BUILDINGTECHNOLOGIESPROGRAMApril29‐30,2014ASRACPumpsWorkingGroupMetric:TestingandCalculations2PrimaryDiscussionReviewofMetricandRelationshiptoStandardOverviewofPERTestProcedureforControlledversusUncontrolledPumpsOtherRemainingIssues/TopicsTestProcedureOptions•Calculation‐basedmethod-Howtoaccountformotorefficiencyatpartloadandcontrols•Testing‐basedmethodLoadPointOptionsWeightingOptionsOtherDenominatorOptionsOverview3MetricGoals1. Beobjectivelymeasureable2. Representtheperformanceofthecoveredproduct3. Differentiateperformanceamongpumpmodelsandpumpconfigurations(e.g.pumpssoldwithcontrols)4. Communicateinformationaboutpumpperformancetotheconsumer–Maynotbealltheinformationaconsumerusestomakeadecision5. ComparetheefficiencyofagivenpumpmodeltoaminimumstandardlevelMetricTestProcedureTestedPerformanceofPumpATestedPerformanceofPumpBEnergyConservationStandardMinimumStandardLevelBarePumpEfficiencyorEnergyUseMotorEfficiencyorEnergyUseControlsEfficiencyorEnergyUse‘Pump’EfficiencyorEnergyUse=4MetricTestProcedureTestedPerformanceofPumpATestedPerformanceofPumpBEnergyConservationStandardMinimumStandardLevelScopeofSlides•ThisslidedeckandthePERCalculatoraddresshowthemetriciscalculatedinthetestprocedureforagivenpumpmodel.5MetricApplicabilitytoPumpConfigurationsPumpConfigurationBare Pump* BarePump+ Motor BarePump+Motor+Controls

Metric CoverageBarePump MEIDoesnotincludemotorefficiencyDoesnotdescribecontrollossesorbenefitsBarePump+DriverPERCL(w/ std.driver)PERCLDoesnotdescribecontrollossesorbenefitsBarePump+Driver+ControlsPERCL(w/ std.driverandcontrols)PERCL(w/std.controls)PERPL

PumpMotor PumpMotorControl Pump•Defineaunique,butsimilar,metricforcontrolledversusuncontrolledpumps•Uncontrolledpumps‐>ConstantLoadPumpEnergyRating(PERCL)•Controlledpumps‐>PartLoadPumpEnergyRating(PERPL)*Pumpssoldwithnon‐electricdrivescouldberatedasbarepumps6PERTestProcedurePumpEnergyRating(PER)CLandFL:equallyweightedaverageelectricinputpowertothe‘pump’measured(orcalculated)atthedriverinputor,whenpresent,controlsinput,overaspecifiedloadprofile:Where:•PER=PumpEnergyRating(hp);•wi=weightateachloadpointi;•LCF=LoadControlFactor(dimensionless);•Pini=powerinputtothe“pump”atthedriver,inclusiveofthecontrolsifpresent,(hp);•Denominator=minimallycompliantuncontrolledpump;and•i=Percentageofflowatthebestefficiencypoint(BEP)ofthepump.•i=110%,100%,75%ofBestEfficiencyPoint(BEP)flowatnominalspeedforuncontrolledpumps•i=25%,50%,75%,and100%ofBEPflowatnominalspeedforpumpssoldwithmotorsandcontrols.