Question

the blades of a windmill sweep out a circle of area 2m^2. if the velocity of wind flows perpendicular to the circle is 18 km h and density of air is 1.2kg/m^3 then find power of windmill

Answer 1

Answer:-

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

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