The power P generated by a certain windmill design depends on its diameter D, the air density P, the wind velocity V, the rotation rate Ω , and the number of blades n.
(a) Write this relationship in dimensionless form. A model windmill, of diameter 50 cm, develops 2.7 kW at sea level when V =40 m/s and when rotating at 4800 r/min.
(b) What power will be developed by a geometrically and dynamically similar prototype, of diameter 5 m, in winds of 12 m/s at 2000 m standard altitude?
(c) What is the appropriate rotation rate of the prototype?