流體力學(xué)課件-第一章08-9chapter

MeteringofItisimportanttobeabletomeasureandcontroltheamountofmaterialenteringandleavingachemicalorotherprocessingplant.Manydifferenttypesofdevicesareusedtomeasuretheflowoffluids.華南理工大學(xué)化工學(xué)院Verywidelyusedforfluidmeteringarethepitottube,venturimeter,orificemeter,andopen-channelweirs華南理工大學(xué)化工學(xué)院Mostmetersoperateonallthefluidinthepipeorchannelandareknownasfull-boremeter.Others,calledinsertionmeters,measuretheflowrate,ormorecommonlythefluidvelocity,atonepointonly華南理工大學(xué)化工學(xué)院InsertionInthistypeofmeterthesensingelement,whichissmallcomparedtothesizeoftheflowchannel,isinsertedintotheflow華南理工大學(xué)化工學(xué)院Afewinsertionmetersmeasuretheaveragevelocity,butthemajoritymeasurethelocalvelocityatonepointonly.華南理工大學(xué)化工學(xué)院PitotThepitottubeisusedtomeasurethelocalvelocityatagivenpointintheflowstreamandnottheaveragevelocityinthe華南理工大學(xué)化工學(xué)院thethestatictubehasitsopeningtothedirectionofTheimpacttubehasitsnormaltothedirectionof華南理工大學(xué)化工學(xué)院 p 2u2p p 2u2pTheopeningofthestatictubeisparalleltothedirectionofflow,wherep0isthestaticpressure華南理工大學(xué)化工學(xué)院andsolvingforuofromtwoequationsuo

2

p0

Itshouldbenotedthatthepitottubemeasuresthevelocityatonepointonly.華南理工大學(xué)化工學(xué)院ThecoefficientCpisusedtotakeintoaccountdeviations,whichgenerallyvariesbetweenabout0.98anduoCp

2ps

po

Foraccurateuse,thecoefficientshouldbedeterminedbycalibrationofthepitottube.華南理工大學(xué)化工學(xué)院Thisequationappliesto pressiblefluidsbutcanbeusedtoapproximatetheflowofgasesatmoderatevelocitiesandpressurechangesofabout10%orlessofthetotal華南理工大學(xué)化工學(xué)院ThevalueofthepressuredropΔpisrelatedtoR,thereadingonthepR(A

)g

whereρAisthedensityofthefluidinthe華南理工大學(xué)化工學(xué)院Sincethepitottubemeasuresvelocityatonlyonepoint,severalmethodscanbeusedtoobtaintheaveragevelocityinthepipe.Inthefirstmethodthevelocityismeasuredattheexactcenterofthetubetoobtainumax.ThenbyusingFig.1.20,theVcanbe華南理工大學(xué)化工學(xué)院Careshouldbetakentohavethepitottubeatleast100diametersdownstreamfromanypipeobstruction.華南理工大學(xué)化工學(xué)院Full-BoreThemostcommontypesoffull-boremetersareventuriandorificemetersandvariable-areameterssuchasRotameters.Otherfull-boremeasuringdevicesincludeV-element,magnetic,vortex-shedding,turbine,andpositive-displacementmeters;ultrasonic華南理工大學(xué)化工學(xué)院VenturimeterisconstructedfromashortflangedinletsectionA,consistingofashortcylindricalportionandatruncatedcone;aflangedthroatsectionandaflangedoutletsectionC,consistingofalongtruncatedcone. 華南理工大學(xué)化工學(xué)院Atthejunctionofthecylindricalandconicalportion,anannularchamberisprovided,andanumberofsmallholesdrilledfromtheinsideofthetubetotheannularchamber.Theannularchamberandthesmallholeshasthefunctionofaveragingindividualpressure,itiscalledpiezometerring.華南理工大學(xué)化工學(xué)院TheaveragepressureistransmittedthroughtheupstreampressureAsecondpiezometerringisformedinthethroatsection.Amanometerorothermeansformeasuringpressuredifferenceisconnectedbetweentwopiezometerring.華南理工大學(xué)化工學(xué)院Intheventurimeter,thevelocityisincreased,andthepressuredecreasedintheupstreamcone.Thepressuredropintheupstreamconeisusedtomeasuretherateofflowthroughtheinstrument.Sinceseparationdoesnotoccurinthecontractingcrosssection,theupstreamconecanbemadeshorterthanthedownstreamconewithbutlittlefriction.華南理工大學(xué)化工學(xué)院ThebasicequationforventurimeterToderivetheequationfortheventurimeter,frictionisneglectedandthepipeisassumedhorizontal.Assumingturbulentflowandwritingthemechanical-energy-balanceequationbetweenpoints1and2foran pressiblefluid,華南理工大學(xué)化工學(xué)院VV 2 ppV22V1 4V2 4(1.6-Thecontinuityequationforconstantρ華南理工大學(xué)化工學(xué)院V2isestimatedfromV 2p1

p2V1 2V1 2D2D1(1.6-D21 2D1華南理工大學(xué)化工學(xué)院Eq(1.6-8)appliesstrictlytothefrictionlessflowofpressiblefluids.Toaccountforthesmallfrictionlossbetweenlocations1and2,Eq(1.6-8)iscorrectedbyintroducinganempiricalfactorCvand2V 2

