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Water from a stream is falling on the bl...

Water from a stream is falling on the blades of a turbine at the rate of `100 kg//s`. If the height of the stram is 100 m, then power delivered to turbine is

A

`1.0 ms^(-1)`

B

`1.4 ms^(-1)`

C

`140 ms^(-1)`

D

`10 ms^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
B
As water falls from a tap, the velocity of water goes on increasing hence from the equation of continuity, the cross section of water-stream goes on decreasing. If `A_(0)`=area of cross-section of the mouth of the tap and `v_(0)` is the velocity of water at this point, and A, v are corresponding quantities at depth h, then
`A_(0)v_(0)=Av=V` (volume rate of flow)
and `v_(2)-v_(0)^(2)=2gh`
`v=A_(0)Asqrt((2gh)/(A_(0)^(2)-A^(2)))=4xx1sqrt((2xx10xx2)/(16-1))`
`=8sqrt((2)/(3))ms^(-1)=6.5 ms^(-1)`
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