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We have Betz's law, an upper bound on power efficiency, for wind-turbines. But there is no theoretical upper limit on hydro-turbines, Why this is so?

Is it mainly due to the incompressibility of water?

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Betz' limit arises from the fact that if the turbine tries to take too much energy out of the flow, the wind will divert and go around the turbine instead of through it. With a hydrothermal system the water is typically behind a dam, so the water has nowhere else to go. The turbines effectively convert gravitational potential energy into work, which can be done (in principle) without any thermodynamic losses.

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If we replace the wind-turbine in air with water-turbine inside the sea, and let the water be the driving force (just like air do with wind-turbine) then would the Betz' law hold same in water as in air ? –  kaka May 16 at 3:43
    
@kaka yes, indeed it would. I'm pretty sure there are some tidal power schemes that work like that, and Betz' law does apply in those cases. (I've been meaning to update my answer to say that, but I'm a bit busy at the moment.) –  Nathaniel May 16 at 13:03

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