Dynamics of the Transient Process Caused by a Change in Flow Rate at the End of a Pipe Section for the Case with and Without Taking into Account the Resistance Force

Within the framework of the non-conservative form of quasi-one-dimensional linearized equations of N.E. Zhukovsky, the problem of the transient process in an elementary relief section of a pipeline with a temporary change in the boundary velocities of an incompressible fluid is considered. The incomplete telegraph equation, composed for the average flow velocity, is solved by the method of separation of variables. The pressure is determined by integrating the original equations using the expression found for the velocity.
Numerical results are given for the case of constant values of initial and boundary conditions. Modes with constant, increasing and decreasing average pressure values in the considered section are identified. Peculiarities of shock wave behavior are noted both with and without taking into account the friction force.