Power windmills turn in response to the force of high-speed drag. For a sphere m

Question

Power windmills turn in response to the force of high-speed drag. For a sphere moving through a fluid, the resistive force, FR is pro- portional to r2v2, where r is the radius of the sphere and v is the fluid speed. The power developed, P = FR v, is proportional to r2v3. The power developed by a windmill can be expressed as P = d r2 v3, where r is the windmill radius, v is the wind speed, and d = 4.72 Ws3/m5 . For comparison, a typical home needs about 3.0 kW of electric power. Note: This representation ignores system efficiency, which is about 25%. For a home windmill with a radius of 1.68 m, calculate the power delivered to the generator if the wind velocity is 12.2 m/s . Answer in units of W

Explanation / Answer

P = 4.72*1.68^2*12.2^3=24190 W

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