Betz's law

Schematic of fluid flow through a disk-shaped actuator. For a constant-density fluid, cross-sectional area varies inversely with speed.

In aerodynamics, Betz's law indicates 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.[1] 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 wind turbine of any mechanism 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 75–80% of the Betz limit.[2][3]

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.

  1. ^ Betz, A. (1966) Introduction to the Theory of Flow Machines. (D. G. Randall, Trans.) Oxford: Pergamon Press.
  2. ^ Cite error: The named reference Enercon was invoked but never defined (see the help page).
  3. ^ Tony Burton et al., (ed), Wind Energy Handbook, John Wiley and Sons 2001, ISBN 0471489972, page 65.