One-dimensional waves - Axial, cylindrical and spherical

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Three geometrically different types of spatially one-dimensional (1-D) wave propagation are considered. The first, namely axial propagation parallel to a single axis, is typical of flows in pipes and channels. The second is cylindrical propagation, as in waves radiating wholly radially from a line source (uniformly along its length). The third is spherical propagation, as in, say, sound waves from a highly localised source in open air. Continuity and momentum equations for the three cases are presented in a common format and are then combined using the Method of Characteristics. It is shown that all three formulations can be expressed in an especially simple manner when the sound speed and the volumetric flow-rate are chosen as the principal variables (as opposed to, say, pressure and velocity).

Differences in the behaviour of the three types of wave propagation are illustrated for
(i) the elementary cases of purely axial, cylindrical, and spherical propagation and
(ii) composite geometries in which radial geometries are coupled with an upstream region of axially 1-D flow-illustrating, for example, radiation from an open end of a pipe.

The outcomes are used as a basis for a short discussion of the fundamental nature of wave propagation.
Original languageEnglish
Title of host publicationProceedings of the 14th International Conference on Pressure Surges
EditorsSarah E. L. Jones
Place of PublicationEindhoven
PublisherEindhoven University of Technology
Number of pages17
ISBN (Print)9789038657103
Publication statusPublished - 2023
Event14th International Conference on Pressure Surges - Eindhoven University of Technology, Eindhoven, Netherlands
Duration: 12 Apr 202314 Apr 2023


Conference14th International Conference on Pressure Surges
Internet address


  • one-dimensional
  • unsteady
  • compressible pipe-flow
  • momentum correction factor
  • energy correction factor


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