Open Channel Flow in a Parabolic Channel

[Gene222]

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. The channel depth and width or any other known depth and width must be entered to describe the curvature of the parabola. Enter any three of the four variables (flow rate, depth, slope, and n) and solve for the fourth variable. 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.

Example. A grassy swale at a slope of 0.008 has water flowing at a rate of 85 cfs. The swale has a parabolic shape and is 2.5 ft deep by 25 ft wide. Assume n = 0.05. Solve for the depth of flow in the swale. Run the program. Select English Units. Enter the channel width (2.5 ft) and depth (25 ft). Enter the flow rate (85 cfs), slope (0.008), and n value (0.05). It does not matter is a value is shown in the depth box. Then select "Solve for depth Y". Press the "OK" tab in the lower right corner. The print terminal will show Depth Y = 1.9022 ft and Velocity V = 3.0735 ft and other information.

[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