Question about Betz limit

Wind & Water General
1

Hi guys,

I just started to learn betz’s law and wanna ask a question about it.
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In betz’s law, the “1/2rhoAtUu^3" is regarded as wind power input, but why don’t we use "1/2rhoAuUu^3” instead? I suppose this is the real wind power input at the very beginning.

Thanks a lot for your comments in advance.

Yanda

2

Dear Yanda,

It is common practice to use the swept area of the rotor (A_t) as the reference in the Betz limit because if the rotor was absent, the flow would not slow down and would pass through that area unaffected. The area A_u is smaller than swept area because the wind slows down due to the presence of the rotor and is not known apriori, but can be solved as part of the solution of momentum equations.

Best regards,

3

Thx Jason. Great clarification. I appreciate your help.

Best regards,
Yanda