Stage-Discharge Relationship for Weir–Orifice Structure Located at the End of Circular Open Channels

Weirs and orifices of different shapes are widely used as flow-measuring devices or adjusting the upstream water level. These water structures can be combined, yielding a simultaneous flow over the weir and through the gate. A combined weir–gate (weir–orifice) structure can be used for flow measurement with the added benefit that sediment deposition behind the structure will be limited. This study introduces a sharp-edged plate installed at the end of a circular open channel in which flow is discharged into the atmosphere as a simple flow-measurement device. This weir–gate system yields a simultaneously free outflow over and under the plate. Most of the floating materials and sediments will pass through this flow-measurement device because the structure has no lateral contraction. The energy principle (results in weir and orifice relations) helps to deduce a suitable mathematical form for the stage-discharge equation. The energy principle and Buckingham’s theorem of dimensional analysis both were used to deduce the stage-discharge relationships. A series of laboratory experiments (626 runs) was conducted in two circular open channels to calibrate the deduced stage-discharge relationships under free-outflow conditions. The results showed that the best model to describe the stage-discharge relationships could be obtained using the energy principle (physically based approach) and dimensional analysis. The proposed general stage-discharge relationship had an average error of 1.89% with a maximum error less than 9.82% for the experimental trials. The results also showed that the dimensional analysis is not powerful enough alone for obtaining an accurate stage-discharge model. The theoretical considerations can make the dimensional analysis powerful enough to obtain an acceptable stage-discharge equation, as shown in this research.