Question

A nozzle of 50mm diameter delivers a stream of water at 20 m/sec perpendicular to a plate that moves away from the jet at 5 m/sec, find 1) The force on the plate. 2) The work done and the efficiency of the jet

Answer 1

The amount of work done will be 2208.9 W and the efficiency is 28.12%.

We are given that:

• Diameter of nozzle = 50 mm
• Speed of water = 20 m/s
• Coefficient of friction (μ) = 5 m/s
• Solution:
• Let's calculate the force exerted on the plate:
• F = ρA [V - μ]^2
• F = 1000 x π/4 x 0.05^2 x 15^2
• F = 441.78 N

• Now the amount of work done will be

• W = F x μ
• W = 441.78 N x 5 m/s
• W = 2208.9 W

Thus the amount of work done will be 2208.9 W

• Now calculate the efficiency:

• η = work done per second/ k.E of jet per second
• K.E / sec = 1/2  ρAv^3 = 1/2 x 1000 x [π/4 x 0.05^2] x 20^3
• K.E/sec = 7853.986 N.m/s
• η =  2208.9 W / 7853.986 N.m/s = 0.2812 x 100
• η = 28.2%

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