Question

What maximum output would you expect from a wind turbine with a blade of radius 15 ft in a 25 mph wind

Answer 1

step 1:
The power that can be extracted from the wind is given by the equation:
P = 0.5*p*A*V^3
where P = kinetic energy extracted from wind
p = density of air, varies with height and temperature (but 1.225 kg/m^3 will be used if
parameters not given)
A = area swept by rotor (A = pi*r^2 = pi*D^2/4) D and r are rotor diameter and radius in meters
V = wind speed in m/s^1

Step 2:
The Wind Turbine converts some of the energy contained in the wind. However, It has been proven that the wind Turbine can't convert no more 59.3% of this wind energy into electrical energy.

As such = Maximum Electrical Power, Pmax = 0.593*(0.5*p*A*V^3)

Convert rotor diameter and wind speed into standard units.
1ft = 0.3048 meters

=> diameter = 15ft = 15*0.3048 = 4.572m

1 mph = 0.44704 meters / second
V = 25 mph = 25*0.44704 = 11.176m/s

NOW:
A = pi*(4.572^2)/4 = 16.41 m^2

Pmax = 0.593*(0.5*1.225*16.41*(11.176^3)) = 8320.10 W = 8.32 kW