Chapt10

107 geometry of a trapezoidal channel section b p

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 P A 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,...
View Full Document

Ask a homework question - tutors are online