A rectangular gate of dimensions 5m ** 1.5m is hinged at its base and inclined at `60^0` with 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 height of water at which gate begins to fall. Neglect weight of gate and frictional effects at 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`