Analytical and empirical models for the acoustic dispersion relations in partially filled water pipes

Sound propagation in a partially filled pipe is a complex and not a well-researched topic. However, this class of pipes is of high importance because it is typical to millions of kilometres of buried sewers and drainage pipes laid across the world. Good knowledge of conditions in these pipes is critical to their successful operation and proactive rehabilitation. Acoustic methods are attractive means for their rapid condition assessment. Therefore, good understanding of sound propagation in this class of pipes is of importance. In response, this paper studies acoustic waves propagation in a pipe with different water filling ratio. Based on a 2-dimensional finite element method (FEM) study, an analytical approximation and empirical model are developed and proposed to predict the acoustic wave dispersion relations (curves) and mode shapes. These two models can be used to predict the acoustic frequency response function of a partially filled pipe with an accuracy of better than 3 dB below twice the first non-axisymmetric mode frequency, but at 1/2000 of computational cost when compared with the FEM. This work paves the way to the development of highly efficient, real-time robotic systems for autonomous inspection of partially filled pipes with acoustic means.