(2.4)--Chapter 2 Fluid Statics - 36号-p4流体力学环境水力学.ppt

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(2.4)--Chapter 2 Fluid Statics - 36号-p4流体力学环境水力学.ppt

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2.6ForceExertedon2DCurvedSurfacebyStaticFluid

and

Shortcut3：1）Thehorizontalforceonacurvedorinclinedsurfaceisequaltothehorizontalforceonaprojectionofthesurface.2）Theverticalforceonacurvedorinclinedsurfaceisequaltotheweightoffluidaboveit.

Notes1）PressureVolumeV:acolumnbetweenthefreesurfaceandthecurvedsurface.

2）Thelineofaction：Thelineofactionoftheresultantforceisalongtheinwardnormalofsurface.Specially,thelineofactionoftheresultantforcepassesthroughthecenterofcylinder.3）Thepointofaction：(a)Thepointofactionoftheverticalforceisthecentroidofthevolume.(b)ThepointofactionofhorizontalforceisthepressurecenterofprojectedareaAx.(c)ThepointofactionoftheresultantFistheintersectionoftheresultantforceandthecurvedsurface.

Example1InthefollowingFigure,D=1m,p=4903.5kPa,neglectingtheweight,fortheallowabletensilestress[σ]=147.1MPa，determinetheleastwallthicknessofpipe.

SolutionForthelengthofpipel,thepipeiscutthroughaxisintotwosections.Theverticalforceonthehalfofpipeis0becausepisuniform.Andthehorizontalforceis

GiventhetensileforceperunitlengthTinthepipewall，thenForguaranteeingthestrengthofpipe,theallowablestressshouldn’tbelessthanrealstress.Combiningthethreeexpressionsabove,so

Example2Acylindricalbarrierholdswaterasshown.Determine1)theresultantpressure2)thepressurecenterandthepointofactionofresultantforceforD=2.4m,L=1m.

Solution1)

2)Assumethepressurecenterisat(xP,yP),then

References(includingbutnotlimitedto):[1]FluidMechanicswithEngineeringApplications,E.J.FinnermoreandJ.B.Franzini,2003,10thediton.[2]FluidMechanicsFundamentalsandApplications,Y.A.CengelandJ.M.Cimbala,2004,3rdediton.