Check out this USGS fact sheet
It's got an very scientific sounding title, but basically it's about side-canyon debris fans and how they evolve through time. The example they present is lava falls.
Figure 2 is side-by-side aerial photos taken in March and April of 1996, before and after the experimental flood.
Figure 4 shows a plot of elevation versus distance for the fastest moving water (the thalweg - more geology speak). Anyway, the plot shows a 4 meter drop through lava, almost all of it occurring in the first 100 meters of the rapid. I imagine that the tail waves will pretty much double that distance, but don't add much to the drop. So much for 37 feet!
It still doesn't answer how fast the water is moving, though.
I haven't tried, but has anyone taken a look with Google Earth? I've looked before and very clearly seen rafts tied up on a beach somewhere (Nankoweap?)
Hydraulic map of Lava Falls Rapids, Grand Canyon, Arizona
scroll to the botoom. either view as images or download the dejavu plug-in.
The highest velocity is about 7 meters/second, which equals about 14 knots, or 15-16 mph. These measurements were taken at 10,000 cfs (see the notes on the right side of the map) sometime in the mid-eighties.
Ain't the web amazing?