Theoretical Analysis of Flow Past Leaf Gate

A theoretical method is developed to predict the mean flow of a two-dimensional turbulent jet spreading in a duct of constant width. The mean velocity distribution in the zone of recirculation is idealized. Integral momentum equations in conjunction with the integral continuity equation are used to calculate the streamwise variations of the mean pressure and three parameters characterizing the mean velocity profile. The theoretical model of the confined jet is then applied to the re-attaching flow past vertical plates of moderate height to determine the streamwise distribution of static pressure. For plates of heights comparable to the depth of the duct, the flow is represented as a plane turbulent wall jet spreading in a duct. The theory is found to predict satisfactorily the point of separation of the boundary layer from the top wall observed in the experiments.