Experiment Bernoulli's Theorem Che486 Uitm

L A B3 :B ER N OULLIST H EO REMN URS Y A FIQ AHB IN TIM OHAM ADF R ID US( 2 022622316)S IT IN ORA FID AHB IN TIL EG IM AN( 2 02289944)I Z D IH ARR A IM IB INI B RA HIM( 2 022664234)M UHAM MADN AQIBB INA BD .N ASIR( 2 022841974)A BST R A CTTheBernoulli'sTheoremDemonstrationApparatuswasusedtocarryouttheexperimenttodemonstrateBernoulli'sTheorem.Aventurimeter ,apadofpiezometertube,apump,andawatertankareallpartoftheequipment,whichisattachedtoapumpwatercontroller ,awaterhose,andtubes.Atubepadisalsoincludedwiththegadget.ThegoalofthisexperimentwastoconfirmtheaccuracyofBernoulli'sTheoreminthecontextofasteadywaterflowwhilealsomeasuringflowrates.Thefundamentalfunctionoftheventuritube'sconver ginganddiver gingsegmentsistochangethefluidvelocityandstaticpressure.Theconver gingsegmentisintendedtoincreasefluidvelocity ,whilstthediver gingsegmentisintendedtodecreasefluidvelocity .Furthermore,theconver gingpartreducesstaticpressurewhereasthediver gingsectionincreasesit.Whendeterminingtherateofwaterflow ,thevolumetricapproachiswidelyused.Theexperimentisrepeatedthreetimes,eachtimewithadif ferentflowrate.ThepressurelevelsofpiezometersA,B,C,D,E,andFareequalizedandstabilizedbeforeeachtrial.Theflowratewascalculatedusingtheprovideddataoncethewaterindicatorreachedtheappropriatewaterlevel.Theamountoftimeittooktofillthetankwiththreelitersofwaterwasmeasuredandnoted.Finally ,theflowrate,velocity ,andvelocitydif ferentialswerecalculatedusingboththesupplieddataandthedatacollectedduringtheinvestigation.Regardlessoftheformofthefloworthepressuregradient,empiricaldatahasdemonstratedthatfluidvelocityriseswhenittransitionsfromabroadertoamuchnarrowerconduit,asevidencedbytheobservedresults.Whenthepressureisincreased,thevelocityofflowforanygiventypeisfoundtorise.ThepresenceofadiscernablepositiveoutcomeintermsofvelocitydisparitysupportsthesuitabilityofusingBernoulli'sequationinthisparticularexperiment.I .I N TR O DUCTIO NBernoulli'sTheoremstatesthatincreasingthevelocityofaflowingairorfluidstreamresultsinadecreaseinthepressureexertedbythestream.Thisphenomenonisunaf fectedbythemovementoftheairorfluid.Inacademiccircles,theaforementionedtheoremisknownas"Bernoulli'sprinciple."AccordingtotheBernoulliprinciple,theriskofwindowssplittingintoshardsrather .thancollapsingisgreaterduringstormoccurrences.Hurricanesgeneraterapidflowofairnearwindows,resultinginadecreaseinexternalairpressurerelativetotheconstantinternalairpressurewithinastructure.Theforceimbalancecausesthewindowstobeejectedinanoutwardtrajectory ,resultingintheirbreakage.Asaresult,itisadvisedtokeepallwindowsopenduringastorm.Inanotherpracticalapplication,theBernoulliprinciplecanbeusedtodeterminethevelocityoffluidflow .Aventurimeteroranorificeplatearetwoexamplesofequipmentthatcanbeusedtoreducethediameterofaflowwithinapipeline.AccordingtoBernoulli'sprinciple,adecreaseindiametercausesanincreaseinfluidvelocity ,whichcausesadecreaseinpressure.Between1700and1782,DanielBernoulli,anotableSwissscientist,conductedresearchandproducedascholarlypaperdemonstratingempiricalproofoftherelationshipbetweenrisingvelocityandlowerpressureinliquidsorgasses.Theaforementionedideawasconceivedintheyear1738,anditsoriginatorelaboratedonitinascholarlyworktitled"Hydrodynamic,"whichwaspublishedin1748.Thebookinvestigatestheobservablephenomenonofwaterflowwithinatubeandthedischar geofwaterfromanaperturepositionedinacontainertoinvestigatethetheoreticalconstructofhydrodynamicpressure.Furthermore,thebookexaminesandcomparesthesetwodistinctwaysofwaterdisplacement.Thetopicunderexaminationwasconnectedtothefundamentalunderstandingoffluiddynamics,namelythemotionoffluidcausedbyapressuredif ference.Inanormalcase,fluidflowoccursmostlyinahorizontalorientation,whereitencountersadetectablepressuredif ferential.Thepressuredif ferencewilleventuallyresultinthedevelopmentofaresultantforce,which,accordingtoNewton'sSecondLaw ,willcausethefluidtoaccelerate.TheuseoftheFM24model,specificallyBernoulli'sTheorem,canbeusedtoestablishBernoulli'sPrinciple.Inthisexperimentalinvestigation,acustomizedapparatusisusedfordemonstration.ThemaincomponentofthisgadgetisatypicalV enturitubemadeoftransparentacrylic.Asequenceofwalltappingsallowsforthemeasurementofstaticpressuredistributionintheconver gingduct.Thetestportionalsohasathoroughheadtubethatrunsparalleltoitscentralaxis.Thetapingsunderconsiderationareforapiezometerbank,whichincludesamanifoldandanairbleedvalve.T opressurizethepiezometers,amanualhand-operatedpumpisused.Thiscourseallowsstudentstoinvestigatethepropertiesoffluidflowinbothconver