How Does Bertz Law Calculate Wind Turbine Power?

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SUMMARY

The discussion focuses on calculating wind turbine power using Bertz's Law. The density of air is established at 1.2 kg/m³, and a wind speed of 10 m/s is used for calculations. The total wind power is calculated to be 600W, while the maximum extractable power, based on Bertz's limit, is determined to be 59% of the total wind power. The power coefficient of the wind turbine is specified as 0.46, which is essential for calculating the actual power extracted.

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Homework Statement



The density of air under normal conditions is about 1.2 kg/m^3. For a wind speed of 10 m/s find

a) the actual power carried by the wind

b) the maximum possible power (Bert'z limit) extractable by a wind turbine with a blade area of 10 m^2 and

c) the actual power extracted by a wind turbine with a blade area of 10 m^2 and a power coefficient of 0.46


Homework Equations



Maximum extractable wind power = 2a(1-a)^2pv^3

The maximum extractable power is 59%

Total wind power= 1/2pv^3


The Attempt at a Solution



A) total wind= 1/2 (1.2 kg/m^3)(10m/s)^3
= 600W

B) I would use the formula 2a(1-a)^2pv^3

but how do I know what a is?

I'm not sure if I did part a right and am confused on part b
 
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Can someone please help me with part B?
 

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