Enhancing Friction Models for Starting Up Water Installations Containing Trapped Air

Starting up water installations is typically a task that falls within the purview of water utility companies. These operations involve the presence of two separate fluids (water and air) that can be analyzed in terms of consideration two distinct behaviors (hydraulic and thermodynamic). During a filling process, trapped air pockets exhibit a trend of declining volume, generating pressure surges that are typically not addressed under current worldwide regulations. This research introduces an innovative mathematical approach based on physical equations to investigate filling operations in water installations involving trapped air, incorporating an unsteady friction model (using the Brunone friction coefficient), in combination with the rigid water column model. The validation of the proposed model is carried out in an experimental facility measuring 7.36 m in length. The proposed model is then applied to a case study involving a 460 m long pipeline with an internal pipe diameter of 150 mm, featuring an undulating profile composed of three branches, to demonstrate how the gravity term should be calculated in real-world water installations. The results showed that the proposed model, considering an unsteady friction model, is suitable for simulating the start up of water pipelines for the experimental facility analysis and the case study. The Swamee–Jain formula yielded the best results compared to other formulations for computing the friction factor.