A mixing length model for estimating channel conveyance

Abstract

This paper describes a simple, physically based mixing length model that explains the functional form of Manning's equation for mean velocity in open channels. Manning's equation has been used to describe mean velocity for over 100 years and is essentially an empirical result rather than being based on an understanding of physical processes. The model described in this paper uses Prandtl's mixing length hypothesis, with mixing length modelled at each point within the cross-section being proportional to the distance to the nearest solid boundary. The model solves equations for the along-stream velocity field using a simple numerical method on regular and irregular finite-difference meshes. The results of the model are compared with Manning's equation and the Colebrook–White formula, giving good agreement across a range of channel sizes, roughnesses and geometries. The results and comparison are used to draw useful insights into open channel flows.