Scale effects of round-crested weir flow

Scale effects of round-crested weir flow originate from viscosity and surface tension. No general weir flow equation accounting for these is available in the literature. In this work an equation is developed accounting for scale effects. Given the lack of knowledge on the laminar boundary layer development for these flows, detailed two-dimensional and integral laminar boundary layer solutions were obtained, from which an analytical solution results. The surface tension effect is included by allowing for high streamline curvature effects, as is typical for flow over very small weir models. The developments were used to successfully predict the discharge characteristics of circular weirs of small crest radius of curvature. The research indicates a minimum of R=0.01 m. Provided that 0.01 m<R<0.30 m, a minimum overflow head of 0.04 m keeps the discharge curve free from significant scale effects. The equations are also applied to the broad-crested weir using a flow analogy for the separation bubble.