We are given laboratory data, taken by Prof. Robert Kirchhoff and his students at the University of Massachusetts, for the spin rate of a 2-cup anemometer. The anemometer was made of ping-pong balls (d =1.5 in) split in half, facing in opposite directions, and glued to thin ( -in) rods pegged to a center axle. (See Fig. P7.91 for a sketch.) There were four rods, of lengths = 0.212, 0.322, 0.458, and 0.574 ft. The experimental data, for wind tunnel velocity U and rotation rate
, are as follows:

     

Assume that the angular velocity Ω of the device is a function of wind speed U, air density and viscosity µ, rod length , and cup diameter d. For all data, assume air is at 1 atm and 20°C. Define appropriate pi groups for this problem, and plot the data in this dimensionless manner. Comment on the possible uncertainty of the results. As a design application, suppose we are to use this anemometer geometry for a large-scale (d 30 cm) airport wind anemometer. If wind speeds vary up to 25 m/s and we desire an average rotation rate Ω 120 r/min, what should be the proper rod length? What are possible limitations of your design? Predict the expected Ω  (in r/min) of your design as affected by wind speeds from 0 to 25 m/s.