流體力學(xué)期中考試

流體力學(xué)期中考試PartI(5pointsperquestion)1.Onasea-levelstandardday,apressuregage,mooredbelowthesurfaceoftheocean(SG1.025),readsanabsolutepressureof1.5MPa.Howdeepistheinstrument?2.Afireboat-pumpdeliverswatertoaverticalnozzlewitha3:1diameterratio,asinFig.1.Iffrictionisneglectedandtheflowrateis0.02m3/sFig.13.Giventhesteady,incompressiblevelocitydistributionVx+y)iC(x+y)j0k,whereCisaconstant,ifconservationofmassissatisfied,findthevalueofC.WritedownthestrainratetensorSij(=0.5(ui,j+uj,i))andthevorticityvector(V).4.Afootball,meanttobethrownat60mi/hinsea-levelair(1.22kg/m3,1.78E-5Ns/m2)istobetestedusingaone-quarter(1/4)scalemodelinawatertunnel(998kg/m3,0.0010Ns/m2).Fordynamicsimilarity,whatistheratioofprototypeforcetomodelforce?PartII(20pointsperquestion)5.ThehemisphericaldomeinFig.2weighs36kNandisfilledwithwaterandattachedtothefloorbysixequallyspacedbolts.Whatistheforceineachboltrequiredtoholdthedomedown?Fig.26.Considerincompressibleflowintheentranceofacirculartube,asinFig.3.Theinletflowisuniform,u1Uo.Theflowatsection2isdevelopedpipeflow.FindthewalldragforceFasafunctionof(p1,p2,,Uo,R)iftheflowatsection2is:(a)Laminar:,(b)Turbulent:Fig.37.Aviscousliquidofconstantdensityandviscosityfallsduetogravitybetweentwoparallelplatesadistance2hapart,asinFig.4.OneplateismovingatspeedW0.Theflowisfullydeveloped,thatis,ww(x)only.Therearenopressuregradients,onlygravity.SetupandsolvetheNavier-Stokesequationforthevelocityprofilew(x).Fig.48.TheperiodofoscillationTofawatersurfacewaveisassumedtobeafunctionofdensity,wavelength,depthh,gravityg,andsurfacetension.Rewritethisrelationshipindimensionlessform.Whatresultsifisnegligible?PartIIIAdditionalProblem(20pointsperquestion)9.AliquidjetofvelocityVjandareaAjstrikesasingle180°bucketonaturbinewheelrotatingatangularvelocityΩ.FindanexpressionforthepowerPdelivered.AtwhatΩisthe