Numerical Investigation of Free Overfall from a Circular Pipe Flowing Full Upstream

Abstract

Results are presented for a computational study of free overfall from a smooth, horizontal, circular pipe that is flowing full upstream. The limiting discharge value that delineates the partially full and full pipe flows was established. Two different flow regimes for partially full pipe outflows were observed: cavity outflow in which an air bubble intrudes into the pipe and the water has a horizontal surface at some distance from the outfall, and bubble washout flow in which the cavity is shorter and the water surface is never horizontal. The outflow water depth and cavity length were expressed as functions of the discharge. The simulated data for several controlling parameters provided good agreement with available data in the literature. The end-depth ratio (EDR), i.e., the ratio of the brink depth to the critical depth (the depth at which the Froude number is one for the given flow rate and pipe diameter), was found to be 0.75 for the cavity outflow regime. For the bubble washout regime, the EDR is shown to vary linearly with the dimensionless critical depth. The simulation results were used to calculate several governing parameters, i.e., the Froude number at the brink, upstream and downstream pressure coefficients, and the minimum slope of the water surface in the cavity. Each of these parameters behaved differently in the two flow regimes. However, the nondimensional pressure distribution at the brink was the same for both flow regimes. The momentum equation was applied to the flow using appropriate pressure and momentum coefficients derived from this study to accurately predict the discharge as a function of the brink depth for the bubble washout regime. These findings provide insights into the mechanics of a free overfall from partially full pipes at the outlet, and explain the transition between the cavity flow and bubble washout regimes.