The power P generated by a certain windmill design depends upon its diameter D, the air density ρ, 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, devel ops 2.7 kW at sea level when V = 40 m/s and when rotating at 4800 rev/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?