8108392 15 or yc 2 gyc cot 503 2q2 g cot2 50 15 237

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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 open-channel 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 two-dimensional 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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