A rectangular sluice door Fig below is hinged at the top A a

A rectangular sluice door (Fig below) is hinged at the top A and kept closed by a weight fixed to the door. The door is 120 cm wide and 90 cm deep, and the center of gravity of the complete door and the weight is at 0, the combined weight being 9810 N. Find the height of water, h, on the inside of the door which will just cause the door to open.

Solution

the door opens when torque due to weight = torque due to water

torque due to water = d x g x (h -0.9 sin 60 /2 )

= 1000 x 9.8 x ( h - 0.39)

9810 x 0.3 = 9800(h - 0.39)

h = 0.69m = 69 cm