Question

The blades of a windmill sweep out a circle of area A.

1. 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?
2. What is the kinetic energy of the air?
3. 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?

Answer 1

(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`