流体力学课后作业

流体力学课后作业1.1Apressureof2106N/m2isappliedtoamassofwaterthatinitiallyfilleda1,000cm3volume.Estimateitsvolumeafterthepressureisapplied.将2106N/m2的压强施加于初始体积为1,000cm3的水上，计算加压后水的体积。(999.1cm3)1.2AsshowninFig.1-9,inaheatingsystemthereisadilatationwatertank.Thewholevolumeofthewaterinthesystemis8m3.Thelargesttemperatureriseis500Candthecoefficientofvolumeexpansionisv=0.00051/K,whatisthesmallestcubageofthewaterbank?如图1-10所示，一采暖系统在顶部设一膨胀水箱，系统内的水总体积为8m3，最大温升500C，膨胀系数v=0.0051/K，求该水箱的最小容积(0.2m3)Fig.1-9Problem1.21.3Whentheincrementofpressureis50kPa,thedensityofacertainliquidis0.02%.Findthebulkmodulusoftheliquid.当压强增量为50kPa时，某种液体的密度增加0.02%。求该液体的体积模量。(2.5108Pa)1.4Fig.1-10showsthecross-sectionofanoiltank,itsdimensionsarelengtha=0.6m,widthb=0.4m,heightH=0.5m.Thediameterofnozzleisd=0.05m,heighth=0.08m.Oilfillstotheupperedgeofthetank,find:(1)Ifonlythethermalexpansioncoefficientv=6.510-41/Koftheoiltankisconsidered,whatisthevolumeFig.1-10Problem1.4ofoilspilledfromthetankwhenthetemperatureofoilincreasesfromt1=-200Ctot2=200C?Ifthelinearexpansioncoefficientl=1.210-51/Koftheoiltankisconsidered,whatistheresultinthiscase?(2)图1-10为一油箱横截面，其尺寸为长a=0.6m、宽b=0.4m、高H=0.5m，油嘴直径d=0.05m，高h=0.08m。由装到齐油箱的上壁，求：(1)如果只考虑油液的热膨胀系数v=6.510-41/K时，油液从t1=-200C上升到t2=200C时，油箱中有多少体积的油溢出？如果还考虑油箱的线膨胀系数l=1.210-51/K，这时的情况如何？(2)((1)2.49210-3m3(2)2.3210-3m3)1.5Ametallicsleeveglidesdownbyselfweight,asshowninFig.1-11.Oilof=310-5m2/sand=850kg/m3fillsbetweenthesleeveandspindle.TheinnerdiameterofthesleeveisD=102mm,theouterdiameterofthespindleisd=100mm,sleevelengthisL=250mm,itsweightis100N.Findthemaximumvelocitywhenthesleeveglidesdownfreely(neglectairresistance).Fig.1-11Problem1.5有一金属套由于自重沿垂直轴下滑，如图1-11所示。轴与套间充满了=310-5m2/s、=850kg/m3的油液。套的内径D=102mm，轴的外径d=100mm，套长L=250mm，套重100N。试求套筒自由下滑时的最大速度为多少(不计空气阻力)。(50m/s)1.6Thevelocitydistributionforflowofkeroseneat200C(=410-3Ns/m2)betweentwowallsisgivenbyu=1000y(0.01-y)m/s,whereyismeasuredinmetersandthespacingbetweenthewallsis1cm.Plotthevelocitydistributionanddeterminetheshearstressatthewalls.在200C时，煤油(=410-3Ns/m2)在两壁面间流动的速度分布由u=1000y(0.01-y)m/s确定，式中y的单位为m，壁面间距为1cm。画出速度分布图，并确定壁面上的剪应力。(410-2Pa)1.7AsshowninFig.1-12,thevelocitydistributionforviscousflowbetweenstationaryplatesisgivenasfollows:Fig.1-12Problem1.7Ifglycerinisflowing(T=200C)andthepressuregradientdp/dxis1.6kN/m3,whatisthevelocityandshearstressatadistanceof12mmfromthewallifthespacingByis5.0cmWhataretheshearstressandvelocityatthewall如图1-12所示，两固定平板间粘性流动的速度分布由给出。