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 m^{2} and the density of the air is 1.2 kg m^{-3}. What is the electrical power produced?

Asked by Pragya Singh | 1 year ago | 151

Area = A

Velocity = V

Density = ρ

**(a)** Volume of the wind through the windmill per sec = Av

Mass = ρAv

Mass m through the windmill in time t = ρAvt

**(b) **kinetic energy = \( \dfrac{1}{2}mv^2\)

= \( \dfrac{1}{2} (ρAvt)v^2 \)

**(c)** Area = 30 m^{2}

Velocity = 36 km/h

Density of air \(\)ρ = 1.2 kg m^{-3}

Electric energy = 25 % of wind energy

= \( \dfrac{25}{100}\) x kinetic energy

= \( \dfrac{1}{8}ρAv^3t\)

Power = \( \dfrac{Electric\;energy}{Time}\)

= \( \dfrac{1}{8}\dfrac{\rho Av^{3}t}{t}= \dfrac{1}{8}ρAv^3\)

= \( \dfrac{1}{8} \times 1.2 \times 30 \times 10^3\)

= 4.5 x 10^{3} W =4.5 kW

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