Note that the direction of is normal to the surface area and the negative sign shows that the pressure force acts against the surface. The total hydrostatic force on the surface can be computed by integrating the infinitesimal forces over the entire surface area.

                               
If h is the depth of the element, from the horizontal free surface as given in Equation (L2.9) becomes

                                                                 L-9.1

If the fluid density is constant and P 0 is the atmospheric pressure at the free surface, integration of the above equation can be carried out to determine the pressure at the element as given below

                                                              L-9.2