Abstract

A revised derivation of the discharge coefficient for flows over thin weirs and sills in the limits of wall overflow to a free overfall is given. Using dimensional analysis, we show that the discharge coefficient, (Formula presented), in the classical weir-discharge equation is best understood as a weir Froude number, (Formula presented), which accounts for the combined effects of inertia, contraction and viscous energy losses within the flow field. A comprehensive set of experimental data from historical studies is complimented by new data from the authors, featuring both laboratory flume experiments and three-dimensional numerical simulations of weir flows. Synthesis of these data elucidates the interaction between the coupled pressure and velocity fields, and the balance between inertial and contraction effects as (Formula presented) varies. Analysis of the vertical pressure gradient reveals that the thickness of the nappe initially widens with increasing inertia but then contracts again towards the free overfall limit due to diminishing flow separation at the base of the weir. These insights allow for a physical explanation of the transition between weir and sill flows using the channel Froude number. Practical limitations on predicting weir discharge and a description of characteristic flow regimes are also set forward.

Department(s)

Civil, Architectural and Environmental Engineering

Publication Status

Open Access

Keywords and Phrases

free jet overfall; free-surface flows; hydraulics; hydrodynamics; sill flow; weir flow

International Standard Serial Number (ISSN)

2633-4259

Document Type

Article - Journal

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 2025 Cambridge University Press, All rights reserved.

Creative Commons Licensing

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

Publication Date

08 Aug 2025

Download

Full Text Link

Share

 
COinS