Skip to main content
SpringerLink
Log in

Comparison between two different derivations of the differential equations for free vibration of the ideal fluid column in a communication tube

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

How would the ideal fluid column in a communication tube moves, the present paper presents two different solutions, one of which has been existing in the literature not less than a half century, while the second is recommended by us with this article. We have deduced the differential equation anew and given the main motion features.

According to our opinion, the hitherto, for a long time broadly used, derivation is not undisputable. Noticeably, the results of our new derivation can duely degenerate into Newton-, John Bernoulli- and Daniel Bernoulli-period laws of vibration.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Isaac Newton, Philosophiae Naturalis Principia Mathematica, London, 1687.

  2. Johann Bernoulli, Commentarii Academiae Scientiarum Petropolitanae, 1727.

  3. H. de Lagrené, Cours de Navigation intérieure, Paris, 1869.

  4. Danielis Bernoulli, Hydrodynamica, Argentorati, 1738.

  5. Hsien-Chih Liu, Beitrag zur Kenntnis der Eigenschwingung einer idealen Flüssigkeit in kommunizierenden Röhren, ZAMP, vol. IV, 1953.

  6. F. Wittenbauer, Aufgaben aus der Technischen Mechanik, III. Band, Julius Springer, Berlin 1921.

    Google Scholar 

  7. Hsien-Chih Liu, Eigenschwingungen einer idealen Flüssigkeit in Rohrleitungen mit verschiedenen Endquerschnitten, Ing.-Archiv, 1952.

  8. Hsien-Chih Liu, Über Schwingungen einer idealen Flüssigkeit in ellipsen- und kreisbogenförmigen, kommunizierenden Röhren, Ing.-Archiv, 1952.

  9. A Handbook on torsional Vibration, B.I.C.ER.A. Cambridge.

  10. Liu Hsien-chih: The singularities of the non-linear Vibration of an ideal fluid column within a communication tube with different end cross sections, to be published.

Download references

Author information

Authors and Affiliations

  1. Shantung Institute of Technology, Jinan

    Liu Hsien-chin

Authors
  1. Liu Hsien-chin
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hsien-chin, L. Comparison between two different derivations of the differential equations for free vibration of the ideal fluid column in a communication tube. Appl Math Mech 1, 319–332 (1980). https://doi.org/10.1007/BF01874555

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01874555

Keywords

Search

Navigation