Question

What is the maximum output you would expect from a wind turbine with a blade diameter of 20 ft in a 15-mph wind?

Answer 1

Diameter of the blade d = 20 ft

radius of the blade r = d/2

                             = 10 ft

                             = 10 x0.3048 m

                             = 3.048 m

The power that can be extracted from the wind P = (1/2) $\rho$A v ³
where P = kinetic energy extracted from wind
         $\rho$ = density of air =1.225 kg/m ³
A = area swept by rotor

    = $\pi$r ²

    = 29.18 m ²

v = wind speed

   = 15 miles/ h

   = 15 x1609 m / 3600 s

   = 6.704 m/s
The wind Turbine can't convert no more 59.3% of this wind energy into electrical energy.

So, Maximum Electrical Power, P_max = 0.593 (1/2) $\rho$A v ³
   = 0.593x(0.5)x1.225x29.18*(6.704 ³)

                                                       = 3189.8 W

                                                       = 3.189 kW

                                                       = 3.2 kW Two significant figures