40 the numerator of eq 1049 changes sign according as

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Unformatted text preview: 2.208 for BG units. | v v Classification of Solutions | It is customary to compare the actual channel slope S0 with the critical slope Sc for the same Q from Eq. (10.38). There are five classes for S0, giving rise to twelve distinct types of solution curves, all of which are illustrated in Fig. 10.14: e-Text Main Menu | Textbook Table of Contents | Study Guide 684 Chapter 10 Open-Channel Flow Slope class S0 S0 S0 S0 S0 Slope notation Sc Sc Sc 0 0 Steep S0 > Sc Fr > 1 Fr > 1 S-1, S-2, S-3 C-1, C-3 M-1, M-2, M-3 H-2, H-3 A-2, A-3 yn yn yn imaginary y (x) Fr < 1 yn Solution curves yc yc yc yn yn Steep Critical Mild Horizontal Adverse yc (a) Depth class S–1 y (0) S–2 S–3 yn = yc (b) Fr < 1 C–1 Critical S0 = Sc Fr > 1 C–3 yn yc (c) Fr < 1 M–1 Fr< 1 Mild S0 < Sc M–2 Fr > 1 M–3 (d ) Horizontal S0 = 0 yn = ∞ Fr < 1 yc Fr > 1 Fr < 1 | v v Fig. 10.14 Gradually varied flow for five classes of channel slope, showing the twelve basic solution curves. Adverse (e) S0 < 0 yn = imaginary | e-Text Main Menu yc H–2 H–3 A–2 A–3 Fr > 1 | Textbook Table of Contents | Study Guide 10.6 Gradually Varied Flow 685 The solution letters S, C, M, H, and A obviously denote the names of the five types of slope. The numbers 1, 2, 3 relate to the position of the initial point on the solution curve with res...
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