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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# [Physics] Why is there no upper-bound on power-efficiency of Hydro-turbines

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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?

## Best Answer

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.