Chapt10

601 flow downstream of the bump is subcritical these

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Unformatted text preview: r bump is hmax E1 E2,min 1.115 0.918 0.197 m Ans. (b) For this bump, the solution of Eq. (10.39) is y2 yc 0.612 m, and the Froude number is unity at the crest. At critical flow the surface level has dropped by y1 y2 h 0.191 m. Flow under a Sluice Gate A sluice gate is a bottom opening in a wall, as sketched in Fig. 10.10a, commonly used in control of rivers and channel flows. If the flow is allowed free discharge through the gap, as in Fig. 10.10a, the flow smoothly accelerates from subcritical (upstream) to critical (near the gap) to supercritical (downstream). The gate is then analogous to a converging-diverging nozzle in gas dynamics, as in Fig. 9.12, operating at its design condition (similar to point H in Fig. 9.12b). For free discharge, friction may be neglected, and since there is no bump ( h 0), Eq. (10.39) applies with E1 E2: y3 2 V2 1 2g V 2y2 11 2g y1 y2 2 0 (10.40) Given subcritical upstream flow (V1, y1), this cubic equation has only one positive real solution: supercritical flow at the same specific energy, as in Fig. 10....
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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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