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1,FluidDynamics,APPhysicsB,2,FluidFlow,Uptillnow,wehaveprettymuchfocusedonfluidsatrest.NowletslookatfluidsinmotionItisimportantthatyouunderstandthatanIDEALFLUID:Isnonviscous(meaningthereisNOinternalfriction)Isincompressible(meaningitsDensityisconstant)ItsmotionissteadyandNONTURBULENTAfluidsmotioncanbesaidtobeSTREAMLINE,orLAMINAR.Thepathitselfiscalledthestreamline.ByLaminar,wemeanthateveryparticlemovesexactlyalongthesmoothpathaseveryparticlethatfollowsit.IfthefluidDOESNOThaveLaminarFlowithasTURBULENTFLOWinwhichthepathsareirregularandcalledEDDYCURRENTS.,3,MassFlowRate,A,A,v,v,L,L,Considerapipewithafluidmovingwithinit.,ThevolumeoftheblueregionistheAREAtimesthelength.LengthisvelocitytimestimeDensityismasspervolumePuttingitalltogetheryouhaveMASSFLOWRATE.,4,WhathappensiftheAreachanges?,A1,A2,v1,v2,L1=v1t,L2=v2t,ThefirstthingyouMUSTunderstandisthatMASSisNOTCREATEDORDESTROYED!ITISCONSERVED.,TheMASSthatflowsintoaregion=TheMASSthatflowsoutofaregion.,UsingtheMassFlowrateequationandtheideathatacertainmassofwaterisconstantasitmovestoanewpipesection:,WehavetheFluidFlowContinuityequation,5,Example,Thespeedofbloodintheaortais50cm/sandthisvesselhasaradiusof1.0cm.Ifthecapillarieshaveatotalcrosssectionalareaof3000cm2,whatisthespeedofthebloodinthem?,0.052cm/s,6,BernoullisPrinciple,TheSwissPhysicistDanielBernoulli,wasinterestedinhowthevelocitychangesasthefluidmovesthroughapipeofdifferentarea.Heespeciallywantedtoincorporatepressureintohisideaaswell.Conceptually,hisprincipleisstatedas:Ifthevelocityofafluidincreases,thepressuredecreasesandviceversa.,ThevelocitycanbeincreasedbypushingtheairoverorthroughaCONSTRICTION,AchangeinpressureresultsinaNETFORCEtowardsthelowpressureregion.,7,BernoullisPrinciple,Funnel,PingpongBall,Constriction,8,BernoullisPrinciple,TheconstrictionintheSubclavianarterycausesthebloodintheregiontospeedupandthusproduceslowpressure.ThebloodmovingUPtheLVAisthenpushedDOWNinsteadofdowncausingalackofbloodflowtothebrain.ThisconditioniscalledTIA(transientischemicattack)or“SubclavianStealSyndrome.,Oneendofagopherholeishigherthantheothercausingaconstrictionandlowpressureregion.Thustheairisconstantlysuckedoutofthehigherholebythewind.Theairentersthelowerholeprovidingasortofairre-circulatingsystemeffecttopreventsuffocation.,9,BernoullisEquation,Letslookatthisprinciplemathematically.,Workisdonebyasectionofwaterapplyingaforceonasecondsectioninfrontofitoveradisplacement.AccordingtoNewtons3rdlaw,thesecondsectionofwaterappliesanequalandoppositeforcebackonthefirst.ThusisdoesnegativeworkasthewaterstillmovesFORWARD.Pressure*AreaissubstitutedforForce.,X=L,F1on2,-F2on1,10,BernoullisEquation,A1,A2,v1,v2,L1=v1t,L2=v2t,y2,ground,WorkisalsodonebyGRAVITYasthewatertravelsaverticaldisplacementUPWARD.AsthewatermovesUPtheforceduetogravityisDOWN.SotheworkisNEGATIVE.,y1,11,BernoullisEquation,NowletsfindtheNETWORKdonebygravityandthewateractingonitself.,WHATDOESTHENETWORKEQUALTO?ACHANGEINKINETICENERGY!,12,BernoullisEquation,ConsiderthatDensity=MassperunitVolumeANDthatVOLUMEisequaltoAREAtimeLENGTH,13,BernoullisEquation,WecannowcancelouttheAREAandLENGTH,Leaving:,14,BernoullisEquation,Movingeverythingrelatedtoonesideresultsin:,WhatthisbasicallyshowsisthatConservationofEnergyholdstruewithinafluidandthatifyouaddthePRESSURE,theKINETICENERGY(intermsofdensity)andPOTENTIALENERGY(intermsofdensity)yougettheSAMEVALUEanywherealongastreamline.,15,Example,Watercirculatesthroughoutthehouseinahot-waterheatingsystem.Ifthewaterispumpedataspeedof0.50m/sthroug
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