ࡾࡱࡼࡸࡲ/ࡸ࡯ࡲ࡯ࡸ ൌ∑߱௜ܲ௜௡௜௜݌݉ݑܲ	݈݈݁݀݋ݎݐ݊݋ܷ݊ܿ	ݐ݈݅ܽ݊݌݉݋ܥ	ݕ݈݈݅݊݅݉ܽܯ8MinimallyCompliantPump•PERforaminimallycompliantpump–BasedonPERStandardsetthroughStandardsanalysis≈MEI10assumedforthisexample–Assumesapumpcurveshapefortheminimallycompliantpumpandalwaysassumesnocontrols–Motorlossesarethatofaminimallycompliantenclosedmotorfortheappropriatepumptype–Theminimallycompliantpumpefficiencyiscalculatedforeachpumptypebasedonafunctionofflowandspeedܲܧܴ௡௜௠ൌ ߱଴.଻ହܲு௬ௗ௥௢,଴.଻ହ0.95 ∗ ߟ௣௨௠௣൅ ܮ଴.଻ହ൅ ߱஻ா௉ܲு௬ௗ௥௢,஻ா௉ߟ௣௠௨௣൅ ܮ஻ா௉൅ ߱ଵ.ଵܲு௬ௗ௥௢,ଵ.ଵ0.985 ∗ ߟ௣௨௠௣൅ ܮଵ.ଵ



# PERൌܨܥܮ߱଴.଻ହܲ௜௡଴.଻ହ൅ ߱஻ா௉ܲ௜௡஻ா௉൅ ߱ଵ.ଵܲ௜௡ଵ.ଵ߱଴.଻ହܲு௬ௗ௥௢,଴.଻ହ0.95 ∗ ߟ௣௨௠௣൅ ܮ଴.଻ହ൅ ߱஻ா௉ܲு௬ௗ௥௢,஻ா௉ߟ௣௨௠௣൅ ܮ஻ா௉൅ ߱ଵ.ଵܲு௬ௗ௥௢,ଵ.ଵ0.985 ∗ ߟ௣௨௠௣൅ ܮଵ.ଵൌ 113∗ܲ଴.଻ହ൅ ܮ଴.଻ହ൅13∗ܲ஻ா௉൅ ܮ஻ா௉൅13∗ܲଵ.ଵ൅ ܮଵ.ଵ13∗ܲு௬ௗ௥௢,଴.଻ହ0.95 ∗ ߟ௣௨௠௣൅ ܮ଴.଻ହ൅13∗ܲு௬ௗ௥௢,஻ா௉ߟ௣௨௠௣൅ ܮ஻ா௉൅13∗ܲு௬ௗ௥௢,ଵ.ଵ0.985 ∗ ߟ௣௨௠௣൅ ܮଵ.ଵ9DeterminingMinimallyComplaintPumpEfficiencyߟ௣௨௠௣ൌ 88.59 ∗ lnܰݏ ൅ 13.46 ∗ lnܳ௠௘௧௥௜௖െ 11.48 ∗ lnܰݏଶെ 0.85∗ lnܳଶെ 0.38 ∗ lnܰݏ ∗ lnܳ െܥ•Where:–Nsisthespecificspeedofthepumpinmetricunits,–QistheflowrateofthepumpatBEPinm3/hr,–CistheC‐valueofthesurface,whichissetbasedonthespeedofrotationofthepump,and–Allvaluesareforthepumpat50Hz.C‐ValuestoDeterminePumpEfficiencyPumpTypeSpeed MEI10 MEI50ESCC1800 131.75 125.50ESFM1800 131.50 125.50IL1800 134.50 126.50RSVALL 131.50 127.00VTSALL 135.75 129.25ESCC3600 133.75 127.75ESFM3600 134.00 128.00IL3600 140.00 129.7510DeterminingPERFLforaControlledPumpܨܥܮ ൌ ܴܧܲ߱଴.଻ହܲ௜௡଴.଻ହ൅ ߱஻ா௉ܲ௜௡஻ா௉൅ ߱ଵ.ଵܲ௜௡ଵ.ଵܴܧܲ௡௜௠ൌ1η௖௧௥௟߱଴.ଶହܲ௜௡଴.ଶହ൅ ߱଴.ହ଴ܲ௜௡଴.ହ଴൅ ߱଴.଻ହܲ௜௡଴.଻ହ൅ ߱஻ா௉ܲ௜௡஻ா௉ܴܧܲ௡௜௠LCFApproach FullCalculationApproachPumpPerformancePi=measuredshaftinputpowertothepump(speedxtorque)ateachloadpointiWhere:i = 75%,100%,and110%offlowrateatBEPofthepumpandequalweightingPi=calculatedshaftinputpowertothepumpbased onaffinitylawsateachloadpointiWhere:i =25%,50%,75%,and100%offlowrateatBEPofthepumpandequalweightingMotorPerformance(Losses)LratedisthefullloadlossesofamotorthatispairedwiththepumpandlossesarecalculatedforthereducedloadingwithspeedreductionControlsPerformanceLCF=0.56forVFDcontrol,0.67for2‐speedmotor,etc.Accountsforreducedpowerinputatloadpointsof25%,50%,75%and100%ofBEPflowDriveefficiency=96%Benefitiscapturedincalculation ofbareshaftinputpower.Couldstillaccountfordriveefficiency.11PumpHydraulicOutputPower•Pump HydraulicOutputPower–“Denominator”=hydraulicoutputpowerateachloadpointi•Note,thisexamplealsoflipsthenumeratoranddenominatortomakehighervalues“better.”