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Unformatted text preview: . Then our initial condition at x 0, just upstream of the dam, is y(0) Y H 4 1.59 5.59 m. Compare this to the critical depth from Eq. (10.30): Q2 b2g yc 1/3 (30 m3/s)2 (8 m)2(9.81 m/s2) 1/3 1.13 m Since y(0) is greater than yc, the flow upstream is subcritical. Finally, for reference purposes, estimate the normal depth from the Chézy equation (10.19): Q 30 m3/s n 1.0 8yn (8 m)yn 0.025 8 2yn 2/3 byRh S1/2 0 2/3 (0.0004)1/2 By trial and error or EES solve for yn 3.20 m. If there are no changes in channel width or slope, the water depth far upstream of the dam will approach this value. All these reference values y(0), yc, and yn are shown in Fig. E10.10b. Since y(0) yn yc, the solution will be an M-1 curve as computed from gradually varied theory, Eq. (10.51), for a rectangular channel with the given input data: dy dx S0 1 4/3 n2Q2/( 2A2Rh ) Q2b0 /(gA3) 1.0 A 8y n 0.025 Rh 8 8y 2y b0 8 Beginning with y 5.59 m at x 0, we integrate backward to x 2000 m. For the RungeKutta method, four-figure 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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