形状阻力公式大全形阻公式.docx

形状阻力公式大全形阻公式.docx

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形状阻力公式大全形阻公式

Flowinvalvesandfittings

ResistancecoefficientK,valvesandfittingsheadlossandflowvelocity|PipeequivalentlengthL/D

Pressuredroporheadlossisproportionaltothevelocityinvalvesorfittings.Forthemostengineeringpracticesitcanbeassumedthatpressuredroporheadlossduetoflowoffluidsinturbulentrangethroughvalvesandfittingsisproportionaltosquareofvelocity.

Toavoidexpensivetestingofeveryvalvesandeveryfittingsthatareinstalledonpipeline,theexperimentaldataareused.ForthatpurposeresistancecoefficientK,equivalentlengthL/DandflowcoefficientCv,Kvareused.Thesevaluesareavailablefromdifferentsourcesliketablesanddiagramsfromdifferentauthorsandfromvalvesmanufacturersaswell.

Kineticenergy,whichisrepresentedasheadduetovelocityisgeneratedfromstaticheadandincreaseordecreaseinvelocitydirectlyisproportionalwithstaticheadlossorgain."Velocityhead"is:

whereis:

hL-headloss;v-velocity;gn-accelerationofgravity;

Thenumberofvelocityheadslostduetoresistanceofvalvesandfittingsis:

whereis:

hL-headloss;K-resistancecoefficient;v-velocity;gn-accelerationofgravity;

Theheadlossduetoresistanceinvalvesandfittingsarealwaysassociatedwiththediameteronwhichvelocityoccurs.

TheresistancecoefficientKisconsideredtobeconstantforanydefinedvalvesorfittingsinallflowconditions,astheheadlossduetofrictionisminorcomparedtotheheadlossduetochangeindirectionofflow,obstructionsandsuddenorgradualchangesincrosssectionandshapeofflow.

HeadlossduetofrictioninstraightpipeisexpressedbytheDarcyequation:

whereis:

hL-headloss;f-frictionfactor;L-length;D-internaldiameter;v-velocity;gn-accelerationofgravity;

Itfollowsthat:

whereis:

K-resistancecoefficient;f-frictionfactor;L-lengt;D-internaldiameter;

TheratioL/Disequivalentlengthinpipediametersofstraightpipethatwillcausethesamepressuredroporheadlossasthevalvesorfittingsunderthesameflowconditions.AstheresistancecoefficientisKisconstanttheequivalentlengthL/Dwillvaryinverselywiththechangeinfrictionfactorfordifferentflowconditions.

Forgeometricallysimilarvalvesandfittings,theresistancecoefficientwouldbeconstant.Actuallytherearealwayssmallerorbiggergeometricalnonsimilarityinvalvesandfittingsofdifferentnominalsize,sotheresistancecoefficientisnotconstant.TheresistancecoefficientKforagiventypeofvalvesorfittings,tendstovarywithsizeasdoesfrictionfactorforstraightcleancommercialsteelpipeatthesameflowconditions.

Someresistancesinpipinglikesuddenorgradualcontractionsandenlargements,aswellaspipeentrancesorexistsaregeometricallysimilar.ThereforetheresistancecoefficientorequivalentlengthL/Disfortheseitemsindependentofsize.

ThevaluesforresistancecoefficientorequivalentlengthL/Darealwaysassociatedwithinternalpipediameterwheretheresistanceisoccurring.

IftheresistancecoefficientorequivalentlengthL/Dshouldbeusedfordifferentinternalpipediameterthanthediameterforwhichexistingvaluescanbefoundfollowingrelationshipcanbeused:

whereis:

K-resistancecoefficient;D-internaldiameter;

wheresubscript"a"definesKanddwiththereferencetointernalpipediameter,andsubscript"b"definesKanddwiththereferencetotheinternaldiameterforwhichvaluesofKcanbefoundintablesordiagrams.

ThisequationcanalsobeusedifthepipingsystemhasmorethanonesizeofvalvesandfittingstoexpresstheresistancecoefficientorequivalentlengthL/Dintermsofonesize.

ResistancecoefficientKcalculatorforvalvesandfittingscanbeused.

ResistancecoefficientKforinternaldiametersuddenandgradualcontractionandenlargement

Usingmomentum,continuityandBernoulliequationtheresistanceduetosuddenenlargementsmaybeexpressedas:

andtheresistancefactorduetosuddencontractionas:

whereis:

K1-resistancecoefficient;d1-internaldiameter（smaller）;d2-internaldiameter（larger）;

Usingβasdiameterratio,bothequationcanbeexpressedas:

whereis:

K1-resistancecoefficient;β-diameterratiod1/d2;

Inordertoexpresstheresistancecoefficientintermsoflargerpipediameter,followingrelationshouldbeused:

whereis:

K1-resistancecoefficientbasedonsmallerinternaldiameter;K2-resistancecoefficientbasedonlargerinternaldiameter;β-diameterratiod1/d2;

Iftheenlargementisnotsuddenbutgradual,orifangleofgradualenlargementisdifferentfrom180O,GibsoncoefficientCecanbeusedfordifferentangleofdivergenceasfollows:

Inotherwords,ifangleofdivergenceisbiggerthan45O,theresistancecoefficientisequaltooneforsuddenenlargement.

