Hydrostatic Pressure Force on a Plane Surface

When a plane surface is submerged in a fluid, hydrostatic forces develop on the surface due to the fluid's pressure. For horizontal surfaces, the pressure exerted by the fluid is uniform because the depth remains constant. The resultant force is determined by the pressure at the given depth multiplied by the area of the surface, and it acts through the centroid of the surface. For vertical surfaces, the pressure varies with depth, increasing as the distance from the fluid's free surface increases. The resultant force is calculated as the product of the fluid's specific weight, the area of the vertical surface, and the depth of the centroid from the fluid surface.

In the case of an inclined surface, the force acting on each small element of the surface is influenced by its depth and the fluid's specific weight. To find the total force, the contributions from all the surface elements are integrated. Though it may seem that the resultant force acts through the centroid of the surface, it actually acts through a point called the center of pressure, which is located below the centroid. This is the point where the total hydrostatic pressure can be considered to act.