Analytical modelling of a pipe with flowing medium subjected to an impulse load

Pipes transporting gas or liquid can be subjected to impulse loading as a result of an accident. In many previous studies the effects of the flowing media on the transient response of pipes were largely ignored or considered to be negligible. This paper aims to shed light on the significance of these effects. First, we present a simplified mathematical model of a pipe filled with a flowing liquid or gas and subjected to dynamic loading. This model is based on the well-known Bernoulli–Euler beam theory, but also incorporates forces generated by the internal flow which follows the pipe lateral deflections and generates the inertia, centrifugal and Coriolis flow accelerations. Further, we develop asymptotic analytical and numerical methods for the analysis of the governing equation. Finally, as example, we investigate in detail the effect of the flow parameters on the dynamic response of a cantilever pipe subjected to impulse loading. Special attention is given to the pipe whip phenomenon, which causes growing unlimited displacements of the pipe regardless of how small the value of the applied loading is. The developed theoretical methods provide a framework for analysis of many other dynamic problems of pipes with flowing media subjected to arbitrary boundary and loading conditions.