Computation of Normal Depth in Horseshoe Shaped Tunnel 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 calculation of the normal depth in open channels, including the horseshoe profile. Current methods are either iterative or approximate. They also consider, unreasonably, Chezy’s coefficient or Manning’s roughness coefficient as a given data of the problem, despite the fact that these coefficients depend on the normal depth sought. In this study, a new analytical method is presented for calculating the normal depth in a horseshoe shaped tunnel. The method takes into account, in particular, the effect of the absolute roughness which is a readily measurable parameter in practice. In a first step, the method is applied to a referential rough model in order to establish the relationships that govern its hydraulic characteristics. In a second step, these equations are used to easily deduce the required normal depth by introducing a non-dimensional correction factor. A practical example is considered to better explain the advocated method and to appreciate its simplicity and efficiency.