, 44:101 | Cite as

Estimation and examination of linepack pressures in long liquid pipelines



In the past, many researchers have carried out water-hammer pressure analysis using Joukowsky equation. However, it has been observed that the computed pressure surge is no longer applicable based on the equation. The Joukowsky equation cannot be used even within the reflection time of the long pipeline. In such cases, the actual pressure rise due to the sudden closure of a quick acting valve will be several times more than that of the sudden increase in pressure as calculated by the Joukowsky equation. The phenomenon of rising pressure at the upstream of an instantaneously closed valve with the passage of time caused by the pipe friction is commonly called as linepacking. In this paper, various parameters affecting the linepack pressure have been thoroughly investigated. As the relative roughness increases, the resulting non-dimensional linepack pressure \( \left( {P_{LP} /P_{o} } \right) \) significantly increases and the proportionality constant was equal to 1.5. The linepack pressure was determined to be decreasing with increasing valve closure time. The dominant parameter that influences the linepack pressure is found to be the Reynolds number as compared to the Mach number, and the relative roughness. Furthermore, the linepack pressure is found to be proportional to frictional head loss \( \left( {h_{L} /D} \right) \), and inversely proportional to inlet pressure \( \left( {P_{o} /\left( {\gamma L_{o} } \right)} \right) \). Finally, a linear regression equation was developed in terms of non-dimensional variables to estimate the linepack pressure using hand calculations without undergoing numerical modeling procedures. The proposed equation was validated for sudden valve closure pressure histories available in the literature. The proposed method is applicable to long distance water supply pipelines where the linepack pressures are significant.


Pressure surge water-hammer linepack pressure Joukowsky formula instantaneous valve closure numerical modeling 


  1. 1.
    Joukowski N E 1898/1900 Mem. Imperial Academy Soc. of St. Petersburg, vol. 9. no. 5, (in Russian. translated by O. Simin, Proc. Amer. Water Works Assoc., vol. 24, 1904. pp. 341–424.) Kerensky, G., 1965–1966, DiscussionGoogle Scholar
  2. 2.
    Kaplan M, Streeter V L and Wylie E B 1967 Computation of oil pipeline transients. J. Pipeline Div. Am. Soc. Civil Eng. 93(4): 59–72Google Scholar
  3. 3.
    Kries J von 1892 Studien zur Pulslehre (Studies of the pulse), (Akademische Verlagsbuchhandlung von) JCB Mohr (Paul Siebeck), Germany: Freiburg im Breisgau und Tübingen (in German)Google Scholar
  4. 4.
    Tijsseling A and Anderson A 2007 Johannes von kries and the history of water-hammer. J. Hydraul. Eng. 133: 1–8CrossRefGoogle Scholar
  5. 5.
    Jung B S, Boulos P F and Wood D J 2009 Effect of pressure-sensitive demand on surge analysis. J. Am. Water Works Assoc. 101: 100–111CrossRefGoogle Scholar
  6. 6.
    Jung B S, Karney B W, Boulos P F and Wood D J 2007 The need for comprehensive transient analysis of distribution systems. J. AWWA, 99:112CrossRefGoogle Scholar
  7. 7.
    Watters G Z 1984 Analysis and control of unsteady flow in pipelines, London: ButterworthsGoogle Scholar
  8. 8.
    Fox J S 1989 Transient flow in pipes, open channels and sewers. Chichester: Ellis Horwood LimitedGoogle Scholar
  9. 9.
    Thorley A R D 2004 Fluid transients in pipeline systems, 2nd edition, Jon Wiley and Sons LtdGoogle Scholar
  10. 10.
    Wylie E B and Streeter V L 1993 Fluid transients in systems, Englewood Cliffs: Prentice-HallGoogle Scholar
  11. 11.
    Hanmaiahgari P R, Elkholy M and Riahi-Nezhad 2017 Identification of partial blockages in pipelines using genetic algorithms. Sādhanā. 42: 1543–1556. Scholar
  12. 12.
    Balamurugan M and Bhallamudi S M 2016 Flood routing in an ephemeral channel with compound cross-section. Sādhanā 41: 771–785. MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Chaudhry M H 2013 Applied hydraulic transients, 3rd ed, New York: SpringerGoogle Scholar
  14. 14.
    Martin C S 2000 Hydraulic transient design in pipeline systems. In: Mays L W (ed) Water Distribution Systems Handbook. New York: McGraw-HillGoogle Scholar
  15. 15.
    White F W 2006 Fluid mechanics, New York: McGraw-HillGoogle Scholar
  16. 16.
    Gudmundsson J, Durgut I, Rønnevig J, Korsan,K and Celius H 2002 Pressure pulse analysis of flow in tubing and casing of gas lift wells. Spring ASME/API Gas Lift Workshop, HoustonGoogle Scholar
  17. 17.
    Liou C P 1991 Maximum pressure head due to linear valve closure J. Fluids Eng. 113: 643–647. CrossRefGoogle Scholar
  18. 18.
    Ghidaoui M S, Zhao M and McInnis D A 2005 A review of water-hammer theory and practice, Appl. Mech. Rev. 58: 49–76. CrossRefGoogle Scholar
  19. 19.
    Adamkowski A and Lewandowski M 2006 Experimental examination of unsteady friction models for transient pipe flow simulation. J. Fluids Eng., ASME. 128: 1351–1363CrossRefGoogle Scholar
  20. 20.
    Ellis J 2008 Pressure transients in water engineering, a guide to analysis and interpretation of behaviour. London: Thomas Telford LimitedCrossRefGoogle Scholar
  21. 21.
    Kucienska B, Seynhaeve, J and Giot M 2008 Friction relaxation model for fast transient flows application to water-hammer in two-phase flow—The WAHA code. Int. J. Multiph. Flow. 34: 188–205CrossRefGoogle Scholar
  22. 22.
    Kucienska B 2004 Friction relaxation model for fast transient flow. Universite´ catholique de Louvain (UCL). Doctoral thesisGoogle Scholar

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© Indian Academy of Sciences 2019

Authors and Affiliations

    • 1
    Email author
    • 2
    • 3
  1. 1.Department of Civil EngineeringIndian Institute of Technology KharagpurKharagpurIndia
  2. 2.Aker SolutionsFornebuNorway
  3. 3.Department of Aerospace EngineeringIndian Institute of Technology KharagpurKharagpurIndia

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