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.'.'•.~"ALASKAPOWERAOTE~lilTYRESPONSETG~GENCYCC~ME~TSCNLICENSEAPPLICATION;EEEEBENCETOCO~MEN!(S):I.IOSAWATERRESOURCESTECHNICAL.PUBLICATIONENGINEERINGMONOGRAPHNO..41EXCERPTFROM/j}[]&IRl~&c~~&©©@SusitnaJointVentureDocumentNumberPleaseReturnToDOCUMENTCONTROLz..-o-f2~_----_..-..AIR-WATERFLOWIN--··~~I···RAULICSTRUCTURES.]'81UNITEDSTATESDEPARTMENTno.2905bjOFTHEINTERIORWATERANDPOWERRESOURCESSERVICE ..;AstheNation'sprincipalconservationagency.theDepartmentoftheInteriorhastheresponsibilityformostofournationaUyownedpubliclandsandnaturalresources.protectingourfishandwildlife,preservingtheenvironmentalandculturalvaluesofournationalparksandhistoricalplaces.andprovidingfortheenjoymentoflifethroughoutdoorrecreation.TheDepartmentassessesourenergyandmineralinterestsofallourpeople.TheDepartmentalsohasamajorresponsibilityforAmericanIndianreservationcommunitiesandforpeoplewholiveinIslandTerritoriesunderU.S.administration.ENGINEERINGMONOGRAPHSarepublishedinlimitededitionsforthetechnicalstaffoftheWaterandPowerResourcesServiceandinterestedtechnicalcirclesinGovernmentandprivateagencies.Theirpurposeistorecorddevelopments,innovations,andprogressintheengineeringandscien-tifictechniquesandpracticeswhichareusedintheplanning,design,con-struction,andoperationofwaterandpowerstructuresandequipment.}O~irs(Printing:19HUmJS1I1ETRICARLIs.AlaskaRLIbrary&Jut;eso~cesonnationSeAn"hQr"8~,A.1askl:tIV1cesU.S.GOVERNMENTPRINTINGOFFICEDENVER.COLORADOFor5al('bytheSIl~rint('nd(,111orDocuments.u.s.GovemmentPrintingOffice.Wa~hinglon.D.C.2U402..ortill"WillerandJ10werResourcesService.Attention922.P.O.Box2;}()1I'i.Denver.Colorado80225.rII II~-I,,IIr--IIII,-IiIIII<XlI~0'<t'<t'<t0I00LOLOr-..I(V)(V)I~-"tjPrefaceThematerialassembledinthisreportistheresultofstudiesextendingovermanyyearsbyalargenumberofengineers.EllisPicketattheU.S.ArmyEngineerWaterwaysExperimentStationinVicksburg,Mississippi,suppliedareferencelistdealingwithair-waterproblems.PersonneloftheWaterandPowerResourcesServiceE&RCenter.WaterConveyanceBranchmadetheirfilesanddrawingonairdesigncriteriainpipelinesavailableforpublica-:tioninthisreport.Priortopublication,thereportwasreviewedbyEllisPickettandTedAlbrechtwiththeU.S.ArmyEngineers;andbyengineersintheDams,Mechanical,andWaterConveyanceBranches,E&RCenter,WaterandPowerResourcesService.ThemanyconstructivecommentsbytheseindividualsandtheassistanceofRichard-Walterswhoprovidedcon-tinuityandtechnicaleditingisgreatlyappreciated.vARLIS.AlaskaResourcesLIbrary&InfonnationServIcesAnchorage,Alaska SymbolQuantitySymbol.QuantityACrosssectionalareaofwaterprismdFlowdepthA.CrosssectionalareaofairflowdbBnlkedflowdepthpassagede·DeflectorheightAcCrosssectionalareaofaircoreinadnNappethicknessverticalshaftdo()ri£icediameter=AdCrosssectionalareaofconduitd,TotaldepthofunderlyingandairAo.()rificeareafreezonesApCrosssectionalareaofpenstockd.sBubblediameterforwhich95AvCrosssectionalareaofventpercentoftheair,byvolume,isaRatioofbubbleterminalvelocityincontainedinbubblesofthisIturbulentflowtoterminalvelocitydiameterorsmaller.instillwaterERelativewidthofthefrequency.