New assessment of friction factor correlations for power law fluids in turbulent pipe flow: A statistical approach

  • Gao Peng  (高鹏)
  • Zhang Jin-jun  (张劲军)Email author


A new statistical approach to assessing the friction factor correlations was presented. Fourteen correlations, published from 1959 to 2003, were collected to calculate friction factors for power law fluids in turbulent pipe flow. A series of Fanning friction factors, f, were computed from these equations. Then the relations between the calculated values of f and ReMR (Metzner-Reed Reynolds number) were analyzed, when the rheological behavior index, n, was given. To verify the foregoing analysis result, in addition, the relations between the calculated values of f and n were analyzed, when ReMR was given. The f value calculated from each equation was compared with each mean value of all the f values from the 14 equations, when each combination (n, ReMR) (n ranging from 0.4 to 1.4 and ReMR from 4 000 to 100 000) was set. The comparison results were surveyed in the relative deviation table of the calculated f values. It shows that the overall mean relative deviation (OMRD) of the Dodge-Metzner correlation is the minimum, 1.5%. Therefore, the Dodge-Metzner correlation is recommended for predicting the friction factors for the turbulent pipe flow of power law fluids.

Key words

friction factor turbulence power law fluids hydraulic analysis fluid mechanics 


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  1. [1]
    DODGE D W, METZNER A B. Turbulent flow of non-Newtonian systems[J]. AICHE Journal, 1959, 5(2): 189–204.CrossRefGoogle Scholar
  2. [2]
    HEYWOOD N I. Pipeline design for non-newtonian fluids[J]. Transactions of the Institute of Chemical Engineering Symposium, 1984(6): 33–45.Google Scholar
  3. [3]
    HANKS R W, RICKS B L. Transitional and turbulent pipe flow of pseudoplastic fluids[J]. Journal of Hydronautics, 1975(9): 39–44.CrossRefGoogle Scholar
  4. [4]
    DARBY R. Hydrodynamics of slurries and suspensions. In: Encyclopedia of Fluid Mechanics, Vol.5 (Slurry Flow Technology) [M]. Houston: Gulf Pub Co, 1986.Google Scholar
  5. [5]
    DARBY R. Laminar and turbulent pipe flows of non-Newtonian fluids. In: Encyclopedia of Fluid Mechanics, Vol.7 (Rheology and Non-Newtonian Flows)[M]. Houston: Gulf Pub Co, 1988.Google Scholar
  6. [6]
    SZILAS A P. Flow mechanics and production, Part A In: Production and Transport of Oil and Gas, Vol.18A in Developments in Petroleum Science[M](2nd ed). Amsterdam: Elsevier Science Pub Co, 1985.Google Scholar
  7. [7]
    BOBOK E. Fluid Mechanics for Petroleum Engineers. Vol.32 in: Developments in Petroleum Science[M]. Amsterdam: Elsevier Science Pub Co, 1993.Google Scholar
  8. [8]
    KAWASE Y, SHENOY A V, WAKABAYASHI K. Friction and heat and mass transfer for turbulent pseudoplastic non-Newtonian fluids flowing in rough pipes[J]. Canadian Journal of Chemical Engineering, 1994(72): 798–804.Google Scholar
  9. [9]
    DESOUKY S M, EL-EMAM N A. A generalized pipeline design correlation for pseudoplastic fluids[J]. Journal of Canadian Petroleum Technology, 1990, 29(5): 48–54.CrossRefGoogle Scholar
  10. [10]
    HEMEIDA A M. Friction factor for yieldless fluids in turbulent pipe flow[J]. Journal of Canadian Petroleum Technology, 1993, 32(1):32–35.CrossRefGoogle Scholar
  11. [11]
    EL-EMAM N, KAMEL A H, EL-SHAFEI M, et al. New equation calculates friction factor for turbulent flow of non-Newtonian fluids[J]. Oil & Gas Journal, 2003, 101(36): 74–83.Google Scholar
  12. [12]
    GOVIER G W, AZIZ K. The Flow of Complex Mixtures in Pipes[M]. New York: Van Nostrand Reinhood Co, 1972.Google Scholar
  13. [13]
    GONG J, YAN D F. Comparison of the friction factor methods for non-Newtonian fluids in pipe flow[J]. Petroleum Planning & Engineering, 1994, 5(3): 28–32. (in Chinese)Google Scholar

Copyright information

© Central South University Press, Sole distributor outside Mainland China: Springer 2007

Authors and Affiliations

  • Gao Peng  (高鹏)
    • 1
  • Zhang Jin-jun  (张劲军)
    • 1
    Email author
  1. 1.Beijing Key Laboratory of Urban Oil and Gas Distribution TechnologyChina University of PetroleumBeijingChina

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