Commenced in January 2007
Paper Count: 32579
Numerical Solution of Manning's Equation in Rectangular Channels
Authors: Abdulrahman Abdulrahman
Abstract:When the Manning equation is used, a unique value of normal depth in the uniform flow exists for a given channel geometry, discharge, roughness, and slope. Depending on the value of normal depth relative to the critical depth, the flow type (supercritical or subcritical) for a given characteristic of channel conditions is determined whether or not flow is uniform. There is no general solution of Manning's equation for determining the flow depth for a given flow rate, because the area of cross section and the hydraulic radius produce a complicated function of depth. The familiar solution of normal depth for a rectangular channel involves 1) a trial-and-error solution; 2) constructing a non-dimensional graph; 3) preparing tables involving non-dimensional parameters. Author in this paper has derived semi-analytical solution to Manning's equation for determining the flow depth given the flow rate in rectangular open channel. The solution was derived by expressing Manning's equation in non-dimensional form, then expanding this form using Maclaurin's series. In order to simplify the solution, terms containing power up to 4 have been considered. The resulted equation is a quartic equation with a standard form, where its solution was obtained by resolving this into two quadratic factors. The proposed solution for Manning's equation is valid over a large range of parameters, and its maximum error is within -1.586%.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1340204Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2140
 Bakhmeteff, B. A. (1932). Hydraulics of open channels. McGraw-Hill Book Co. Inc., New York, N.Y.
 Chow, V. T. (1958). Open Channel Hydraulics, McGraw-Hill Book Co. Inc., New York, N. Y.
 French, R. H. (1987). Open Channel Hydraulics, McGraw-Hill Book Co. Inc., New York, N. Y.
 Heading, J. (1970). Mathematical Methods in Science and Engineering, p. 40, 2nd Ed., Edward Arnold, London.
 Hendeson, F.M. (1966). Open Channel Hydraulics, Macmillan Company, New York, N. Y.
 Sturm, Terry W. (2001). Open Channel Hydraulics, P. 33, 1st Ed., McGraw-Hill Company, Inc., 1221 Avenue of the Americas, New York, N. Y. 10020.