Wind power; it transforms the kinetic energy of wind into electrical energy. According to Newton’s law of “conservation of mass and energy” the sum of the energy entering a system is equal to the sum of the output energy. Not all winds coming into kinetic energy in the wind turbine. According to this situation, in 1926, Albert Betz`s found theoretically how much kinetic energy we can convert the power of wind into the following equation.

The kinetic energy of this moving mass can be extracted from the power relation expressed by Equation (1):

…… (1)

It is the mass flow of air expressed by and is shown as in (2);

……. (2)

If equation (2) is substituted in equation (1):

…….. (3)

As can be seen, power is directly proportional to the cube of speed.

The power generated in the wind turbine is proportional to the difference between the input (Vi) and output (Vo) speeds. This average speed is:

……… (4)

Then the mass flow of air is as follows:

………. (5)

Given all the above equations:

……… (6)

If equation (6) is arranged:

…….(7)

According to Vo max. min. points are found:

As a result, equation (8) emerges:

…….. (8)

If the found result is substituted in equation (7): it is seen that its value is 0.59.

The components that make up the first part in equation (7) are expressed as the power factor.

………… (9)

the expressed power factor equation is replaced by 7;

…………(10)

the maximum power that can be produced from a turbine;

As a result, the max. power only equals 0.59 of incoming energy.

## Assumptions on which Betz law is based:

-the wind is steady and constantly strong according to altitude

– air compressibility is not considered (density is assumed to be constant)

-the top and bottom pressure is equal to atmospheric pressure

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