A windmill is designed to operate at 20 rpm in a 15 mph wind and produce 300 kW of power. The blades are 1.75 ft in diameter. A model 1.75 ft in diameter is to be tested at 90 mph wind velocity. What rotor speed should be used, and what power should be expected.
This question is in a chapter on "dimensional analysis" so I assume it wants me to use dimensional analysis to solve this. The problem is that I don't know how to begin.
Would I say that the rotor speed, w = f(rho, blade diameter, wind velocity)
power, P = f(rho, blade diameter, wind velocity, w) ?
I could then find the PI groups but I'm not sure how this helps me answer the question.
Could it be much more simple than that and have nothing to do with dimensional analysis?
Also, I'm aware of the equation: Power = 0.5*rho*swept area*Velocity^3 => for wind turbines
The Attempt at a Solution
Other than what I have above, I have been unable to come up with much.
Any help would be appreciated!