Question. In the system shown below, the force exerted by the free jet issuing from the sharp-edged circular nozzle and impinging on the small circular plate is just su±cient to keep the (iscoceles) triangular door closed against the water pressure. The depth of the water in the tank is kept fixed by using top-up water. The mass of the arm, the circular plate and door are negligible. The door and the plate are each rigidly fixed to the arm, through their centroids.

Neglect friction in both the water flow and the pivot, and take ½ ¼ 1000 kg/m3 the density of water, and g ¼ 9:81m/s2 the acceleration due to gravity. Give full details of your assumptions, symbolic working and numerical calculations.

(a) Neglecting fluid motion (you can use results from Qu. 1) find (i) the horizontal hydrostatic force FN acting on the door, and (ii) the line of action of the hydrostatic force.

(b) Using Bernoulli's equation find the jet speed VJ .

(c) Draw a control volume focussed only on the circular plate, and analyze the linear momentum equation to find the horizontal hydrodynamic force FR acting on the plate in terms of nozzle diameter d.

(d) Finally, use moments to find the value of the diameter d.