Introduction to Engineering Fluid Mechanics Introduction to Engineering Fluid Mechanics Marcel Escudier 3 3 GreatClarendonStreet,Oxford,OX26DP, UnitedKingdom OxfordUniversityPressisadepartmentoftheUniversityofOxford. ItfurtherstheUniversity’sobjectiveofexcellenceinresearch,scholarship, andeducationbypublishingworldwide.Oxfordisaregisteredtrademarkof OxfordUniversityPressintheUKandincertainothercountries ©MarcelEscudier2017 Themoralrightsoftheauthorhavebeenasserted FirstEditionpublishedin2017 Impression:1 Allrightsreserved.Nopartofthispublicationmaybereproduced,storedin aretrievalsystem,ortransmitted,inanyformorbyanymeans,withoutthe priorpermissioninwritingofOxfordUniversityPress,orasexpresslypermitted bylaw,bylicenceorundertermsagreedwiththeappropriatereprographics rightsorganization.Enquiriesconcerningreproductionoutsidethescopeofthe aboveshouldbesenttotheRightsDepartment,OxfordUniversityPress,atthe addressabove Youmustnotcirculatethisworkinanyotherform andyoumustimposethissameconditiononanyacquirer PublishedintheUnitedStatesofAmericabyOxfordUniversityPress 198MadisonAvenue,NewYork,NY10016,UnitedStatesofAmerica BritishLibraryCataloguinginPublicationData Dataavailable LibraryofCongressControlNumber:2016954938 ISBN978–0–19–871987–8(hbk.) ISBN978–0–19–871988–5(pbk.) Printedandboundby CPIGroup(UK)Ltd,Croydon,CR04YY LinkstothirdpartywebsitesareprovidedbyOxfordingoodfaithand forinformationonly.Oxforddisclaimsanyresponsibilityforthematerials containedinanythirdpartywebsitereferencedinthiswork. TomywifeAgnes,oursonStephen,andthememoryofmyMother andGrandmother Preface Afluidisamaterialsubstanceintheformofaliquid,agas,oravapour.Themostcommon examples,tobefoundinbotheverydaylifeandinengineeringapplications,arewater,air,and steam,thelatterbeingthevapourformofwater.Theflow(i.e.motion)offluidsisessentialto thefunctioningofawiderangeofmachinery,includingtheinternal-combustionengine,the gasturbine(whichincludestheturbojet,turbofan,turboshaft,andturbopropengines),wind and hydraulic turbines, pumps, compressors, rapidly rotating discs (as in computer drives), aircraft, spacecraft, road vehicles, and marine craft. This book is concerned primarily with Newtonianfluids,suchaswaterandair,forwhichtheviscosityisindependentoftheflow.The quantitativeunderstandingoffluidflow,termedfluiddynamics,isbasedupontheapplication ofNewton’slawsofmotiontogetherwiththelawofmassconservation.Toanalysetheflow ofagasoravapour,forwhichthedensitychangesinresponsetopressurechanges(known ascompressiblefluids),itisalsonecessarytotakeintoaccountthelawsofthermodynamics, particularlythefirstlawintheformofthesteady-flowenergyequation.Thesubjectoffluid mechanicsencompassesbothfluidstaticsandfluiddynamics.Fluidstaticsconcernsthevari- ationofpressureinafluidatrest(aswillbeseeninChapter4,thislimitationneedstobestated moreprecisely),andisthebasisforasimplemodeloftheearth’satmosphere. This text is aimed primarily at students studying for a degree in mechanical engineering oranyotherbranchofengineeringwherefluidmechanicsisacoresubject.Aeronautical(or aerospace),chemical,andcivilengineeringarealldisciplineswherefluidmechanicsplaysan essential rôle. That is not to say that fluid flow is of no significance in other areas, such as biomedical engineering. The human body involves the flow of several different fluids, some quiteordinarysuchasairintherespiratorysystemandwater-likeurineintherenalsystem. Otherfluids,likebloodinthecirculatorysystem,andsynovialfluid,whichlubricatesthejoints, havecomplexnon-Newtonianproperties,asdomanysyntheticliquidssuchaspaint,slurries, and pastes. A brief introduction to the rheology and flow characteristics of non-Newtonian liquidsisgiveninChapters2,15,and16. As indicated in the title, this text is intended to introduce the student to the subject of fluid mechanics. It covers those topics normally encountered in a three-year mechanical- engineering-degreecourseorthefirstandsecondyearsofafour-yearmechanical-engineering- degreecourse,aswellassometopicscoveredingreaterdetailinthefinalyears.Thefirstten chapters cover material suitable for a first-year course or module in fluid mechanics. Com- pressible flow, flow through axial-flow turbomachinery blading, internal viscous fluid flow, laminarboundarylayers,andturbulentflowarecoveredintheremainingeightchapters.There aremanyothertextbookswhichcoverasimilarrangeofmaterialasthistextbutoftenfrom a much more mathematical point of view. Mathematics is essential to the analysis of fluid flowbutcanbekepttoalevelwithinthecapabilityofthemajorityofstudents,asisthein- tentionherewheretheemphasisisonunderstandingthebasicphysics.Theanalysisofmany viii PREFACE flowsituationsrestsuponasmallnumberofbasicequationswhichencapsulatetheunderly- ingphysics.Betweenthesefundamentalequationsandthefinalresults,whichcanbeapplied directlytothesolutionofengineeringproblems,canbequiteextensivemathematicalmanip- ulationanditisalltooeasytolosesightofthefinalaim.Abasicunderstandingofvectorsis requiredbutnotofvectoranalysis.Tensornotationandanalysisisalsonotrequiredandthe useofcalculusiskepttoaminimum. Theapproachtocertaintopicsmaybeunfamiliartosomelecturers.Aprimeexampleisdi- mensionalanalysis,whichwesuggestisapproachedusingthemathematicallysimplemethod ofsequentialeliminationofdimensions(Ipsen’smethod).Theauthorbelievesthatthistech- niquehasclearpedagogicaladvantagesoverthemorewidelyusedRayleigh’sexponentmethod, whichcaneasilyleavethestudentwiththemistaken(andpotentiallydangerous)ideathatany physicalprocesscanberepresentedbyasimplepower-lawformula.Theimportanceofdimen- sionsanddimensionalanalysisisstressedthroughoutthebook.Theauthorhasalsofoundthat thedevelopmentofthelinearmomentumequationdescribedinChapter9ismorestraightfor- wardtopresenttostudentsthanitisviaReynoldstransporttheorem.Theapproachadopted here shows very clearly the relationship with the familiar F = ma form of Newton’s second lawofmotionandavoidstheneedtointroduceanentirelynewconceptwhichisultimately onlyasteppingstonetotheendresult.Thetreatmentofcompressibleflowisalsosubtlydif- ferent from most texts in that, for the most part, equations are developed in integral rather thandifferentialform.Theanalysisofturbomachineryislimitedtoflowthroughtheblading ofaxial-flowmachinesandreliesheavilyonChapters3,10,and11. ‘Whydoweneedafluidmechanicstextbookcontaininglotsofequationsandalgebra,given thatcomputersoftwarepackages,suchasFLUENTandPHOENICS,arenowavailablewhich can perform very accurate calculations for a wide range of flow situations?’ To answer this questionweneedfirsttoconsiderwhatismeantbyaccurateinthiscontext.Thedescriptionof anyphysicalprocessorsituationhastobeintermsofequations.Inthecaseoffluidmechanics, thefullsetofgoverningequationsisextremelycomplex(non-linear,partialdifferentialequa- tionscalledtheNavier-Stokesequations)andtosolvepracticalproblemswedealeitherwith simplified,orapproximate,equations.Typicalassumptionsarethatallfluidpropertiesremain constant,thatviscosity(theessentialpropertywhichidentifiesanymaterialasbeingafluid) playsnorole,thattheflowissteady(i.e.therearenochangeswithtimeatanygivenlocation withinthefluid),orthatfluidandflowpropertiesvaryonlyinthedirectionofflow(so-called one-dimensionalflow).ThederivationoftheNavier-Stokesequations,andtheaccompanying continuityequation,isthesubjectofChapter15.Exactanalyticalsolutionoftheseequations ispossibleonlyforahandfulofhighlysimplified,idealisedsituations,oftenfarremovedfrom the real world of engineering. Although these solutions are certainly mathematically accur- ate,duetothesimplificationsonwhichtheequationsarebasedtheycannotbesaidtobean accuraterepresentationofphysicalreality.Evennumericalsolutions,howevernumericallyac- curate, are often based upon simplified versions of the Navier-Stokes equations. In the case of turbulent flow, the topic of Chapter 18, calculations of practical interest are based upon approximateequationswhichattempttomodelthecorrelationswhicharisewhentheNavier- Stokesequationsaretimeaveraged.Itisremarkablethatvaluableinformationaboutpractical engineeringproblemscanbeobtainedfromconsiderationsofsimplifiedequations,suchasthe PREFACE ix one-dimensionalequations,atminimalcostintermsofbothtimeandmoney.Whatisessen- tial,however,isagoodphysicalunderstandingofbasicfluidmechanicsandaknowledgeof whatanycomputersoftwareshouldbebasedupon.Itistheaimofthistexttoprovidejustthat. Already in this brief Preface the names Navier, Newton, Rayleigh, Reynolds, and Stokes have appeared. In Appendix 1 we provide basic biographical information about each of the scientistsandengineerswhosenamesappearinthisbookandindicatetheircontributionsto fluidmechanics.