Fluid Dynamics

, Volume 10, Issue 3, pp 447–451 | Cite as

Propagation of perturbation waves in infinitely long viscoelastic pipes

  • Yu. M. Blitshtein
  • M. G. Khublaryan


Until recently, almost all investigations of unsteady fluid flow in pipes involved Hooke deformation. Flow conditions in pipes made from materials with viscoelastic and relaxation properties have received little attention [1–3], Because of the rapid utilization of new polymer materials, the study of fluid motion in pipes made of non-Hooke materials is of definite practical and theoretical interest. An experimental and theoretical investigation of hydraulic shock with stream separation has been carried out in [4]. Below, the deformation of pipes in which perturbation waves of an elastic liquid propagate is described using a Boltzmann-Volterra elastic-memory theory, which gives a good description of the strength of many polymer materials and metals [5–7]. The problem is solved by means of integral transformations and discontinuous waves.


Polymer Fluid Flow Flow Condition Polymer Material Theoretical Investigation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    I. P. Ginzburg, “Hydraulic shock in viscoelastic tubes,” Vestn. Leningr. Univ., Ser. Mat. Mekh. Astronom., No. 13 (1956).Google Scholar
  2. 2.
    R. F. Gromova, “Hydraulic shock in viscoelastic tubes,” Uch. Zap Kuibyshev. Ped. Inst., No. 21 (1958).Google Scholar
  3. 3.
    E. Rientord and A. Blanchard, “Influence d'un comportement viscoelastique de la conduite dans le phenomene du coup de belier,” C. R. Acad. Sci.,274, No. 26 (1972).Google Scholar
  4. 4.
    T. Tanahashi and E. Kasahara, “Comparisons between experimental and theoretical results of the waterhammer with water column separations,” Bull. JSME,13, No. 61 (1970).Google Scholar
  5. 5.
    Yu. N. Rabotnov, Creep of Structural Elements [in Russian], Nauka, Moscow (1966).Google Scholar
  6. 6.
    A. A. Il'yushin and B. E. Pobedrya, Principles of the Mathematical Theory of Thermal Viscoelasticity [in Russian], Nauka, Moscow (1970).Google Scholar
  7. 7.
    A. R. Rzhanitsyn, Theory of Creep [in Russian], Stroiizdat, Moscow (1968).Google Scholar
  8. 8.
    I. A. Charnyi, “Steady Flow of a Real Fluid in Tubes [in Russian], Gostekhteoretizdat, Moscow (1951).Google Scholar
  9. 9.
    H. S. Carslaw and J. C. Jaeger, Operational Methods in Applied Mathematics, Oxford University Press, London (1948).Google Scholar
  10. 10.
    T. Y. Thomas, Plastic Flow and Fracture in Solids, Academic Press, New York (1961).Google Scholar
  11. 11.
    J. D. Achenbach and D. P. Reddy, “Shear waves of finite deformations excited at the surface of a visco-elastic half-space,” in: Mechanics [Russian translation], No. 6 (1967).Google Scholar
  12. 12.
    B. D. Coleman, M. E. Gurtin, and J. Herrera, “Waves in materials with memory. I The velocity of one-dimensional shock and acceleration waves,” Arch. Ration. Mech. Anal.,19, No. 1 (1965).Google Scholar

Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • Yu. M. Blitshtein
    • 1
  • M. G. Khublaryan
    • 1
  1. 1.Moscow

Personalised recommendations