TY - JFULL
AU - Abdulrahman Abdulrahman
PY - 2017/7/
TI - Numerical Solution of Manning's Equation in Rectangular Channels
T2 - International Journal of Civil and Environmental Engineering
SP - 739
EP - 743
VL - 11
SN - 1307-6892
UR - https://publications.waset.org/pdf/10007232
PU - World Academy of Science, Engineering and Technology
NX - Open Science Index 126, 2017
N2 - 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%.
ER -