DEVELOPMENT OF FLOW EQUATION FOR HYPERBOLICALLY SHAPED SHARP CRESTED WEIRS

摘要

Experiments are performed in an open channel under uniform steady flow conditions to generate basic head discharge data for three hyperbolically shaped sharp crested weir sections of varying flatness; having eccentricities 1.1, 1.15 and 1.2 respectively. The computation of flow obtained by integrating the discharge through infinitesimal small arbitrary strip of the section gives rise to complicated elliptical integrals. A multivariate regression analysis is therefore performed to develop the flow equation. A dimensional analysis is carried out to establish independent parameters:a/H, b/H and a_w/H~2 and dependent parameter Q/H~(2.5) g~(0.5). The first two independent parameters a/H and b/H are dimensionless heads causing the flow whereas the term a_w/H~2 is the relative area of the weir section. In addition the terms a/b relating purely to the weir geometry and a_w/A_c the ratio of wetted area of weir section to the wetted channel area are also analyzed to check their utility. A flow equation is developed to give a relationship between dependent discharge and the independent parameters affecting the flow. The computed data fits well to the experimental data giving a coefficient of correlation equal to 0.97. Literature on sharp crested weirs was reviewed, but to the best of knowledge of the authors the hyperbolic shape does not find mention in existing literatures.