The blades of a windmill sweep out a circle of area A. (a) If the wind flows at a velocity `upsilon` perpendicular to the circle, what is the mass of air passing through it in time t? (b) What is K.E. of the air ? (c) Assume that the wind mill converts `25%` of the wind's energy into electrical energy , and that `A=30m^(2), upsilon=36km//h` and the density of air is `1.2kg//m^(3)`. What is electrical power produced ?

Explanation

(a) Volume of wind flowing `//` sec `=Aupsilon`
Mass of wind flowing `//` sec `=Aupsilonrho`
Mass of air passing in t sec, `m=Aupsilon rho t`
(b) K.E. of air `=(1)/(2)m upsilon^(2)=(1)/(2)(Aupsilonrhot)upsilon^(2)=(1)/(2)Aupsilon^(3)rhot`
(c) Electrical energy produced `=((25)/(100))xx` K.E. of air `=(1)/(4)xx(1)/(2) Aupsilon^(3)rhot`
Electrical power `=(1)/(8)(Aupsilon^(3)rhot)/(t)=(1)/(8)Aupsilon^(3)rho`
`P=(1)/(8)xx30xx(10)^(3)xx1.2=4500 wat t =4.5kW`