如果流体为甘油(T=200C)且压强梯度dp/dx为1.6kN/m3，间距By为5.0cm，距平板12mm处的速度与剪应力为多少平板处的剪应力与速度为多少(u12=0.59m/s；τ12=20.8N/m2；u0=0；τ0=40.4N/m2)WhatistheratioofthedynamicviscosityofairtothatofwateratstandardpressureandT=200CWhatistheratioofthekinematicviscosityofairtowaterforthesameconditions1.8在 标准 excel标准偏差excel标准偏差函数exl标准差函数国标检验抽样标准表免费下载红头文件格式标准下载 大气压、T=200C时，空气与水的动力粘度之比为多少同样条件下它们的运动粘度之比又为多少(A/W=0.0018；A/W=15.1)1.9ThedeviceshowninFig.1-13consistsofadiskthatisrotatedbyashaft.Thediskispositionedveryclosetoasolidboundary.Betweenthediskandboundaryisviscousoil.(1)Ifthediskisrotatedatarateof1rad/s,whatwillbetheratiooftheshearstressintheoilatr=2cmtoFig.1-13Problem1.9theshearstressatr=3cm?Iftherateofrotationis2rad/s,whatisthespeedofoilincontactwiththediskatr=3cm?(2)Iftheoilviscosityis0.01Ns/m2andthespacingyis2mm,whatistheshearstressfortheconditionnotedin(b)(3)图1-13所示装置由绕一根轴旋转的圆盘构成。圆盘放置在与固体边界很近的位置。圆盘与边界间为粘性油。(1)如果圆盘的旋转速率为1rad/s，问半径为r=2cm与r=3cm处的剪应力之比为多少？(2)如果旋转速率为2rad/s，r=3cm处与圆盘接触的油层的速度为多少？如果油的粘度为0.01Ns/m2、且间距y为2mm，(b)情况下的剪应力为多少？(3)((1)2:3；(2)6cm/s；(3)0.3Pa)1.10AsshowninFig.1-14,aconerotatesarounditsverticalcenteraxisatuniformvelocity.Thegapbetweentwoconesis=1mm.Itfilledwithlubricantwhich=0.1Pas.IntheFigure,R=0.3m,H=0.5m,Fig.1-14Problem1.10=16rad/s.Whatisthemomentneededtorotatethecone?如图1-14所示，一圆锥体绕竖直中心轴等速旋转，锥体与固定的外锥体之间的隙缝=1mm，其中充满=0.1Pas的润滑油。已知锥体顶面半径R=0.3m，锥体高度H=0.5m，当旋转角速度=16rad/s时，求所需要的旋转力矩。(39.6Nm)2.1Twopressuregaugesarelocatedonthesideofatankthatisfilledwithoil.Onegaugeatanelevationof48mabovegroundlevelreads347kPa.Anotheratelevation2.2mreads57.5kPa.Calculatethespecificweightanddensityoftheoil.两个测压计位于一充满油的油箱的一侧。一个测压计高于地面的位置高度为48m，读数57.5kPa。另一个位置高度为2.2m，读数347kPa。计算油的重度与密度。(=6.32kN/m3,=644kg/m3)2.2Twohemisphericalshellsareperfectlysealedtogether,andtheinternalpressureisreducedto20kPa,theinnerradiusis15cmandtheouterradiusis15.5cm.Iftheatmosphericpressureis100kPa,whatforceisrequiredtopulltheshellsapart?两半球壳完美密闭在一起，内压减至20kPa，内径15cm，外径15.5cm。如果大气压强为100kPa，求要将半球拉开所需的力为多少。(24.5kN)2.3Asshowninthefigure,thereisaquantityofoilwithdensityof800kg/m3,andaquantityofwaterbelowitinaclosedcontainer.Ifh1=300mm,h2=500mm,andh=400mmHg,findthepressureatthefreesurfaceoftheoil.如图所示，密闭容器中油的密度为800kg/m3，其下方为水。如果h1=300mm,h2=500mm,及h=400mmHg，求油的自由 表 关于同志近三年现实表现材料材料类招标技术评分表图表与交易pdf视力表打印pdf用图表说话 pdf 面上的压强。(46.1kPa)Problem2.32.4Accordingtothediagram,oneendofatubeconnectedtoanevacuatedcontainerandtheotherendisputintoawaterpoolwhosesurfaceisexposedtonormalatmosphericpressure.Ifhv=2m,whatisthepressureinsideofcontainerA?如图，一根管子一端与一抽空的容器相连，另一端插入暴露于大气的水池中。