Let be the wind velocity approaching a windmill, D be the windmill rotor disk diameter, and

Let Ѵ be the wind velocity approaching a windmill, D be the windmill rotor disk diameter, and ρ the air mass density. Show that the rate of kinetic energy flow through the windmill disk area is ρπD²Ѵ³/8. Defining η as the fraction of this energy that is converted into electrical energy (the efficiency), give the expression for the electrical power output. Apply your results to a windmill with D = 5 m, η = 0.6, using ρ ≈ 1 kg/m³, plotting the power in W versus the wind speed for velocities from 0 to 15 m/s. At 10 m/s, how many windmills are required by a city that needs 100 MW of electrical power? What is the power available to this city when the wind speed drops to 5 m/s?