An analytical solution of the nonlinear storage routing equation is presented. The solution is applicable for the particular case of a constant-area reservoir and a culvert outlet. It allows for arbitrary inflow hydrographs, which can be approximated by a series of linear segments. The resulting solution is an implicit expression relating the outflow or storage with time. Explicit algebraic equations for the maximum storage and outflow in terms of the reservoir and inflow parameters have also been obtained. The analytical results have been applied to a specific inflow hydrograph to formulate simple design equations for a circular culvert outlet and a constant-area reservoir which compared well with similar published equations.
