Wind Turbine © D Hoult 2010.

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Presentation transcript:

Wind Turbine © D Hoult 2010

Consider a cylinder of air moving towards the turbine

Consider a cylinder of air moving towards the turbine

Consider a cylinder of air moving towards the turbine

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 =

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

K. E. possessed by this air is

K. E. possessed by this air is ½ m u2

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

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

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

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

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

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

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

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

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

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

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