Calculating Power Output of Wind Turbine

[JosephF]

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]

This link might be useful:
http://www.otherpower.com/windbasics1.html

 

[JosephF]

Thanks for the link.

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]

Thanks for the link.

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,

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.

 

[tyco05]

You have calculated your "swept area" incorrectly.

You have used the diameter, not the area.

Remember area of circle = pi*r^2