Filling of Pipelines with Undulating Elevation Profiles

The authors develop a model that describes the unsteady motion of a lengthening rigid water column filling an empty pipeline with an undulating elevation profile. The model provides time histories of the water column's length, velocity, and pressure at various sites. A criterion to evaluate the applicability of the model is given in terms of air intrusion at the advancing front. The early phase of filling was examined experimentally. The model yields velocities comparable with the experimental data. A high but short-lived peak velocity is possible when the inlet submergence is large, the entrance head loss small, and the length of water column short. With column lengthening comes acceleration or deceleration according to the undulating profile, the inertia of the column, and the velocity history. The model captures the interaction of the variables. Applications of the model for evaluating the velocity history and for judging the occurrence of column separation in filling an undulating pipeline are illustrated in an example.