# Wind power

## Homework Statement

1. A wind turbine with a swept diameter of 20m and an efficiency of extracting energy from the wind of 40% is subjected to an average wind speed of 10m/s.
(a) How much power might the turbine produce?

Please can some one point me to the right equation as everyone I can find includes cut-in speeds etc....

LowlyPion
Homework Helper
http://www.otherpower.com/windbasics1.html [Broken]

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P=0.5 * air density * swept area * wind velocity3

Taking air density as 1.23kg per cubic meter.

P=0.5 * 1.23 * 20 * 103

P=12,300Watts

40% efficent so output power is 4,920Watts.

Is this correct as the value seems quite high? Also there was no mention of air density in the question... Thanks,

LowlyPion
Homework Helper

P=0.5 * air density * swept area * wind velocity3

Taking air density as 1.23kg per cubic meter.

P=0.5 * 1.23 * 20 * 103

P=12,300Watts

40% efficent so output power is 4,920Watts.

Is this correct as the value seems quite high? Also there was no mention of air density in the question... Thanks,

Wikipedia said:
At sea level and 20 °C, air has a density of approximately 1.2 kg/m3.

They are after all 30 foot blades. That's a big area and a hefty chunk of air at 10m/s. I haven't calculated it out, but you would expect power in the kilowatts I would think.

You have calculated your "swept area" incorrectly.

You have used the diameter, not the area.

Remember area of circle = pi*r^2