First slide

Fluid dynamics

Question

The blades of a wndmill sweeps out a circle of area 'A'. If the wind flows at a velocity 'v' perpendicular to the circle (denisity of air = $\large \rho$ )
   A)   the mass of the air passing through it in time 't' is AV $\large \rho$ t
   B)   the kinetic energy of the air is $\large \frac{1}{2}A{v^3}\rho t$
   C)   If the windmill converts 25% of the wind energy into electrical energy and $\large A = 30{m^2},V = 36kmph,\rho = 1.2kg{m^{ - 3}}$ then the electrical power produced is 4.5 kw

Moderate

A

A, B are true, C is false
B

A, B, C are false
C

A false, B & C are true
D

A, B, C are true

Solution

Q = rate of volume flow
m = rate of mass flow = ρQ = ρAV
Rate of generation of K.E. = 1/2 mV² = 1/2 ρAv³.
Total kinetic energy delivered to the air in time t = 1/2 ρ Av³ . t.
Power = η x 1/2 ρ AV³
= 0.25 x 1/2 x 1.2 x 30 x (36 x 5/18)³ W
= 4.5 KW

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