American Society of Civil Engineers


Economic Shape of Trapezoidal Open Channel Sections with Freeboard


by Warren E. Howland, M.ASCE, (Emeritus Prof. of San. Engrg., Purdue Univ., Lafayette, Ind.) and Howard C. Howland, (Assoc. Prof., Div. of Biological Sci., Cornell Univ., Ithaca, N.Y.)

Journal of the Hydraulics Division
, Vol. 101, No. 5, May 1975, pp. 639-643

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Document type: Technical Note
Abstract: It can be proved mathematically that the maximum flow by the Manning formula is an open channel of trapezoidal cross section of fixed side slopes and with a fixed freeboard occurs r=(5/2)fx/q, in which r = the hydraulic radius of the wetted section; x = the bottom width of channel section; and q=2L-W, the difference between the total length of the side slopes, 2L, and the top width, W, of the excavated section; and f, herein called freeboard, is the vertical distance between the present or undisturbed ground surface and the proposed water surface in the finished channel. It is assumed to be below the original ground surface.


ASCE Subject Headings:
Open channel flow
Water flow
Hydraulics
Channels