Force Exerted on Hinged Plate - Ishwaranand

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Force Exerted on Hinged Plate

Force exerted on the jet toward a hinged plate

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Fig. Force on a hinged plate 
Let,
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) 
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
ρav^2 x x = W x x x sinθ 
sinθ = (pav^2/W)

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