Hydrostatic

2.2.0    Hydrostatic Forces:

2.2.1 Hydrostatic forces on plane surfaces:

            The center of mass also called the “center of gravity” (CG), is a point in space or inside the body (Fig) where the weight of a body acts as if it were concentrated there.

  v Center of Pressure:

   For inclined surfaces the “point of action for hydrostatic force” is not the centroid, but a point called   “pressure center” (PC) which is ALWAYS shifted towards the high pressure area (with respect to the   centroid). Consider a plate of arbitrary shape completely submerged in a liquid, as shown below. The   centroid of the plate is shown by CG, which is chosen to be the origin of the coordinate system on the     surface.

The position of center of pressure on the surface can be calculated from,

   v Gage pressure formulas:

        Most of the time the atmospheric pressure P_atm is neglected, because of its equal acts on both sides of the plate. In this case, according to Eq. Pressure is  

2.2.2 Hydrostatic forces on curved surfaces:

            Consider an arbitrary curved surface as shown in Fig. For the comparison sake, a flat surface is shown as well. Free-body diagrams of the surfaces and column of the fluid above the surfaces are shown.

The difficulty of the force calculation on a curved surface is rooted in its geometry, i.e., finding its centroid (center of gravity) and center of pressure.

         The horizontal force, F_H equals the force on the plane area formed by the projection of the curved surface onto a vertical plane normal to the component.

                   The vertical force, F_V equals to the weight of the entire column of fluid, both liquid and                   atmospheric, above the curved surface. For the shown surface.