Analytical Solution for Normal Depth Problem in a Vertical U-shaped Open Channel Using the Rough Model Method

Abstract

Normal depth plays a significant role in the design of open channels and in the analysis of the non-uniform flow as well. Currently there is no analytical method for calculating the normal depth in the open channels. Current methods are either iterative or approximate and consider, unreasonably, Chezy’ coefficient or Manning’s roughness coefficient as a given data of the problem. Yet, both of these coefficients depend in particular on the normal depth sought and it is therefore unjustified to fix them beforehand. To overcome this drawback, the rough model method (RMM) seems to be the most appropriate tool. The RMM takes into account, in particular, the effect of the absolute roughness which is a readily measurable parameter in practice. The method is based on known referential rough model characteristics used to deduce the normal depth by means of a non-dimensional correction factor.