A windmill is rotated by air flow to produce power to pump water. It is desired to find the power output P of the windmill. Assume that P is a function of the density of the air ρ, viscosity of the air μ , diameter of the windmill d, wind speed v, and the rotational speed of the windmill ω (measured in radians per second). Thus,

a. Using dimensional analysis, find a relationship for P. Be sure to check your products to make sure that they are dimensionless.

b. Do your results make common sense? Explain.

c. Discuss how you would design an experiment to determine the nature of your function.