Discussion
The power obtained from a horizontal wind turbine operating at maximum efficiency is proportional to its diameter (D) as
Answer: B
The power obtained from a horizontal wind turbine at maximum efficiency is proportional to the square of its diameter, option B. The power in the wind passing through the rotor is proportional to the swept area, and the area is proportional to the square of the diameter.
\[ P = \tfrac{1}{2}\,\rho A v^{3} C_{p} \]
\[ A = \frac{\pi D^{2}}{4} \Rightarrow P \propto D^{2} \]
Option A, a linear dependence, and option C, the power of three halves, do not follow from the formula. Option D, the square root, is the inverse relation. At maximum efficiency the coefficient is the Betz limit, a constant, and so does not change the dependence on diameter.
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