Show that the resultant of the hydrostatic forces acting on a sub­merged plane area A is a...

Show that the resultant of the hydrostatic forces acting on a sub­merged plane area A is a force P perpendicular to the area and of magnitude , where  is the specific weight of the liquid and  is the pressure at the centroid C of the area. Show that P is applied at a point CP, called the center of pressure, whose coordinates are (see Sec. 9.8). Show also that the difference of ordinates is equal to and thus depends upon the depth at which the area is submerged.