Fluid-dynamic loading of pipes conveying fluid with a laminar mean-flow velocity profile

The fluid-conveying pipe is a fundamental dynamical problem in the field of fluid-structure interactions. The possibility of modelling such a system analytically is mainly dependent on the availability of suitable analytical models for the fluid-dynamic loading acting on a vibrating pipe. The aim of this paper is an analytical study of the velocity profile effects for a straight pipe. The main contribution is the derived asymptotic model for the fluid-dynamic loading of the laminar and uniform mean flows that is applicable for any circumferential wavenumber of the mode shape of the pipe. The velocity profile effects are expressed in terms of the correction factors for the fluid-dynamic loading, which consists of three components being related to the translational, Coriolis and centrifugal accelerations of the fluid. This model also takes into account the effects of the fluid compressibility and the finite pipe length. The asymptotic model is derived from the solutions of the Pridmore-Brown equation for the Fourier transform of the vibrational fluid pressure. The solution procedure is based on the Frobenius power series method. The results about the velocity profile effects are compared with the previous, accessible studies in this field. As an application case, the discussed model is used to predict the flow effects on the first-mode natural frequency of a beam-type pipe with both ends clamped.