英文工程流体力学第二章

White: Chapter2Chapter2

PressureDistribution

inafluid

(FluidStatics

Basic)1Definition:Unit:(SI)(PoundperSquireInch)Verticaltothesurfaceandpointintoit.Atanypoint,pressureisindependentoforientation.PropertiesofPressurePressure2Atanypointinastaticfluid,pressureisindependentoforientation.Verification:When(up)Forcesonleftandupsurface:3FluidMechanicsAerodynamicsFluidatrestFluidStaticsFluidDynamicsFluidinmotion4Pressureistheonlysurfaceforce.Pressuredistributionrelatestobodyforceonly.Dams（水坝）Buoyancyrelatedinstrument（利用浮力的装置）Fluidpowersystem（液压驱动系统）Connectedvessel（连通器）……Applications:§2.1Fluid@rest5Consideracubeinastaticfluid Pressureatthecenterisp; Bodyforcesaredxdydz§2.2EquilibriumofaFluidElement6dxdydzdxdydzPressure:Bodyforce:7Inxdirection:ForceonleftsurfaceForceonrightsurfaceBodyforceinxdirectionEulerEquilibriumEquations(Euler1775)8Pressureincreaseinthedirectionofbodyforce.Surfacesinfluidwithsamepressure,verticaltobodyforceeverywhere,ingravityfielditisahorizontalplane.Equipressuresurface（等压面）9xzzhz0p01Basicrule:Generalsolution2Boundarycondition:§2.3

PressureDistributionunderGravity10PressureatfreesurfacePressureduetoweightontopAnypointwiththesamedepthhunderfreesurfacehasthesamepressure.equipressuresurface（等压面）Freesurfaceisanequipressuresurface11p0Watermanometer（水柱压力计）phPressuresourceConnectedwatertubeApplication?Absolutepressure（绝对压力）Relativepressure（相对压力）Gaugepressure（表压力）Vacuumdegree（真空度）Pressuremeasurementh(mmH2O)h+p0

(mmH2O)pA

绝压pG

表压12P2.7Homework:13Centroid（形心，重心）hcycChyxAαyxp0FindtotalforceP§2.4HydrostaticForceonPlaneSurface14hc:

depthofcentroidTheforceonasubmergedplaneequalsthepressureattheplatecentertimestheplatearea,independentoftheshapeoftheplateortheangle

.CenterofpressureIsthecenterofpressureatcentroid?hcycChdydDhyxAαyxp015hcycChdydDhyxAαyxp0Momenttoxaxis16ExampleThegateis5mwide,ishingedatpointB,andrestagainstasmoothwallatpointA.FindTheforceonthegateexertedbyseawaterpressure,ThehorizontalforcePxexertedbythewallatpointA17(a)Centroid:3maboveBSolution:(b)LcL18HooverDamChannel

SelectadAandfindthethreeforcesonitIntegration§2.5HydrostaticForcesonCurvedSurfaces19Conclusion:x1.Horizontalforces:xOzAAx2.Verticalforces:OzV20Example:Findtheforcesactingonthehemi-sphericalcovers.RFOxyH45o

Solution:21§2.6.1UniformLinearAcceleration（恒加速度直线运动）aX=-agxGravityBodyforceInertiaForce§2.6Fluidinrigidbodymotion22Boundarycondition:Atfreesurface（自由液面）Equipressuresurface（等压面）EulerEquilibriumEquations23Acupofcoffeeis7cmdeepatrest.1.Whetheritwillspilloutwhileax=7m/s2?2.GagepressureofpointA?Example:Solution:Itwillnotspillout!24§2.6.2Rigidbodyrotation（整体旋转）gω2rzfOω2yωxyROfω2xryxθBodyforce:Equipressur