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109b the flow at the crest will be exactly critical

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Unformatted text preview: a depression ( h 0): Subcritical approach flow will cause a water-level rise and supercritical flow a fall in depth. Point 2 will be h to the right of point 1, and critical flow cannot occur. EXAMPLE 10.6 Water flow in a wide channel approaches a 10-cm-high bump at 1.5 m/s and a depth of 1 m. Estimate (a) the water depth y2 over the bump and (b) the bump height which will cause the crest flow to be critical. Solution Part (a) First check the approach Froude number, assuming C0 1.5 m/s (9.81 m/s2)(1.0 m) V1 gy1 Fr1 gy: 0.479 (subcritical) For subcritical approach flow, if h is not too large, we expect a depression in the water level over the bump and a higher subcritical Froude number at the crest. With h 0.1 m, the specific-energy levels must be V2 1 2g E1 y1 (1.5)2 2(9.81) 1.0 1.115 E2 E1 h 1.015 m This physical situation is shown on a specific-energy plot in Fig. E10.6. With y1 in meters, Eq. (10.39) takes on the numerical values y3 2 1.015y2 2 0.115 0 0.859 m, 0.451 m, and 0.296 m. The third (ne...
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