Optimizing an Open Channel

by Michael Perry

Submitted : Spring 2011

The goal of this project was to minimize the wetted perimeter and find optimal values of the height and width of an open channel for a specific case of Q =20 m3/s, S = 0.02, and n = 0.012 (smooth concrete). Where Q is the volumetric flow rate, S is the slope of the channel (dimensionless), and n is the roughness parameter.

To accomplish this task I used a series of substitutions into equations to get quadratic function for h (height) in terms of P (perimeter). Then I used the quadratic formula to solve for h in terms of P. Then I took the derivative dh/dP. Then I found where this equals infinity, in order maximize P.

Finding a value for P, I was able to substitute it back into the expression for h and solve using the quadratic formula. Considering only the positive value for h, I was able to substitute and solve for w (width).  

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