Betz' Law
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Betz' Law

from Wikipedia

Betz' law is a theory about the maximum possible energy to be derived from a wind turbine. It was developed in 1919 by German physicist Albert Betz. According to the rule, no turbine can capture more than 59.3 percent of the potential energy in wind.

betz-law.pngCp
Where:
  • P = Power in Watts
  • p = Air Density in kg/m3
  • S = Turbine Area in m2
  • v1 = Wind Speed in m/s
  • Cp = Coefficient of performance = 0.593 or 59.3%
Assumptions
  1. The rotor does not possess a hub, this is an ideal rotor, with an infinite number of blades which have 0 drag. Any resulting drag would only lower this idealized value.
  2. The flow into and out of the rotor is axial. This is a control volume analysis, and to construct a solution the control volume must contain all flow going in and out, failure to account for that flow would violate the conservation equations.
  3. This is incompressible flow. The density remains constant, and there is no heat transfer from the rotor to the flow or vice versa.
DescriptionValue
Betz' Efficiency Percentage59.3%
Blades Diameterm
Air Speedm/s
Density of Airkg/m3
Air Temperature oC