•Units=dimensionlessൌ ܴܧܲ1ܨܥܮ߱ ෍௜ܲ௜,௢௥ு௬ௗܲ௜ܮ ൅௜௜12HouseofEfficiencyversusWeightedAverageHouseofEfficiency WeightedAverageCharacteristics•Definespump performanceuniquelyatindividualloadpoints•Weightspumpperformanceatallloadpoints todetermineasinglemetricPros•Potentially moreinformativeforthemarket•SimilartoEUapproach•Moreaccommodating ofdifferentpumpcurves•SimplertocomparepumpsCons•Lessflexible, sinceamanufacturerhastomeetallloadpoints•Masks performanceofpumpatindividualloadpointsOtherComments•Could potentiallyreportallloadpointsonlabelorinDOEdatabaseWorkingGroupRecommendation=13MetricNomenclature•PumpEnergyRating(PER)•PumpEfficiencyRating(PER)•PumpSystemEnergyRating(PSER)•PumpSystemEfficiencyRating(PSER)•Others?14PERTestProcedureOptionsPumpConfigurationBare Pump*BarePump+Motor BarePump+Motor+Controls

Test Procedure OptionsTestedBarePump+CalculationsTestedbarepumpperformance +DOEminimumefficiencymotorwithassumedpartloadlossesTested barepumpperformance+manufacturermotorwithassumedpartloadlossesTestedbarepumpperformance+manufacturermotorwithassumedpartloadlosses+LoadControlFactorTestedPumpwithManufacturerMotorN/ATested performanceofbarepumpwithmanufacturermotor(wiretowater)Tested performanceofbarepumpwithmanufacturermotor(wiretowater)+LoadControlFactorTestedPumpwith MotorandControlsN/A N/ATested performanceofbarepumpwithmanufacturermotorandcontrols(followsystemcurve)

PumpMotor PumpMotorControl Pump*Pumpssoldwithnon‐electricdrivescouldberatedasbarepumps15DeterminingPumpInputPowerPowerinputtothepumpataspecificloadpoint(Pini)canbe:(A) measuredusingawiretowatertest;or(B) calculatedasthepowerinputtothepump(Pi)plusthemotorlossesatthatloadpoint:Where:•Pini=powerinputtothe“pump”atthedriver,inclusiveofthecontrolsifpresent(hp);•Pi=theshaftinputpowertothebareshaftpump(hp);•Li=thefractionalloadmotorlosses(hp);and•i=Percentageofflowatthebestefficiencypoint(BEP)ofthepump.ExpandingthePERequationyieldsthefollowingequation:ܲ௜௡௜ܲ ൌ௜ܮ ൅௜ܨܥܮ ൌ ܴܧܲ∑߱௜ܲ௜ܮ ൅௜௜ݎ݋ݐ݉݅݊ܽ݋݁݊ܦ16AccountingforMotorLossesThefractionalmotorlossesateachloadpointi(Li)arecalculatedastheratedfullloadmotorlosses(Lrated)multipliedbythepart‐loadlossfactor(yi),whichiscalculatedasacubicpolynomial*oftheloadfractiononthemotor(xi):ܮ௜ൌ ܮ௔௥௧௘ௗ∗ ݕ݅ ൌ ܮ௔௥௧௘ௗ∗ܽ∗ݔ௜ଷ൅ܾ∗ݔ௜ଶ൅ܿ∗ݔ௜൅ ݀ൌ ܮ௔௥௧௘ௗ∗ܽ ∗ܲ௜݁ݖܵ݅ݎ݋ݐ݋ܯଷ൅ܾ∗ܲ௜݁ݖܵ݅ݎ݋ݐ݋ܯଶ൅ܿ∗ܲ௜݁ݖܵ݅ݎ݋ݐ݋ܯ݀ ൅Where:•Li=thefractionalloadlossofthemotoratloadpointi(hp);•Lrated=theratedfullloadmotorlossesasdeterminedinaccordancewiththeDOEtestprocedureformotorsat10CFR431subpartB(hp);•yi=thepart‐loadlossfactor;•xi=theloadfractionforthemotorateachloadpointi;•Pi=theshaftinputpowertothebareshaftpump(hp);•MotorSize =thenominalratedoutputpowerofthemotor(hp);and•i=Percentageofflowatthebestefficiencypoint(BEP)ofthepump.*Adifferentcubicpolynomial(i.e.differenta,b,c,anddcoefficients)areassumedbasedontherotatingspeed(2‐polevs.4‐pole)andmotordesign(ODPvs.TEFC)17TestingBarePumpPerformancePerformHI40.6todeterminebareshaftinputpowerateachloadpointi:•7pointssweptfromshutofftomaximumflowrate,withflowrate(GPM),Head(ft),rotationalspeed(rpm),torque(in‐lbf)recordedinfollowingtable•Hydraulicpumpefficiencyiscalculatedateachflowpoint–Inputpower=(torque)x(speed)–Outputpower=(flowrate)x(head)x(specificweightoffluid)–Efficiency=outputpower/inputpower•BEPfoundbydeterminingmaximumofbestfitcurveofefficiencywithrespecttoflowrate•Bareshaftinputpowerateachloadpointfoundbyinterpolatingperformancefrompumpcurveat75%and110%ofBEPflow%ofBEPflowFlowRate(GPM) Head(ft)Speed(RPM)Torque(lb‐in)HydraulicPower(hp)Shaftinputpower(hp)η(%)η[bestfit](%)128 1200.59 141.51 1774.10 1977.14 41.76 55.65 75.04 74.42108 1012.80 157.91 1774.63 1782.87 39.31 50.20 78.31 77.57100 939.62 162.58 1774.80 1721.36 37.55 48.47 77.47 77.8691 851.24 169.44 1775.86 1613.80 35.46 45.47 77.97 77.6576 709.87 178.40 1775.85 1458.85 31.13 41.11 75.73 75.9658 547.19 186.61 1777.84 1251.15 25.10 35.29 71.12 71.2248 449.06 189.67 1778.80 1112.42 20.94 31.40 66.69 66.1818×standardizedmotorefficiencyanddefaultpartloadcurveMOTORpumpperformancedatafrompumptestatratedspeedDeterminingBarePumpPER×standardizedcontrolsperformance=1Controls•Pivaluesarethetestedshaftinputpowertothepump(speedxtorque)ateachloadpointi•i=75%,100%,and110%offlowrateatBEPofthepump•Equalweighting•StandardizedMotorPerformance•EnclosedmotorthatisminimallycompliantwithDOE’smotorregulations(10CFR431.25)forgeneralpurposemotors(subtypeI)forallpumpsexceptESCCandgeneralpurposemotors(subtypeII)forESCCpumps•HPusedwillbenextHPabovebrakehorsepowerat120%ofBEPHP•Poleswillbebasedonspeedatwhichpumpisbeingrated•StandardizedControlsPerformance•LCF=1(nocontrols)•Driveefficiency=100%(sincenodrive)19×manufacturermotorefficiencyatfullandpartloadMOTORBarePump+MotorTestProcedureManufacturercanpairitspumpdatawithmanufacturermotordata.pumpperformancedatafrompumptestatratedspeedstandardizedcontrolsperformance=1Controls×MOTORPUMPManufacturercanmeasurepowerofpump+motorcombo.standardizedcontrolsperformance=1Controls×pump+motor