Assessing Stage-Discharge Relationships for Circular Overflow Structure

Circular overflow structures are used in irrigation and drainage networks as water measuring structures. Different approaches can be found in the literature to formulate the stage-discharge relationship of the circular weir. They are mainly categorized in three groups: (1) methods trying to simplify the complex elliptic integrals coming from the theoretical discharge equation; (2) methods that use the orifice formula and a discharge coefficient specific for the circular weir; and (3) approaches using dimensional analysis and Buckingham’s Theorem. In this study, a nondimensional stage-discharge formula was obtained using Buckingham’s Theorem to define the flow over the sharp-crested circular weir. Then the current available methods and experimental data from the literature were employed to calibrate the theoretically deduced stage-discharge relationship. The effect of the approach channel on the stage-discharge formula was also investigated using the experimental data available in the literature. Finally, the performances of different stage-discharge relationships are discussed and practical suggestions are provided.