AP_Physics_B__Fluid_Dynamicsppt课件.ppt

FluidDynamics APPhysicsB FluidFlow Uptillnow wehaveprettymuchfocusedonfluidsatrest Nowlet slookatfluidsinmotionItisimportantthatyouunderstandthatanIDEALFLUID Isnonviscous meaningthereisNOinternalfriction Isincompressible meaningitsDensityisconstant ItsmotionissteadyandNON TURBULENTAfluid smotioncanbesaidtobeSTREAMLINE orLAMINAR Thepathitselfiscalledthestreamline ByLaminar wemeanthateveryparticlemovesexactlyalongthesmoothpathaseveryparticlethatfollowsit IfthefluidDOESNOThaveLaminarFlowithasTURBULENTFLOWinwhichthepathsareirregularandcalledEDDYCURRENTS MassFlowRate A A v v L L Considerapipewithafluidmovingwithinit ThevolumeoftheblueregionistheAREAtimesthelength LengthisvelocitytimestimeDensityismasspervolumePuttingitalltogetheryouhaveMASSFLOWRATE WhathappensiftheAreachanges A1 A2 v1 v2 L1 v1t L2 v2t ThefirstthingyouMUSTunderstandisthatMASSisNOTCREATEDORDESTROYED ITISCONSERVED TheMASSthatflowsintoaregion TheMASSthatflowsoutofaregion UsingtheMassFlowrateequationandtheideathatacertainmassofwaterisconstantasitmovestoanewpipesection WehavetheFluidFlowContinuityequation Example Thespeedofbloodintheaortais50cm sandthisvesselhasaradiusof1 0cm Ifthecapillarieshaveatotalcrosssectionalareaof3000cm2 whatisthespeedofthebloodinthem 0 052cm s Bernoulli sPrinciple TheSwissPhysicistDanielBernoulli wasinterestedinhowthevelocitychangesasthefluidmovesthroughapipeofdifferentarea Heespeciallywantedtoincorporatepressureintohisideaaswell Conceptually hisprincipleisstatedas Ifthevelocityofafluidincreases thepressuredecreasesandviceversa ThevelocitycanbeincreasedbypushingtheairoverorthroughaCONSTRICTION AchangeinpressureresultsinaNETFORCEtowardsthelowpressureregion Bernoulli sPrinciple Funnel PingpongBall Constriction Bernoulli sPrinciple TheconstrictionintheSubclavianarterycausesthebloodintheregiontospeedupandthusproduceslowpressure ThebloodmovingUPtheLVAisthenpushedDOWNinsteadofdowncausingalackofbloodflowtothebrain ThisconditioniscalledTIA transientischemicattack or SubclavianStealSyndrome Oneendofagopherholeishigherthantheothercausingaconstrictionandlowpressureregion Thustheairisconstantlysuckedoutofthehigherholebythewind Theairentersthelowerholeprovidingasortofairre circulatingsystemeffecttopreventsuffocation Bernoulli sEquation Let slookatthisprinciplemathematically Workisdonebyasectionofwaterapplyingaforceonasecondsectioninfrontofitoveradisplacement AccordingtoNewton s3rdlaw thesecondsectionofwaterappliesanequalandoppositeforcebackonthefirst ThusisdoesnegativeworkasthewaterstillmovesFORWARD Pressure AreaissubstitutedforForce X L F1on2 F2on1 Bernoulli sEquation A1 A2 v1 v2 L1 v1t L2 v2t y2 ground WorkisalsodonebyGRAVITYasthewatertravelsaverticaldisplacementUPWARD AsthewatermovesUPtheforceduetogravityisDOWN SotheworkisNEGATIVE y1 Bernoulli sEquation Nowlet sfindtheNETWORKdonebygravityandthewateractingonitself WHATDOESTHENETWORKEQUALTO ACHANGEINKINETICENERGY Bernoulli sEquation ConsiderthatDensity MassperunitVolumeANDthatVOLUMEisequaltoAREAtimeLENGTH Bernoulli sEquation WecannowcancelouttheAREAandLENGTH Leaving Bernoulli sEquation Movingeverythingrelatedtoonesideresultsin WhatthisbasicallyshowsisthatConservationofEnergyholdstruewithinafluidandthatifyouaddthePRESSURE theKINETICENERGY intermsofdensity andPOTENTIALENERGY intermsofdensity yougettheSAMEVALUEanywherealongastreamline Example Watercirculatesthroughoutthehouseinahot waterheatingsystem Ifthewaterispumpedataspeedof0 50m sthrougha4 0cmdiameterpipeinthebasement