Open Channel Flow Over a Bump is WEIRD, but Bernoulli and Continuity Equations Explain It
This problem uses typical slow moving, sub-critical, incompressible flow. The real mind-bender will come later when you get to Compressible, Supersonic Flow - and discover that everything you think you learned in this video will be totally backwards!
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This Fluid Mechanics Example Problem is solved using the Bernoulli Equation and Continuity Equation to find out what would happen to slow moving, sub-critical, open channel flow over a bump, or open channel flow over a hump. The solution is pretty short, but does sometimes require setting aside your intuition, until you develop new better intuition based on the conservation of energy.
The 2 most common exceptions to the behavior you see in this video are:
1. Hydraulic Jump. When you have fast moving, supercritical open channel flow, and have a bump large enough, you'll create a hydraulic jump, and the whole flow will very rapidly change from shallow and fast to deep and slow. It's a very cool phenomenon that you can see in the bottom of your sink every time you turn on the faucet.
2. Supersonic Nozzles, like at the bottom of a Rocket Ship. You know those flared outward cones at the bottom of rockets? Those are nozzles. We usually think of nozzles as being narrow. In this Bernoulli Problem, smaller area means faster flow. But not with compressible flow at supersonic speeds. In that situation, larger area causes faster flow. That is why the nozzles at the bottom of rockets flare outwards.
TIMECODES
0:00 Open Channel Flow Over a Bump
3:43 Start the Bernoulli Equation Example Problem
5:20 Finish Example Problem using the Continuity Equation