Open Channel Flow in a Parabolic Channel

[Dieter]

(04-03-2018 02:38 AM)Gene222 Wrote:  This program calculates the normal depth of a parabolic channel in the form of y = Cx^2, where C is the x^2 coefficient or curvature coefficient.
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The wetted perimeter P is calculated using the exact formula per Chow as redefined by Merkley. See the included attachment for the formulas and test problems used in writing the program.

Thank you very much, especially for the attached PDF. First of all: I am not an engineer, and my knowledge of open channel design is very limited, but some time ago I wrote a program for the HP67 or HP35s (can't remember exactly) for a similar application. I always wondered why the wetted perimeter of a parabolic channel was mostly given as an approximation: the exact solution can be derived quite easily (just a bit of calculus), and so I set up my own equation. Looking at the result it agrees with the Chow formula in your PDF. It also turned out that P can be written quite elegantly by means of the hyperboldic arsinh function. ;-)

In any case thank you very much for this thorough documentation.

Dieter