How fast does the water travel down river when the discharge gates of a large dam are opened? Can the discharge-wave travel downstream faster than the water? Is this likely to occur for a real river and an actual sudden discharge from a large reservoir?
The Manning Formula is an empirical equation that describes uniform open channel flow. It depends upon several factors, including roughness and sinuosity of the river channel.
This paper: The Colorado River in Grand Canyon; how fast does it flow? describes some dye experiments performed in the Colorado River in the 1990s. Several releases (at different volumetric rates) were made from lake Powell and the time to reach different distances downriver were measured. These experiments showed that the water velocity down river was higher for the higher volume releases (~3 miles/hr for ~30,000 cubic feet/sec.) The discharge waves traveled faster than the water, traveling a distance of ~235 miles in ~1.6 days rather ~4.3 days.