomarySystemandtheSystemInternationald‘Units,andstatesomeofthederivedunitsusedinmechanicalengineering.Understandtheneedforproperbookkeepingofunitswhenmakingengineeringcalculationsandtheimplicationsofnotdoingso.ConvertnumericalquantitiesfromtheUnitedStatesCustomarySystemtotheSystemInternationald‘Units,andviceversa.Checkyourequationsandcalculationstoverifythattheyaredimensionallyconsistent.Understandhowtoperformorder-of-magnitudeapproximations.2UNITSYSTEMSANDCONVERSIONS-UnitSystem

whatisUSCSandSI?6Engineersspecifyphysicalquantitiesintwodifferent,butconventional,systemsofunits:theUnitedStatesCustomarySystem(USCS)andtheInternationalSystemofUnits.Practicingmechanicalengineersmustbeconversantwithbothunitsystems.2UNITSYSTEMSANDCONVERSIONS-anexample

KeepingTrackofUnitsonFright1437InJulyof1983,AirCanadaFlight143wasenroutefromMontrealtoEdmonton.TheBoeing767hadthreefueltanks,oneineachwingandoneinthefuselage,whichsuppliedtheplane'stwojetengines.volume(L),weight(lb),mass(kg)Totalfuel22,300kilograms(kg)

Howmuchfuelshouldbeadded?Fuelintanks7682liters(L)Boeing767pounds(lb);kilograms1.77lb/L1.77kg/L9000liters16,000liters

2UNITSYSTEMSANDCONVERSIONS-BaseandDerivedUnits

whatisbaseunits?

Whatisderivedunits?8Abaseunitisafundamentalquantitythatcannotbefurtherbrokendownorexpressedintermsofanysimplerelements.Baseunitsarethecorebuildingblocksofanyunitsystem.Derivedunits,astheirnameimplies,areconstructedascombinationsofbaseunits.92WHATISENGINEERING?---UnitedStatesCustomarySystemTheUnitedStatesCustomarySystemofunitsisahistoricalandtraditionalsystem,anditsorigintracesbacktotheancientRomanEmpire.WhydoestheUnitedStatesstandoutinretainingtheUSCS?Thereasonsarebothlogisticalandcultural:Thereisalreadyavastcontinent-sizedinfrastructurewithintheUnitedStatesthatisbasedontheUSCS.Conversionawayfromtheexistingsystemwouldbeasignificantandexpensiveburden.Thedimensionsofcountlessexistingstructures,factories,machines,andsparepartshavealreadybeenspecifiedandbuiltintermsoftheUSCS.102WHATISENGINEERING?---UnitedStatesCustomarySystemQuantityUSCSBaseUnitAbbreviationLengthfootftForcepoundlbTimesecondsElectriccurrentampereAThermodynamictemperatureRankineRAmountofsubstancemolemolLuminousintensitycandelacdTABLE2.1BaseUnitsintheUSCS112WHATISENGINEERING?---UnitedStatesCustomarySystemTABLE2.2CertainDerivedintheUSCS.Althoughachangeintemperatureof1Rankinealsoequalsachangeof1degreeFahrenheit,theabsolutevaluesareconvertedusingtheformula.QuantityUSCSDerivedUnitAbbreviationDefinitionLengthmilmil1mil=0.001in.Lengthinchin.1in.=0.0833ftLengthyardyd1yd=3ftLengthmilemi1mi=5280ftVolumeU.S.gallongal1gal=0.1337ft3Massslugslug1slug=1lb·s2/ftForceounceoz1oz=0.0625lbForcetonton1ton=2000lbMomentofaforceft·lbft·lb-------------Pressureorstresspsipsi1psi=1lb/in2Energy,work,orheatft·lbft·lb-------------Energy,work,orheatBtuBtu1Btu=778.2ft·lbPowerhorsepowerhp1hp=550ft·lb/sTemperaturedegreeFahrenheit?F?F=?R-460122WHATISENGINEERING?---InternationalSystemofUnitsTheInternationalSystemofunits(orSI)isthemeasurementstandardbasedinpartonthequantitiesofmeters,kilograms,andseconds.

QuantitySIBaseUnitAbbreviationLengthmetermForcekilogramkgTimesecondsElectriccurrentampereAThermodynamictemperatureKelvinKAmountofsubstancemolemolLuminousintensitycandelacdTABLE2.3BaseUnitsintheSI132WHATISENGINEERING?---InternationalSystemofUnitsQuantitySIDerivedUnitAbbreviationdefinitionLengthmicronμm1μm=10-6mVolumeliterL1L=0.001m3ForcenewtonN1N=1kg·m/s2MomentofaforceN·mN·m-----------PressureorstresspascalPa1Pa=1N/m2

