How thick is the film?
For a thin sheet of water sliding down a wide, smooth slope, classic laminar film theory gives the depth: h = (3 x viscosity x q / (density x g x sin of the slope angle)) raised to the one third power, where q is the flow per meter of channel width.
This model assumes a 10 cm wide channel, water at room temperature, and no roots in the way, so treat the depth as a teaching estimate. Real root mats thicken the film and slow it down.
Why growers keep channels short
As solution travels down a channel, the plants pull out oxygen and nutrients. Very long runs leave the last plants with tired water, which is why many systems keep channels to about 12 meters or feed long runs from the middle as well.