如hv=2m，容器内的压强是多少(81.7kPa)PProblem2.42.5Apressuregaugeisplacedundersealevel.Ifthegaugepressureatapoint300mbelowthefreesurfaceoftheocean,itregisters309kPa,findtheaveragespecificweightofseawater.一测压计置于海平面下，如果在自由表面下300m深处测压计的读数为309kPa，求海水的平均重度。(1.03kN/m3)2.6Ifthelocalatmosphericpressureisgivenby98.1kPaabsolute,findtherelativepressureatpointsa,bandcinwater.(seeattachedfigure)如果当地大气压的绝对压强为98.1kPa，求水中a、b及c点的相对压强。（见附图）(Pa=68.6kPa，Pb=31.3kPa，Pc=-29.4kPa)Problem2.62.7Thereisanappliedloadof5788Nonthepistonwithinacylindricalcontainer,inwhichisfilledwithoilandwater.Theoilcolumnheightish1=30cmwhenthewatercolumnh2=50cm.Thediameterofthecontainerisgiverasd=40cm.Thedensityofoilis1=800kg/m3andthatofmercuryas3=13600kg/m3.ComputetheheightH(cm)ofthemercurycolumnintheU-tube.圆柱形容器的活塞上作用一5788N的力，容器内充有水和油。当水柱高h2=50cm时，油柱高h1=30cm。容器直径d=40cm，油的密度1=800kg/m3，水银密度3=13600kg/m3。求U形管内的汞柱高H(cm)。(14.07cm)Problem2.72.8Accordingtothediagram,aclosedtankcontainswaterthathasarelativepressureonthewatersurfaceofpo=-44.5kN/m2.(1)Whatisthedistanceh?(2)WhatisthepressureatpointMwith0.3mbelowwatersurface?(3)WhatisthepiezometricheadofpointMrelativetodatumplane1-1?如图所示，一密闭容器内盛有自由表面相对Problem2.8压强为po=-44.5kN/m2的水。(1)求距离h；(2)水面下0.3m处的M点的压强为多少？(3)M点相对于基准面1-1的测压管水头是多少？(h=4.54m，Pm=-41.6kPa，hm=-4.24m)2.9AnuprightU-tubeisfixedonthehoodofacarwhichtravelinginastraight-line,withaconstantaccelerationa=0.5m/s2.ThelengthL=500mm.FindtheheightdifferenceofthetwofreesurfacesintheU-tube.一竖直的U形管安装在以匀加速度a=0.5m/s2作直线运行的车罩上，长度L=500mm。求U形管内两自由液面的高度差。(25.5mm)Problem2.92.10Accordingtothediagram,anopentankcontainingwatermoveswithanaccelerationa=3.6m/s2,alongaslopeof30o.Whatistheinclinedanglewiththehorizontalplaneandtheequationofwaterpressurepatthefreesurface?如图所示，一盛水的开口容器以加速度a=3.6m/s2沿30o的斜面运动。求自由液面与水平面的夹角，并写出水的压强p的分布方程。(=15o，p=pa+gh)Problem2.102.11Asshowninthefigure,agateof2mwide,extendsoutoftheplaneofthediagramtowardthereader.ThegateispivotedathingeH,andweighs500kg.Itscenterofgravityis1.2mtotherightand0.9maboveH.ForwhatvaluesofwaterdepthxaboveHwillthegateremainclosed(Neglectfrictionatthepivotpointandneglectthethicknessofthegate)如图所示，闸门宽2m，重500kg，绕铰链H转动。闸门重心在距右端1.2m处且高于H0.9m。问铰链H上方水深x为多少时，闸门将关闭（忽略铰链摩擦及闸门的厚度）(1.25m)Problem2.112.12Aflat1mhighgateishingedatpointO,andcanrotatearoundthepoint(seeattacheddiagram).TheheightofpointOisa=0.4m.WhatisthewaterdepthwhenthegatecanautomaticallyopenaroundpointO?一1米高的平板闸门在O点处用铰链连接，且可绕铰链转动（见附图）。O点的高度为a=0.4m。水深多少时，闸门将自动开启？