Hydrostatische drukkracht op een gebogen oppervlak

Consider a swimming pool with a fluid of a known specific weight having a curved surface at the bottom.

If the volume around the curved surface is isolated with a horizontal and vertical plane along a unit length, the horizontal plane surface and the vertical plane surface will experience forces perpendicular to their planes due to the fluid.

The self-weight of the fluid in the enclosed volume is the product of the fluid's specific weight and the volume of the enclosed space, acting through the center of gravity of the volume.

The force components exerted by the curved surface on the fluid, in both horizontal and vertical directions, can be expressed through the forces developed on the horizontal and vertical planes, along with the self-weight of the fluid in the isolated volume.

Finally, the hydrostatic force acting on the curved surface is given by the square root of the sum of the squares of the force components exerted by the curved surface of the swimming pool on the fluid.