text: Suppose we are interested in finding the maximum power that can be extracted from the fluid. The power in the fluid is given by the following expression:
  where  is the fluid density as before,  is the fluid velocity, and  is the area of an imaginary surface through which the fluid is flowing. The power extracted from the fluid by a rotor in the scenario described above is some fraction of this power expression. We will call the fraction the power co-efficient, . Thus the power extracted,  is given by the following expression:
  Our question is this: what is the maximum value of  using the Betz model?
  Let us return to our derived expression for the power transferred from the fluid to the rotor (). We can see that the power extracted is dependent on the axial induction factor. If we differentiate  with respect to , we get the following result:
  If we have maximised our power extraction, we can set the above to zero. This allows us to determine the value of  which yields maximum power extraction. This value is a . Thus we are able to find that . In other words, the rotor cannot extract more than 59 per cent of the power in the fluid.