(h=1.33m)Problem2.122.13Asshowninthediagram,aclosedtankformingacubeishalffullofwater,find:(a)theabsolutepressureonthebottomofthetank,(b)theforceexertedbythefluidsonatankwallasafunctionofheight,(c)thelocationofthecenterofpressurebywateronthetankwall.如图所示，一密闭立方体水箱装了一半的水，求：(a)箱底的绝对压强；(b)将流体对一侧箱壁的作用力表示为高度的函数；(c)水对箱壁的压力中心位置。Problem2.13(17.8kPa，F=2h(8000+0.5gh)，2/3)2.14Acircularsluicegateofdiameterd=1missubmergedinwaterasshowninthefigure.Theslantangle=60o,thesubmergeddepthhc=4.0m,andtheweightofthegateFG=1kN.DeterminethemagnitudeoftheverticalforceTsoastomakethegaterotateupwardaboutaxisa(neglectfrictionataxisa).如图所示的一直径d=1m圆形闸门淹没于水中。倾角=60o，淹深hc=4.0m，闸门重FG=1kN。求使闸门绕a轴向上转动的铅直力T的大小。(230kN)Problem2.142.15ThegateMshowninthefigurerotatesaboutanaxisthroughN.Ifa=33m,b=13m,d=20mandthewidthperpendiculartotheplaneofthefigureis3m,whattorqueappliedtotheshaftthroughNisrequiredtoholdthegateclosed?图示闸门M绕N轴转动。如a=33m、b=13m、d=20m且与图形垂直的宽度为3m，要使闸门关闭，需要施加多大的力矩在转轴上(666103kNm)Problem2.152.16Findthehorizontalandverticalcomponentsoftheforceexertedbyfluidsonthefixedcircularcylindershowninthefigure,if:(1)thefluidtotheleftofthecylinderisagasconfinedinaclosedtankatapressureof35kPa,and(2)thefluidtotheleftofthecylinderiswaterwithafreesurfaceatanelevationcoincidentwiththeuppermostpartofthecylinder.Assuminginbothcasesthatnormalatmosphericpressureconditionsexisttotherightandtopofthecylinder.求下述流体对图示圆柱体所施加的水平与铅直方向的分力。(1)圆柱体左边是压强为35kPa的密闭气体；(2)圆柱体左边是自由液面刚好与柱顶平齐的水。设两种情况下圆柱体的右边与顶部为标准大气压。Problem2.16((1)Fx=130.5kN，Fz=35kN；(2)Fx=68.1kN，Fz=100.5kN)2.17Thecrosssectionofatankisasshowninthefigure.BCisacylindricalsurfacewithr=6m,andh=10m.Ifthetankcontainsgasatapressureof8kPa,determinethemagnitudeandlocationofthehorizontalandverticalforcecomponentsactingonunitwidthoftankwallABC.图示为一容器的剖面，BC是半径r=6m的圆柱面。容器高h=10m。如果容器装有压强为8kPa的气体，求作用在容器壁ABC上单位宽度的水平分力与铅直分力的大小与作用位置。(Fx=80kN，Fz=48kN)Problem2.172.18Findtheminimumvalueofzforwhichthegateinthefigurewillrotatecounterclockwiseifthegateis:(a)rectangular5mhighby4mwide;(b)triangular,4mbaseasaxis,height5m.neglectfrictioninbearings.Problem2.18当下述情况时，求使图示闸门沿逆时针方向转动的z的最小值：(a)闸门为高5m、宽4m的矩形；(b)闸门为上底4m（转轴）、高5m的三角形。((a)z=307.5m，(b)305m)2.19AcurvedsurfaceisformedasaquarterofacircularcylinderwithR=0.75m,asshowninthefigure.Thecylindersurfaceisw=3.55mwide(outoftheplaneofthefiguretowardthereader).WaterstandstilltotherightofthecurvedsurfacetoadepthofH=0.65m.Determine(1)Themagnitudeofthehydrostaticforceonthesurface.(2)Thedirectionofthehydrostaticforce.Problem2.19一曲面由半径为R=0.75m的四分之一的圆柱体组成，如图所示。圆柱面宽w=3.55m（垂直于图形平面）。曲面右侧静水深度H=0.65m。试求：(1)作用于曲面上静水压力的大小；(2)静水压力的方向。