-aoMeanairdistributionfunctionspectrum~a,MeanairdistributionconstantexpNapierianlogarithmequaltoBWidthofrectangularchute2.71828,approximatelyb·WidthofflowchannelfDarcy-WeisbachfrictionfactorbnNappewidthGGateopening~b,EmpiricalcoefficientaccountingforGgMassvelocityofgassandgrainroughnessG,MassvelocityofliquidCAirconcentrationgGravitationalconstant(acceleration)~C.ActualairconcentrationHHydranlicradiusofprototypeairCbDragcoefficientonabubbleventCdDischargecoefficientbasedon100HIFallheightofawaterjetIIpercentgateopeningHmHeadacrossorificeCI·LocallosscoefficientHnNetheadacrossturbineCIAirconcentrationatd,/2HoDistancefromchannelinverttoCmAirconcentrationmeasuredbya.energygradelinepitottubesamplerH,TotalpotentialandkineticenergyCoC>rificedischargecoefficienthMeanwaveheightC,Dragcoefficientonasphereh.HeightofairflowpassageC,AirconcentrationatthebottomofhiDistancefrominlettothewater.-themixingzonelevelintheverticalshaftCMeanairconcentrationhiHeadlossperunitlengthcWaterhammerwavecelerityhmHeadacrossmanometerDConduitdiameterhwAllowableheadriseinpenstockDbSmallerdimensionofarectangularKeEntrancelossconduitK,Singnlar(form)lossDdDiameterofwaterdropkVonKarmanuniversalconstantDeEquivalentbubblediameterequaLtoO.4D,Largerdimensionofarectangularkr.Coefficientofroughnessconduit,:;.k.Sand·grainroughness,f;'"'.f~::'viLetterSymbolsandQuantities II,,.-LEITERSYMBOLSandQUANTITIES-ContinuedISymbolQuantitySymbol'QuantityILLengthofconduitorventr,RelativeroughnessofconduitLcDistancetostartofself-aeration(rugositytodiameterratio)LrPrototypetomodelscaleratioSSubmergencedepthIL,DistancebetweenstiffenerringsSoPipeslopeMUnitmassSfSlopeofenergygradelinecMoMaximumdifferenceinelevationSRoot-mean-squarevalueofwaveIbetweenawavecrestandtheheightdistributionmeanwaterlevelSwRoot-mean-squarevalueof'water;-mAirconcentrationdistributionsurfacedistributionIcoefficientTTopwidthofflowpassageNSafetyfactortPipewallthicknessr.nManning'sroughnesscoefficientUFreestreamvelocity:noVelocitydistributionpower-lawUdVelocityofwaterdroprelativetoIcoefficientairvelocityPEnergydissipatedUjWaterjetvelOcityf'PgNormaldistribution'functionuLocalairvelocityIPhProbabilitythatthewaveheightisVMeanflowvelocity,equaltogivenheightVfTerminalvelocityofbubblesfPwProbabilitythatthewatersurface.inturbulentflowIisequaltoorgreaterthanthePiNappevelocityatimpactgivenelevationVmMinimumvelocityrequiredto•PPressureintensityentrainairP.AllowableinternalpressureV.MaximumwatersurfacevelocityPatmAtmosphericpressureV.Terminalvelocityofbubblesin•PcCollapsepressureslugflowPinInternalpressureV,TerminalvelocityofbubblesinPoNappeperimeterstillwaterQDischargeWWettedperimeterIQ.VolumeflowrateofairxDistancefromstartofboundaryQcCriticaldischargelayergrowthrQrDischargefromreservoirYDistancenormaltochannelbottomIfQwVolumeflowrateofwater(flowdepth)qUnitdischargeY•.Distancefromwatersurfaceq.InsufflationrateofairperunitYcConjugatedepthIsurfaceareaY.EffectivedepthRBubbleradiusYkCriticaldepthRbEquivalentbubbleradiusY'NormaldistancetothebottomofIiRcRadiusofcurvatureofthe,bubblethemixingzoneI,capzElevationRjThicknessofannularjetIrWaterjetradiusIvii-'1,=-'!