How Does Bertz Law Calculate Wind Turbine Power?

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In summary, the conversation discusses the density of air and its relation to wind power calculations. It includes finding the actual and maximum possible power for a wind turbine with a blade area of 10 m^2 and a power coefficient of 0.46. The maximum extractable wind power is determined to be 59% and the total wind power is calculated using the formula 1/2pv^3. The formula 2a(1-a)^2pv^3 is mentioned for part B, but the value of a is unclear.
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courtneywetts
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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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  • #2
Can someone please help me with part B?
 

Related to How Does Bertz Law Calculate Wind Turbine Power?

1. What is Bertz Law?

Bertz Law is a mathematical formula used in the field of spectroscopy to describe the relationship between the concentration of a substance and the amount of light absorbed or transmitted by that substance.

2. How is Bertz Law written?

The equation for Bertz Law is A = εcl, where A represents absorbance, ε represents the molar absorptivity coefficient, c represents the concentration of the substance, and l represents the path length of the light through the substance.

3. What is the purpose of using Bertz Law in spectroscopy?

Bertz Law is used to determine the concentration of a substance in a solution by measuring the amount of light that is absorbed or transmitted by the substance. This allows scientists to quantitatively analyze the composition of a sample.

4. Can Bertz Law be used for all substances?

Bertz Law can only be used for substances that follow Beer-Lambert Law, meaning that the substance's concentration is directly proportional to its absorbance or transmittance of light. Additionally, the substance must have a known molar absorptivity coefficient.

5. How is Bertz Law applied in real-world situations?

Bertz Law is used in a variety of fields, such as chemistry, biology, and environmental science, to quantitatively analyze the composition of a sample. It is commonly used in drug testing, environmental monitoring, and chemical analysis in industries such as pharmaceuticals and food production.

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