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 P = γ Ay sin θ = pA , where γ is the specific weight of the liquid and p 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 x_p = I_xy/Ay and y_p + = I_x/Ay, where I_xy = ∫ xy dA (see Sec. 9.8). Show also that the difference of ordinates y_p−y is equal to kx²′_x /y and thus depends upon the depth at which the area is submerged.