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Unformatted text preview: near Emin cause a large change in the
depth y, by analogy with small changes in duct area near the sonic point in Fig. 9.7.
Thus critical flow is neutrally stable and is often accompanied by waves and undulations in the free surface. Channel designers should avoid long runs of nearcritical flow. EXAMPLE 10.4
50 ft3/(s ft). (a) What is the criti A wide rectangular cleanearth channel has a flow rate q
cal depth? (b) What type of flow exists if y 3 ft? Solution
Part (a) From Table 10.1, n 0.022 and
yc Part (b) Nonrectangular Channels 0.12 ft. The critical depth follows from Eq. (10.30):
q2
g 502
32.2 1/3 1/3 4.27 ft Ans. (a) If the actual depth is 3 ft, which is less than yc, the flow must be supercritical. Ans. (b) If the channel width varies with y, the specific energy must be written in the form
E y Q2
2gA2 (10.35) The critical point of minimum energy occurs where dE/dy
A A(y), Eq. (10.35) yields, for E Emin,
dA
dy 0 at constant Q. Since gA3
Q2 (10.36) But dA b0 dy, where b0 is the channel width at the free surface. Therefore Eq. (10.36)
is equiv...
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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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