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Q9. (a) Show that the position of the centre of pressure for a rectangular plane, with its edge in surface, is two thirds of the depth of the plane below the surface.  (3)

(b) A dock gate 12 m wide and 8 m has river water of density 1008 kg/m3 on one side to a depth of 3 m and sea water of 1025 kg/m³ on the other side to a depth of 5 m.

Calculate EACH Of the following:

(i) the resultant load; (6)

(ii) the position of the centre of pressure. (4)

(c) The depth of on the river water side of the gate is increased until the load on each side of the gate is equal. Calculate this new depth of water of river water. (3)