A wind turbine with a diameter of 72 m produces an average of 2.04 MW at a certa

Question

A wind turbine with a diameter of 72 m produces an average of 2.04 MW at a certain location (with a particular wind speed distribution). If the diameter were increased to 112 m and all other factors remained constant, what would the power output be in MW? Enter the numerical value without units. All other factors being equal, the output of a turbine is proportional to the diameter squared, and the wind speed cubed. If the ratio of the new diameter to the original diameter were 'r', then the power would increase by x r^2.

Explanation / Answer

Output of turbine propertional to d2

So

P1/P2=d12/d22

So

P2=P1*d22/d12=2.04*(112)2/(72)2=4.9363 MW

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