Energy,work,orheatjouleJ1J=1N·mPowerwattW1W=1JtemperaturedegreeCelsius℃℃=?K-273TABLE2.4CertainDerivedintheSI.Althoughachangeintemperatureof1Kelvinalsoequalsachangeof1degreeCelsius,theabsolutevaluesareconvertedusingtheformula.142WHATISENGINEERING?---InternationalSystemofUnitsTABLE2.5onversionFactorBetweenCertainQuantitiesintheUSCSandSIQuantityToConvertfrom···To···Multipyby···Lengthfoot(ft)meter(m)0.3048Lengthinch(in.)meter(m)0.0254Lengthmile(mi)kilometer(km)1.609Volumegallon(gal)meter3(m3)3.785×10-3Volumegallon(gal)liter(L)3.875Massslugkilogram(kg)14.59Forcepound(lb)newton(N)4.448Pressureorstresspound/inch2(psi)pascal(Pa)6895Energy,work,orheatfoot-pound(ft·lb)joule(J)1.356Powerfoot-pound/second

(ft·lb/s)watt(W)1.356Powerhorsepower(hp)kilowatt(kW)0.7456152WHATISENGINEERING?---InternationalSystemofUnitsTABLE2.6onversionFactorBetweenCertainQuantitiesintheSIandUSCSQuantityToConvertfrom···To···Multipyby···Lengthmeter(m)foot(ft)0.3048Lengthmeter(m)inch(in.)0.0254Lengthkilometer(km)mile(mi)1.609Volumemeter3(m3)gallon(gal)3.785×10-3Volumeliter(L)gallon(gal)3.875Masskilogram(kg)slug14.59Forcenewton(N)pound(lb)4.448Pressureorstresspascal(Pa)pound/inch2(psi)6895Energy,work,orheatjoule(J)foot-pound(ft·lb)1.356Powerwatt(W)foot-pound/second

(ft·lb/s)1.356Powerkilowatt(kW)horsepower(hp)0.7456162WHATISENGINEERING?---InternationalSystemofUnitsTABLE2.6onversionFactorBetweenCertainQuantitiesintheSIandUSCSNamesymbolMultiplicativeFactorteraT1,000,000,000,000=1012gigaG1,000,000,000=109megaM1,000,000=106kilok1000=103hectoh100=102decada10=101decid0.1=10-1centic0.01=10-2millim0.001=10-3microμ0.000,001=10-6nanon0.000,000,001=10-9picop0.000,000,000,001=10-123DIMENSIONALCONSISTENCY17Dimensionalconsistencymeansthattheunitsassociatedwiththenumericalvaluesoneachsideoftheequalitysignmatch.Inpaper-and-pencilcalculations,itisgoodpracticetokeeptheunitsadjacenttoeachnumericalquantityinanequation.performingadouble-checkontheunitsinanyequationisalwaysagoodidea.4SIGNIFICANTDIGITS18Asignificantdigitisanumericalvaluethatisknowntobecorrectandreliableinthelightofinaccuracythatispresentinthesuppliedinformation,anyapproximationsthathavebeenmadealongtheway,andthemechanicsofthecalculationitself.Theprecisionofanumberishalfaslargeasthelastsignificantdigitusedinexpressingthenumber.Thefactorofone-half(

arisesbecausemelastdigitofanumberrepresentstherounding-offprocesseitherhigherorlower,ofthetrailingdigits.43.01mN43.01mN43.02mN5ANERROROFUNITSONTHEWAYTOMARS19TheimportanceofkeepingtrackofunitsinengineeringcalculationswashighlightedbythefailureoftheMarsClimateOrbiterspacecraftin1999.ThespacecraftwastoarriveatMarsonSeptember23,1999,anditwasscheduledtocompleteitsprimarysciencemissiononDecember31,2004.NASAconductedathoroughinvestigation,andtheMarsClimateOrbiterMishapInvestigationBoardidentifiedeightfactorsthatcontributedtothespacecraft'sloss.unitsof(force)×(time)newton-secondspound-seconds6APPROXIMATIONINENGINEERING20Engineersarecomfortablemakingreasonableapproximationssothatthesystemstheyanalyzeareassimpleaspossibleandyetwillyieldaresultthatisaccurateenoughforthetaskathand.Engineersnearlyalwaysmakeapproximationswhentheydesignandsolvetechnicalproblems.Approximationsarealsousefultoremoveextraneousfeaturesthatcomplicatetheproblembutotherwisehavelittleinfluenceonthefinalanswer.6APPROXIMATIONINENGINEERING21Giventheuncertaintypresentinrealsystems,itisoftennecessaryforengineerstomake"order-of-magnitude"approximations.Thesearesometimescalled"back-of-the-envelope"calculationsbecausetheycanbeperformedquicklyandinformally.7PROBLEM-SOLVINGMETHODOLOGY22

1.Makeacleanstart2.Draw3.Givensandunknowns.4.Thinkfirst,thenwrite..5.Becoordinated238.Significantfigures9.Boxit10.Interpretyouranswer6.Neatnesscounts.7.Units.7PROBLEM-SOLVINGMETHODOLOGYSUMMARY24Engineersareoftendescribedasbeing"can-do"peoplewithexcellentproblem-solvingskills.Inthischapterwehavediscussedsomeofthefundamentaltoolsandskillsthatmechanicalengineersusewhentheyanswertechnicalquestions.Numericalvalues,theUSCSandSIsystems,unitconversions,dimensionalconsistency,significan