6.21 The blades of a windmill sweep out a circle of area A.
(a) If the wind flows at a velocity v perpendicular to the circle, what is the mass of the air passing through it 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 = 30 m2, v = 36 km/h and the density of air is 1.2 kg m–3. What is the electrical power produced ?
6.21 The blades of a windmill sweep out a circle of area A.
(a) If the wind flows at a velocity v perpendicular to the circle, what is the mass of the air passing through it 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 = 30 m2, v = 36 km/h and the density of air is 1.2 kg m–3. What is the electrical power produced ?
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1 Answer
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6.21 Given, the area of the windmill sweep = A, Wind velocity = v
The volume of air passing through the blade = Av
Let the density of air be , the mass of air passing through the blade =
(a) The mass of air passing through the blade in time t =
(b) The kinetic energy of air = = = /2 …. (1)
(c) Area, A = 30 , v = 36 km/h = 10 m/s, density of air be = 1.2 kg/
Total wind energy, from eqn. (1) = 18 kW
Electrical energy = 25 % of wind energy = 0.25
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