Theoretical of dynamic loading against water-filled simply supported pipes

Abstract

The primary aim of this study had been to investigate the effects of water-filled flow on the transient response of a simply supported pipe subjected to dynamically applied loading. The importance of this study is manifested in numerous applications, such as oil and gas transportations, where dynamic loading can be the result of an accident. The classical Bernoulli-Euler beam theory was adopted to describe the dynamic behavior of an elastic pipe and a new governing equation of a long pipe transporting gas or liquid was derived. This governing equation incorporated the effects of inertia, centrifugal, and Coriolis forces due to the flowing water. This equation can be normalized to demonstrate that only two non-dimensional parameters governed the static and the dynamic responses of the system incorporating a pipe and flowing water. The transient response of this system was investigated based on a standard perturbation approach. Moreover, it had been demonstrated that the previous dynamic models, which largely ignored the internal flow effects and interactions between the flow and the structure, normally produced a large error and are inapplicable to the analysis of many practical situations. One interesting effect identified was that at certain flow ratio, the system became dynamically unstable and any, even very small, external perturbation led to a growing unstable dynamic behavior. Such behavior, which is called pipe whip, is well-known to everyone who waters a garden using a flexible long hose.