Problem

Consider a wind turbine with a diameter d = 110 m and the airflow streamlines shown, which...

Consider a wind turbine with a diameter d = 110 m and the airflow streamlines shown, which are symmetric relative to the axis of the turbine. Since the airflow is tangent to the streamlines (by definition), these lines can be taken to define the top and bottom surfaces of a control volume. Suppose that pressure measurements indicate that the flow experiences atmospheric pressure at the cross sections A and B (as well as outside the control volume) where the wind speed is υA = 7 m/s and υB = 2.5 m/s, respectively. Furthermore, assume that the average pressure along the streamlines defining the control volume is also atmospheric. Finally, assume that the diameter of the flow cross section at A is 85% of the rotor diameter and that the rotor hub is at a distance h = 75 m above the ground. If the density of air is constant and equal to ρ = 1.25 kg/m3, determine the force exerted by the air on the wind turbine and the reaction moment at the base of the support.