The blades of a windmill sweep out a circle of area A . (a) If the wind flows at a velocity v perpendicular to the circle, what is the mass of the air passing through it in time t ? (b) What is the kinetic energy of the air? (c) Assume that the windmill converts 25% of the wind’s energy into electrical energy, and that A = 30 m 2 , v = 36 km/h and the density of air is 1.2 kg m –3 . What is the electrical power produced?
Area of the circle swept by the windmill = A
Velocity of the wind = v
Density of air = ρ
(a) Volume of the wind flowing through the windmill per sec = Av
Mass of the wind flowing through the windmill per sec = ρAv
Mass m, of the wind flowing through the windmill in time t = ρAvt
(b) Kinetic
energy of air
(c) Area of the circle swept by the windmill = A = 30 m2
Velocity of the wind = v = 36 km/h
Density of air, ρ = 1.2 kg m–3
Electric energy produced = 25% of the wind energy
