Filling of Pipelines with Undulating Elevation Profiles

Abstract

A model is formulated to describe the unsteady motion of a lengthening rigid water column filling an empty pipeline with an undulating elevation profile. The model gives time histories of the water column's length, velocity, and pressure at various locations. A criterion to judge the applicability of the model is given in terms of air intrusion at the advancing front. The early phase of filling was investigated experimentally. The model yields velocities comparable with the experimental data. A high but short-lived peak velocity can occur when the inlet submergence is large, the entrance head loss small, and the length of water column short. As the column lengthens, it accelerates or decelerates according to the undulating profile, the inertia of the column, and the velocity history. The interaction of these variables is captured by the model. Applications of the model for assessing the velocity history and for judging the occurrence of column separation in filling an undulating pipeline are demonstrated by an example.