Power from Wind Problems

It has been a little while since I posted anything in the Cute Problems category so since today is quite a windy day I thought I’d give you this one, which leads to an extimate of the maximum power that can, in theory, be extracted from wind a windmill.

Assume that the wind far upstream and down-stream of the windmill has speed V and αV respectively, with 0≤α≤1, and let the wind speed at the sails of the windmill, which sweep out an area A, be v.

Now for the problems

(i) By equating the power absorbed by the mill to the rate of loss of kinetic energy of the wind, show that v/V=½(1+α).

(ii) Show that the power obtainable is proportional to AρV3 where ρ is the density of air.

(iii)  Show that the maximum power that can be extracted is 16/27 of the power available initially in the wind.

The final result is known as Betz’s Law and it works for any form of turbine, not just a windmill.

 

 

 

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: