Discharge Coefficients for Orifices Cut into Round Pipes

This study focuses on the discharge coefficient ($C_d$) for flow into orifices cut with a circular bit perpendicular to and along the centerline of a round pipe, a common configuration on perforated risers installed as the principal outlets for stormwater detention or sediment basins. When predicting flow, the orifice area is generally defined as the area of the bit used to cut the hole, but the true orifice area is larger than the bit due to the curvature of the riser pipe. Four different descriptions for orifice area were tested while attempting to fit $C_d$ to measured discharge experiments. The tests showed that $C_d$ decreases as the orifice diameter approaches the diameter of the riser. Photographic imagery shows that the reduced $C_d$ is due to lateral flow from the riser’s curved sides decreasing the vena contracta area more than what normally occurs during flow through an orifice in a flat plate. In contrast, but to a lesser extent, $C_d$ increases as the water surface approaches the top of the orifice. Best fit equations to model $C_d$ were developed to better estimate flow, with the most applicable having an $R^2$ of 88.8% and a root-mean squared error of 0.028. Orifice elevation above the tank floor was measured and initially modeled but was ultimately not included in the $C_d$ model because the $R^2$ improved by only 0.6%.