Question

derive the wind power equation starting the kinetic energy equation

Answer 1

Wind energy: The energy harnessed from the source of wind is referred to as wind energy.

Derivation of wind power equation:

The kinetic energy equation,

Ekin = 1/2 mv^2

The air mass m can be determined from the air density ρ and the air volume V,

m = ρv

We get,

Ekin(wind) = 1/2 v ρv^2

The volume can be given by,

ΔV = AvΔt

Then the wind power is,

Pwind = Ekin(wind) / Δt

Pwind = ΔVρv^2 / 2Δt

Pwind = ρAv^3 / 2

Ideal power coefficient is given by ,

Cp ≅ 59