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Calculating Pressure Drops in Straight PipeFebruary14,2013mycheme

INTRODUCTIONProcessEngineersoftenneedtocalculatepressuredropforfluidsflowingdownpipes.Thisarticlepresentsamethodofestimatingpressuredropsinstraightpipe.

Instraightpipelengths,PressureDrop(?P)canbecalculatedusingtheDarcyEquation,whichinSIunitsispresentedbelow:

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Where:

LPipeLength(m)

uFluidVelocity(m/s)

?FluidDensity(kg/m3)

dPipeInternalPipeDiameter(m)

fDarcyFrictionFactor(Dimensionless)

ThisformoftheDarcyEquationcalculatesthepressuredropinPascal.ToconvertintoBar,dividetheanswerby105.

OtherlinksonsimilarsubjectsPressureDropsinPipeFittingsLiquidPressureDropSpreadsheetStandardPipesizes

CALCULATING THE DARCY FRICTION FACTORTheDarcyfrictionfactor(f)givesameasureofthepressurelossesresultingfromenergydissipationasaresultofshearstressesatthepipewall.ThefrictionfactorisafunctionoftheReynoldsNumber,Re.ItisoftenconvenienttoestimatethefrictionfactorusingtheMoodyDiagram.ThisisaplotoftheReynoldsNumberagainsttheFrictionFactor.AcopyoftheMoodyDiagram(takenfromWikipedia)isshownbelow.

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Inlaminarflow(i.e.ReynoldsNumberlessthanapproximately2100),thefrictionfactorisafunctionoftheReynoldsNumberonly(f=64/Re).Inturbulentflow(i.e.ReynoldsNumbergreaterthanapproximately3000),thefrictionfactorisafnctionofboththeReynoldsNumberandtherelativeroughnessofthepipe.

Pipe Roughness

Therelativeroughnessofthepipeisthepiperoughness,?,dividedbytheinternalpipediameter.Thepiperoughness,?,dependsonthepipematerial.TypicalvaluesofpiperoughnessforcommonpipingmaterialsaregivenontheMoodydiagramabove.Pipesmanufacturedfrommaterialswithcoursersurfacefinisheswillhavehigherfrictionfactorsand,allotherfactorsbeingequal,willthereforehavehigherpressuredrops.Asthepipediameterincreases,thepipesurfacewillbecomelessimportant,thus?isdividedbytheinternaldiameterofthepipetogivetherelativepiperoughness.Itshouldbenotedthattherelativepiperoughnessisdimensionlessitisimportanttoensurethatpiperoughnessandtheinternaldiameterareinthesameunits(thevaluesof?givenintheMoodyDiagramaboveareinmillimetres).

FRICTION FACTOR CALCULATION METHODSInadditiontousingtheMoodyDiagram,itispossibletoestimatetheDarcyFrictionFactorbycalculation.Thisisparticularlyusefulforcomputersoftwarewheregraphicalmethodsareinappropriate

Forlaminarflow,aformulafortheDarcyFrictionFactorcanbederivedfromfirstprinciplesusingPoiseuillesLaw.FromPoiseuilleslaw,thefrictionfactorcanbeobtainedusingthefollowingequation:

f = 64 / Re

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Unfortunately,thisequationisonlyapplicabletolaminarflowwhichisamajordrawbackaspipeflowinthemajorityofindustrialapplicationsisturbulent.Consequently,aconsiderableamountofacademicworkhasbeendoneonobtainingempiricalcorrelationstodeterminetheDarcyFrictionFactorinturbulentflow.ThemostwellknownistheColebrookCorrelation,givenbelow:

TheColebrookequationisapplicableforturbulentflowconditions(i.e.Reynoldsnumbers,Re,greaterthan3000).Itsmaindrawbackisthatthefrictionfactorcannotbeexpressedexplicitly,makingitdifficulttosolve.Itshouldbenotedthattheaboveequationisexpressedbase10logorithmsnotnaturallogs.ThereareanumberofothercorrelationswhichallowtheDarcyFrictionFactorinturbulentflowtobesolvedexplicitly:theseincludetheWoodCorrelationandtheJainCorrelation.However,personnallyIbelievethatthemostusefulistheChurchillCorrelation,seebelow:

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Inaddition,toallowingtheDarcyFrictionFactortobesolvedexplicitly,theChurchillCorrelationisapplicableforallReynoldsNumbers(atlowReynoldsNumbersitreducestof=64/Re).Thismakesitparticularlyusefulincomputerprogramsandspreadsheets,asitcanbeappliedtoallflowconditions.

OTHER FRICTION FACTORS

TheDarcyFrictionFactormustnotbeconfusedwithotherfrictionfactors,forexampletheFanningFrictionFactor.TheFanningFrictionFactorisexactlyaquarterofthesizeoftheDarcyFrictionFactorandisusedinamodifiedversionoftheDarcyEquation.IfthewrongformoftheFanningFrictionFactorisusedintheDarcyEquationabove,thepressuredropwillbeoutbyafactoroffour!

Sometimesitisnotclearwhichformthethefrictionfactorisbeingestimated.Ifthisisthecase,checkthevalueofthefrictionfactorataReynoldsNumberof1000whichfortheDarcyFrictionFactorwillgaveavalueof0.064

MyChemEprovideaspreadsheetforcalculatingpressuredropsinliquidpipelines,usingtheFanningFrictionFactor,canbefoundhere.

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