Best trapezoid angle equations 1025 are valid for any

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Unformatted text preview: evaluate dP/d from Eq. (10.24) with A and y held constant. The result is 2 or (1 2 1/2 ) cot 1 31/2 60° (10.27) | v v Thus the very best trapezoid section is half a hexagon. Similar calculations with a circular channel section running partially full show best efficiency for a semicircle, y 1 D. In fact, the semicircle is the best of all possible 2 | e-Text Main Menu | Textbook Table of Contents | Study Guide 10.4 Specific Energy; Critical Depth 671 channel sections (minimum wetted perimeter for a given flow area). The percentage improvement over, say, half a hexagon is very slight, however. EXAMPLE 10.3 What are the best dimensions for a rectangular brick channel designed to carry 5 m3/s of water in uniform flow with S0 0.001? Solution From Eq. (10.26), A 2y2 and Rh 0.015 from Table 10.1, Q 1 2 1.0 2/3 1/2 ARh S0 n y. Manning’s formula (10.19) in SI units gives, with n 1 1.0 (2y2) y 2 0.015 5 m3/s or 2/3 (0.001)1/2 which can be solved for y8/3 y 1.882 m8/3 1.27 m Ans. The proper area and width are...
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