Routing Equations for Detention Reservoirs

Abstract

Routing equations for detention reservoir systems are developed from an approximate analytical solution of the nonlinear storage differential equation. The approximate solution is obtained by a two-term perturbation expansion whereby the zeroth-order term is the linear solution and the first-order term is the correction. The first-order approximation, which allows for arbitrary multievent inflow hydrographs, irregular reservoir configuration, and various types and sizes of outlets, is found to be accurate for all practical purposes. The asymptotic solution allowed the derivation of design equations that can apply for arbitrary reservoir configuration and for various types and sizes of outlet.