Unformatted text preview: analysis of the trapezoid section will show the basic results.
Consider the generalized trapezoid of angle in Fig. 10.7. For a given side angle
, the flow area is
A y2 by cot (10.22) The wetted perimeter is
P b 2W b 2 1/2 ) (10.23) 2 1/2 (10.24) 2y(1 Eliminating b between (10.22) and (10.23) gives
y y 2y(1 To minimize P, evaluate dP/dy for constant A and
A 2 2 1/2 y [2(1 ) P ) and set equal to zero. The result is
2 1/2 4y(1 ) 2y Rh 1
2 y (10.25) The last result is very interesting: For any angle , the most efficient cross section for
uniform flow occurs when the hydraulic radius is half the depth.
Since a rectangle is a trapezoid with
0, the most efficient rectangular section
is such that
2y2 A P 4y Rh 1
2 y b 2y (10.26) To find the correct depth y, these relations must be solved in conjunction with Manning’s flow-rate formula (10.19) for the given discharge Q. Best Trapezoid Angle Equations (10.25) are valid for any value of . What is the best value of for a given
depth and area? To answer this question,...
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- Spring '08
- Fluid Dynamics, Fig, e-Text Main Menu, subcritical flow