Head-discharge relationship of flumes: Energy loss versus boundary layer

Long-throated flumes are measurement structures often used in water and wastewater systems to determine the flow discharge. The head-discharge relationship of long-throated flumes is traditionally determined following the critical flow theory and the boundary layer concept. After a review of the traditional approach and an analysis of the approximate assumptions of the boundary layer approach, this study revisits the energy loss approach as an alternative to the questionable boundary layer concept for the determination of the discharge in long-throated flumes. Computational fluid dynamics (CFD) is used for determining the kinetic energy correction coefficient and the piezometric energy correction coefficient along the throat of the flume (especially in the critical section); CFD is also used for locating the critical section and determining the energy loss between the measurement section and the critical section. A new method based on the kinetic energy correction coefficient, the piezometric energy correction coefficient and the energy loss between the measurement section and the control section is proposed. A step-by-step procedure is given for the head-discharge calculation. It appears that the proposed alternative is a simple and promising method to accurately determine the discharge coefficient.