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 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=30m^2`, `v=36kmh^-1` and the density of air is `1.2kgm^-3`, what is the electrical power produced?

Explanation

Velocity of wind = v
Volume of wind flowing/sec = Av
Mass of wind flowing per sec . = Avp
Mass of air passing in time t = Avpt
v = 36 km/h = 10 m/s
(b) K.E of air ` = 1/2 mv^(2)`
` = 1/2 (Avrhot)v^(2)`
` = 1/2 Av^(3) rhot `
(c ) Electric energy
`25/100 ` (K.E of air)
` = 25/100 xx1/2 Av^(3) rhot`
`= 1/8 Av^(3) rhot`
Electric power ` = 1/8 (Av^(3)rhot)/t `
`= 1/8 Av^(3)rho`
` P = 1/8 xx30 xx(10)^(3) xx1.2 `
` 1/8 xx30 xx1000 xx1.2`
` = 4,500 W `
`= 4.5 ` kW