A wind turbine with a rotor diameter of 40 m produces 90 kW of electrical power when the wind speed is 8 m? s?1. The density of air impinging on the turbine is 1.2 kg? m?3. What fraction of the kinetic energy of the wind impinging on the turbine is converted to electrical energy?
What will be an ideal response?
If we take a cylinder of 40 m diameter and wind speed of 8 m/s, then the volumetric flow rate of the air impinging on the turbine is 8 m/s? (40 m)2/4? ? = 10050 m3/s. The corresponding mass flow rate is
10050 m3/s? 1.2 kg/m3 = 12060 kg/s. The kinetic energy per unit mass is 
= 32 m2/s2 = 32 J/kg. Thus, the total kinetic energy per time is 12060 kg/s? 32 J/kg = 386000 J/s = 386 kW. The fraction of this converted to electrical power is 90/368 = 0.233. That is, 23.3% of the kinetic energy of the oncoming wind is captured.
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