(Fx=7357N，Fz=6013N)2.20Asshowninthediagram,thereisacylinderwithdiameterD=4mandlengthL=12minwater.Thedepthofwaterontherightandleftsideofthecylinderare4mand2mrespectively.Findthemagnitudeanddirectionoftheforceonthecylinderexertedbywater.如图所示，直径D=4m、长L=12mProblem2.20的圆柱体放于水中，圆柱体左右两边水的深度分别为4m和2m。求水对圆柱体的作用力的大小与方向。(Fx=706kN，Fz=1579kN)2.21Asshowninthefigure,determinethepivotlocationyoftherectangulargate,sothatthegatewilljustopen.如图所示，求闸门刚好开启时转轴的位置y为多少。(y=0.44m)Problem2.21Problems3.1Atwo-dimensional,incompressibleflowfieldisgivenbyFindthevelocityandaccelerationatpoint(1,2).二维不可压缩流动由确定。试求点（1，2）处的速度与加速度。(vx=5，vy=30；ax=75，ay=150)3.2SupposevelocitydistributionofaflowfieldisgivenbyFind:(1)theexpressionoflocalacceleration;(2)theaccelerationofthefluidparticleatpoint(1,1)whent=0.设流场的速度分布为。求：（1）当地加速度的表达式；（2）t=0时在点（1，1）处流体质点的加速度。((1)vx/t=4,vy/t=0；(2)ax=3,ay=1)3.3ThevelocitycomponentsofaflowfieldisDeterminethestreamlineequationthroughpoint(x0,y0)att=t0.一流场的速度分量为确定在t=t0时刻通过点(x0,y0)的流线方程。(x2yAty+C=0)3.4Atwo-dimensionalvelocityfieldisgivenbyWhatisthestreamlineequationinthisflowfield?已知二维速度场，求流线方程。(x1+t=cy)3.5ItisknownthevelocityfieldisTrytofindthestreamlineequationpassingthroughpoint（2，1，1）.已知速度场，求通过点（2，1，1）的流线方程。(x=2，5-z=2z)3.6Anoiltransportationpipeline,thevelocityatthesectionofdiameter20cmis2m/s,whatisthevelocityandmassflowrateatthesectionofdiameter5cmThedensityoftheoilis850kg/m3.有一输油管道，在内径为20cm的截面上流速为2m/s，求在另一内径为5cm的截面上的流速以及管内的质量流量。油的密度为850kg/m3。(32m/s，53.4kg/s)3.7Inapipelineofinnerdiameter5cm,themassflowrateofairis0.5kg/s,pressureatacertainis5105Pa,thetemperatureis1000C.Findtheaverageairflowvelocityonthissection.在内径为5cm的管道中，流动空气的质量流量为0.5kg/s，在某一截面上压强为5105Pa，温度为1000C。求该截面上气流的平均速度。(54.5m/s)3.8Thevelocitydistributionofanincompressiblefluidis，Trytodeducetheexpressionofvzbyadoptingcontinuityequation.已知一不可压缩流体的速度分布为，。试用连续方程推导出vz的表达式。(vz=-z(2x+2y+z+1)+c(x,y))3.9AsshowninFig.3-25,waterflowssteadilyintoatwo-dimensionaltubeatauniformvelocityv.Sincethetubebendsanangleof900,velocitydistributionattheoutletbecomes.Assumingthewidthhofthetubeisconstant,findconstantC.如图3-25所示，水以均匀速度v定常流入一个二维通道，由于通道弯曲了900，在出口端速度分布变为。设通道宽度h为常数，Fig.3-25Problem3.9求常数C。(C=v/3)3.10Waterisflowinginariver,asshowninFig.3-26.TwoPitottubesarestackedandconnectedtoadifferentialmanometercontainingafluidofspecificgravity0.82.FindvAandvB.水在河道中流动，如图3-26所示。两个重叠的皮托管与一装有比重为0.82的流体的压差计连接。试求vA及vB。