Critical flow over spillway profiles

Abstract

One of the oldest problems of critical flow in open-channel hydraulics is rise in the channel bottom, which causes a critical flow at the weir crest. Although the classic hydraulic theory for parallel flow shows the usefulness of critical flow leading to unique head–discharge relations over the weir, in practice the parallel flow condition is unreal; theoretical analysis of round-crested weirs is thus restricted to teaching purposes or is used as a rough indication of flow characteristics before using more complete methods. The spillway problem has been treated previously with more laborious methods, either using two-dimensional (2D) hydrodynamic flow nets or accurate physical model experiments. A new extended Bernoulli energy equation, which is valid for moderately curved channel flows, is presented. From this equation, a higher-order critical flow condition suitable for a curved streamline flow has been developed. As a practical application, the flow over spillway profiles used in dam engineering has been studied. The proposed new critical flow theory makes it possible to simulate flow features with a reasonable agreement up to design conditions of the spillway, thus obtaining accurate results in situations in which the velocity is non-uniform, the pressure is non-hydrostatic and conventional critical flow theory is not valid.