Abdulrahman Abdulrahman
Numerical Solution of Manning&039;s Equation in Rectangular Channels
740 - 743
2017
11
6
International Journal of Civil and Environmental Engineering
https://publications.waset.org/pdf/10007232
https://publications.waset.org/vol/126
World Academy of Science, Engineering and Technology
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&39;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 trialanderror solution; 2) constructing a nondimensional graph; 3) preparing tables involving nondimensional parameters. Author in this paper has derived semianalytical solution to Manning&39;s equation for determining the flow depth given the flow rate in rectangular open channel. The solution was derived by expressing Manning&39;s equation in nondimensional form, then expanding this form using Maclaurin&39;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&39;s equation is valid over a large range of parameters, and its maximum error is within 1.586.
Open Science Index 126, 2017