Stage-discharge relationship for a pipe overflow structure in both free and submerged flow

Many facilities for urban drainage systems are equipped with a pipe overflow structure that can often be treated as a circular broad-crested weir. Thus it is possible to evaluate the overflow discharge through this device by measuring the water levels in the upstream tank and at the outlet of the pipe. In the present study, computational fluid dynamics (CFD) is used to determine a relationship between the discharge and the water levels upstream and downstream of the orifice for a range of diameters between 200 and 600 mm and a relative head up to 2. Over 50 numerical simulations are performed to take into account all the operating conditions of the system: free flow, submerged flow and pressurized flow. A regression is applied to the resulting data in order to obtain an orifice equation valid in both free-flow and submerged-flow regimes. Specific formulas, derived from Bernoulli's theorem, are also given for pressurized flows. The proposed methodology is applied to two examples.