Betz Limit Applied to hydro turbine?

[rmm5]

Just wondering if the Betz limit is applicable to hydro turbines or if there is some analogous limit for hydro turbines?

 

[Bob S]

This article claims that water turbines can exceed the Betz limit (for windmills) with the proper venturi.
http://www.freeenergynews.com/Direc...Technical_Report_on_Davidson-Hill_turbine.pdf
I can also see that a penstock with a large elevation drop will also exceed the Betz limit (about 60% for HAWT wind turbines). As a matter of fact, the pumped water storage system at Ludington, Michigan has about a 80% round trip efficiency. See
http://en.wikipedia.org/wiki/Ludington_Pumped_Storage_Power_Plant
Bob S

 

[Franco_v]

The Betz limit commonly applies to wind turbines and to underwater turbines which are made to turn by the bulk movement of water (e.g. tidal power). This theoretical efficiency limit is around 60%, where at most 60% of the wind (or water) kinetic energy is converted to mechanical energy in the rotor.

Hydro turbines are different, in that they use gravitational potential energy of falling water to turn turbines. The physics is different in that the water is channeled into the turbine, but for a wind turbine you have the blades spinning in open air, or in the case of an underwater turbine, open water. This is why hydro turbines (in particular Francis turbines), can reach higher efficiencies, more than 85%.

That's the word explanation. I'm sure there's a more rigorous mathematical way of proving it, but off the top of my head I don't know of one.

Just wondering if the Betz limit is applicable to hydro turbines or if there is some analogous limit for hydro turbines?

 

[rmm5]

Thanks for the info.