Critical Depth Relations for Flow Measurement Design

Abstract

Long-throated flumes and broad-crested weirs are becoming widely used for open-channel flow measurement, primarily because of their simplicity and numerical predictability. These flumes and weirs are constructed such that flow in the throat or crest is nearly parallel, i.e., no streamline curvature. Under these conditions, standard critical depth relationships apply (i.e., hydrostatic pressures). Design is based on determining the amount of contraction from the approach section to the throat that is needed to produce critical flow. The existing design procedure is to determine an acceptable contraction amount by trial and error. In this paper, mathematical relationships are developed for precisely determining the amount of contraction needed. These relationships are solved with a convergent-iterative procedure. Several new relationships for critical flow are also developed.