Question

A type 3 wind turbine has rated wind speed of 13 m/s. Coefficient of performance of this turbine is 0.3. Calculate the rated power density of the wind that is hitting the turbine. Calculate the mechanical power developed at the shaft connecting rotor and generator. Assume rotor diameter 100 m and air density 1.225 kg/m^3.

Answer 1

Rated power = 1345.66 W/m²

Mechanical power developed = 3169035.1875 W

Step-by-step explanation:

Wind speed, V = 13 m/s

Coefficient of performance of turbine,
`C_p` = 0.3

Rotor diameter, d = 100 m

or

Radius = 50 m

Air density, ρ = 1.225 kg/m³

Now,

Rated power =
`(1)/(2)\rho V^3`

or

Rated power =
`(1)/(2)*1.225*13^3`

or

Rated power = 1345.66 W/m²

b) Mechanical power developed =
`(1)/(2)\rho AV^3C_p`

Here, A is the area of the rotor

or

A = π × 50²

thus,

Mechanical power developed =
`(1)/(2)*1.225*\pi*50^2*13^3*0.3`

or

Mechanical power developed = 3169035.1875 W