AP_Physics_B_-_Hydrostatics

.,FluidMechanics-Hydrostatics,APPhysicsB,.,StatesofMatter,BeforewebegintounderstandthenatureofaFluidwemustunderstandthenatureofallthestatesofmatter:The3primarystatesofmatter-solid-Definiteshapeandvolume.-liquid-Takestheshapeofitscontainer,yethasadefinitevolume.-gas-Takestheshapeandvolumeofitscontainer.Specialstates-Plasma,Bose-EinsteinCondensate,.,Density,The3primarystateshaveadistinctdensity,whichisdefinedasmassperunitofvolume.,DensityisrepresentedbytheGreekletter,“RHO”,r,.,WhatisaFluid?,Bydefinition,afluidisanymaterialthatisunabletowithstandastaticshearstress.Unlikeanelasticsolidwhichrespondstoashearstresswitharecoverabledeformation,afluidrespondswithanirrecoverableflow.Examplesoffluidsincludegasesandliquids.,.,Whyfluidsareusefulinphysics?,Typically,liquidsareconsideredtobeincompressible.ThatisonceyouplacealiquidinasealedcontaineryoucanDOWORKontheFLUIDasifitwereanobject.ThePRESSUREyouapplyistransmittedthroughouttheliquidandovertheentirelengthofthefluiditself.,.,Pressure,Oneofmostimportantapplicationsofafluidisitspressure-definedasaForceperunitArea,.,Example,Awaterbedis2.0monasidean30.0cmdeep.(a)Finditsweightifthedensityofwateris1000kg/m3.(b)Findthepressurethethatthewaterbedexertsonthefloor.Assumethattheentirelowersurfaceofthebedmakescontactwiththefloor.,1.2m3,1200kg,11760N,2940N/m2,.,HydrostaticPressure,SupposeaFluid(suchasaliquid)isatREST,wecallthisHYDROSTATICPRESSURETwoimportantpointsAfluidwillexertapressureinalldirectionsAfluidwillexertapressureperpendiculartoanysurfaceitcompacts,NoticethatthearrowsonTOPoftheobjectsaresmallerthanattheBOTTOM.ThisisbecausepressureisgreatlyaffectedbytheDEPTHoftheobject.Sincethebottomofeachobjectisdeeperthanthetopthepressureisgreateratthebottom.,.,Pressurevs.Depth,Supposewehadanobjectsubmergedinwaterwiththetopparttouchingtheatmosphere.IfweweretodrawanFBDforthisobjectwewouldhavethreeforcesTheweightoftheobjectTheforceoftheatmospherepressingdownTheforceofthewaterpressingup,mg,Fatm,Fwater,Fwater=Fatm+mg,.,Pressurevs.Depth,Butrecall,pressureisforceperunitarea.Soifwesolveforforcewecaninsertournewequationin.,Note:Theinitialpressureinthiscaseisatmosphericpressure,whichisaCONSTANT.Po=1x105N/m2,.,AcloserlookatPressurevs.Depth,ABSOLUTEPRESSURE,InitialPressureMayorMAYNOTbeatmosphericpressure,Depthbelowsurface,GaugePressure=CHANGEinpressureortheDIFFERENCEintheinitialandabsolutepressure,.,Example,a)Calculatetheabsolutepressureatanoceandepthof1000m.Assumethatthedensityofwateris1000kg/m3andthatPo=1.01x105Pa(N/m2).b)Calculatethetotalforceexertedontheoutsideofa30.0cmdiametercircularsubmarinewindowatthisdepth.,9.9x106N/m2,2.80 x106N,.,Aclosedsystem,IfyoutakealiquidandplaceitinasystemthatisCLOSEDlikeplumbingforexampleoracarsbrakeline,thePRESSUREisthesameeverywhere.Sincethisistrue,ifyouapplyaforceatonepartofthesystemthepressureisthesameattheotherendofthesystem.Theforce,ontheotherhandMAYorMAYNOTequaltheinitialforceapplied.ItdependsontheAREA.YoucantakeadvantageofthefactthatthepressureisthesameinaclosedsystemasithasMANYapplications.TheideabehindthisiscalledPASCALSPRINCIPLE,.,PascalsPrinciple,.,AnotherExample-Brakes,Inthecaseofacarsbrakepads,youhaveasmallinitialforceappliedbyyouonthebrakepedal.Thistransfersviaabrakeline,whichhadasmallcylindricalarea.ThebrakefluidthenentersachamberwithmoreAREAallowingaLARGEFORCEtobeappliedonthebrakeshoes,whichinturnslowthecardown.,.,Buoyancy,Whenanobjectisimmersedinafluid,suchasaliquid,itisbuoyedUPWARDbyaforcecalledtheBUOYANTFORCE.,WhentheobjectisplacedinfluidisDISPLACESacertainamountoffluid.Iftheobjectiscompletelysubmerged,theVOLUMEoftheOBJECTisEQUALtotheVOLUMEofFLUIDitdisplaces.,.,ArchimedessPrinciple,Anobjectisbuoyedupbyaforceequaltotheweightofthefluiddisplaced.,Inthefigure,weseethatthedifferencebetweentheweightinAIRandtheweightinWATERis3lbs.Thisisthebuoyantforcethatactsupwardtocanceloutpartoftheforce.Ifyouweretoweightthewaterdisplaceditalsowouldweigh3lbs.,.,ArchimedessPrinciple,.,Example,Abargainhunterpurchasesagoldcrownatafleamarket.Aftershegetshome,shehangsitfromascaleandfindsitsweightinairtobe7.84N.Shethenweighs