A $$wind-powered$$ generator converts wind energy into electric energy. Assume that the generator converts afixed fraction of the wind energy intercepted by its blades into electric energy. For wind speed v, the electric power output will be proportional to

Question

A $$wind-powered$$ generator converts wind energy into electric energy. Assume that the generator converts afixed fraction of the wind energy intercepted by its blades into electric  energy. For wind speed v, the electric power output will be proportional to

Infinity Learn · Accepted Answer

The force F exerted by the wind on the blades of the generator is given $$byF=$$ρ$$Av2$$  where, ρ$$=$$ density of air  $$A=$$ area of $$cross-section$$ of blade  $$V=$$ velocity of wind  ∴  Power output, $$P=$$∫Fdv $$=$$∫ρ$$Av2dv=$$ρ$$Av3/3$$ ρ∝$$v3$$

A wind-powered generator converts wind energy into electric energy. Assume that the generator converts a
fixed fraction of the wind energy intercepted by its blades into electric energy. For wind speed v, the electric power output will be proportional to

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A wind-powered generator converts wind energy into electric energy. Assume that the generator converts afixed fraction of the wind energy intercepted by its blades into electric energy. For wind speed v, the electric power output will be proportional to

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A wind-powered generator converts wind energy into electric energy. Assume that the generator converts a
fixed fraction of the wind energy intercepted by its blades into electric energy. For wind speed v, the electric power output will be proportional to