Show that the system of hydrostatic forces acting on a submerged plane area A can be reduced to a force P at the centroid C of the area and two couples. The force P is perpendicular to the area and is of magnitude P = γ Ay sin θ, where γ is the specific weight of the liquid, and the couples are Mx′ = (γ Ix′ sin θ)i and My′=(γ Ix′y′ sin θ)j, where Ix′y′ = ∫ x′y′ dA (see Sec. 9.8). Note that the couples are independent of the depth at which the area is submerged.

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A' M, y'