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Chapter 7 - Establishing an empirical formula which is correct. The ratio friction velocity to mean velocity has no significant influence on the scour but is almost constant at about 0.1. 7 6 5 h 12,max Computed 4 3 2 Table 7.5: 1 ID 101 0 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 Plots of the maximum relative scour depth obtained with GPKernel with macro-roughness (ID 101 corresponds to eq. 7.58, ID 112 to eq. 7.59, ID 124) ID 112 Replacing V∗ ⁄ V by a constant of 0.2, leads to almost the same correlation ( R 2 = 0.885 ). If we regroup the two terms θ to form Cst + θ 2 , and adjust the constant, the correlation is even increased to R 2 = 0.887 . The constant has a value of 0.002. Since the square of θ cr = 0.047 gives exactly the same result, it is tempting to write: h -------------- smax , 0.95 e s = ⋅ ----- ⋅( θ2 , (7.62) h m R cr + θ 2 ) ⋅Fr + 1.83 R 2 = 0.887 h The problem is that θ2 cr + θ 2 has not directly a physical signification. But if we write ( θ– θ cr ) 2 = θ 2 – 2 ⋅θ⋅θ cr + θ2 cr , we find a physical explanation (unfortunately with a worse correlation). Some additional simplifications and optimizations result in: h -------------- smax , 7.7 e s = ⋅ ----- ⋅ Fr ⋅( 0.001 + ( θ– θ , (7.63) h m R cr ) 2 ) + 1.7 R 2 = 0.876 h If we check this equation with the data set without macro-roughness, (admitting e s = 11.3 m for the tests without ribs), we find R 2 = 0.766 . Considering only the data set with macro-roughness, the correlation is rather poor ( R 2 = 0.537 ) (see Figure 7.12) but still much better compared to directly computed scour depth (see § 7.4). This poor correlation is due to the fact that the tests performed with ribs cover only a limited range of the hydraulic parameters. In average, the prediction capability is quite well (see Figure 7.12). All parameters in equation 7.63 have a physical meaning. The scour depth grows with increasing rib spacing, Froude number and Shields parameter. A possible explanation for the constant 0.001 is that the Shields parameter θ is computed in the inlet reach; but in the bend, the erosive power is more important, which is translated by the constant 0.001. page 180 / November 9, 2002 Wall roughness effects on flow and scouring
Establishment of the scour formula Computed 7 6 5 4 3 2 1 3 ±10% ±20% Computed 2 1 ±10% ±20% 0 0 1 2 3 4 5 6 7 Measured 0 0 1 2 3 Measured Figure 7.12: Comparison of maximum relative scour depth computed with equation 7.63 with the complete dataset (R 2 = 0.876) (left) and the one without Peter’s tests (right). EPFL Ph.D thesis 2632 - Daniel S. Hersberger November 9, 2002 / page 181
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WALL ROUGHNESS EFFECTS ON FLOW AND
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Abstract By applying vertical ribs
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Résumé En disposant des nervures
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Zusammenfassung • Ein markanter S
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Acknowledgments page x / November 9
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Table of contents 4. Smart & Jäggi
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Table of contents 7.6 Summary and c
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Chapter 1 - Introduction 1.1 Contex
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Chapter 2 - State of the art Theref
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Index of Keywords parameter 77 Pete
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Publications (continued) 1997 Hersb
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