Hydrostatic Forces on Submerged Plane Surfaces

Abstract

A fluid at rest in contact with a surface exerts only a normal force per unit area, called pressure. The pressure is isotropic (at a given point it is the same regardless of the orientation of the infinitesimal surface containing the point and on which it is evaluated) and once the pressure field has been determined, it is possible to calculate the total force acting on a surface of finite dimensions. For planar surfaces the analysis is simplified because the direction of the hydrostatic force is normal to the surface, and the force always enters the surface. The magnitude of the force can be calculated by integration and, only for homogeneous fluids, also as a product of the pressure in the centroid of the surface and the surface area. The force is applied to the pressure centre, which generally differs from the centroid of the surface, and which can be calculated by imposing the equivalence of the moments of the force and the vectorial sum of the elementary moments of the elementary forces. Pressure centre is always below the centroid, with respect to the water line, except for horizontal surfaces.