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A unified theory of turbulent flow III

Pipe flow

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Summary

A general theory of turbulent flow is applied to incompressible flow in a circular pipe. The theoretical mean velocity distribution is found to be in good agreement with experiment, but there is some discrepancy in the normal stress distribution. The available pressure drop data are used to estimate the value of the apparent wall velocity as a function of Reynolds number and roughness. It is found that the results can be represented by simple expressions which in turn imply simple expressions for the pressure drop as a function of Reynolds number and roughness. However, it has not been possible to derive these results from fundamental considerations. The basis of Reynolds analogy and the application of the theory to channel flow are also discussed.

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References

  1. Squire, W., Appl. Sci. Res. A 8 (1959) 158.

    Article  MathSciNet  Google Scholar 

  2. Squire, W., Appl. Sci. Res. A 9 (1960) 393.

    Article  Google Scholar 

  3. Goldstein, S. (Editor), Modern Developments in Fluid Dynamics, p. 193, Oxford Press 1938.

  4. Broszko, M., Ann. Acad. Pol. Sci. Techn. 7 (1946) 75.

    Google Scholar 

  5. Stanton, T. E., Proc. Roy. Soc. A 85 (1911) 366.

    ADS  Google Scholar 

  6. Nikuradse, J., Laws of Flow in rough Pipes, NACA Technical Memo. 1292, November 1950.

  7. Izakson, A., Techn. Phys. USSR 4 (1937) 239.

    Google Scholar 

  8. Finniecome, J. R., The Friction Coefficient for Circular Pipes at Turbulent Flow. Emmot and Company, London 1954.

    Google Scholar 

  9. Laufer, J., The Structure of Turbulence in fully developed Pipe Flow, NACA Rept 1174, 1955.

  10. Bradshaw, P. and M. Gregory, The Determination of Local Turbulent Skin Friction From Observations in the Viscous Sub-Layer, Aeronautical Research Council Rept 20, 895, March 26, 1959.

  11. Squire, W., An Extended Reynolds Analogy, Proc. 6th Midwestern Conf. Fluid Mechanics, pp. 16–33, Univ. of Texas, Austin 1959.

    Google Scholar 

  12. Frank-Kamenetsky, D. A., Diffusion and Heat Exchange in Chemical Kinetics, Princeton Univ. Press, 1955.

  13. Chou, P. Y., Quart. Appl. Math. 3 (1945) 128.

    Google Scholar 

  14. Rotta, J., Z. Phys. 129 (1951) 547.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  15. Robertson, J. K., The Turbulent Velocity Distribution in Rough Pipe, Proc. Midwestern Conf. Fluid Mechanics, University of Michigan, 1957.

  16. Taylor, G. I., Proc. Roy. Soc. A 157 (1936) 537; also, The Scientific Papers of G. I. Taylor, II, pp. 372–379, Cambridge University Press, 1960.

    ADS  Google Scholar 

  17. Burka, E. Archiwum Hydrotechnicki 4 (1957) 95, (in Polish).

    Google Scholar 

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Authors and Affiliations

  1. Southwest Research Institute, San Antonio, Texas, U.S.A.

    William Squire

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  1. William Squire
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Squire, W. A unified theory of turbulent flow III. Appl. sci. Res. 10, 23 (1961). https://doi.org/10.1007/BF00411896

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  • DOI: https://doi.org/10.1007/BF00411896

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