I am not very familiar with particular calculations related to the applications of wind for producing energy. However some general features of the relation can be formulated without the particular knowledge.

1. The wind as a moving matter takes some kinetic energy with density \rho_e = \pho_m*v^2 / 2 where rho_m is the mass density (say in kg/m^3) and v is the speed (in m/sec) which gives the result in Joule/m^3.

2. Its power can be exploited only in account of loosing its energy: the more effective is the transition of the energy from the air into the engine using this energy, the more is the power obtained from the wind by the appliance. For simple example, let us imagine, that the wind is caught into a pipe with cross-section say S [m^2] and that its energy is transfered to the engine in p percent. This means, that during 1 second the air flow is S*v [m^3/sec] which contains kinetic energy in amount

S*v*\rho_e = S*\rho_m*v^3/2 [J/sec = W]. Thus the power obtained by the engine is p*S*\rho_m*v^3/200 [W].

Possible error: the percentage depends on the velocity, usually decreses with increse of the speed.

3. In practical applications, say in sailing, the problem is not that simple. Let us stay at sailing: First, it is not simple to determine the equivalent cross section of the "pipe" of air cought by the boat, then counts only the relative speed of the wind i.e. difference between the speed of the wind and the boat, the effective cross section depends on the speeds and the current shape of the sail etc. Additionally, in a no-resistant motion, the difference between the speed would be low causing that almost no power will be exploited by the boat. That means for instance, that say a wind power-station will be supplied with a great power at the moment it starts, and decreasing until the resistance (caused by the load of the electrical network) balances the two powers.

4. Many details are omitted in this brief elementary physical introduction. Wouldn't it be useful to look at pages devoted to wind-power-stations "How does it work?" ? Perhaps this link is useful:

https://www.turbinegenerator.org/wind/how-wind-turbine-works/

Regards, Joachim

For more detailed information see e.g.

https://www.raeng.org.uk/publications/other/23-wind-turbine

http://mragheb.com/NPRE%20475%20Wind%20Power%20Systems/Wind%20Energy%20Conversion%20Theory%20Betz%20Equation..pdf

JoD

Dear Aqsa, for a wind turbine of cross section A you can use Betz' Law:

Power = 1/2 Cp rho A V3,

where rho = air (fluid) density, V = upstream velocity and Cp = power coefficient (which is computable using V and U = downstream velocity).

Gianluca

I'm not a mathematician or a physicist, but somewhere along the school I learned an equation; p = mv

where

p is momentum

m is mass

v is velocity (speed with direction)

Air does have mass. I hope that helps.

Dear Gianluca, Thanks for the name of the formula derived by me within the first answer (which I recognized later on when searching for sources with some deeper presentation of this Betz's Law). The real problem is how to find/calculate the efficiency and how to count the effective cross section. If there are some known relations, please share with the Followers. For instance, it would be very interesting to find the rules giving the value of a wind power station with given geometry of its blades. Since the efficiency is not a constant (it should be known that it decreases with increasing wind; seemingly due to greater losses caused by the possibility that the additional preasure kicks out from the active region more fluid; thus one can expect in the practical formulas the exponent 3 replaced by some smaller value).

Regards, Joachim