Study of Transient Modes of Incompressible Fluid Flow in Relief Sections of Pipelines with Changes in Velocity at Their Boundaries

The paper considers modeling of unsteady flow of incompressible fluid in an elementary section of a pipeline with changing relief, in which the boundary conditions for velocity change over time. The study is based on linearized quasi-one-dimensional equations modified based on the approach of N.E. Zhukovsky. To analyze the flow velocity, the method of separation of variables is used, which allows solving a simplified telegraph equation. The pressure is determined by integrating the equations of motion taking into account the found velocity distribution.
Numerical modeling of transient processes was performed for various variants of initial and boundary conditions, including cases with constant functions. Scenarios of average pressure change along the section were analyzed: stable, increasing and decreasing. Particular attention was paid to the influence of friction on the formation and evolution of shock waves in comparison with the model where the friction force is not taken into account.