动力学2MicrosoftPowerPoint演示文稿.ppt

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1、DynamicsofFluidMotion一EulerEquationofMotion二Bernoulli’sEquation三Bernoulli’sEquationforStreamtube四MomentumEquation五MomentofMomentumEquation一EulerEquationofMotion1.EulerEquation*Considerasmallelement*Bodyforce:*Foridealfluid:Therearenoshearingstresses.*

2、ApplicationofNewton’ssecondlawinXdirectionSimplifyingtheequationabove,wecanobtainxyzdxdydzxp+(p/x)dxfxfyfzyzpinasimilarmanner,wehaveEulerEquationNotethat:①Eulerequationmustapplyateverypointthroughoutthefluid.②Itisvalidonlyforanidealfluid.③Itisapplic

3、abletobothcompressibleandincompressibleflow.2.EulerEquationinSreamlineCoordinates（流线坐标）*Streamline(Natural)CoordinatesStreamlinecoordinateisusuallyconfinedtoflowsthatcanbespecifiedbytwocoordinatedirections.Thecoordinatedirectionsisalongastreamlineandi

4、stakenaspositiveinthedirectionofflow.Thenormaldirectionnispositiveinward.s,沿流线方向为“正”n,垂直s,且内向为“正”Theadvantageofthissystemisthatthereisnovelocitycomponentinndirection,thevelocitymustbetangenttothestreamline.∴的分量形式可表达为：加速度：其中,srdsdθdθ*Considerasmallelem

5、entwhichiscylindricaltubewithcrosssectiondAandlengthdl.(l:anarbitrarydirectioninflowfield)ApplicationofNewton’ssecondlawinldirectionNow,picktheldirectionasthestreamlinedirectionforasteadyflowpdAylθweightdlLettheldirectionbendirectionofstreamlinecoordi

6、nates:forincompressibleflow分析：①若流动发生在水平方向，得到：上式说明：沿着压力降的方向上将有加速度产生，也就是说沿着等压线的方向上无加速度，如果有加速度的话，只可能发生在与等压线垂直的方向上。②记——piezometrichead（测压水头）对于不可压缩流体：Wemayimmediatelynotethattherecanbenoaccelerationalongalineofconstantpiezometrichead.Theaccelerationingener

7、almustbeperpendiculartolinesofconstantpiezometricheadandinthedirectionofdecreasingvaluesofh.二Bernoulli’sEquationDanielBernoulli(1700-1782),Swiss,mathematician,publishedthisequationinhisHydrodynamica(1738).上式即为伯努利方程。应用条件：①理想，②不可压，③定常，④重力流体，⑤同时在一条流线上。*伯

8、努利方程还可写作：各项的物理意义：三项分别是单位重量流体的压力势能、位置势能和动能，或压力头（pressurehead）、位置头（elevationhead）和速度头（velocityhead），三项之和称为totalhead。伯努利方程的物理意义：Thetotalheadisaconstantalongastreamlineinsteady,incompressible,frictionlessflows.Example:BothtanksofFig.2havealiquidde