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ReynoldsexperimentAimoftheexperiment1.Observethelaminarandturbulentflow,andtheprocessoftransitionfromonestatetotheother.2.MeasurethecriticalReynoldsnumberanddeveloptheskillsonhowtodistinguishthepipeflowstate.3.Studythedimensionalanalysismethodtoanalyzetheexperiment,confirmingthecriterionnumberofflowstateforanon-circularpipe.Experimentalapparatus1.ThefigureoftheapparatusFigure1showstheexperimentalapparatusandthenameofeachpart.Figure1.1:Self-circulatingwatersupply,2:Hydraulicbench,3:Speedcontroller,4:Constantheadwatertank,5:Colouredwaterpipe,6:Perforatedplate,7:Overflow,8:Experimentpipe,9:Flowratecontrolvalve2.Theillustrationofinstallationandthemethodofoperation.Thewaterflowrateiscontrolledbyaspeedcontroller3,makingconstantpressurewatertank4keepthestatewhichmicrooverflowinordertoimprovethestabilityofwaterflow.Therearemanyclapboardstokeepwaterstabilityinthisexperimentaldevice,shortenthetimespendonstabilizethewaterto3-5min.Colurewaterflowintopipe8throughcolurewaterpipe5,wecandistinguishtheflowstateaccordingtowhetherthecolurewaterdisperse.Inordertoavoidpollutionofwaterduetotheself-circulation,weusethespecialcolurewater.Theflowrateintheexperimentiscontrolledbyvalve9.Theory.In1883,OsborneReynoldsusingtheexperimentaldevicewhichissimilarwiththedeviceshowninFigure4.2.1,observedthelaminarstateandturbulentstateinfluidflow:Thecoloredfilamentisstraightandsmoothforlowspeeds,thisstateislaminarflow.However,thecoloredfilamentbreaksoffanddispersesalmostuniformlyforhighvelocities,andthisstateisturbulentflow.Reynoldsalsofoundthatthereisacriticalvelocityvcfromlaminartoturbulentstate.vcdependsontheviscosityofthefluidνandthediameterofpiped.Thevalueofvcshouldbeknownindifferentsituationswhenwewanttoknowtheflowstate.ThecontributionofReynoldsisnotonlytofindthetwoflowstates,butalsouseddimensionalanalysistoanalyzetheexperimentandgettheReynoldsnumberwhichsimplifiestheproblem.Thefollowingisdimensionalanalysis.Since:v=f(ν,d)Accordingtothedimensionalanalysismethod:v=kν d LT=LT L α=1,α= −1v= kork= Reynoldsconcludedthemeasurementofthecriticalvaluefromlaminarflowtoturbulentflowstateinpipeflow,validatingkisconstant.So,canbeusedtodistinguishbetweentheflowstateinanysituation.BecauseofReynoldscontribution,iscalledtheRenumber.So,thereisRe= vdν= 4q!πνd=KqV:velocityofflowν:kinematicviscosityofflowd:diameteroftubeq!:flowrateinpipeK:calculationconstant,K=$%.ThereisalowercriticalRenumberwhenflowtransitsfromturbulenttolaminarstate.ThereisanuppercriticalRec’numberwhenflowtransitsfromlaminartoturbulentstate.ThevalueofuppercriticalRecnumberisnotstablebecauseofexternaldisturbances.However,thevalueoflowercriticalnumberisstable.Hence,generallythelowercriticalRecnumberisusedtodistinguishbetweentheflowregimes.ThevalueofRecnumberis2300accordingtothemeasurementfromReynolds.ItislaminarstateflowwhenReRec,whiletheflowisturbulencewhenReRec.Foranon-circularpipe,itcanbeshownthatRenumberRe= vRνR:hydraulicradius,R=A/PA:areaofsectionofsurfaceP:wettedperimeterRenumberthatisusingthehydraulicradiustodenotethecharacteristiclength.Thecontentandmethodofexperiment1.QualitativeobservationofthetwoflowstatesOpenthepumptosupplywater,makingwatertankoverflow,opentheflowcontrolvalveafterstable.Openthevalvetoinjectthecolouredwater.Itcanbeseenthatthecolouredfilamentisstraightandsmooth,thisislaminarstate.Thecolouredfilamentbreaksoffanddispersesalmostuniformlywhenturnuptheflowcontrolvalve,thisisturbulentflow.2.MeasurementofthelowercriticalReynoldsnumber.Makesurethatflowstateisturbulent,closetheflowcontrolvalvegradually,Flowstatetransitsfromturbulenttolaminarstatewhenthecolouredfilamentbecomestraightandsmooth.Measuretheflowratebyusingthegravimetricmethodandwritedowntemperatureofwater.LowerRenumbercanbeobtained.3.MeasurementofthehighercriticalReynoldsnumber.Makesurethatflowstateislaminar,andopentheflowcontrolvalvegradually.Flowstatetransitsfromlaminarstatetoturbulentwhenthecolouredfilamentbreaksoffanddispersesalmostuniformly.Measuretheflowratebyusingthegravimetricmethodandwritedowntemperatureofwater.UpperRenumbercanbeobtained.4.AnalyseanddesigntheexperimentDeterminethegeneralReynoldsnumberforanycross-sectionshapebyusingdimensionalanalysis.DesigntheexperimenttomeasurelowerReynoldsnumberforanopenchannelandgetthevalueoflowerReynoldsnumberonthebaseoftheresultthatcomesfromtheexperiment.DataprocessingThenameoftheequipment:Experimenter:Date:Diameter(D):(m)Temperature(T):(oC)Kinematicviscosity,ν=.'(()×'+,-'.'..(/-'.'''/=(m2/s)ConstantK:(s/m3)2.RecorddataandresultofcalculationRuntheexperiment5timesforeachcase.Thedatathatneedtobecollectedare:Volume(10-6m3),time(s),flowrate(10-6m3/s),Re,Degreeofopeningofvalve,Remarks.TheaveragevalueisthecriticalReynoldsnumber.3.Results1.MeasurethelowercriticalReynoldsnumber.2.MeasuretheuppercriticalReynoldsnumber.3.DeterminetheexpressionofgeneralReynoldsnumberandthemeasuredvalueoflowercriticalReynoldsnumberofcircularpipeflow.Questions1.WhythereisnosignificancefortheuppercriticalReynoldsnumber?WhydoweusethelowercriticalReynold