The rotor blades of a wind turbine have a disc diameter of 20 m. If the wind speed is 10 m/s, calculate the theoretical maximum power that can be extracted by the turbine. What is the Betz limit? Explain the difference between this power and the Betz limit. Density of air = 1.225 kg/m3.

A wind turbine converts some of the kinetic energy of the wind intoelectric energy. Suppose that the blades of a small wind turbinehave length L = 3.7 m.

(a) When a 11 m/s (24.607 mi/h) wind blows head-on, what volume ofair (in m3) passes through the circular area swept out by theblades in 1.0 s?

(c) What is the translational kinetic energy of this mass ofair?

(d) If the turbine can convert 43% of this kinetic energy intoelectric energy, what is its electric power output?

(e) What happens to the power output if the wind speed decreases to1/2 of its initial value?

What maximum output would you expect from a wind turbine with a blade of diameter 20ft in a 15-mph wind?

Modern wind turbines are larger than they appear, and despite their apparently lazy motion, the speed of the blades tips can be quite high-many times higher than the wind speed. A typical modern turbine has blades 56 m long that spin at 13 rpm. At the tip of a blade, what are

(a) the speed and

(b) the centripetal acceleration?