1= 0.212 1= 0.322 1= 0.458 1= 0.574 U, ftls n, r/min U, ft/s n, r/min U, ft/s n, r/min U, ft/s N, r/min 18.95 435 18.95 225 20.10 140 23.21 115 22.20 545 23.19 290 26.77 215 27.60 145 25.90 650 29.15 370 31.37 260 32.07 175 29.94 760 32.79 425 36.05 295 36.05 195 38.45 970 38.45 495 39.03 327 39.60 215
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 ( 1/4
-in) rods pegged to
a center axle. There were four
rods, of lengths l = 0.212, 0.322, 0.458, and 0.574 ft. The
experimental data, for wind tunnel velocity U and rotation
rate Ω , are as follows:
Assume that the angular velocity Ω of the device is a
function of wind speed U , air density ρ and viscosity μ , rod
length l , and cup diameter d . For all data, assume air is at
1 atm and 20 ° C. Defi ne appropriate pi groups for this
the 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.
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