Extraction of the Flow Rate Equation under Free and Submerged Flow Conditions in Pivot Weirs with Different Side Contractions

Pivot weirs are used in irrigation networks to regulate water surface elevation and flow rate measurements. For ease of operation, this type of weir can be implemented in automatic operations of irrigation networks. However, little research has been performed to determine the head-discharge equation for this type of weir. In this research, two equations are used to calculate discharge over the pivot weir. The first equation is Kindsvater-Carter’s discharge equation, which is commonly used as the normal rectangular weir equation. The second is derived from energy and critical depth equations. To determine the coefficients of these equations, some tests were performed on an experimental model using three pivot weirs with different angles ($\theta =0$, 20, 40, 60, 80, and 90°) and side contractions of 0.4, 0.6, and 0.8. The experimental data were then compiled with the United States Bureau of Reclamation (USBR) data, and based on dimensional analysis, the discharge coefficients were estimated for free and submerged flow conditions. The accuracy of two equations under free-flow conditions was within $\pm 15$ and $\pm 10\%$, respectively. The range of error for the second equation in submerged flow condition was less than $\pm 20\%$, and the submergence factor was between 0.2 and 0.9, which is acceptable for application.