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MA_775_DIABLO [31]
2 years ago
12

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 pow

er 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.
Engineering
1 answer:
Anna [14]2 years ago
8 0

Answer:

Rated power = 1345.66 W/m²

Mechanical power developed = 3169035.1875 W

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 = \frac{1}{2}\rho V^3

or

Rated power = \frac{1}{2}\times1.225\times13^3

or

Rated power = 1345.66 W/m²

b) Mechanical power developed =  \frac{1}{2}\rho AV^3C_p

Here, A is the area of the rotor

or

A = π × 50²

thus,

Mechanical power developed = \frac{1}{2}\times1.225\times\pi\times50^2\times13^3\times0.3

or

Mechanical power developed =  3169035.1875 W

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