reynold numberWord文件下载.docx

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reynold numberWord文件下载.docx

laminarflowoccursatlowReynoldsnumbers,whereviscousforcesaredominant,andischaracterizedbysmooth,constantfluidmotion;

turbulentflowoccursathighReynoldsnumbersandisdominatedbyinertialforces,whichtendtoproducechaoticeddies,vorticesandotherflowinstabilities.

Contents

[hide]

∙1Definition

o1.1Significance

o1.2FlowinPipe

o1.3Flowinanon-circularduct(annulus)

o1.4FlowinaWideDuct

o1.5FlowinanOpenChannel

o1.6Objectinafluid

▪1.6.1Sphereinafluid

▪1.6.2Oblongobjectinafluid

▪1.6.3Fallvelocity

o1.7PackedBed

o1.8StirredVessel

∙2TransitionReynoldsnumber

∙3Reynoldsnumberinpipefriction

∙4Thesimilarityofflows

∙5Reynoldsnumbersetsthesmallestscalesofturbulentmotion

∙6ExampleoftheimportanceoftheReynoldsnumber

∙7Reynoldsnumberinphysiology

∙8Reynoldsnumberinviscousfluids

∙9Derivation

∙10Seealso

∙11Referencesandnotes

o11.1Furtherreading

∙12Externallinks

[edit]Definition

Reynoldsnumbercanbedefinedforanumberofdifferentsituationswhereafluidisinrelativemotiontoasurface(thedefinitionoftheReynoldsnumberisnottobeconfusedwiththeReynoldsEquationorlubricationequation).Thesedefinitionsgenerallyincludethefluidpropertiesofdensityandviscosity,plusavelocityandacharacteristiclengthorcharacteristicdimension.Thisdimensionisamatterofconvention–forexamplearadiusordiameterareequallyvalidforspheresorcircles,butoneischosenbyconvention.Foraircraftorships,thelengthorwidthcanbeused.Forflowinapipeoraspheremovinginafluidtheinternaldiameterisgenerallyusedtoday.Othershapes(suchasrectangularpipesornon-sphericalobjects)haveanequivalentdiameterdefined.Forfluidsofvariabledensity(e.g.compressiblegases)orvariableviscosity(non-Newtonianfluids)specialrulesapply.Thevelocitymayalsobeamatterofconventioninsomecircumstances,notablystirredvessels.

[4]

where:

isthemeanvelocity,

oftheobjectrelativetothefluid(SIunits:

m/s)

isacharacteristiclineardimension(travelledlengthofthefluid;

hydraulicdiameterwhendealingwithriversystems)(m)

isthedynamicviscosityofthefluid(Pa·

sorN·

s/m²

orkg/(m·

s))

isthekinematicviscosity(ν=μ/ρ)(m²

/s)

isthedensityofthefluid(kg/m³

NotethatmultiplyingtheReynoldsnumber,

by

yields

whichistheratio,

.[5]

[edit]Significance

[edit]FlowinPipe

Forflowinapipeortube,theReynoldsnumberisgenerallydefinedas:

[6]

isthehydraulicdiameterofthepipe;

itscharacteristiclength,

(m).

isthevolumetricflowrate(m³

/s).

isthepipecross-sectionalarea(m²

).

oftheobjectrelativetothefluid(m/s)

s)).

[edit]Flowinanon-circularduct(annulus)

Forshapessuchassquares,rectangularorannularducts(wheretheheightandwidtharecomparable)thecharacteristicdimensionforinternalflowsituationsistakentobethehydraulicdiameter,DH,definedas4timesthecross-sectionalarea(ofthefluid),dividedbythewettedperimeter.Thewettedperimeterforachannelisthetotalperimeterofallchannelwallsthatareincontactwiththeflow.[7]ThismeansthelengthofthewaterexposedtoairisNOTincludedinthewettedperimeter

Foracircularpipe,thehydraulicdiameterisexactlyequaltotheinsidepipediameter,ascanbeshownmathematically.

Foranannularduct,suchastheouterchannelinatube-in-tubeheatexchanger,thehydraulicdiametercanbeshownalgebraicallytoreduceto

DH,annulus=Do−Di

where

Doistheoutsidediameteroftheoutsidepipe,and

Diistheinsidediameteroftheinsidepipe.

Forcalculationsinvolvingflowinnon-circularducts,thehydraulicdiametercanbesubstitutedforthediameterofacircularduct,withreasonableaccuracy.