ForgradualcontractiontheresistancecoefficientonthesamebasisbasedonCranetestdata,contractioncoefficientCccanbeusedfordifferentanglesofconvergence,asfollows:

Usingaboveexpressionsforenlargementandcontractioncoefficient,resistancecoefficientcanbecalculatedas:

Forgradualenlargement:

whereis:

Ce-coefficientofenlargement;K1-resistancecoefficientbasedonsmallerinternaldiameter;β-diameterratiod1/d2;θ-enlargementangle;

Forgradualcontraction:

whereis:

Cc-coefficientofcontraction;K1-resistancecoefficientbasedonsmallerinternaldiameter;β-diameterratiod1/d2;θ-enlargementangle;

Forresistancecoefficientbasedonthelargepipediameterexpression:

shouldbeused,withaboveequations.

whereis:

K1-resistancecoefficientbasedonsmallerinternaldiameter;K2-resistancecoefficientbasedonlargerinternaldiameter;β-diameterratiod1/d2;

Equationsforgradualenlargementandcontractioncanbeusedforresistancecoefficientcalculationforreducedborestraight-throughvalveslikeballvalvesandgatevalves.Thetotalresistancecoefficientforthistypeofballandgatevalvesisthesummationofresistancecoefficientforgradualcontractionandgradualenlargement.

YoucancalculateresistancecoefficientusingresistancecoefficientKandequivalentlengthl/dcalculator.

FlowcoefficientCv,pressuredrop,controlvalveflowrate

Selectingthecorrectvalvesizeforagivenapplicationrequiresknowledgeofprocessconditionsthatthevalvewillactuallyseeinservice.Intheindustryofcontrolvalvesitispracticetouseflowcoefficientandflowcharacteristics.

IntheUKandintheUSAcoefficientCvisusedanditisdefinedasflowrateofwateringpmat60OFthatcreatespressuredropof1psiacrossthevalve.Basicequationforvalvesizingforliquidserviceis:

whereis:

Cv-flowcoefficient[gpm];q-flowrate[gpm];Δp-pressuredrop[bar];S-specificgravity（relativedensity）[-];

ToaidinestablishinguniformmeasurementofliquidflowcoefficientsCv,standardizedtestingfacilitybyFluidControlInstitute（FCI）areusedbymanufacturers.Theeffectofviscosityoffluidsotherthanwatershouldbeconsideredwhenselectingthevalve,asincreasedviscosityoffluidisreducingthevalvecapacity.

AnothercoefficientKvisusedinsomecountries,particularlyinEuropeandisdefinedasflowrateofwaterinm3/hthatcreatespressuredropof1kg/cm2acrossthevalve（1kg/cm2isequalto0.980665bar）.

Controlvalvesizingisbasedonthecalculationofflowcoefficientforgivenpressuredropandflowrate.LiquidflowcapacityofavalveinmetricunitscanbeconvertedtoCvas:

whereis:

Cv-flowcoefficient[gpm];qm-flowrate[l/m];ρ-density[kg/m3];Δp-pressuredrop[bar];

Also,liquidflowcapacityofavalvecanbeconvertedtoKvas:

whereis:

Kv-flowcharacteristic[m3/h];qh-flowrate[m3/h];S-specificgravity（relativedensity）[-];Δp-pressuredrop[bar];

AboveequationsareusedinflowcoefficientCv,pressuredropandcontrolvalveflowratecalculator.

Flashingandcavitation,vaporpressureatvalvevenacontracta

Flashingorcavitationinsideavalvecanhaveasignificantinfluenceonvalvecapacity.Flashingandcavitationcanreducetheflowthroughvalveinmanyliquidservices.Also,damagecanbemadetothevalveaswellastothepipingsystem.Theeffectisrepresentedbythechangefromliquidtovaporstateoffluid,resultinginthevelocityincreasedownstreamfromthevalve.

Asliquidpassesthroughtherestrictionareainsidethevalveflowstreamiscontracted.Thesmallestcrosssectionareaofstreamisjustdownstreamoftheactualphysicalrestrictionatapointcalledvenacontracta.Atthatpointthevelocityisatitsmaximumandpressureattheminimum.

Asthefluidexitsthevalve,awayfromvenacontracta,velocitydecreaseandpressureincrease,sothecriticalpointforflashingandcavitationisatthepointwherethepressureissmallestwhichisinvenacontracta.Ifpressureatvenacontractadropsbellowsthevaporpressureofthefluid,duetoincreasedvelocityatthispoint,bubbleswillformintheflowstream.

Ifpressuredownstreamofthevenacontractaincreaseabovethevaporpressure,bubbleswillcollapseorimplodeproducingcavitation.Cavitationreleasesenergyandproducesanoise.Ifcavitationoccursclosetosolidsurfaces,theenergyreleasedgraduallywearsthematerialleavingtheroughsurface.Cavitationcanalsodamagethedownstreampipeline,ifatthatplacethepressurerisesabovethevaporpressureandbubblescollapse.

Chockedflowvalvepressuredropandcavitationinhighpressurerecoveryvalve

Formationofbubblesinthevalveresultingofflashing