912b for free discharge friction may be neglected and

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Unformatted text preview: 10b. The flow rate varies with the ratio y2/y1; we ask, as a problem exercise, to show that the flow rate is a maximum when y2/y1 2 . 3 The free discharge, Fig. 10.10a, contracts to a depth y2 about 40 percent less than the gate’s gap height, as shown. This is similar to a free orifice discharge, as in Fig. 6.38. If H is the height of the gate gap and b is the gap width into the paper, we can approximate the flow rate by orifice theory: Q CdHb 2gy1 where Cd 0.61 1 0.61H/y1 (10.41) | v v in the range H/y1 0.5. Thus a continuous variation in flow rate is accomplished by raising the gate. If the tailwater is high, as in Fig. 10.10c, free discharge is not possible. The sluice gate is said to be drowned or partially drowned. There will be energy dissipation in the exit flow, probably in the form of a drowned hydraulic jump, and the downstream flow will return to subcritical. Equations (10.40) and (10.41) do not apply to this situation, and experimental discharge correlations are necessary [2, 15]. See Prob. 10.77. | e-Text Main Menu | Text...
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