[edit]FlowinaWideDuct

Forafluidmovingbetweentwoplaneparallelsurfaces(wherethewidthismuchgreaterthanthespacebetweentheplates)thenthecharacteristicdimensionistwicethedistancebetweentheplates.[8]

[edit]FlowinanOpenChannel

Forflowofliquidwithafreesurface,thehydraulicradiusmustbedetermined.Thisisthecross-sectionalareaofthechanneldividedbythewettedperimeter.Forasemi-circularchannel,itishalftheradius.Forarectangularchannel,thehydraulicradiusisthecross-sectionalareadividedbythewettedperimeter.Sometextsthenuseacharacteristicdimensionthatis4timesthehydraulicradius(chosenbecauseitgivesthesamevalueofRefortheonsetofturbulenceasinpipeflow),[9]whileothersusethehydraulicradiusasthecharacteristiclength-scalewithconsequentlydifferentvaluesofRefortransitionandturbulentflow.

[edit]Objectinafluid

TheReynoldsnumberforanobjectinafluid,calledtheparticleReynoldsnumberandoftendenotedRep,isimportantwhenconsideringthenatureofflowaroundthatgrain,whetherornotvortexsheddingwilloccur,anditsfallvelocity.

[edit]Sphereinafluid

Forasphereinafluid,thecharacteristiclength-scaleisthediameterofthesphereandthecharacteristicvelocityisthatofthesphererelativetothefluidsomedistanceawayfromthesphere(suchthatthemotionofthespheredoesnotdisturbthatreferenceparceloffluid).Thedensityandviscosityarethosebelongingtothefluid.[10]NotethatpurelylaminarflowonlyexistsuptoRe=0.1underthisdefinition.

UndertheconditionoflowRe,therelationshipbetweenforceandspeedofmotionisgivenbyStokes'

law.[11]

[edit]Oblongobjectinafluid

Theequationforanoblongobjectisidenticaltothatofasphere,withtheobjectbeingapproximatedasanellipsoidandtheaxisoflengthbeingchosenasthecharacteristiclengthscale.Suchconsiderationsareimportantinnaturalstreams,forexample,wheretherearefewperfectlysphericalgrains.Forgrainsinwhichmeasurementofeachaxisisimpractical(e.g.,becausetheyaretoosmall),sievediametersareusedinsteadasthecharacteristicparticlelength-scale.BothapproximationsalterthevaluesofthecriticalReynoldsnumber.

[edit]Fallvelocity

TheparticleReynoldsnumberisimportantindeterminingthefallvelocityofaparticle.WhentheparticleReynoldsnumberindicateslaminarflow,Stokes'

lawcanbeusedtocalculateitsfallvelocity.WhentheparticleReynoldsnumberindicatesturbulentflow,aturbulentdraglawmustbeconstructedtomodeltheappropriatesettlingvelocity.

[edit]PackedBed

ForflowoffluidthroughabedofapproximatelysphericalparticlesofdiameterDincontact,ifthevoidage(fractionofthebednotfilledwithparticles)isεandthesuperficialvelocityV(i.e.thevelocitythroughthebedasiftheparticleswerenotthere-theactualvelocitywillbehigher)thenaReynoldsnumbercanbedefinedas:

LaminarconditionsapplyuptoRe=10,fullyturbulentfrom2000.[10]

[edit]StirredVessel

Inacylindricalvesselstirredbyacentralrotatingpaddle,turbineorpropellor,thecharacteristicdimensionisthediameteroftheagitatorD.ThevelocityisNDwhereNistherotationalspeed(revolutionspersecond).ThentheReynoldsnumberis:

ThesystemisfullyturbulentforvaluesofReabove10000.[12]

[edit]TransitionReynoldsnumber

[citationneeded]Inboundarylayerflowoveraflatplate,experimentscanconfirmthat,afteracertainlengthofflow,alaminarboundarylayerwillbecomeunstableandbecometurbulent.Thisinstabilityoccursacrossdifferentscalesandwithdifferentfluids,usuallywhen

wherexisthedistancefromtheleadingedgeoftheflatplate,andtheflowvelocityisthefreestreamvelocityofthefluidoutsidetheboundarylayer.

ForflowinapipeofdiameterD,experimentalobservationsshowthatfor'

fullydeveloped'

flow(Note:

[13]),laminarflowoccurswhenReD<

2000andturbulentflowoccurswhenReD>

4000.[14]Intheintervalbetween2300and4000,laminarandturbulentflowsarepossible('

transition'

flows),dependingonotherfactors,suchaspiperoughnessandflowuniformity).Thisresultisgeneralisedtonon-circularchannelsusingthehydraulicdiameter,allowingatransitionReynoldsnumbertobecalculatedforothershapesofchannel.

ThesetransitionReynoldsnumbersarealsocalledcritical

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