Question

Jet of water enters and leaves a moving curved vane tangentially the force of jet along normal to vane is

Answer 1

Answer:

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Answer 2

Force of the jet along normal to vane is $F{x}$ = 2 ρ a $(V-U)^{2}$Cos θ

• Consider a jet of water entering a symmetrical moving curved vane at its one end tangentially
• Let us assume the following data from the above figure.
• V = Velocity of jet
• U = Velocity of vanes
• So, relative velocity = ( V-U)
• θ = Angle made by jet with the x-axis at the inlet and outlet tip of the curved plate
• Assume a frictionless plate so that the velocity at the entry and exit are the same
• Force exerted in the x-direction by the water jet
• $F_{x}$ = Mass per second  x   [$V_{1x}$  – $V_{2x}$ ]
• mass per second = ρ a (V-U)
• Where,
• $V_{1x}$ = Initial velocity in the x direction = (V-U) Cos θ
• $V_{2x}$ = Final velocity in the x direction = -( V-U) Cos θ
• $F{x}$ = ρ a (V-U) x [(V-U) Cos θ -{- (V-U) Cos θ}]
• $F{x}$ = 2 ρ a $(V-U)^{2}$Cos θ