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Unformatted text preview: ic, since they postulate constant bottom slopes. In practice, channel slopes can vary greatly, S0 S0(x), and the solution curves can cross between two regimes. Other parameter changes, such as A(x), b0(x), and n(x), can cause interesting composite-flow profiles. Some examples are shown in Fig. 10.15. Figure 10.15a shows a change from a mild slope to a steep slope in a constant-width channel. The initial M-2 curve must change to an S-2 curve farther down the steep slope. The only way this can happen physically is for the solution curve to pass smoothly through the critical depth, as shown. The critical point is mathematically singular [3, sec. 9.6], and the flow near this point is generally rapidly, not gradually, varied. The flow pattern, accelerating from subcritical to supercritical, is similar to a convergingdiverging nozzle in gas dynamics. Other scenarios for Fig. 10.15a are impossible. For example, the upstream curve cannot be M-1, for the break in slope would cause an S-1 curve which would move a...
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This note was uploaded on 10/27/2009 for the course MAE 101a taught by Professor Sakar during the Spring '08 term at UCSD.

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