performancedataAB20pumpperformancefrompumptestatratedandreducedspeed×motor/driveperformancedataBCVFDMOTORControlsMOTORPUMPBarePump+Motor+ControlsTestProcedureManufacturercanpairitspumpdatawithtestedmotor+VFD data.Manufacturercanmeasurepowerofpump+motor+controlscombo.×manufacturerordefaultmotorefficiencyAMOTORManufacturercanpairitspumpdatawithmanufacturermotordataanddefaultfactorforcontrols.pumpperformancedatafrompumptestatratedspeeddefaultcontrolsperformanceControls×21LoadControlFactor:BasisLCFisdefinedastheratioofPERofaspeedcontrolledpumptothePERofanuncontrolledpump•ܨܥܮ ൌ௉ாோ಴೚೙೟ೝ೚೗೗೐೏௉ாோೆ೙೎೚೙೟ೝ೚೗೗೐೏•LoadcontrolfactorfortheVFDprovidedinPERcalculationexamplevariesdependingonloadprofileandweightingPERofpump+motor willbeusedtodeterminetheLCFforeachcontroloptionUseanassumedconservativesystemcurveforallthreeoptionswithfollowingvariationstodeterminetheLoadControlFactorAssumptions:•Efficiencyofcontrol=96%ࡽ૚ࡽ૛ൌ࢔૚࢔૛ࡴ૚ࡴ૛ൌ࢔૚࢔૛૛ࡼ૚ࡼ૛ൌ࢔૚࢔૛૜22LoadControlFactorOptions•Othercontroloptionstobeconsidered?•MakeLCFafunctionofefficiencytodistinguishsimilarcontroloptionswithdifferentefficiencies?ControlEfficiencyofControlOtherAssumptions LCFVFD 96% Followdefined systemcurve 0.56ECM 96% 0.602‐speed motor 96%25% and50%loadpointareatlowerspeed&75%and100%loadpointsareatfullspeed0.6723ControlLoadCurve•LoadcurveinPERcalculator:dynamicheadbasedloadcurve–Headvsflowisproportional:ܪ	 ∝ 	ܳ2•Proposed:loadprofilewithastaticoffset–Headwithflowisoffset:ܪ ൌ ߙܳଶ൅ ܪௌ௧௔௧௜௖–Assume:staticoffsetis20%ofBEPhead(otheroffsetscouldbeconsidered)–GivenQBEPandHBEP,thesystemcurvebecomes:•ܪ ൌ 0.8ுಳಶುொಳಶುమܳଶ൅ 0.2ܪ஻ா௉•ThiscurvepassesthroughbothBEPandthepumpheadinterceptat20%ofHBEP0501001502002503003500 200 400 600 800 1000 1200 1400

Head (ft)flowrate(GPM)OriginalVFDloadprofileNewVFDLoadProfileExamplePumpCurveBestEfficiencyPoint20%ofBEPHeadRealized potential savingsUnrealizedsavings24ImpactofStaticLoadProfile•Morerealisticrepresentationofhowcontrolsareusedinfield•UsingstaticoffsetcurvewillproducemoreconservativeestimateofPERusingcalculationmethod–Testingwillproceedwithclosedloop(dynamicsystemcurve),thereforetestedPERvaluesshouldconsistentlyoutperformvaluesobtainedfromcalculationmethod25ImpactofStaticOffsetonPER•ResultsofPERcalculationforbareshaftpumpwithmotorandcontroloriginalloadcurveiscomparedtostaticoffsetloadprofiletoshowtheincreasedenergyconsumptionduetounrealizedsavingsLoad