(vA=1.212m/s，vB=1.137m/s)Fig.3-26Problem3.103.11AsshowninFig.3-27,apipeofdiameter1misinstalledhorizontally,ofwhichapartbendsanangleof300.Oilofspecificgravity0.94flowsinsidethepipewithaflowrateof2m3/s.Assumepressureinthepipeisuniform,thegaugepressureis75kPa,findthehorizontalforceexertingontheelbowpipe.直径为1m的水平装置的管Fig.3-27Problem3.11道有一段300的弯管，如图3-27所示。管内比重为0.94的油以2m3/s的流量流动。设弯管内压强均匀，表压为75kPa，求弯管受到的水平力。(Fx=8.64kN，Fy=31.9kN)3.12TheheightofthemercurycolumninU-tubeis60mm,asshowninFig.3-28.Assumethediameteroftheconduitis100mm,findthevolumeflowrateofwaterthroughtheconduitatsectionA.如图3-28所示，U形管内汞柱高度为60mm。设排水管的直径为100mm，求在截面A处通过排水管的体积流量。(0.0314m3/s)Fig.3-28Problem3.123.13Anozzleisconnectedatoneendofawaterpipe,asshowninFig.3-29.Theoutletdiameterofthewaterpipeisd1=50mm,andthatofthenozzleisd2=25mm.Thenozzleandthepipeareconnectedbyfourbolts.Thegaugepressureatinletofthenozzleis1.96105Pa,volumeflowrateis0.005m3/s,trytofindthetensionappliedoneachbolt.在水管的端部接有喷嘴，如图3-29所示。水管出口直径d1=50mm，喷嘴出口直径d2=25mm。喷嘴与Fig.3-29Problem3.13管之间用四个螺栓连接。喷嘴入口处的表压为1.96105Pa，流量为0.005m3/s，求每个螺栓所受到的拉力。(86.75N)3.14Acentrifugalpumpdrawswaterfromawell,asshowninFig.3-30.Assumetheinnerdiameteroftheslouchisd=150mm,volumeflowrateisqv=60m3/h,andthevacuumvalueatpointAwheretheslouchandthepumpareconnectedispv=4104Pa.Neglectheadloss,whatisthesuctionheightHsofthepump?离心式水泵从井里抽水，如图3-30所示。设吸水管内径d=150mm，流量为qv=60m3/h，吸水管与水泵接头处A点的真空值为pv=4104Pa。不计水头损失，求水泵的吸水高度Hs。(4.03m)Fig.3-30Problem3.143.15AsshowninFig.3-31,anoilofspecificgravity0.83rushestowardsaverticalplateatvelocityv0=20m/s,findtheforceneededtosupporttheplate.如图3-31所示，相对密度为0.83的油水平射向直立的平板，已知v0=20m/s，求支撑平板所需的力F。(652N)Fig.3-31Problem3.153.16Ahorizontaljetflowwithvolumeflowrateqv0rushestowardsaninclinedplateatvelocityv0,asshowninFig.3-32.Neglecttheeffectsofgravityandimpactlossofthefluid,thepressureandvelocityofthejetflowremainthesameafteritsplitsintotwodistributaries.Findtheformulasofthetwodistributaries’flowrateqv1andqv2,andtheforceactingontheplate.如图3-32所示，一股速度为v0、体积流量为qv0的水平射流，射到倾斜的光滑平板上。忽略流体撞击的损失和重力的影响，射流的压强与速度在分流后也没有变化，求沿板面向两侧的分流流量qv1与qv2的表达式，以及流体对板面的作用力。Fig.3-32Problem3.16()3.17AsshowninFig.3-33,acartcarryinganinclinedsmoothplatemovesatvelocityvagainstajetflow,thevelocity,flowrateanddensityofthejetflowarev0,qv，andrespectively.Ignorethefrictionbetweenthecartandground,whatisthepowerWneededfordrivingthecart?如图3-33所示，带有倾斜光滑平板的小车逆着射流方向以速度v运动，射流的速度和流量分别为v0和qv，射流的密度为，不计小车与地面的摩擦力，求推动小车所需的功率W。Fig.3-33Problem3.17()3.18Acrookedpipestretchesoutfromabigcontainer,asshowninFig.3-34,thediameterofthepipeis150mm,andthatofthenozzleis50mm.Ifneglecttheheadloss,trytofindtheflowrateofthepipe,andpressuresatpointA,B,C,andD.