Why dimensional analysis and self-similarity are useful to determine a stage-discharge relationship: A review

The stage-discharge relationship of weirs, gates, and flumes is generally deduced by applying classical physics and using the experimental analysis to study the flow characteristics and correct the deviations of the theoretical discharge from the measured one by an empirical discharge coefficient. For these measurement devices, the classical hydraulic approach continues to be widely applied, notwithstanding studies applying dimensional analysis to investigate the flow over the weirs, under the gates, and in a flume are available and useful to obtain accurate theoretical stage-discharge relationships. This paper presents the state of the art on the application of dimensional analysis and self-similarity theory for different types of weirs, gates, and measurement flumes. The main aim is to demonstrate the usefulness of this approach, in comparison with the classic hydraulic one, to deduce a theoretically based stage-discharge relationship.