Force Exerted on Hinged Plate

Force exerted on the jet toward a hinged plate

• Think a jet of water striking a vertical plate at 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.

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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. 

• That dotted lines show the position of the plate before the jet strikes the plate. 
• The 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 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)