Applicability of the Elastic Water Column Method to Pressurized Pipeline Emptying: Dimensionless Pressure Analysis Under Different Air Pocket Configurations

Pressurized pipelines are critical components in hydraulic engineering systems, including urban water supply networks and hydroelectric power plants. These systems are susceptible to air entrapment during operations such as filling and emptying, which can reduce the effective flow area and trigger critical pressure surges or sub-atmospheric conditions. One-dimensional approaches, namely the Rigid Water Column (RWC) and Elastic Water Column (EWC) models, are the most widely used due to their balance between physical accuracy and computational practicality. EWC models have been widely used to analyze transient phenomena in pipe filling and water hammer processes; however, their application to emptying operations is limited. For this reason, this study develops an EWC-based formulation for emptying operations and assesses pressure behavior through a dimensionless analysis for different air pocket configurations. The developed model couples the Method of Characteristics (MOC) with a polytropic air pocket model, enabling the representation of wave propagation effects that RWC-based models cannot capture. The formulation is verified against 24 experimental cases, yielding a mean absolute error of 0.35% in minimum pressure prediction. The results show that dimensionless air pocket ratios 𝑥0/𝐿𝑇
between 0.17 and 0.83 produce minimum pressures between 0.309 and 0.877 𝑝∗𝑎𝑡𝑚
, confirming that smaller initial air pocket volumes generate the most severe depressurization conditions. The inclusion of an air valve in the most critical scenario effectively prevents sub-atmospheric pressure development, underscoring the protective role of air admission devices. These findings provide a dimensionless framework for characterizing transient pressure risk during pipeline emptying across different operational conditions.