A gate supporting water takes form of an inclined shield which swings around a hinged axis O as shown in figure.Determine:

• The position x of hinge at which a water level of h = 5.1 m on left would cause gate to tip over hinge.
• The magnitude of hydrostatic free on gate just before it opens (tips about hinge) automatically

Neglect frictional effects.

SOLUTION:

The gate would tip about the hinge point O when the line of action of the resultant pressure force lies from O to B anywhere on the gate; the limiting condition being the situation when the resultant force passes through the hinged point O. Hence for the given condition point O becomes the centre of pressure.

SOLUTION:

The gate would tip about the hinge point O when the line of action of the resultant pressure force lies from O to B anywhere on the gate; the limiting condition being the situation when the resultant force passes through the hinged point O. Hence for the given condition point O becomes the centre of pressure.

The resultant also passes through the centroid of the pressure diagram, and the centroid lies at a distance `1/3** (AB) ` from the bottom point A.

Thus,

`x=â??*(AB)`

or, `AB=3*x`... (i)

Also,

`h=AB*sin45`

or,`h=3*x*sin45`

or,`h=2.4 m`

Now, the hydrostatic pressure force P is,

P = area of pressure diagram ** width of gate.

Assuming unit width of the gate,

`P=(1/2 *AB*wh*h)*1`

`=180.11 KN`