Discharge coefficients formulae of grate inlets of complicated conditions for urban floods simulation and urban drainage systems design

With the acceleration of climate change and urbanization, all over the world is widely facing serious urban flooding problems. Grate inlets are key elements for the discharge exchange of surface flows and underground sewer flows in urban floods, so the accurate calculation of the overflow discharges of the grate inlets is related to the accurate simulation of the urban flood evolution process, which also plays an important role in the design of sustainable urban drainage systems. This study investigated the discharge coefficients of six types of grate inlets under different approaching discharges, transverse and longitudinal road slopes through 285 indoor 1:1 tests, mainly focusing on the supercritical flow conditions with less attention before. The experimental results show that: (1) With all other parameters being equal, as the interception discharge Q increases, the discharge coefficient increases. When the approaching Froude number increases, the discharge coefficient also decreases. The performance of parallel grate inlets in terms of discharge coefficients is not significantly different from that of vertical grate inlets. (2) Using Buckingham's theorem of dimensional analysis, 12 groups of accurate grate inlets discharge coefficient calculation formulae were creatively proposed. The average relative errors of the 12 groups of formulae are 0.37% ∼ 5.41%, indicating that the calculated values of the formulae and the measured values are in good agreement. (3) The discharge coefficients of grate inlets were found to show a strong dependence on the Froude number of the approaching discharge, being in agreement with previous study result. But the relative error of individual data in this method is large, so the use of equations with more influencing parameters is recommended. A novel and effective method was also proposed to calculate the interception discharge of the grate inlets by iteration. This study can provide important references for the design and selection of grate inlets for urban drainage systems and also provide support for accurate simulation of urban floods.