• LEITERSYMBOLSandQUANTITIES-ContinuedSymbolQuantitySymbolQuantityaalphaAnglechuteinvertmakesEElltvllsnumber-YD'withhorizontal0f3betaRatioofvolumetricairflowE"Eulernumber/ill-ratetowaterflowrate-l'J'"YgammaSpecificforceofwaterddeltaBoundarylayerthicknessFFroudenumber-I'£epsilonMasstransfercoefficientI~I>1'"ofbubblesPPrandtlvelocity~zetaAirconcentrationratio-Fdistributionconstant11,'/(>1"2YJetaNormalizedwaveheightI,,,"Idp/dxlfithetaVoidfractionP"Poiseuillenumber-lCkappaGasconstant~J1V}.lambda'DensityratioRReynoldsnumber1'1)Dynamicviscosity-J1muvII'J1.'DynamicviscosityofairJ1wDynamicviscosityofwaterRxDistanceReynoldsVx,vnuKinematicviscosity..number-,VIWaterviscosityv~11pi'RatioofthecircumferenceWWebernumberIIofanycircletoits-(o/,!/),'",radius,3.14159...erhoDensitye.AirdensityewWaterdensityegGasdensityelLiquiddensityemDensityofmanometerfluid~asigmaInterfacialsurfacetensionTotauWallsbearstressTjShearstressatwaterjetU.tmupsilonSpecificvolumeofairatatmosphericpressureIu.'Shearvelocity1jJpsiMuiticomponentflowparametercoomegaVolumeofgasbubbleco.VolumeofairCOwVolumeofwater,00Infinity1_"_viii viI3'577881012141616191919212224283637374141424444485152545457575757575759ixPagePreface;. . . . •. . . . . . . . . . . . . . vLetterSymbolsandQuantities.•......'.'.......•......~.Introduction...•......•..•..•................................PurposeandApplications.SummaryandConclusions.•.........•...,..•.........•...•...OpenChannelFlow......•.•...•.........•.••.•..........•..'..Introduction•.........•...•.....•.••..•...•.............•.BubbleDynamics'.TerminalVelocityofaSingleBubbleinStillWater.BubbleSizeinShearFlows.....:.....•..............•..TerminalVelocityofBubblesinTurbulentFlow......•....VerticalandLongitudinalFlowStructure.....•....•...........DesignParameters....•..•..'.. . . .... . ....... . . . . . . . ........LocationofBeginningofAeration..••...•.........•....••LocationofFullyAeratedFlow•••.••..••.•......•...•'••.AirConcentrationProfiles..••••.•••.•...••.........•••.Definitionofconcentration•..•••.••..•.........••••.AirdistributioninthemixingZOD.Airdistributionintheunderlyingzone•....••...•••...Meanairconcentration.••••••.......'.'..••....•....WaterSurfaceLocation..EffectofAirEntrainmentFlowonStillingBasinPerformance......••..••••..•.......................ClosedConduifFlow'.'•.•'...••.......••.............ClassificationofFlow......•:.FlowinPartiallyFilledConduits....••.......•.•..•..........ModelPredictions......•.•.................•.......•••Airventnotdesigned..Airventdesigned..AnalyticEstimates.FlowHavingaHydraulicJumpThatFillstheConduit.......••.FlowsFromControlDevices,.FlowsFromValves••••••.•.•.••••...•••.....•••••.•••.FlowsFromGates••.•....•...•.•.•..•.........•••.••••FallingWaterSurface...••.••...•....•..••.....;..•...••...AirVentDesignCriteriaforClosedConduits........••:..••••.Purpose.Location.....•••.••....•••••••••••....•...•••..•••.••MaximumAirflowRate.StructuralConsiderations•.••.•..•.•...•....••...•..••.•PhysiologicalEffects.SafetyofPersonnel.•••.••......•••.••....•...•...•..•...\.Aontents:;,,.IIIII,,II,.I*II•IIIIi[IIII- xiiCONTENTS-ContinuedFIGURES-ContinuedNumlJerPage36Pipelineconfigurations...........•.........