The blades of a windmill sweep out a circle of area `30m^(2)`. If the wind flows at a velocity `10ms^(-1)` at right angles to the circle, what is the mass of the air passing through it in time t? What is the kinetic energy of the air? If the density of air is 1.2 `kgm^(-3)`, then calculate the electric power produced if the windmill converts 25% of wind energy into electrical energy.

Explanation

`A=30m^(2),v=10ms^(-1),s=1.2kgm^(-3)`
volume of (fluid) air passing/sec = V = Av where 'v' is the velocity of air.
Mass of air passing in one sec = `Avrho`
(a) Mass of air passing in t sec = `Avrhot`
(b) K.E. of air = `(1)/(2)mv^(2)=(1)/(2)(Avrhot)v^(2)=((1)/(2))Arhotv^(3)`
At 25% efficiency
K.E. produced = `0.25xx(1)/(2)Arhotv^(3)=((1)/(8))Arhotv^(3)`
Power produced = `("energy")/("time")=(Arhotv^(3))/(8t)=(1)/(8)Arhov^(3)`
i.e. `P=0.125xx30xx1.2xx(10)^(3)=4500W`
`P=4.5kW`.