Theoretical and Numerical Analysis of the Pressure Distribution and Discharge Velocity in Flows Under Sluice Gates

The flow under sluice gates is well known in open channel hydraulics. There are theoretical, semi-empirical and empirical equations to determine the flow rate under a sluice gate Most of these formulas are based on the Bernoulli equation applied at the inflow cross section and in the vena contracta behind the gate. In 2017 Malcherek [1] showed that it is also possible to apply the integral momentum balance to the sluice gate. When assuming hydrostatic pressure distributions in the inflow cross section and on the weir’s plate then the simple formula $VA=(3/4) g h0=0.6122 g h0$ is obtained, which is in perfect agreement with the classical vena contracta theory for small opening ratios h₀/a. In the outflow cross section under the gate the bottom pressure was assumed to be the mean of the hydrostatic bottom pressure before and behind the sluice gate. In this paper Malcherek’s momentum balance theory will be investigated in further detail with numerical CFD RANS computations of the free surface flow below sluice gate. The exact pressure distributions on the bottom as well as on the gate were obtained for different openings ratios and flow conditions at the sluice gate in a systematic parameter study. These pressure distributions have been introduced into the integral momentum equation and the discharge velocity as well as the flow rate at the sluice gate were investigated and compared with the pure numerical results. These results were also compared with the theoretical and empirical approaches of the literature and a detailed analysis is given.