Transcription of Lecture6 Hydrostatic Force on curved Surfaces
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Lecture6 Hydrostatic Force on curved Surfaces
Hydrostatic Force on a curved SurfacesHenryk Kudela1 Hydrostatic Force on a curved SurfaceOn a curved surface the forcesp Aon individual elements differ in direction, so a simplesummation of them may not be made. Instead, the resultant forces in certain directionsmay be determined, and these forces may then be combined vectorially. It is simplest tocalculate horizontal and vertical components of the total component of Hydrostatic forceAny curved surface may be projected on to a vertical plane. Take, for example, the curvedsurface illustrated in Fig. 1: Hydrostatic Force on a curved surfaceIts projection on to the vertical plane shown is representedby the trace AC. LetFxrepresent the component in this direction of the total forceexerted by the fluid on thecurved act through the center of pressure of the vertical projection andis equal in magnitude to the Force F on the fluid at the any given direction, therefore, the horizontal Force on any surface equals the forceon the projection of that surface on a vertical plane perpendicular to the given line of action of the horizontal Force on the curved surface is the same as that of theforce on the vertical component of Hydrostatic forceThe vertical component of the Force on a curved surface may bedetermined by consideringthe fluid enclosed by the curved surface and vertical projection lines extending to t
4 m) and its centroid is 1 + d/2 = 2 m below the free surface. Therefore horizontal force F H is equal F H = ρgz sA = 1000 ·9.81 · 2· (5 ·2) = 1.962 ·105 N Its line of action passes through the center of pressure of the vertical projection, that is, at a distance I x/Az s below the free surface, given by: I x Az s = I s +Az2 s Az s = bd3 ...
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