Hydrostatic Pressure Force on a Plane Surface

Consider plane surfaces submerged in a fluid with a specific weight. Forces are developed on the surfaces because of the fluid.

The resultant of the forces developed on the horizontal surface is given by the product of pressure exerted by the fluid on the surface and the area of the surface acting through the centroid of the area.

The resultant of the forces on the vertical surface is given by the product of the specific weight of the fluid, the area of the vertical surface, and the depth of the centroid of the area from the fluid surface.

For an inclined submerged surface, the force acting on a small element is the product of the fluid's specific weight, the element's depth from the fluid surface, and its area.

Integrating the force acting on the patch gives the resultant of the pressure acting on the entire incline surface.

The resultant appears to be acting through the centroid, but it actually acts through the point below the centroid called the center of pressure.