VARIED FLOW THROUGH SYSTEM OF GUTTERS AND GRATES

An adaptation of the Newton Method is used to solve the combined system of ordinary differential and algebraic equations that describe the spatially varied flows that occur from lateral inflow with periodic outflow along open channels. The application selected is lateral inflow into gutters with periodically spaced grates in its bottom through which the accumulated flow is discharged. The occurrence of critical flow may allow the lateral inflow to be solved as a separate problem, and the outflow to be handled separately. Where subcritical flow exists, the composite system of differential and algebraic equations resulting from a series of gutter-grates must be solved simultaneously. Solutions to such example applications are given. Keywords– Open channel flow, differential equations, gutters, grates, hydraulics, lateral inflow/outflow, numerical analysis, system of equations, varied flow, water flow 1. AN INTRODUCTION TO EQUATION FOR SPATIALLY OF VARIED FLOWS Spatially varied flows occur when the flow rate in an open channel increases or decreases in magnitude because there is either lateral inflow or outflow from the channel. Such flows are governed by the following first order ordinary differential (ODE) that can be found in text books [1-4]. (This equation can be obtained from the energy principle for the outflow situations, but requires the momentum principle for lateral inflow.)