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The minimum Reynolds number for a turbulent boundary layer and the selection of a transition device

  • J. H. Preston (a1)


In the case of turbulent flow in a pipe there is a lower experimental number to the Reynolds limit for which fully developed turbulent flow occurs. From the similarity and close agreement of the curves showing the coefficient of skin friction cf as a function of the Reynolds number Rθ (based on the momentum thickness θ) for the circular pipe and flat plate, it is suggested that there should be a lower limit to Rθ for fully developed turbulent flow on a flat plate. Rather limited experimental data confirm this and place the lower limit at Rθ = 320. The choice and size of transition device is examined in relation to this minimum Rθ and an approximate theory leads to a ‘wire’ Reynolds number in fair agreement with experience.



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Arie, M. & Rouse, H. 1956 J. Fluid Mech. 1, 129.
Coles, D. 1954 Z. angew. Math. Phys. 5, 181.
Dutton, R. A. 1955 Ph.D. Dissertation, University of Cambridge.
Dutton, R. A. 1956 The accuracy of the measurement of turbulent skin friction by means of surface pitot tubes and the distribution of skin friction on a flat plate, Aero. Res. Counc., Lond., Rep. & Mem. (to be published).
Landweber, L. 1953 Trans. Soc. Nav. Archit., N.Y., 61, 5.
Nikuradse, J. 1932 Forschungsh. Ver. Dtsch. Ing. 356.
Nikuradse, J. 1933 Forschungsh. Ver. Dtsch. Ing. 361.
Ross, D. 1952 Turbulent flow in smooth pipes (a reanalysis of Nikuradse's experiments), Pennsylvania State College, Report Nord. 7958–246.
Sacks, G. M. 1956 M.Sc. Dissertation, University of Cambridge.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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