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Betz's law
Betz's law calculates the maximum power that can be extracted from the wind, independent of the design of a wind turbine in open flow. It was published in 1919, by the German physicist Albert Betz.〔Betz, A. (1966) ''Introduction to the Theory of Flow Machines.'' (D. G. Randall, Trans.) Oxford: Pergamon Press.〕 The law is derived from the principles of conservation of mass and momentum of the air stream flowing through an idealized "actuator disk" that extracts energy from the wind stream. According to Betz's law, no turbine can capture more than 16/27 (59.3%) of the kinetic energy in wind. The factor 16/27 (0.593) is known as Betz's coefficient. Practical utility-scale wind turbines achieve at peak 75% to 80% of the Betz limit.〔〔Tony Burton et al., (ed), ''Wind Energy Handbook'', John Wiley and Sons 2001 ISBN 0471489972 page 65〕
The Betz limit is based on an open disk actuator. If a diffuser is used to collect additional wind flow and direct it through the turbine, more energy can be extracted, but the limit still applies to the cross-section of the entire structure.〔Burton et. al, ''Wind Energy Handbook'', chapter 5 ''Shrouded Turbines''〕
==Concepts==
Betz' Law applies to all Newtonian fluids, but this article will use wind as an example. Consider that if all of the energy coming from wind movement through a turbine was extracted as useful energy the wind speed afterwards would drop to zero. If the wind stopped moving at the exit of the turbine, then no more fresh wind could get in - it would be blocked. In order to keep the wind moving through the turbine there has to be some wind movement, however small, on the other side with a wind speed greater than zero. Betz' law shows that as air flows through a certain area, and when it slows from losing energy to extraction from a turbine, it must spread out to a wider area. As a result geometry limits any turbine efficiency to 59.3%.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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