Equations and methodologies of inlet drainage system discharge coefficients: A review

Abstract

Accurate determination of grate inlet discharge coefficients is crucial in reducing modeling uncertainties and mitigating urban flooding hazards. This review critically examines the methods, equations, and recommendations for determining the weir/orifice discharge coefficients, based on the inlet parameters and flow conditions. Reviewing previous studies for inlets showed that the discharge coefficient of rectangular inlets under subcritical flow ranges from 0.53 to 0.6 for weirs and from 0.4 to 0.46 for orifices, while in grated circular inlets, it falls between 0.115 and 0.372 for weirs and between 0.349 and 2.038 for orifices. For circular non-grated inlets under subcritical flow, the weir and orifice coefficients are in the range of 0.493–0.587 and 0.159–0.174, respectively. However, the orifice discharge coefficients of grated and non-grated inlets with unknown Froude number range between 0.14–0.39 and 0.677–0.82, respectively. For supercritical flow, the weir and orifice discharge coefficients of grated and non-grated rectangular inlets are 0.03–0.47 and 1.67–2.68, respectively. Previous studies showed that it is recommended to correlate the discharge coefficients with the approaching flow and Froude number under subcritical and supercritical flows, respectively. Yet, additional studies are recommended for a better understanding of the limits and parameters governing the flow transitional stage between weir and orifice and between subcritical and supercritical conditions. Moreover, further research is required to determine the weir and orifice discharge coefficients of circular inlets under supercritical flow as well as the orifice discharge coefficient range of rectangular non-grated inlets under subcritical flow. Finally, it is recommended to increase the road surface roughness to reduce Froude number, and thereby, increase discharge coefficients of street inlets. The aim of this review is to help inlet designers and authorities promote sustainable cities with resilient urban drainage systems and reduce the environmental, economic, health, and social impacts of urban drainage failure.