Question

Does anyone know the equation I should use?

At a different wind speed, the wind turbine has a power output of 388 kW. The mass of air passing the wind turbine each second is 13 800 kg.
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Calculate the speed of the air passing the blades each second. Assume that the process is 100% efficient.

Answer 1

Explanation:

Given, Power output of wind turbine P = 388 kW

Mass of air passing per second = 13800 kg

Efficiency = 100%

Principle:

In a wind turbine, the kinetic energy of the wind passing through the air blades is converted into the energy stored in wind turbine (electrical energy or mechanical energy)

As efficiency is 100%, Kinetic energy of wind is completely converted into Energy produced in the turbine.

So,

$\frac{1}{2} mv {}^{2} = energy \: produced$

But we don't know the mass, but we know mass of wind passing per second. Using this we can calculate speed of wind (v)

$\frac{1}{2} \frac{mv {}^{2} }{t} = \frac{e}{t} = p$

so,

v² = 2P/(m/t)

v² = 2×388000/13800

v ≈ 7.5 m/s

Thank you.