•.........•..6137Planandprofileofagravitypipeline.......................6238Ventstructure..........................................6339Typicalirrigationsystemairvalveinstallation........•......6440Ventlocationatchangesinpipeslope......................6541Airbindinginapipeline..................................6642Large-orificeairvalve...........•...•....•....••........6743Performancecurvesforlarge-orificeairreleasevalves........•6844Typicalsmall-orificeairreleasevalve.••.•...."..........•...6945Performancecurvesforsmall-orificeairreleasevalves......•..7146Typicalfrostprotectioninstallation...•.•......•..•..•.....7247C;ollapsingpressureofasteelpipewithstiffenerrings........•7348Performancecurvesforlarge-orificevacuumreliefvalves....•.7449Specificvolumeandbarometricpressureofairasafunctionofelevation......•...•.....••...........••..7550Requiredairrelief orificediametertopreventcollapseofsteelpipelines....................................7651Observedairblowbackinmorninggloryspillwayat~OwyheeDam,Oregon...............................n52Typicaltypesofverticalshaftinletstructures.........••.....7853Verticalshaftspillwaydischargecharacteristics...••.••......78~54Breakupofawaterjetfromahollow-jetvalve...............8455Waterdropbreakup......•..........••.........".•.......8556Velocitydistributionforflowoveraflatplate,Bormann[11)...86IAPPENDIX~I-IElectronicsschematic...........................•....•...961-2Probeschematic.:....•........••...•...•....••....••..•961-3Controlsinutilitybox....................................96III-IDefinitionsketchatpenstockintake•..•.••...••.....•.••..114IIF2Typicalturbinecharacteristicsofrunnerspecificspeed230•.•.116III-3Turbinelosscoefficient........•....•.•~....••..•..•.....117III-4Airvolumeinpenstock........•.....••••••....••....••..•118III-5Watersurfacearea.......................................118 IrI,I.I.I(,IrIrI*IIIIiIIIII'~~.IntroductionInmanyengineeringprojectsastronginter-actiondevelopesbetweenthewaterflowingthroughastructureandtheairwhichisadja-centtothemovingwater.Sometimestheinter-actionproducesbeneficialeffects.However,moreoftenthannot,theeffectsarenotbeneficialandtheremedialactionrequiredtoreducetheeffectscanbecostly.Casesinwhichair-waterinteractiondevelopinclude:•Openchannelswithfastflowingwaterthatrequiredepthsadequatetocontaintheairwhichisentrainedwithinthewater•Morning-gloryspillwaysthatmusthaveacapacitytoconveythedesignfloodanditsentrainedair•Verticalshaftsthatentrainlargequan-titiesofairatsmallwaterdischarges•Measuringweirsthatneedadequateven-tilationtopreventfalsereadingsandtoeliminatesurging•Outletgatesthatrequireadequateaerationtopreventthedevelopmentoflowpres-sures-whichcanleadtocavitationdamage•Emergencygatesatpenstockentrancesthatrequireventilationtopreventex-cessivenegativeinternalpressuresduringdrainingoremergencygateclosuresI•Sagpipes(invertedsiphonsI'thatcanbedamagedduetoblowbackofentrainedair•LongpipelinesthatrequireairreleaseandvacuumreliefvalvesFromthesecasesitisnotedthatair-waterflowscanbegeneralizedintothreebasicflowtypes:1.Air-waterflowsinopenchannels,2.Air-waterflowsinclosedconduits,and3.Free-fallwaterflows.Thefirsttypeusuallyiscalledair·entraining.flowbecauseairisentrainedintothewatermass.Thesecondbasicflowtypegenerallyisreferredtoasair-demand.Thetermair-'demandisbothmisleadingandtechnicallyin-correct,sinceanairventdoesnotdemandairanymorethananopenvalvedemandswater.However,sincethetermhasbeenincommonuseforover20years,effortstoimprovethenomenclatureseemratherfutile.Thethirdtypeisreferredalsotoasair-entrainingflow.'''siphon,inverted-Apipelinecrossingoveradepressionorunderahighway,railroad;canal,elc.Thetermiscom-monbutinappropriate,asnosiphonicactionisinvolved.Thesuggestedterm,sagpipe.isveryexpressiveandap-propriate.toNomenclatureforHydraulics,Comm.onHyd,Str..Hyd.Div••ASCE.1962, PurposeandApplication~..~I."I~II,•Effectsofturbulenceandairconcentrationonbubbledynamics•Fluiddynamicsinthedevelopingaerationregimeoffree-surfaceflow•EffectsofhydraulicandconduitpropertiesI'/onprobabilisticdescriptionofwatersur-/faceinfree-surface,high-velocityflow•Effectofpressuregradientsonairflowinpartially-filled,closedconduits•Bubblemotioninclosed-conduitflowsforconduitslopesexceediIig45-degrees•Effectsofambientpressurelevelsoncavitationcharacteristicsofgatesandvalvesdischargingintoaclosedconduit•Interactionbetweentheairandafreejet:lThepurposeofthisreportistosummarizetheworkthathasbeendoneonair-entrainmentandair-demandregardingthemostrecenttheoriesandtosuggestwaysinwhichtheresultscanbeappliedtodesign.Theintentwastoproduceaconcisereferenceofmaterialfromwhichdesignmanuals,nomographs,andchartsforspecificapplicationscouldbeprepared..Althoughmanygeneralizationsofthedatacanbemade,sometypesofflowconditions'thatareencounteredinpracticecanbetreatedonlybyindividualstudieswithphysicalmodels.Thesecasesareidentifiedwhentheyoccur.Additionalstudiesareneededinmanyareas.Someofthemostcriticalareasrequiringfur-therresearchincludethefollowing: SummaryandConclusions2IIi,III,-IrI-.•r-•-,-IIItiI;::>Rf,III...._:I,-Methodshavebeendevelopedtopredictthemeanairconcentrationandtheconcentrationdistributionwithopenchannelflow.Anewdescriptionofthefreewatersurfaceinhighvelocity-f[ow'isproposeawhich-moreaccuiiitelL_representSactualconditionsinhighveio~ityflow.Theeffectofairentrainmentontheper-formanceofastillingbasincanbeestimatedusingabulkedflowconcept.Acomputerpro-gram(app.II)ispresentedwithwhichthemeanairconcentration'insteepchutesandspillwayscanbeestimated.Withexceptionofafalling-watersurfaceanddecreasingflowinpipelines,closedconduitflowsrequiremodelstudies.Whenproperlyconductedandanalyzed,modelstudieswillyieldaccuratedataforestimatingair-flow5rates.Experimentalmethodsarediscussed.Acomputerprogram(app.III)ispresentedwhichcimbeusedtopredicttheairflowratewithafalling-watersurface.Designchartsarepresentedforsizingairreliefvalvesandvacuumvalvesonpipelines.Theairflowrateinverticalshaftswasfoundtobeextremelydependentupontheflowcondi-tionsattheshaftinlet.Equationsareincludedforestimatingtheairflowratehavingvariousinletconditions.Factorsinfluencingtheairflowratearoundfreefallingjetsarediscussed.Thisareaisiden-tifiedasoneneedingadditionalresearch.Equa-tionsarepresentedfromwhichtheairentrain-ingcharacteristicsofajetenteringapoolcanbeestimated.