A horizontal-axis wind turbine must deliver 2 kW shaft power at 7 m/s wind speed. Power coefficient is .36,drivetrain efficiency .90,and air density $1.225\,\mathrm{kg/m^3}$. Ignore other losses and use π=3.14. If rotor diameter is X m and shaft power at 6 m/s is Y kW, choose the nearest pair.
Use $P=\tfrac12\rho A v^3C_p\eta$. Required area is $A=2000/[0.5(1.225)(7^3)(.36)(.90)]\approx29.38$ m². Thus $D=\sqrt{4A/3.14}\approx6.12$ m. With unchanged coefficients, power scales as speed cubed:$P_6=2(6/7)^3=1.2595$ kW, nearest 1.28 kW. Hence **A**.
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