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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.  eText Main Menu  Text...
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 Spring '08
 Sakar

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