The windmill sweeps a circle of area A with their blades. If the velocity of the wind is perpendicular to the circle, find the air passing through it in time t and also the kinetic energy of the air. 25 % of the wind energy is converted into electrical energy and v = 36 km/h, A = 30 m2 and the density of the air is 1.2 kg m-3. What is the electrical power produced?
Density of air =ρ kg/m3 Time taken = t sec Velocity of air = v m/s Mass of the air = density × volume =ρAvt (b) KE=21mv2 =21(ρAvt)v2 =21(ρAv3t) (c) Velocity, v= 36 km/hr = 10 m/s ρ=1.2kg/m3 A=30m2 Work done = change in kinetic energy =21×1.2×30×103tNm =18000tJ Power = work/t=18000W Efficiency = 25% Actual power=18000×25/100=4500W
