Force exerted on curved plate - Ishwaranand

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Force exerted on curved plate

Force exerted by a jet on a fixed curved plate

Jet strikes the curved plate at the centre
  • Sign a jet of water strikes a fixed curved plate at the middle as shown in Fig. 
  • Some jet after striking the plate comes out with the identical velocity if the plate is smooth and there is never a loss of energy due to impact of the jet, into the tangential direction of the curved plate. 
  • This velocity at the outlet of the plate can be resolved within two components, one in the direction of jet also other perpendiculars over the direction of the jet.
  • Component of velocity in the direction of jet = -v cosθ. 
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Fig. Jet striking a fixed curved plate at the centre 

(-ve sign is taken as the velocity at an outlet is in the opposite direction of the jet of water coming out from nozzle). 

Force exerted on the jet into the direction of jet, 

@ Fx = Mass per secx (Vx1 - Vx2) 
where,
Vx2 = Final velocity in the direction of jet = - v cosθ 
Fx = ρav {v - (-v cosθ)}
= ρav (v + v cosθ)
= ρav^2 (1 + cosθ)

@ Fy = Mass per secx (Vy1 - Vy2)
where,
Vy1 = Initial velocity into the direction of y = 0
Vy2 = Final velocity into the direction of y = v sinθ 
Fy = ρav [0 – vsinθ] 
= ρav^2 sinθ 

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