Статья
2019

Further Thoughts on Turbulent Flow in a Pipe


John Newman John Newman
Российский электрохимический журнал
https://doi.org/10.1134/S1023193519010105
Abstract / Full Text

Nikuradse’s 1932 paper on turbulent flow in a smooth pipe contains a wealth of information on flow resistance (friction factor) and profiles of velocity and eddy viscosity. The goal here is to study this information in detail with the objective of applying it to other turbulent-flow situations. In particular, reverse engineering supports a value of n = 2 for the exponent on the volumetric dissipation in the decay term of the equation of the dissipation theorem. Of equal importance, integration of Nikuradse’s profiles of eddy viscosity does not lead to his formula for the universal resistance law; instead the presence of the viscous sublayer has an overt effect on the result even though we had thought that such a region influenced only the form of mass transfer at high values of the Schmidt number. A formula is proposed for the decay of dissipation for turbulent flow in smooth pipes.

Author information
  • Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California, 94720-1462, USA

    John Newman

References
  1. Newman, J., Theoretical analysis of turbulent mass transfer with rotating cylinders, J. Electrochem. Soc., 2016, vol. 163, p. E191.
  2. Newman, J., Application of the dissipation theorem to turbulent flow and mass transfer in a pipe, Russ. J. Electrochem., 2017, vol. 53, p. 1061.
  3. Nikuradse, J. Gesetzmässigkeitem der turbulentem Strömung in glaten Rohren, Forschungsheft 356, Beilage zu Forschung auf dem Gebiete des Ingenieurwesens, Edition B, Volume 3, September/October, 1932 (Berlin NW7:VDI-Verlag GMBH, 1932). Translated as Nikuradse J., Laws of turbulent flow in smooth pipes, NASA TT F-10, 359, Washington: National Aeronautics and Space Administration, Oct. 1966.
  4. Cahn, J. W. and Hilliard, J. E., Free Energy of a nonuniform system. I. Interfacial free energy, J. Chem. Phys., 1958, vol. 28, pp. 258–267. doi 10.1063/1.1744102
  5. Martemianov, S.A., Statistical theory of turbulent mass transfer in electrochemical systems, Russ. J. Electrochem., 2017, vol. 53, p. 1076.