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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
convergingdiverging 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.
 Spring '08
 Sakar

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