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  1. The question is written to allow for a rather simple solution, unlike the challenges of real wind turbine power and energy estimation.

    Energy = Power x Time

    Electric power produced = conversion efficiency x gross wind power

    Gross wind power = power density x turbine swept area

    So, with all the equations at hand, we can solve the problem.

    Turbine swept area = 2 x pi x (25 m)^2 = 3927 m^2
    Wind power density = 500 W/m^2

    Thus, Gross wind power = 500 W/m^2 x 3927 m^2 = 1.9635 x10^6 W = 1.9635 MW

    Electric power produced = 0.25 * 1.9635 MW = 0.49087 MW

    Since the problem identifies the wind power as long-term average, we can calculate the average energy produced in a year.

    Energy (Joules) = Watts x seconds
    Energy = 0.49087 MW x 31536000 s = 15.487 x10^6 MJ
    But the question asked for energy measured in kilowatt-hours (kWh).

    So, Energy = 490.87 kW * 8760 h = 4300100 kWh produced in 1 year.

    Unfortunately, a real wind turbine would produce this energy in an unscheduleable manner, typically peaking when the demand (load) is lowest. That’s the challenge of wind energy.

How much electrical energy (in kWh) can the wind turbine generate in a year?

Assume a wind turbine with a hub 50.0 m above the ground, a rotor diameter of 50.0 m, and a wind-power conversion efficiency of 25%. The turbine operates in an area with an average wind-power density of 500 watts/m2 at 50 m altitude. How much electrical energy (in kWh) can the wind turbine generate in a year?