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

4.3155 kW

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 = 137 kg/s

According to the law of conservation of energy

Energy generated = change in kinetic energy

Hence,energy generated in 1 sec can be given by

`E\ =\ (1)/(2).m.V^2\ -\ (1)/(2).m.U^2`

`=\ (1)/(2)* 137* 12^2\ -\ (1)/(2)* 137* 9^2`

`=\ 9864\ -\ 5548.5`

= 4315.5 J

So, the power generated in 1 sec will be given by

`P\ =\ (energy\ generated)/(time)`

`=\ (4315.5)/(1)`

= 4315.5 W

= 4.13 kW

So, the power generated will be 4.13 kW.