A rectangular gate of dimensions 5m ** 1.5m is hinged at its base and inclined at `60^0` with the horizontal. The gate is kept in stable position by hanging 50 KN weight at its upper end through a pulley system as shown in figure. Find the height of the water at which the gate begins to fall. Neglect the weight of the gate and the frictional effects at the hinge and pulley.

SOLUTION:

Here, the  pressure intensity varies from zero at point D to `wh` at the hinge point A.

Plotting the pressure diagram,

SOLUTION:

Here, the  pressure intensity varies from zero at point D to `wh` at the hinge point A.

Plotting the pressure diagram,

Now, the side AD of the pressure diagram is,

`AD=h/(sin60)=1.1547h`

Now the total hydrostatic force on the gate is,

F= (area of pressure diagram ) ** width of gate

`F=(1/2**1.1547h**wh)**1.5`

`F=0.866 wh^2`

This force acts at point C, which is at a distance,

`AC=(AD)/3`

`=(1.1547h)/3`

or,`AC=0.3849 h` from point A.

Now, Taking the moments about the hinge point A, we get,

`50**10^3**5=0.866wh^2**0.3849h`

or,`h=4.244 m`