从一大容器引出一弯曲的管道如图3-34所示，管径为150mm，喷嘴直径为50mm，不计水头损失，求管的输水流量，以及A、B、C、D各点的压强。(0.0174m3/s，68.2、-0.47、-20.1、38.8kPa)Fig.3-34Problem3.183.19AVenturiflowmeterisinstalledbiasasshowninFig.3-35,diameterattheinletisd1,anddiameteratthethroatisd2,trytodeduceitsflowrateexpression.文丘里管流量计倾斜安装如图3-35所示，入口直径为d1，喉部直径为d2。试推导出其流量的计算公式。()Fig.3-35Problem3.193.20AsshowninFig.3-36,waterflowsoutfromabigcontainerandintoanothersmallcontainer.Supposethatthefreesurfaceelevationsofthetwocontainerskeepunchanged,findthevelocityveattheoutlet.如图3-36所示，大容器中的水由小孔流出，流入另一盛水小容器。若两容器的水面高度保持不变，求小孔流出的速度ve。()Fig.3-36Problem3.203.21APitottubeissubmergedinaprismaticpipeline,whichisshownasinFig.3-37.Ifthedensityofthefluidinsidethepipelineis,andthatintheU-tubeis’,theelevationdifferenceintheU-tubeish,findthevelocityinthepipeline.一皮托管置于等截面的管路中，如图3-37所示。若管内流体的密度为，U形管内流体的密度为’，液面高度差为h，求管流速度。()Fig.3-37Problem3.213.22AsshowninFig.3-38,transportwaterfromcontainerAtocontainerBbymeansofasiphon.Ifthevolumeflowrateis100m3/h,H1=3m,z=6m,andneglecttheheadloss,findthediameterofthesiphonandthevacuumvalueintheupperpartofthesiphon.如图3-35所示，利用虹吸管把水从容器A引到容器B。已知体积流量为100m3/h，H1=3m，z=6m，不计水头损失，求虹吸管的管径，以及上端管中的真空值。Fig.3-38Problem3.22(0.068m，5.89104Pa)3.23AwatersprinklerisshownasinFig.3-39,thelengthsofitstwoarmsarel1=1mandl2=1.5mrespectively,ifthediameterofthenozzleisd=25mm,donottakethefrictionalmomentintoaccount,findtherotatingspeedn.洒水器如图3-39所示，两臂长分别为l1=1m、l2=1.5m，若喷口直径d=25mm，每个喷口的流量qv=3L/s，不计摩擦阻力矩，求转速n。(44.9r/min)Fig.3-39Problem3.233.24AsymmetricalsprinklerisshownasinFig.3-40.TherotatingradiusisR=200mm,=450,thenozzlediameterisd=8mm,thetotalflowrateisqv=0.563L/s,ifthefrictionalmomentis0.2Nm,findtherotatingspeedn.Andwhatisthemagnitudeofthemomentneededtoholdthesprinkleratrestwhileitisinoperation?对称洒水器如图3-40所示。旋转半径Fig.3-40Problem3.24R=200mm，=450，喷口直径d=8mm，总流量qv=0.563L/s，若已知摩擦阻力矩为0.2Nm，求转速n。若喷水时不让其旋转，应受到多大的力矩(103r/min，0.441Nm)Problems1.1ThevelocityfieldofarotationalflowisgivenbyFindtheaverageangularrotatingvelocityatpoint(2,2,2).已知有旋流动的速度场为求在点（2,2,2）处平均旋转角速度。(x=0.5，y=2，z=0.5)1.1Determinewhetherthefollowingflowfieldisrotationalfloworirrotationalflow.确定下列流场是有旋运动还是无旋运动：(1)(2)((1)有旋，(2)无旋)4.3Thevelocitydistributionofaflowfieldisdescribedbyv=x2yixy2jIstheflowirrotational?流场的速度分布为v=x2yixy2j该流动是否无旋(有旋)4.4Foracertainincompressible,two-dimensionalflowfieldthevelocitycomponentintheydirectionisgivenbyvy=x2+2xyDeterminethevelocitycomponentinthexdirectionsothatthecontinuityequationissatisfied.某一不可压缩平面流场在y方向的速度分量为vy=x2+2xy确定x方向的速度分量，以满足连续性方程。