TalkingAboutTheDesignofHydraulicConductorsEricSandgrenThispaperisaccountforuncertaintyMechanicalEngineering,UniversityofCalifornia,SanFrancisco,avialon503WestMainStreet,P.O.Box9625311.1INTRODUCTIONInahydraulicsystem,thefluidflowsthroughadistributionsystemconsistingofconductorsandfittings,whichcarrythefluidfromthereservoirthroughoperatingcomponentsandbacktothereservoir.Sincepoweristransmittedthroughoutthesystembymeansoftheseconductinglines(conductorsandfittingsusedtoconnectsystemcomponents),itfollowsthattheymustbeproperlydesignedinorderforthetotalsystemtofunctionproperly.Thechoiceofwhichtypeofconductortousedependsprimarilyonthesystemsoperatingpressuresandflowrates.Inaddition,theselectiondependsonen-vironmentalconditionssuchasthetypeoffluid,operatingtemperatures,vibration,andwhetherornotthereisrelativemotionbetweenconnectedcomponents.Conductinglinesareavailableforhandlingworkpressuresupto10,000Paorgreater.Ingeneral,steeltubingprovidesgreaterplumbingflexibilityandneaterappearanceandrequiresfewerfittingsthanpiping.However,pipingislessexpensivethansteeltubing.Plastictubingisfindingincreasedindustrialusagebecauseitisnotcostlyandcircuitscanbeveryeasilyhookedupduetoitsflexibility.Flexiblehosesareusedprimarilytoconnectcomponentsthatexperiencerelativemotion.Theyaremadefromalargenumberofelastomeric(rubberlike)compoundsandarecapableofhandlingpressuresexceeding10,000Pa.Stainlesssteelconductorsandfittingsareusedifextremelycorrosiveenvi-ronmentsareexpected.However,theyareveryexpensiveandshouldbeusedonlyifnecessary.Copperconductorsshouldnotbeusedinhydraulicsystemsbecausethecopperpromotestheoxidationofpetroleumoils.Zinc,magnesium,andcadmiumconductorsshouldnotbeusedeitherbecausetheyarerapidlycorrodedbywater-glycolfluids.Galvanizedconductorsshouldalsobeavoidedbecausethegal-vanizedsurfacehasatendencytoflakeoffintothehydraulicfluid.Whenusingsteelpipeorsteeltubing,hydraulicfittingsshouldbemadeofsteelexceptforinlet,return,anddrainlines,wheremalleableironmaybeused.Conductorsandfittingsmustbedesignedwithhumansafetyinmind.Theymustbestrongenoughnotonlytowithstandthesteady-statesystempressuresbutalsotheinstantaneouspressurespikesresultingfromhydraulicshock.Whenevercontrolvalvesareclosedsuddenly,thisstopsthefluid,whichpossesseslargeamountsofkineticenergy.Thisproducesshockwaveswhosepressurelevelscanbetwoorfourtimesthesteady-statesystemdesignvalues.Pressurespikescanalsobecausedbysuddenstoppingorstartingofheavyloads.Thesehigh-pressurepulsesaretakenintoaccountbytheapplicationofanappropriatefactorofsafety.1.2CONDUCTORSIZINGFORFLOW-RATEREQUIREMENTSAconductormusthavealargeenoughcross-sectionalareatohandletheflow-raterequirementswithoutproducingexcessivefluidvelocity.Wheneverwespeakoffluidvelocityinaconductorsuchasapipe,wearereferringtotheaveragevelocity.Theconceptofaveragevelocityisimportantsinceweknowthatthevelocityprofileisnotconstant.AsshowninChapter5thevelocityiszeroatthepipewallandreachesamaximumvalueatthecenterlineofthepipe.Theaveragevelocityisdefinedasthevolumeflowratedividedbythepipecross-sectionalarea:AQvInotherwords,theaveragevelocityisthatvelocitywhichwhenmultipliedbythepipeareaequalsthevolumeflowrate.Itisalsounderstoodthatthetermdiameterbyitselfalwaysmeansinsidediameterandthatthepipeareaisthatareathatcorrespondstothepipeinsidediameter.Themaximumrecommendedvelocityforpumpsuctionlinesis4ft/s(1.2m/s)inordertopreventexcessivelylowsuctionpressuresandresultingpumpcavitation.Themaximumrecommendedvelocityforpressurelinesis20ft/s(6.1m/s)inordertopreventturbulentflowandthecorrespondingexcessiveheadlossesandelevatedfluidtemperatures.Notethatthesemaximumrecommendedvaluesareaveragevelocities.EXAMPLE1-1Apipehandlesaflowrateof30gprn.Findtheminimuminsidediameterthatwillprovideanaveragefluidvelocitynottoexceed20ft/s.SolutionRewriteEq.(3-26),solvingforD:invQD782.0612.02030408.0408.0EXAMPLE1-2Apipehandlesaflowrateof0.002sm/3.Findtheminimuminsidediameterthatwillprovideanaveragefluidvelocitynottoexceed6.1m/s.SolutionPerEq.3-35)wesolvefortheminimumrequiredpipeflowarea:232000328.01.6002.0msmvsmQmATheminimuminsidediametercannowbefound,because42DASolvingforDwehavemmmAD4.200204.0000328.0441.3PRESSURERATINGOFCONDUCTORSAconductormustbestrongenoughtopreventburstingduetoexcessivetensilestress(calledhoopstress)inthewalloftheconductorunderoperatingfluidpressure.Themagnitudeofthistensilestress,whichmustbesustainedbytheconductormaterial.weseethefluidpressure(P)actingnormaltotheinsidesurfaceofacircularpipehavingalength(L).ThepipehasoutsidediameterD0,insidediameterDi,andwallthicknesst.Becausethefluidpressureactsnormaltothepipesinsidesurface,apres-sureforceiscreatedthatattemptstoseparateonehalfofthepipefromtheotherhalf.FigureshowsthispressureforcePFpushingdownwardonthebottomhalfofthepipe.Topreventthebottomhalfofthepipefromseparatingfromtheupperhalf,theupperhalfpullsupwardwithatotaltensileforceF.One-halfofthisforce(orF/2)actsonthecross-sectionalarea(tL)ofeachwall,asshown.Sincethepressureforceandthetotaltensileforcemustbeequalinmagnitude,wehavewhereAistheprojectedareaofthelowerhalf-pipecurved-wallsurfaceontoahor-izontalplane.Thus,AequalstheareaofarectangleofwidthDiandlengthL,asshowninFigure4-1(b).Hence,Thetensilestressinthepipematerialequalsthetensileforcedividedbythewallcross-sectionalareawithstandingthetensileforce.Thisstressiscalledatensilestressbecausetheforce(F)isatensileforce(pullsontheareaoverwhichitacts).Substitutingvariableswehavewhere=Greeksymbol(sigma)=tensilestress.AscanbeseenfromEq.thetensilestressincreasesasthefluidpressureincreasesandalsoasthepipeinsidediameterincreases.Inaddition,asexpected,thetensilestressincreasesasthewallthicknessdecreases,andthelengthofthepipedoesnothaveanyeffectonthetensilestress.BurstPressureandWorkingPressureTheburstpressure(BP)isthefluidpressurethatwillcausethepipetoburst.Thishappenswhenthetensilestress()equalsthetensilestrength(S)ofthepipematerial.Thetensilestrengthofamaterialequalsthetensilestressatwhichthematerialruptures.Noticethatanaxialscribelineissho