The non-inertia wave model in its linearized form with a space- and time-dependent lateral inflow is solved for a finite-length channel. The study is performed for two kinds of upstream boundaries with a stage hydrograph at the downstream end. The limit of convergence of the flow rate is found to be dependent on the observed location for the positions between the boundaries of the lateral inflow, while the same for the stage depends on the location of observation throughout the channel. The backwater effect caused by the lateral inflow decreases the flow rate in the upstream direction and increases the stage along the channel. The higher values of the stage are found either between the two boundaries of the lateral inflow or for the locations downstream of it. The location of the lateral inflow is more influential on the flow behavior than the distance between the two boundaries of the lateral inflow segment. When a stage hydrograph is imposed at both ends of the channel and as the downstream boundary effect reduces, the effect of the lateral inflow added in the upstream section becomes dominant over the lateral inflow added closer to the downstream end. Corresponding to a Péclet number greater than 2.5, the lateral inflow responses for the semi-infinite-length channel present a suitable approximation in predicting the flow rate in the finite-length channel at the locations nearer the upstream end, but the same cannot be termed appropriate for the locations near the downstream boundary.
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