Discharge Coefficient of Rectangular Short-Crested Weir with Varying Slope Coefficients

Rectangular short-crested weirs are widely used for simple structure and high discharge capacity. As one of the most important and influential factors of discharge capacity, side slope can improve the hydraulic characteristics of weirs at special conditions. In order to systemically study the effects of upstream and downstream slope coefficients S-1 and S-2 on overflow discharge coefficient in a rectangular short-crested weir the Volume of Fluid (VOF) method and the Renormalization Group (RNG) kappa-epsilon turbulence model are used. In this study, the slope coefficient ranges from V to 3H:1V and each model corresponds to five total energy heads of H-0 ranging from 8.0 to 24.0 cm. Comparisons of discharge coefficients and free surface profiles between simulated and laboratory results display a good agreement. The simulated results show that the difference of discharge coefficients will decrease with upstream slopes and increase with downstream slopes as H-0 increases. For a given H-0, the discharge coefficient has a convex parabolic relation with S-1 and a piecewise linearity relation with S-2. The maximum discharge coefficient is always obtained at S-2 = 0.8. There exists a difference between upstream and downstream slope coefficients in the influence range of free surface curvatures. Furthermore, a proposed discharge coefficient equation by nonlinear regression is a function of upstream and downstream slope coefficients.