Question

Find the power from the wind turbine at a height of 300 M for a rotor diameter of 90m. Velocity of wind at 10m is given as 2m/s and shear ratio is given as .15 and Betz limit (or efficiency factor) is given by 0.45.

Assume density of air as 1.23 Kg/m³

Answer 1

To calculate the power from a wind turbine, use the formula P = (1/2) * rho * A * v^3 * Cp. Given a rotor diameter of 90m and wind speed at 10m of 2m/s, use the shear ratio equation to find the wind speed at a height of 300m. Then, plug the values into the power formula to find the power output, which is 7530.91 kW.

Step-by-step explanation:

To calculate the power from a wind turbine, we can use the formula P = (1/2) * rho * A * v^3 * Cp, where P is the power, rho is the density of air, A is the swept area of the rotor, v is the wind speed, and Cp is the power coefficient.

Given the rotor diameter of 90m, we can calculate the swept area as A = pi * (diameter/2)^2. The swept area would be 6362.56 square meters.

The wind speed at a height of 300m can be calculated using the shear ratio. The wind speed at 10m is given as 2m/s and the shear ratio is given as 0.15. Using the equation v2/v1 = (z2/z1)^alpha, where v2 is the wind speed at a height of 300m, v1 is the wind speed at 10m, z2 is the height of 300m, z1 is the height of 10m, and alpha is the shear exponent (0.15), we can solve for v2. Plugging the values into the equation, we get v2 = 2 * (300/10)^0.15 = 4.032m/s.

Now, we can calculate the power using the formula P = (1/2) * rho * A * v^3 * Cp. Plugging in the values, we get P = (1/2) * 1.23 * 6362.56 * (4.032)^3 * 0.45 = 7530.91 kW.