Question

a wind - powered generator converts wind energy into electrical energy. assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. for wind speed the electrical power output will be proportional to

Answer 1

Solution:

Wind Power Generator:

Let ρ be the density of the air and A be the cross-section area of the blades.

Consider a cylindrical volume V with cross - sectional area A and length x.

The mass of air contained in volume V is:

Mass =ρAx.

kinetic energy is:

K. E = 1/2mV²

K. E =1/2mV² =1/2ρAxV².

The time taken by this volume to intersect the blades is:

Δt = x/v.

The air transfers its entire kinetic energy to the blades (assuming 100% efficiency).

Thus, the power generated is,

P = K. E Δt =1/2ρAV³.