Question

Please help ASAP will rate.

3. The wind speed, V, in a wind farm follows a boundary layer distribution of V = 8 15 hodhi (m/s) ---100 -100 where h is the height from ground. The wind turbine efficiency reaches to 90% of the ideal efficiency. If a turbine blade length is 60m, in order to have a power output of 1.5 MW for this turbine, what is the wind velocity and the height that the turbine should be set? Air density is 1.0 kg/m? Assume the wind velocity at the height of the turbine axis is the wind velocity for the entire turbine. 20 point.

Answer 1

the power produced by wind turbine P =

where A is area = 0.785*60^2 = 2827.43m^2

V is velocity of air

Cp is the efficiency of turbine = 0.90

1.5*10^6 = 0.5*1*2827.43*0.9 *v^3

v = 10.56m/s

putting the value of velocity into the velocity height relation we get

10.56=8(1.5(h/100)-.5(h/100)^3)

so the solutions for h are

h1 = 206.79941
h2 = -103.3997 + i * 45.54663
h3 = -103.3997 - i * 45.54663

hence the only real solution is h = 206.79m

is the height of the wind turbine