Question

A wind turbine is located at the top of a hill where the wind blows steadily at 12 m/s, and stands 37 m tall. The air then exits the turbine at 9 m/s and the same elevation. Find the power generated by the wind if the mass flow rate is 137 kg/s. Report your answer in kW and to 2 decimal places.

Answer 1

Answer:

Power generated = 4.315 kW

Step-by-step explanation:

Given,

• speed of wind when enters into the turbine, V = 12 m/s

• speed of wind when exits from the turbine, U = 9 m/s

• mass flow rate of the wind, m = 137 kg/s

According to the law of conservation of energy

Energy generated = change in kinetic energy

Since, the air is exiting at same elevation. So, we will consider only kinetic energy.

Energy generated in one second will be given by,

$E\ =\ \dfrac{1}{2}.mV^2-\dfrac{1}{2}.m.U^2$

   $=\ \dfrac{1}{2}\times 137\times (12)^2-\dfrac{1}{2}\times 137\times (9)^2$

   =4315.5 J

   = 4.315 kJ

So, energy is generated in one second = 4.315 kJ

Power generated can be given by,

$P\ =\ \dfrac{\textrm{energy generated}}{time}$

And the energy is generated is already in per second so power generated will be 4.315 kW.