Calculadora de Peso de Aço
Calcule o peso de perfis e chapas de aço para projetos estruturais.
Turbine Power Output
630.5 kW
Turbine Power Output vs Wind Speed
Formula
Wind Turbine Power
Wind power depends on the cube of wind speed and the swept area of the rotor.
Formula
P_available = 0.5 rho A V^3 (total wind power)
P_output = 0.5 rho A V^3 Cp (extracted power)
where rho is air density, A is the swept area (pi D^2/4), V is wind speed, and Cp is the power coefficient. The Betz limit states maximum Cp = 16/27 = 59.3%. Practical turbines achieve 35-45%.
Exemplo Resolvido
An 80 m rotor diameter turbine in 8 m/s wind, Cp = 0.40.
- 01Swept area = pi x 40^2 = 5,027 m^2
- 02Available power = 0.5 x 1.225 x 5027 x 8^3 = 0.5 x 1.225 x 5027 x 512
- 03Available = 1,576,461 W = 1,576 kW
- 04Output = 1,576 x 0.40 = 630.6 kW
Perguntas Frequentes
Why does power depend on wind speed cubed?
The kinetic energy in wind is 0.5 m v^2. The mass flow rate through the rotor is rho A v. Power = energy x flow rate = 0.5 rho A v^3. So doubling wind speed increases power 8-fold. This is why site selection (average wind speed) is critical.
What is the Betz limit?
Albert Betz proved in 1919 that no turbine can extract more than 59.3% of the kinetic energy in the wind. This is because the wind must continue flowing downstream; extracting all energy would require stopping the wind entirely.
What wind speed is needed for viable wind power?
Annual average wind speed above 5-6 m/s is generally required for economic viability. Most utility-scale turbines are rated for 10-15 m/s wind and cut in at 3-4 m/s.
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