On Boussinesq and Coriolis coefficients and implications for the Joukowsky equation

Alan E. Vardy, Arris S. Tijsseling

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


The purpose of this paper is to show how derivatives of the Boussinesq and Coriolis coefficients, /J and o., can be handled formally in 1-D analyses of unsteady flow. In the case of low Mach number flows typical of liquid flows in many pipes, it is usual to disregard differences between these coefficients and unity, thereby simplifying expressions such as the Joukowsky equation. When this is deemed to be unacceptable - e.g. in moderate and high Mach number flows -a different approach is usually followed, namely allowing for the actual values of the coefficients, but disregarding derivatives of them. It is shown herein that this approach is not only unnecessary, but is actually less accurate than disregarding the coefficients altogether (i.e. using plug-flow approximations). Mathematically, the new result is obtained by deriving expressions that relate derivatives of /J and o. to derivatives of the principal flow parameters (pressure p, density p and mean velocity U). Because these relationships involve derivatives, they do not enable actual values of /J and o. to be deduced. However, it is shown rigorously that inertial waves do not change the product p2 U2(/J-1) and so, if /J is known a priori before a wave-induced velocity change, its value after the change can be deduced.
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 pages16
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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