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?

Asked by Pragya Singh | 1 year ago |  151

##### Solution :-

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 m2

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 103 W =4.5 kW

Answered by Pragya Singh | 1 year ago

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