Theoretical Analysis of the Reduction of Pressure Wave Velocity by Internal Circular Tubes

  • Michał KubrakEmail author
  • Apoloniusz Kodura
Conference paper
Part of the GeoPlanet: Earth and Planetary Sciences book series (GEPS)


This study presents a theoretical analysis of the influence of the insertion of circular tubes into a pipeline on the rapid water hammer phenomenon. Three types of circular tubes are distinguished: a thin-walled tube, a thick-walled tube and a solid cylindrical tube. For each case, by applying the work-energy principle, a formula for the pressure wave velocity is derived. The differences between the derived formulas are analyzed. It is shown that the insertion of a tube with a low bulk elastic modulus may have a damping effect on the water hammer phenomenon, i.e., it reduces the pressure wave velocity and maximum pressure increase.


Water hammer Pressure wave velocity Pressure increase Elastic tube 


  1. Bergant A, Tijsseling A, Vitkovsky J et al (2008) Parameters affecting water-hammer attenuation, shape and timing—Part 1: mathematical tools. J Hydraul Res 46(3):377Google Scholar
  2. Grote K, Antonsson E (2009) Springer handbook of mechanical engineering, 1st edn. Springer, Berlin, p 947Google Scholar
  3. Kubrak M, Kodura A, Imiełowski S (2018) Analysis of pressure wave velocity in a steel pipeline with inserted fiber optic cable. Free Surface Flows and Transport Processes/GeoPlanet: Earth and Planetary Sciences, pp 281–292Google Scholar
  4. Mitosek M, Szymkiewicz R (2016) Reservoir influence on pressure wave propagation in steel pipes. J Hydraulic Eng 132(8):1–5Google Scholar
  5. Streeter VL (1958) Fluid mechanics. McGraw-Hill Companies, Columbus, OHGoogle Scholar
  6. Tijsseling AS, Kruisbrink ACH, Pereira da Silva A (1999) The reduction of pressure wavespeeds by internal rectangular tubes. In: Proceedings of 3rd ASME/JSME joint fluids engineering conference, San FranciscoGoogle Scholar
  7. Wylie EB, Streeter VL (1993) Fluid transients in systems. Prentice-Hall, Upper Saddle River, NJGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Faculty of Building Services, Hydro and Environmental EngineeringWarsaw University of TechnologyWarsawPoland

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