A rectangular opening in a vertical face of a dam impounding water is closed by

Question

A rectangular opening in a vertical face of a dam impounding water is closed by a gate mounted on horizontal trunnions passing through its centre, as shown schematically in Figure Q2 below.
The height of the gate d is 1 m and its width b is 1.25 m. The top edge of the gate is at a depth h of 2 m.
The density of water is 1000 kg/m³ and the acceleration due to gravity is 9.81 m/s².

(a)    Determine the magnitude, direction and position of line of action of the water hydrostatic force acting on the gate.

(b)   Determine the magnitude and direction of the moment that is required to keep the gate closed.

Explanation / Answer

Thinks about force, and pressure. Pressure = F/A in fluids the formula for pressure is P = ro * g * h, where ro is the density of the liquid, g is graviational pull due to gravity, and h is the depth of the liquid at which we measure the pressure. Also be mindful that liquid pressure effects on all directions at a certain depth. So if you have the area over which this force acts (per se the door frame etc.) you can proceed easily from there.

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