Question by BishopSherry:
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?


——————————————

Answer by Steve W
The question is written to grant for a rather easy 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 compute 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 is the challenge of wind energy.

——————————————
Add your own answer in the comments!

Related posts:

  1. HOW MUCH MONEY WOULD AN AVERAGE WIND TURBINE SAVE ON A $240 ENERGY BILL ON AN AVERAGE $31 DAY MONTH?
  2. HOW TO ESTIMATE THE ENERGY OF A WIND TURBINE?
  3. HOW DOES A WIND TURBINE CONVERT THE WIND INTO ENERGY WE CAN YOU USE?