Flow separation at the upstream edge of a square-edged broad-crested weir

Abstract

A simple model is suggested to explain the flow mechanism at the upstream edge of a square-edged broad-crested weir. The separation bubble that may be seen to occur at this point is treated as an area of constant static head, while the main flow outside the bubble is deemed to be irrotational and divided from the bubble by a free streamline. If this model is accepted, the flow pattern will be such that energy requirements will be met along the free surface and the streamline bounding the bubble while, within these boundaries, the Laplace equation will be satisfied at every point. Accordingly, a solution satisfying these conditions is established by the use of a relaxation technique.In practice, it is likely that the cavity flow within the bubble will be bounded not by a single streamline but by a turbulent mixing zone and that there will be some increase in pressure near the point of re-attachment. Nevertheless, the surface profile and flow pattern observed in experiments show fair agreement with those predicted using the simple model. Whilst acknowledging, then, that the bubble and the zone bounding it are in fact of a more complex character, we may say that this simplified treatment affords a sound model of the main flow and so permits a better understanding of the action of the square-edged broad-crested weir.