One Dimensional Momentum Theory and the Betz Limit for Maximum Power Production

In this lecture Prof. Jens N. Sørensen presents a derivation of the Betz limit, which gives the theoretical upper limit for the power production of a horizontal-axis wind turbine. The derivation is based on 1D momentum theory and shows that no more than 59.3% of the available power in the wind can be exploited in the rotor of a wind turbine.

[samtheman]

Prof Sorenson,

Thanks for a great derivation of the Betz limit. However, I am struggling to understand something - In the control volume analysis slide, in the axial momentum balance, you have a term -mout*U0 representing the axial momentum of the air going out of the domain, ie the red top far-field boundary. I am guessing that the velocity here is (U0, v, 0) where v is a small y component, without which mout =0.

Sam

[grahamflowers]

There is something wrong with Betz limit if kinetic energy in the wind is 1/2 mass or 50% then were can the other 0.926% come from regards Graham Flowers MEng