Show that the system of hydrostatic forces acting on a submerged plane area A can be

Chapter 9, Problem 9.65

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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 sin , Ay = where is the specific weight of the liquid, and the couples are ( sin ) xx I = Mi and ( sin ) , y x y I = Mj where xyI x y dA = (see section 9.8). Note that the couples are independent of the depth at which the area is submerged.

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