(vx=x2+C)4.5Foracertainincompressibleflowfielditissuggestedthatthevelocitycomponentsaregivenbytheequationsvx=x2yvy=4y3zvz=2zIsthisaphysicallypossibleflowfield?某一不可压缩流场流场的速度分量由下列方程给出vx=x2yvy=4y3zvz=2z试问该流场在物理上是否可能(不可能)4.6Itisknownthatstreamlinesareconcentriccircles,andvelocitydistributionis已知流线为同心圆族，其速度分布为Findthevelocitycirculationalongcirclex2+y2=R2,wheretheradiusesofthecircleare(1)R=3；(2)R=5；(3)R=10respectively.求沿圆周x2+y2=R2的速度环量，其中圆的半径R分别为(1)R=3；(2)R=5；(3)R=10。((1)18/5，(2)10，(3)10)4.7Assumethereisavortexof=0locatingatpoint(1，0),andanothervortexof=-0atpoint(-1，0).Findthevelocitycirculationalongthefollowingroutes:(1)x2+y2=4；(2)(x-1)2+y2=1；(3)Squareofx=2，y=2；(4)Squareofx=0.5，y=0.5.设在点(1，0)处置有=0的旋涡，在点(-1，0)处置有=-0的旋涡。试求下列路线的速度环量：(1)x2+y2=4；(2)(x-1)2+y2=1；(3)x=2，y=2的方形框；(4)x=0.5，y=0.5的方形框。((1)0，(2)0，(3)0，(4)0)4.8Forincompressiblefluid,determineifthereexiststreamfunctionsinthefollowingflowfields,whereKisaconstant.对于不可压缩流体，试确定下列流场是否存在流函数？式中K为常数。(1)vx=Ksin(xy)，vy=-Ksin(xy)(2)vx=Kln(xy)，vy=-Ky/x((1)不存在，(2)存在)4.9Demonstratethefollowingplanarflowofanincompressiblefluidsatisfiescontinuityequation,andisapotentialflow,thenfindthepotentialfunction.试证明以下不可压缩流体平面流动满足连续性方程，是有势流动，并求势函数。(=x2/2+x2yy2/2y3/3)4.10Avelocityfieldisgivenbyvx=x2y+y2，vy=x2xy2，vz=0，questions：(1)Ifthereexiststreamfunctionandpotentialfunction?(2)Findtheexpressionsofstreamfunctionandpotentialfunctioniftheyexist.给定速度场vx=x2y+y2，vy=x2xy2，vz=0，问：(1)是否存在流函数和势函数？(2)如果存在，求其具体表达式。((1)存在流函数，不存在势函数；(2)=x2y2/2+y2/3x2/3)4.11Thevelocitypotentialinacertainflowfiledis=4xyDeterminethecorrespondingstreamfunction.某流场的速度势为=4xy求相应的流函数。(=2x22y2)4.12Thevelocitypotentialforanincompressible,planarflowis=x2y2+xFinditsstreamfunction.不可压缩流体平面流动的势函数为=x2y2+x试求流函数。(=2xy+y)4.13Thestreamfunctionforanincompressible,planarflowis=xy+2x3yFindthepotentialfunction.不可压缩流体平面流动的流函数为=xy+2x3y试求势函数。(=(x2y2)/23x2y)4.14Demonstratethefollowingtwoflowfieldsareidentical:(1)thepotentialfunctionis=x2+xy2(2)thestreamfunctionis=2xy+y证明下列两个流场是相同的。(1)势函数=x2+xy2(2)流函数=2xy+y4.15Giventhevelocitydistributionofaflowfieldasvx=Ax+Byvy=Cx+DyIftheflowisincompressibleandirrotational,findWhatrelationshipshouldcoefficientsA、B、C、Dsatisfy?(1)(2)Thestreamfunctionoftheflowfield.已知流场的速度分布为vx=Ax+Byvy=Cx+Dy若流体不可压缩，且流动无旋，试问(1)系数A、B、C、D应满足怎样的关系？(2)求流场的流函数。((1)A=D，B=C；(2)=B(y2x2)/2+Axy)4.16Thereisafixedpointvortexofcirculationanddistanceatoastationarywall.Findthevelocitypotentialfunctionoftheflowandpressuredistributiononthewall.有一环量为的固定点涡，离一静止壁面的距离为a。试求流动的速度势和壁面上的压强分布。(，)4.17Give