ProfilePER(hp) PercentIncreaseinPERwithStatic LoadCurveOriginal LoadCurveStaticOffsetLoadCurve50,75,100,110(equalweighting)34.61 36.37 5.1%25,50,75,100(equalweighting)21.36 23.70 11.0%75,100,110(equalweighting)43.07 44.16 2.5%26ApplicationofCalculationandTestingBasedMethods•Isphysicaltestingmoreappropriateforsomeequipmentclasseswhileacalculationmethodismoreappropriateforothers?–e.g.ESCCpumps,pumpssoldwithnon‐DOEmotorsTestMethod Pros ConsCalculationMethodRepeatable;LessburdensomeDoes notdifferentiatedifferentcontrolsperformance;Assumptionsregarding changeinmotor/controlsefficiencywithchangingloadrequired;DecreasedaccuracyPhysical TestMethodAccurate;Differentiatesperformanceofdifferent motor/controlsequipmentatfullandpartloadBurdensome;AHRI1210test datanotavailable27•Loadpointsassumingequalweighting:•Choiceofloadpointsdoesnotimpactranking,onlyrelativemagnitude–Fewerlow‐endloadpointsde‐emphasizesimpactofcontrolsImpactofDifferentLoadPointsLoad ProfilePump EnergyRating(PER)inhpBarePumpPump& 95%Eff.MotorPump, MinEff.Motor&VFD75%,100%, 110%ofBEPflow49.48 48.65 27.4025%, 50%,75%,100%ofBEPflow39.31 38.51 21.9150%,75%,100%,110% ofBEPflow45.95 45.14 25.4928LoadProfiles•Verylittlefielddataisavailableregardingtypicalloadprofilesandloadprofilesareextremelyvariablebasedonapplication•PERcalculatedbasedon4typicalloadprofiles–LP0:BEPonly–LP1:equallyweightedat75%BEP,BEP,110%BEP–LP2:increasingload,peakatBEP–LP3:increasingload,peakatBEP,withoverloadat110@BEP00.20.40.60.8150%BEP 75%BEP 100%BEP 110%BEP

WeightsLP0LP1LP2LP329•Assumeloadpointsof50%,75%,100%and110%ofBEPflow:•WeightingsimpactmagnitudeofcalculatedPERandchangerelativeimpactofcontrols,butdonotchangerelativecomparisonofpumpconfigurationsorrankingImpactofDifferentWeightingsLoad ProfilePump EnergyRating(PER)inhpBarePumpPump& 95%Eff.MotorPump, MinEff.Motor&VFDLP0:100%BEPFlow Only51.06 50.21 28.37LP1:EqualWeighting45.95 45.14 25.49LP2:IncreasingLoad,PeakatBEP45.93 45.12 25.36LP3:IncreasingLoad,PeakatBEP withOverloadat110@BEP46.65 45.84 25.8530BigchangeinrankingneedtoconsidernonBEPloadpointsRelativelyconsistentrankingaslongasmultipleloadpointsareconsidered02004006008001000120014001600180020000 500 1000 1500 2000

Ranking based on PER LP3RankingbasedonPERLP1[0.33@0.75BEP,BEP,1.1BEP]02004006008001000120014001600180020000 500 1000 1500 2000

