GENERAL STAGE–DISCHARGE RELATIONSHIP FOR SHARP‐CRESTED POWER‐LAW WEIRS: ANALYTICAL AND EXPERIMENTAL STUDY

Abstract

AbstractThe efficient use of water for irrigation and agriculture projects depends mainly on measurement of water. Weirs are widely used in irrigation networks to measure flow discharge. Flow estimation through weirs of different shapes is very important in irrigation engineering. Weirs are characterized by a relation between the water head and discharge, which mainly depends on the shape and dimensions of the weir. A power‐law weir is very versatile and allows modelling of weirs with different shapes. The generic results of the power‐law weir can also be applied to its special forms such as triangular, semi‐cubic, parabolic, cubic and rectangular weirs. Up to now, the hydraulic behaviour of a general power‐law weir has not been studied. In this study, sharp‐crested power‐law weirs were studied experimentally and theoretically. For this, weir (Model I) and critical flow (Model II) theories along with Buckingham's theorem of dimensional analysis were used to deduce the stage–discharge relationship of power‐law weirs. A series of laboratory experiments (502 runs) were performed to calibrate the deduced theoretical stage–discharge relationships under free‐flow conditions. The proposed general stage–discharge relationships have an average error less than 1.7%; thus, actual discharge through the channel can be simply and reliably estimated. © 2019 John Wiley & Sons, Ltd.