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Q.

The blades of a windmill sweep out a circle of area A. If the wind flows at a velocity v perpendicular to the circle, then power developed by air is

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a

12AρV

b

12Aρv2

c

12Aρv3

d

2Aρv3

answer is C.

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Detailed Solution

m = Mass flow rate of air through the blades = ρ(Av). It is assumed that air comes to rest after passing through blades.
 

\large \therefore

The rate at which air is losing kinetic energy = 

\large \left ( \frac 12mv^2-0 \right )=\frac 12\rho Av^3


 

\large \therefore

Power developed =

\large \frac 12\rho Av^3
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