An Implicit Formulation for Calculating Final Conditions in Drainage Maneuvers in Pressurized Water Installations

Emptying processes are typical maneuvers that should be performed by water distribution companies for operation purposes. These processes involve a complex numerical analysis, since a set of algebraic and ordinary differential equations needs to be solved for the intricacy of hydraulic and thermodynamic formulations for two analyzed phases (liquid and gas). This research provides an implicit equation to compute exactly the final conditions in water emptying operations in single pipelines without an air valve (or admitted air). The implicit expression was developed by considering that for all final conditions, the water velocity is null, and thus, the water column length and air pocket pressure can be computed. The friction factor, internal pipe diameter, and opening maneuvers of drain valves do not disturb the final conditions in draining processes. The developed implicit formulation was validated using experimental measurements in a pipeline with a total length of 4.36 m. The equation is of utmost importance, since it can be utilized for engineers to easily plan for future conditions in water distribution networks.