Ranking based on PER LP2RankingbasedonPERLP1[0.33@0.75BEP,BEP,1.1BEP]02004006008001000120014001600180020000 500 1000 1500 2000

Ranking based on PER LP1RankingbasedonPERLP0[1.00@BEP]ImpactofWeightingonRelativeRanking31“Denominator”Options“Denominator” Units Pros ConsNoDenominator Hp orkWhRepresentativeoftheenergyconsumptionofthatpumpinthefield.Strong function offlowandspecificspeed.Notcomparableacrosspumpsofdifferentflows/specificspeeds.Less strong function offlowandspecificspeed.ReferenceshaftpowerforminimallycompliantbarepumpwithminimallycompliantmotorDimensionlessResultsinvaluebetween0and1(moreintuitive).Clearlyindicatesperformance ofapumprelativetoabaseline.Inherentlyrequiresdesignationofminimallycompliantpump(i.e.,MEI).Mayover‐orunder‐representthebaselineefficiencyforsomepumps.MarketaverageshaftpowerwithminimallycompliantormarketaveragemotorDimensionless Indicatesperformanceofapumprelativetothemarket.Locksinthemetrictotheperformanceofpumpsinthemarketatagivenpointintime.Doesn’tlimitmetricvaluesbetween0and1.Testedpump’shydraulic poweratBEPDimensionlessAccountsfordifferencesinpumpefficienciesbetweenmodels.Hassimilarratedvaluesforpumpsofdifferentsizes.LowerPERratingforsmallerpumpsbecauselowercapacityequipmentisinherentlylessefficient.32DenominatorOptionsComparison•Assumptions–Loadpoint•75%,100%,and110%ofBEPflowforbarepumpandbarepump+motor•25%,50%,75%and100%forcontrolledpump–Weighting•equalweighting–SystemCurve•AffinitylawsDenominatorScalingOptionsValue(hp)Pump energyrating(PER)BareShaftPumpPump &95%Eff.MotorPump, MinEff.Motor&VFDNoDenominator N/A 49.48 48.65 21.91HydraulicpowerCalculatedateachloadpoint0.719 0.732 3.297MinimallyCompliant(MEI10)52.74 0.938 0.922 0.415MarketAverage(MEI50)48.89 1.012 0.995 0.43233MarketAveragePump•MarketAveragePump–Denominator=PERforamarketaveragepump•Basedon≈MEI50forU.S.market•Assumesapumpcurveshapefortheminimallycompliantpumpandalwaysassumesnocontrols•Motorlossesarethatofaminimallycompliantenclosedmotorfortheappropriatepumptype•Themarketaveragepumpefficiencyiscalculatedforeachpumptypebasedonafunctionofflowandspeed•Units=dimensionlessܴܧܲ௚ ௩௔ܨܥܮ ൌ߱଴.଻ହܲ௜௡଴.଻ହ൅ ߱஻ா௉ܲ௜௡஻ா௉൅ ߱ଵ.ଵܲ௜௡ଵ.ଵ߱଴.଻ହܲு௬ௗ௥௢,଴.଻ହ0.95 ∗ ߟ௣௨௠௣൅ ܮ଴.଻ହ൅ ߱஻ா௉ܲு௬ௗ௥௢,஻ா௉ߟ௣௨௠௣൅ ܮ஻ா௉൅ ߱ଵ.ଵܲு௬ௗ௥௢,ଵ.ଵ0.985 ∗ ߟ௣௨௠௣൅ ܮଵ.ଵൌ 113∗ܲ଴.଻ହ൅ ܮ଴.଻ହ൅13∗ܲ஻ா௉൅ ܮ஻ா௉൅13∗ܲଵ.ଵ൅ ܮଵ.ଵ13∗ܲு௬ௗ௥௢,଴.଻ହ0.95 ∗ ߟ௣௨௠௣൅ ܮ଴.଻ହ൅13∗ܲு௬ௗ௥௢,஻ா௉ߟ௣௨௠௣൅ ܮ஻ா௉൅13∗ܲு௬ௗ௥௢,ଵ.ଵ0.985 ∗ ߟ௣௨௠௣൅ ܮଵ.ଵ