ginganddiver gingsections.ThismaterialisintendedtobeexaminedinconjunctionwiththeHydraulicsBench.Duringtheexperimentalprocedure,waterissuppliedbyahoseconnector ,andparticipantscancontroltheamountofwaterflowingthroughtheexperimentbymanipulatingaflowregulatorvalvelocatedatthetestarea'sexit.AccordingtoBernoulli'sTheorem,thetotalener gyofanincompressibleandnon-viscousfluidinasteadyflowinapipeisconstantalongitswholelength,assumingnofluidsourcesorsinks.Theabsenceofviscosityinanincompressibleandnon-viscousfluid,whichwouldotherwiseimpedeitsflowthroughthepipe,istheunderlyingreasonforthisevent.Theexplanationisbasedonthepremisethatfrictiondoesnotresultinener gydissipation.I I.O BJE C TIV ESTheobjectiveofthisexperimentistoinvestigatethevalidityoftheBernoulliequationwhenitisappliedtoasteadyflowofwaterthroughataperedduct.I II.T H EO RYBernoulli'sprinciple,whichstatesthattotalener gydoesnotchangeinanidealfluidorwhentheinfluenceofviscosityisignoredandnoworkisdoneonthefluid,islar gelyaworkener gyconservationprinciple.Thisprinciplestatesthattotalener gydoesnotchangeinanidealfluidorwhenneitherworknortheinfluenceofviscosityisperformedonthefluid.Thisisbecausethefluidunder goesnoworkinalltheseconfigurations,whichisthereasonwhythisresultisobtained.Accordingtothistheory ,thetotalener gyofafluidthatismovingalonganenclosedpath(astreamline)isthesameatanytwoplacesplacedinthesamedirectionalongthatpath.Therelationshipbetweenpressure,speed,andheightattwolocationsinanon-viscous,incompressiblefluidthatisflowingsteadilycanbeexpressedbythefollowingequation:....................(Eq1.1)Theequationprovidedrepresentsthesumofkineticener gy,potentialener gy,andgravitationalener gyataparticularheight.Whenthevolumeismultipliedbytheequation,thedensitymaybesubstitutedwiththemass,andthepressurecanbeexpressedastheproductofforceanddistance.Inthiscontext,itisevidentthatthepressuredif ferentialdoeswork,henceenablingthemanipulationofthefluid'skineticandpotentialener gywithinthegivenequation.Thecontinuityequationpostulatesthattherateatwhichmassistransportedbyanincompressiblefluidthroughatubewithvaryingcross-sectionalareaisconstantatallpointsalongthetube.Thecontinuityequationcanbeexpressedinthefollowingmanner:........(Eq1.2)Thedensityremainsconsistent,andtheflowrate(A v)isthesoleconstant.Theutilizationofthecontinuityequationresultsinagreaterfluidvelocitywithintheconstrictedsegment.Bernoulli'sprinciplealsosuggeststhatinthecaseofanon-viscousflowconductedviaaconduitwithachangeablecrosssection.Thevelocityofthefluidexhibitsadirectrelationshipwiththedecreaseinpressureorthedeclineinthefluid'spotentialener gy.Conversely ,thepressureexperiencesanincreasewhenthepipeisopened,andthefluidreachesastateofstagnation.Inthecontextoffluiddynamics,ithasbeenshownthatariseinvelocityisaccompaniedwithadecreaseinpressure.Themathematicalrepresentationofthisstatementisasfollows:............(Eq1.3)Where,Theaggregatehead(h*)iscomposedofthecumulativepressurehead(h),velocityhead(hv),andelevationhead(z).AsperBernoulli'stheorypertainingtothefluidflowwithinaconduit,thetotalheadremainsconstantatanygivencross-sectionalarea.Inpracticalfluiddynamics,itiscommonfortheobservedoutcomestodeviatefromthetheoreticalpredictionsasaresultoffactorssuchasfriction,inherentimperfections,anduncertaintiesassociatedwithmeasurements.Allthecrosssectionsbeingexaminedarealignedalongacommonhorizontalplane,whichcanbedesignatedasthedatumwithaz-coordinateofzero.Consequently ,allthez-valuesintheprecedingequationbecomezero,resultinginasimplifiedequation..........(Eq1.4)Thisrepresentsthetotalheadatcrosssection.I V .A PPA RATU SFigure1.1Bernoulli'sApparatusT estEquipmentV .P R O CED URE1 .TheGeneralStart-upProcedurewasperformed.2.Thehypodermictubewaswithdrawnfromthetestsection.3.Thedischar gevalvewasadjustedtothemaximummeasurableflowrateoftheventuri.Thiswasachievedwhentube1and3gavethemaximumobservablewaterheaddif ference.4.5.Whenthelevelstabilizes,thewaterflowratewasmeasuredusingvolumetricmethodandthemanometerreadingswererecorded.6.Step4wererepeatedwithatleastthreedecreasingflowratesbyregulatingtheventuridischar gevalve.7.Theactualflowrate,Qawasobtainedfromthevolumetricflowmeasurementmethod.8.Theidealflowrate,Qwascalculatedfromtheheaddif ferencebetweenhiandh3usingtheequationgiven.9.QaVsQwasplottedandfinallythedischar gecoef ficient,Cawasobtainedwhichistheslope.V I.R ESU LTD is ch arg eC oeffic ie n tD ete rm in atio nQA( L P M )hA( m )hB( m )hC( m )hD( m )hE( m )hF( m )Qi( L P M)F lo wr a teQi( L P M)5 .7 910 .1 790 .1 650 .1 400 .1 530 .1 570 .1 601