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## 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 at O.
• Due to the force exercised by the jet toward the plate, that plate will swing through some angle on the hinge.
 Image Source ~ Crafted With ©Ishwaranand – 2020 ~ Image by ©Ishwaranand
Fig. Force on a hinged plate
Let,
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
where,
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)

Last updated on Tuesday - May 30th, 2023

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