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Unformatted text preview: nd b0c 3.41 m/s Textbook Table of Contents Ans. (b)  Study Guide 10.4 Specific Energy; Critical Depth 675 Part (c) With n 0.018, we compute from Eq. (10.38) a critical slope
Sc Frictionless Flow over a Bump gn2P
1
Rh /3b0 9.81(0.018)2(6.18)
1.0(0.760)1/3(3.97) 2 0.00542 Ans. (c) A rough analogy to compressible gas flow in a nozzle (Fig. 9.12) is openchannel flow
over a bump, as in Fig. 10.9a. The behavior of the free surface is sharply different according to whether the approach flow is subcritical or supercritical. The height of the
bump also can change the character of the results. For frictionless twodimensional
flow, sections 1 and 2 in Fig. 10.9a are related by continuity and momentum:
V1y1 V2
1
2g V2y2 V2
2
2g y1 y2 h Eliminating V2 between these two gives a cubic polynomial equation for the water
depth y2 over the bump:
y3
2 V2y2
11
2g E2y2
2 0 where E2 V2
1
2g y1 h (10.39) This equation has one negative and two positive solutions if h is not too large. Its behavior is illustrated in Fig. 10.9b and depends upon whether condition 1 is on the upper or lower leg of the energy curve. The specific energy E2 is exactly h less than the
approach energy E1, and p...
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 Spring '08
 Sakar

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