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## Homework Statement

Consider a wind turbine farm that uses turbines with a blade span diameter of 80 m at a site subjected to wind speeds over the range of 4 to 32 m/s. Taking the overall efficiency of each turbine to be 25% and the air density to be 1.112 kg/m

^{3}, determine the electric power generated by a single turbine.

## Homework Equations

I know that, for an average wind speed, the equation I need is:

**W**=

**m**(V

^{2}/2)*η (the bold variables are per unit time), but I'm not sure exactly how to modify this equation for a range of velocities. I at first thought that I could take the integral of the equation with respect to velocity, but then I end up with the wrong units.

**W**=

**m**(V

^{2}/2)*η = ρVA(V

^{2}/2)*η = ρπr

^{2}(V

^{3}/2)*η = ρπ(d/2)

^{2}(V

^{3}/2)*η = ρπ(d

^{2}/4)(V

^{3}/2)*η = ρπ(d

^{2}/8)V

^{3}*η

## The Attempt at a Solution

Since I'm not sure what equation to use, I can't attempt to find the solution.If someone could help me, I would really appreciate it. Thanks.