Problem 1 (35 points, CCO #4, CCO#1) The power output, P, of a commercial wind turbine is a function of the density of air, p, wind speed at hub height, V, and diameter of the turbine blades, D. (a) If a non-dimensional parameter II for the system can be written as P paDbyc' determine a, b, and c. (b) At the location of a wind farm, it is known that atmospheric wind speed increases with height (z) following the relation, V - 0.05z + 0.0001z2, where z is in m and V in m/s. The density of the atmosphere is independent of height. Two turbines, Turbine #1 and #2, are known to have the same power output. If Turbine #1 has a hub height of z = 100 m and blade diameter D = 20 m, and Turbine #2 has a hub height of 120 m, what is the blade diameter of Turbine #2? (Assume that all turbines in the wind farm have the same design, characterized by the same value of the II parameter.)