The flow under sluice gates is nowadays frequently still determined by empirical approaches, based on the Bernoulli equation and a specific discharge coefficient which depends on the geometry of the sluice gate. This discharge coefficient is determined from a selection of tables and charts, which are based on a variety of experimental series. In 2016 Malcherek developed a fundamentally new approach to describe hydraulic structures based on integral momentum balance instead of Bernoulli’s energy conservation principle. In this approach a flow is described as the result of the integral momentum balance including pressure forces on open boundaries as well as closed walls, momentum fluxes through open boundaries and gravitational and frictional forces. In this theoretical approach, the discharge under inclined sluice gates can be described as a result of the acting pressure forces and momentum fluxes. To apply the theory, the pressure integral at the sluicegate and under the sluice gate and also the momentum integral of the flow under the sluice gate have to be known. For the determination of these values, multiphase CFD simulations for different angles of inclination and waters levels upstream of the sluicegate were done by the authors in the paper “Theoretical and numerical analysis of the pressure distribution and discharge velocity in flows under inclined sluice gates” (AJKFLUIDS2019 5020).
Using the values determined in this previous paper, parametrized model equations for the pressure and momentum integrals in dependency of the angle of inclination and upstream water levels were derived in this work. These polynomial approaches have been used to determine the three unknown physical quantities in the integral momentum balance: the pressure integral at the sluice gate, the pressure integral under the sluice gate and the momentum integral of the flow under the sluicegate. The polynomial approaches are shown in detail in this work.