1. Wind Turbine
© D Hoult 2010

3. Consider a cylinder of air moving towards the turbine

4. Consider a cylinder of air moving towards the turbine

5. Consider a cylinder of air moving towards the turbine

6. Consider a cylinder of air moving towards the turbine
If all the air in a cylinder of length L interacts with the turbine in time t, then the speed of the air is u =

7. Consider a cylinder of air moving towards the turbine
If all the air in a cylinder of length L interacts with the turbine in time t, then the speed of the air is u = L/t

8. K. E. possessed by this air is

9. K. E. possessed by this air is ½ m u2

10. K. E. possessed by this air is ½ m u2
mass of air in the cylinder is

11. K. E. possessed by this air is ½ m u2
mass of air in the cylinder is r V

12. K. E. possessed by this air is ½ m u2
mass of air in the cylinder is r V =

13. K. E. possessed by this air is ½ m u2
mass of air in the cylinder is r V = r A L

14. K. E. possessed by this air is ½ m u2
mass of air in the cylinder is r V = r A L
Therefore the power (theoretically) available from this cylinder of air is given by

15. K. E. possessed by this air is ½ m u2
mass of air in the cylinder is r V = r A L
Therefore the power (theoretically) available from this cylinder of air is given by
½ r A L u2 = t

16. K. E. possessed by this air is ½ m u2
mass of air in the cylinder is r V = r A L
Therefore the power (theoretically) available from this cylinder of air is given by
½ r A L u2 =
½ r A u3 t

17. If the average speed of the air in the cylinder after it has interacted with the turbine is v then the efficiency of the turbine is given by

18. If the average speed of the air in the cylinder after it has interacted with the turbine is v then the efficiency of the turbine is given by
power in air before – power in air after
power in air before

19. If the average speed of the air in the cylinder after it has interacted with the turbine is v then the efficiency of the turbine is given by
½ r A u3 -
½ r A v3
½ r A u3

20. If the average speed of the air in the cylinder after it has interacted with the turbine is v then the efficiency of the turbine is given by
u3 – v3 u3