# Question about Betz limit

**URL:** <https://forums.nlr.gov/t/question-about-betz-limit/2023>\
**Category:** General\
**Created:** [April 16, 2019, 5:20pm UTC](https://forums.nlr.gov/t/question-about-betz-limit/2023 "2019-04-16T17:20:23Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![Yanda.Jiang](https://avatars.discourse-cdn.com/v4/letter/y/f17d59/32.png) [@Yanda.Jiang](https://forums.nlr.gov/u/Yanda.Jiang)\
**Post date:** [April 16, 2019, 5:20pm UTC](https://forums.nlr.gov/t/question-about-betz-limit/2023/1 "2019-04-16T17:20:23Z")

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Hi guys,

I just started to learn betz’s law and wanna ask a question about it.  
 ![Capture.PNG](https://europe1.discourse-cdn.com/nrel/original/2X/f/f29d2ebf752e7f55f7369ada58fa8141ed91cf85.png)

![Capture2.PNG](https://europe1.discourse-cdn.com/nrel/original/2X/4/403ca99def7491ff346406e37cfdd488dc76ee61.png)

In betz’s law, the “1/2_rho_At_Uu^3" is regarded as wind power input, but why don’t we use "1/2_rho_Au_Uu^3” instead? I suppose this is the real wind power input at the very beginning.

Thanks a lot for your comments in advance.

Yanda

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**Author:** ![Jason.Jonkman](https://dub1.discourse-cdn.com/nrel/user_avatar/forums.nlr.gov/jason.jonkman/32/3086_2.png) [@Jason.Jonkman](https://forums.nlr.gov/u/Jason.Jonkman)\
**Post date:** [April 16, 2019, 6:25pm UTC](https://forums.nlr.gov/t/question-about-betz-limit/2023/2 "2019-04-16T18:25:19Z")

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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,

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**Author:** ![Yanda.Jiang](https://avatars.discourse-cdn.com/v4/letter/y/f17d59/32.png) [@Yanda.Jiang](https://forums.nlr.gov/u/Yanda.Jiang)\
**Post date:** [April 16, 2019, 8:04pm UTC](https://forums.nlr.gov/t/question-about-betz-limit/2023/3 "2019-04-16T20:04:07Z")

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> [@Jason.Jonkman](#):
>
> 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,

Thx Jason. Great clarification. I appreciate your help.

Best regards,  
Yanda