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A Jet of water strikes on series of cup shaped vanes which defects through 165degree If the velocity of jet is that corresponding to head of 40 m & velocity of vanes is such that efficiency is maximum. Find the work done on vane per kg of water?
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A Jet of water strikes on series of cup shaped vanes which defects thr...
Analysis of Work Done on Vane per kg of Water

Given Data:
- Deflection angle of vanes: 165 degrees
- Velocity of jet: corresponding to a head of 40 m
- Maximum efficiency condition for vanes

Calculations:
- Efficiency of the vane, η = (Actual work done on the vane) / (Work done by the jet)
- Maximum efficiency occurs when the kinetic energy of water leaving the vane is minimum
- Therefore, the velocity of vanes should be equal to the velocity of water leaving the vane

Work done on the vane per kg of water:
- Work done on the vane = Change in kinetic energy of water
- Change in kinetic energy = (Initial kinetic energy) - (Final kinetic energy)
- Since the vane velocity is equal to the water velocity, the change in kinetic energy is zero
- Therefore, the work done on the vane per kg of water is zero

Conclusion:
- In this case, when the efficiency of the vane is maximized by adjusting the vane velocity to be equal to the water velocity, the work done on the vane per kg of water is zero. This implies that all the kinetic energy of the water jet is transferred to the vane without any work being done.
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A Jet of water strikes on series of cup shaped vanes which defects through 165degree If the velocity of jet is that corresponding to head of 40 m & velocity of vanes is such that efficiency is maximum. Find the work done on vane per kg of water?
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