Fluid Statics

Hydrostatic force on a Curved Submerged surface

 

On a curved submerged surface as shown in Fig. L-9.3, the direction of the hydrostatic pressure being normal to the surface varies from point to point. Consider an elementary area in the curved submerged surface in a fluid at rest. The pressure force acting on the element is

 
       

                                 

The total hydrostatic force can be computed as

                                  

   
Fig. L-9.3: Hydrostatic force on a curved surface

Note that since the direction of the pressure varies along the curved surface, we cannot integrate the above integral as it was carried out in the previous section. The force vector is expressed in terms of its scalar components as

                           

in which represent the scalar components of F in the x , y and z directions respectively.

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