Question

Assume that the generator converts a fixed fraction of the wind energy interdepted by its blades into electrical energy. For wind speed u. The electrical power output will be proportional to

Answer 1

According to Bernouli's Theorm the net trust experienced propotional to the velocities difference above and below the wing of the areoplane Thus P1-P2= (1/2) *d *(V2^2-V1^2) And net force experienced Fnet= A * (1/2) *d *(V2^2-V1^2).....Eq 1 Where A= Total area of the of the wings and d = density of air and V1 and V2 are velocities above and below the wings. Now the shape of the wind turbines is similar to that of the aeroplane . Thus, the power output P = Fnet*Velocity of the wind = A * (1/2) *d *V^2 * V (Since we can assume that the wind mill has V2=0 as maximum amount of the air flow takes place in the bulged part of the wings as shown in the figure thus giving V2 = V (velocity of the wind) This implies Output power is proportional to V^3 where all the terms in the expression[A*(1/2)*d] can be assumed to be constant Please feel free to post as many doubts on our discussion forum as you can.
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