Question

The blades of windmill sweep out a circle of area A . (a) if the wind flows at a velocity v perpendicular to circle , what is the mass of the air passing through 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 = 30m³ , v = 36 km / h and the density of air is 1.2 kg m^-3 . What is the electric power produced ?

Answer 1

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 = (1/2) mv²
= (1/2) (ρAvt)v² = (1/2)ρAv³t


(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
= (25/100) × Kinetic energy of air
= (1/8) ρ A v³t
Electrical power = Electrical energy / Time
= (1/8) ρ A v³t / t
= (1/8) ρ A v³
= (1/8) × 1.2 × 30 × (10)³
= 4.5 kW