Wind Engineering Power!

Now, let's delve deeper into the delicate engineering of wind power . (You may want to refer to the wind power note to have a clearer idea on wind energy)

The diagram above shows how a wind turbine is used to produce electricity in a typical power station both internally and externally. The wind turns the wind turbines which are connected to a generator to generate electricity.

One day, An physicist, James Prescott Joule who came up with The Principle of Conservation of Energy has risen from the grave near a wind power station. He then saw a majestic wind turbine and discovered that the power available to a wind turbine depends on the kinetic energy of a column of air with the same cross sectional area $A$ as the wind turbine blades.

As James had risen from the grave, he had the capability of observing that the steady supply of strong wind is necessary to use the power in the wind. Modern wind turbines are designed to operate when the speeds are within the domain, $10m s^{-1}$ to $15m s^{-1}$ . Many wind turbines are designed to remain stationary when the wind speed is below $5m{s}^{-1}$ .

Hence, determine the available power from the Wind if the wind speed is at its minimum for the turbines to operate. James Prescott Joule : Can you figure it out?

Details :

1. Assume that the density of air is $1.2kg\ { m }^{ -3 }$ .

2. Assume that the wind blades have a length of $22m$ . Do not use the length given by the diagram, it's just for visualization.

3. Round your answer off to $2s.f.$ .

4. This is part of the set, Beauty of the natural wind, #MajesticWind.