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Question
The blades of a windmill sweep out a circle of area 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?
- What is the kinetic energy of the air?
- 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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Solution
(a) Volume of wind flowing per second = Av Mass of wind flowing per second = Avρ
Mass of air passing in second = Avρt
(b) Kineic energy of air = `1/2mv^2 = 1/2 (Avrhot)v^2 = 1/2 Av^3rhot`
(c) Electrical energy produced = `25/100 xx 1/2 Av^3 rhot = (Av^3rhot)/8`
Electrical power = `(Av^3rhot)/"8t" = (Av^3rho)/8`
Now
`A = 30m^2`
`v = 36 kmh^(-1) = 36 xx 5/18 ms^(-1) 10 ms^(-1) `
`rho = 1.2 kg ms^(-1)`
∴ Electrical power =`((30xx10xx10xx10xx1.2)/8)W`
`= 4500 W = 4.5 KW`
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