Application of Newton–Raphson Method for Computing the Final Air–Water Interface Location in a Pipe Water Filling

The estimation of thermodynamic behavior during filling processes with entrapped air in water pipelines is a complex task as it requires solving system algebraic-differential equations. A lot different numerical methods have been used for this purpose literature including the rigid column (RWC) model. main advantage RWC model its acceptable accuracy very low computational load. In that context, research presents computation critical points physical equations describe phenomenon. These provide information about final position air–water interface. Newton–Raphson method was then applied to obtain unique equation can be by engineers directly compute variables such pocket pressure and length at end hydraulic event. case study analyzed compare results mathematical obtained computing points. Both provided same values sensitivity analysis conducted identify dependent non-dependent parameters evaluating proposed formulation validated through an experimental set data.