Available Wind Energy Calculation

[keith0101]

TL;DR

Why we take area of disc, instead of area of ambient air in the assumption of mass flow rate when calculating the available wind energy? Isn't it a contradiction to conservation of mass?

For the avaliable power to be harvested in free-streaming wind:
P=1/2QU^2_infinite (Q: mass flow rate, U_infinite: velocity of free-streaming wind)
And
Q is defined as: p x U_infinite x A_d. (p: density of air, A_d: Area of disc)

I cannot understand the reason of taking the area of disc, A_d, instead of area of ambient air, A_infinite, in the assumption of Q, since under the conservation of mass:
p*U_infinite*A_infinite = p*U_d*A_d = p*U_w*A_w

 

[berkeman]

Welcome to PF, Keith.

here in the 2nd slide

What 2nd slide? What presentation? Please always provide links to your source material when posting on PF (and to avoid copyright violations). Thanks.

 

[keith0101]

Hi,

For 2nd slide I mean the equation of avalible power in wind, which is:
P=1/2QU^2_infinite (Q: mass flow rate, U_infinite: velocity of free-streaming wind)
And
Q is defined as: p x U_infinite x A_d. (p: density of air, A_d: Area of disc)

I cannot understand the reason of taking the area of disc, A_d, instead of area of ambient air, A_infinite, in the assumption of Q, since under the conservation of mass:
p*U_infinite*A_infinite = p*U_d*A_d = p*U_w*A_w

 

[berkeman]

Please post links to your sources for that material, Keith, or your post will be deleted for a copyright violation.

UPDATE - it appears that the OP's solution was to delete the attachments...

 

[cjl]

You use disk area because the only air you can harvest is that which flows through the disk. Yes, there's much more total air power, but you don't care about the air flowing around the disk, you only care about the air that you could theoretically capture.