2p1p2D 4D1 2D1

(1.6-華南理工大學(xué)化工學(xué)院(1.6-Whend2islessthand1/4,theDvelocityandtheterm 2D1

canbesincetheerrorislessthan0.2FormanymetersandaRe>104atpoint1,Cvisabout0.98forpipediametersbelow0.2mand0.99forlargersizes.However,thesecoefficientscanvary,andindividualcalibrationis mendedifthemanufacturer'scalibrationisnotavailable.華南理工大學(xué)化工學(xué)院FlowTheflowrateofpracticalinterestisthemassandvolumetricflowratesthroughthemeter.Tocalculatethevolumetricflowrate,thevelocityV2ismultipliedbytheareaA2qVA

2p1

p24 4D D1 2D1華南理工大學(xué)化工學(xué)院PressureFrictioncannotbecomple yeliminated,andapermanentlossinpressureandacorrespondinglossinpowerdooccur.Becauseofthesmallangleofdivergenceintherecoverycone,thepermanentpressurelossfromventurimeterisrelativelysmall.華南理工大學(xué)化工學(xué)院2.12C.OrificeTheventurimeterhascertainpracticaldisadvantagesforordinaryplantpractice.Itisexpensive,itoccupiesconsiderablespace,anditsratioofthroatdiameterandpipediametercannotbe華南理工大學(xué)化工學(xué)院Foragivenmeteranddefinitemanometersystem,the ummeasurableflowrateisfixed,soiftheflowrangeischanged,thethroatdiametermaybetoolargetogiveanaccuratereadingortoosmallto thenext umflowrate.華南理工大學(xué)化工學(xué)院Theorificemetermeetstheseobjectionstotheventuributatthepriceofalargerpower華南理工大學(xué)化工學(xué)院Theprincipleoftheorificemeterisidenticalwiththatoftheventuri.Thereductionofthecrosssectionoftheflowingstreaminpassingthroughtheorificeincreasingthevelocityheadattheexpenseofthepressurehead,andreductioninpressurebetweenthetapsismeasuredbythemanometer.華南理工大學(xué)化工學(xué)院華南理工大學(xué)化工學(xué)院Atypicalsharp-edgedorificeisshowninfigure.AdrilledplatehavingaholeofdiameterD0ismountedbetween華南理工大學(xué)化工學(xué)院Pressuretapsatpoints1upstreamand2downstreammeasurep1-p2.Theexactpositionsofthetwotapsaresomewhatarbitrary:inonetypeofmeterthetapsareinstalledabout1pipediameterupstreamand0.3to0.8pipediameter華南理工大學(xué)化工學(xué)院Theequationfortheorificeissimilartoequationfortheventuri2V 2

2p1p2D4

121 0D1whereV2isthevelocityintheorifice,D0istheorificediameter,andC0istheorificecoefficientandalwaysdeterminedexperimentally.華南理工大學(xué)化工學(xué)院華南理工大學(xué)化工學(xué)院ItvariesconsiderablywithchangesinD0/D1andwithReynoldsnumberattheorifice.CoisalmostconstantandindependentofD0/D1providedReisgreaterthanabout20000andD0/D1islessthanabout0.5.UndertheseconditionsComaybetakenas0.61forbothflangetapsandvena-contractataps.華南理工大學(xué)化工學(xué)院Furthermore,ifD0/D1islessthan0.25,the differsnegligiblyfromunity,andEq.(1.6-12) V

