# Wind Energy Formula

Wind energy is a kind of solar energy. Wind energy describes the process by which wind is used to produce electricity. The wind turbines convert the kinetic energy present in the wind to mechanical power.

Wind energy is a renewable source of energy that determines the total power in the wind. The wind turbines which convert kinetic energy to mechanical power, wherein the mechanical power is converted into electricity which acts as a useful source.

The wind energy formula is given by,

$P=\frac{1}{2}\rho AV^{3}$

Where,

P = power,

ρ = air density,

A = swept area of blades given by $A=\pi r^{2}$

V = velocity of the wind.

Example 1

Determine the power in the wind if the wind speed is 20 m/s and blade length is 50 m.

Solution:

Given:

Wind speed v = 20 m/s,

Blade length l = 50 m,

Air density ρ = 1.23 kg/m.

The area is given by, $A=\pi r^{2}$

A = π × 2500

= 7850 m

The wind power formula is given as,

$P=\frac{1}{2}\rho AV^{3}$

$P=\frac{1}{2}(1.23)(7850)20^{3}$

P = 38622 W

Example 2

A wind turbine travels with the speed is 10 m/s and has a blade length of 20 m. Determine wind power.

Solution:

Given:

Wind speed v =10 m/s,

Blade length l = 20 m,

air density ρ = 1.23 kg/m3,

area ,$A=\pi r^{2}$

= π × 400

= 1256 $m^{2}$

The wind power formula is given as,

$P=\frac{1}{2}\rho AV^{3}$

= 0.5 × 1.23 × 1256 × 1000

P = 772440 W.