...
This was our first plot of theoretically predicted Rossby number with our experimental data. Note that the fit is terrible!
We think that this result was due primarily to the angular momentum not actually being constant. After all, there is a net loss of mass through the hole in the center of the tank. If we look at a plot of angular momentum per unit mass versus radius, we see that it is, in fact, not constant.
In all of our calculations, the radius was computed as a normalized radius equal to the measured radius divided by the total radius of our bucket, which was 190 pixels in the camera units. Since all of our other data was in pixels, there was no need to convert to "real world" units for a meaningful comparison.
If the radius is scaled to an effective radius of 0.53 the normalized radius, we get a much better fit.
...