Water quality modeling for a sinusoidally varying waste discharge concentration

Abstract

Biochemical oxygen demand modeling in a river involves derivation and solution of the governing partial differential equation which describes concentration change with time and space brought on by convective, dispersive, and decay processes and the loading function. In this study, a sinusoidal variation in waste discharge concentration is considered. The governing partial differential equation is solved analytically by a transform method and by assuming that the solution varies periodically in time. The concepts of memory length and memory time are used to indicate when the solution becomes quasi-steady (periodic). The analytical solution is compared with two other solutions. The three solutions produce comparable results. However, the analytical solution is much easier to apply. The analytical solution extends the number of boundary conditions which a modeler can apply to describe real engineering problems.