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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  eText 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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 Spring '08
 Sakar

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