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.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
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