Modern wind turbines can convert up to 30% of the kinetic energy of the incoming wind blowing through their blades to electricity. Assuming that the wind at a proposed offshore location blows steadily at 20 knots, how much electrical power can be generated from a turbine with rotor diameter d=80 m? By how much is the wind slowed when going through the turbine? Temperature of the air is 300K and its pressure is 1 bar. Air can be considered an ideal gas with Cv=5R/2.
Given: u=20 knots ~10.2889 m/s d=80 m T= 300k P= 1 bar Cv=5R/2
With out being given any information of the output stream how do I determine output velocity?
Am I right by making certain assumptions, such as, T and V are constant, and that there is no internal energy and if so wouldn't Cv change to Cp? If T is constant would the system be adiabatic?
The Attempt at a Solution
I have attached a pdf of the work I have done solving for mass flow rate, Kinetic Energy of input, general equation trying to solve for velocity decrease of output and an attempt at creating an overall general energy equation.