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(I) For a trapezoidal channel with a fixed cross-sectional area of 10m2, bottom width b, depth y, and side slopes of 2H:1V, confirm that the most efficient (optimal) cross-section occurs with b / У = 21 V1+ m2-m | , where ,n=2 in this case. To do this, it is easiest to make a Matlab or Excel program with different b/y ratios and 10m2 cross-sectional area, and determine the relative flow rates. Then normalize this by the optimal flow rate and plot (x-axis (b/y)/(b/y)opt) (y-axis QlQopt). From your plot, how much does the optimal cross-section increase flow rates? If you want, you can also solve this analytically -it follows closely the derivation in class for a rectangular channel.

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