Force Exerted on Hinged Plate
Force exerted on the jet toward a hinged plate
- Think of a jet of water striking a vertical plate in the middle which is hinged plate at O.
- Due to the force exercised by the jet toward the plate, that plate will swing through some angle on the hinge.
x = distance of the centre of a jet from hinge O,
θ = angle of swing about a hinge,
W = weight of plate acting at C.G. of the plate.
- The dotted lines show the position of the plate before the jet strikes the plate.
- Point A on the plate will be at A’ after the jet strikes the plate.
- The distance OA = OA’ = x.
- Let the weight of the plate is acting at A’.
- If the plate is in equilibrium after the jet strikes the plate, the moment of all the forces about the hinge must be zero.
- Two forces are acting on the plate. They are….!
Force due to a jet of water, normal to the plane,
Fn = ρav^2 sinθ1
θ1 = Angle between jet and plate
= (90o – θ)
Weight of plate, W
Moment of force Fn about hinge
= Fn x OB
= ρav^2 sin(90o – θ) x OB
= ρav^2 cosθ x OB
= pav^2 cosθ x (OA/cosθ)
= ρav^2 x OA
= ρav^2 x x
Moment of weight W about hinge
= W x O A’ sinθ
= W x x x sinθ
For equilibrium of the plate,
ρav^2 x x = W x x x sinθ
sinθ = (pav^2/W)