A mixing length model for estimating channel conveyance

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 b...

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Bibliographic Details
Published in:Proceedings of the Institution of Civil Engineers. Water management 2013-04, Vol.166 (4), p.165-174
Main Authors: HORRITT, Matthew S, WRIGHT, Nigel G
Format: Article
Language:English
Subjects:
Applied sciences
Boundaries
Buildings. Public works
Channels
Cross sections
Exact sciences and technology
Finite difference method
Hydraulic constructions
Mathematical analysis
Mathematical models
Open channel flow
Open channels
River flow control. Flood control
Water management
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Summary: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.
ISSN:1741-7589
1751-7729
DOI:10.1680/wama.11.00066