2p1

p2 TheThemassflowrateisgiven

o

o

11D/D401華南理工大學(xué)化工學(xué)院Unlessconsiderableprecisionisdesired,equationisadequatefororificedesign.AcheckonthevalueoftheReshouldbemade,however,sincethecoefficient0.61isnotaccuratewhenReislessthanabout20000.華南理工大學(xué)化工學(xué)院Itisespeciallyimportantthatenoughstraightpipebothaboveandbelowtheorificetoensureaflo tternthatisnormalandundisturbedbyfittings,valves,orotherequipment.華南理工大學(xué)化工學(xué)院PressureThepressurerecoveryinanorificeispoor,whichisonedisadvantageoftheorificeThefractionoforificedifferentialthatispermanentlylostdependsonthevalueoftheβ.華南理工大學(xué)化工學(xué)院2.12D.Flow-NozzleAtypicalflownozzleisshowninfigure.Itisessentiallyashortcylinderwiththeapproachbeingellipticalinshape.Thismeterhascharacteristicssimilartothoseoftheventurimeterbutisshorterandmuchlessexpensive.華南理工大學(xué)化工學(xué)院Thelengthofthestraightportionofthethroatisaboutone-halfthediameterofthethroat,D2.Theupstreampressuretapp1is1pipediameterfromtheinlet-nozzleface,andthedownstreamtapp2is1/2pipediameterfromtheinlet-nozzleface.華南理工大學(xué)化工學(xué)院Theequationforthenozzlemeteristhesameasventurimeter,withthecoefficientCnforthenozzlereplacingCvfortheventuri.FortheflownozzlethecoefficientCnrangesfrom0.95atapipeReof104,0.98at105,and0.99at106orabove.Thepermanentpressurelossiscalculatedbyequation華南理工大學(xué)化工學(xué)院2.12E.Variable-AreaFlowIntheorifice,nozzle,orventuri,thevariationofvelocitythroughaconstantareageneratesavariablepressuredrop,whichisrelatedtotheflowrate.華南理工大學(xué)化工學(xué)院Anotherclassofmeters,calledareameters,consistsofdeviceinwhichthepressuredropisconstant,ornearlyso,andtheareathroughwhichthefluidflowvarieswithflowrate.Theareaisrelated,throughpropercalibration,totheflowrate.華南理工大學(xué)化工學(xué)院Rotameterconsistsessentiallyofagraduallytaperedglasstubemountedverticallyinaframewithlargeendup.Thefluidflowupwardthroughthetaperedtubeandsuspendsfreelyafloat.Theentirefluidstreammustflowthroughtheannularspacebetweenthefloatandthetubewall.華南理工大學(xué)化工學(xué)院Thetubeismarkedindivisions,andthereadingofthemeterisobtainedfromthescalereadingatthereadingedgeofthefloat,whichistakenatthelargestcrosssectionofthefloat.華南理工大學(xué)化工學(xué)院TheoryandcalibrationofForagivenflowrate,theequilibriumpositionofthefloatinarotameterisestablishedbyabalanceofthreeforces:Thegravityofthefloat:thebuoyantforceofthefluidonthefloat:vfρgVthethedragforceonthe

AfCD華南理工大學(xué)化工學(xué)院FDFDAfCD2vffgvfVForagivenmeteroperatingonacertainfluid,theright-handsideofequationaboveisconstantandindependentoftheflowrate.Therefore,whentheflowrateincreases,thepositionofthefloatmustchangetokeepthedragforceconstant.華南理工大學(xué)化工學(xué)院Ifthechangeindragcoefficientissmall,thetotalflowrateisproportionaltotheannularareabetweenthefloatandtheq

d

d2fForalinearlytaperedtubewithadiameteratthebottomaboutequaltothefloatdiameter,theareaforflowisaquadraticfunctionoftheheightofthefloat.f華南理工大學(xué)化工學(xué)院tt

d2

d

2df

a2h2fffWhentheclearancebetweenfloatandtubewallissmall,theterma2h2isrelativelyunimportantandtheflowalmostalinearfunctionoftheheighth.fffThereforerotameterstendtohavealinearrelationshipbetweenflowrateandpositionofthefloat.華南理工大學(xué)化工學(xué)院Foragivenfloatofdensityρfandadensityρ,thevolumetricflowrateqisgivenq

ff

volumetricflowrateqisthereadingontherotameter,andKisaconstantwhichisdetermined華南理工大學(xué)化工學(xué)院IfafluidρBisusedinsteadofρ,atthesameheightorreadingofqontherotameterandassumingKdoesnotvaryappreciably,thefollowingapproximationcanbeused:m

ff

1.6- qBB B BForgaseswhereρf﹥﹥?chǔ)補(bǔ)nd BB華南理工大學(xué)化工學(xué)院Notethatthereadingontherotameteristakenatthehighestandwidestpointofthefloat.華南理工大學(xué)化工學(xué)院orificeandventurimetersmeasure velocityoftheentirestreamofThepitottubemeasuresthe velocityofRotametermustbe installedinthepipeline,andthefluidmustflow throughthetaperedtubeandsuspendsfreelyafloat.華南理工大學(xué)化工學(xué)院DisadvantagesforVenturimeterThedisadvantagefororificemeter華南理工大學(xué)化工學(xué)院Intheorificeandventurimeter,thevariationofvelocitythrough( areageneratesa( )pressureIntherotameter,thevariationofflowratethrough( )areageneratesa )pressuredrop.華南理工大學(xué)化工學(xué)院Foraorifice,nozzleandventurimeter,whentheReynoldsnumberisgreaterthancriticalRe,thenorificecoefficientCois )oftheReynoldsnumberagiven華南理工大學(xué)化工學(xué)院ExampleSulphuricacidofspecificgravity1.3isflowingthroughapipeof50mminternaldiameter.Athin-li