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Applicability tests for empirical formulas: Analysis of turbulent flows and general comments

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Abstract

Direct and differential-invariant methods for processing experimental data are used to analyze Nikuradse’s results for a turbulent flow of a viscous liquid in round smooth tubes for various Reynolds numbers. It is found that direct testing ratios do not make it possible to draw a correct inference about the applicability of the Prandtl logarithmic profile. The explanation of this paradoxical result is given. It is shown that although direct applicability tests for empirical formulas do not generally ensure the necessary conditions of their applicability, they make it possible to draw subtle qualitative inferences that cannot be reached using the least-squares method.

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Authors and Affiliations

  1. Institute for Problems of Mechanics, Russian Academy of Sciences, Moscow, Russia

    A. D. Polyanin & E. A. Vyazmina

  2. Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences, Leninskii pr. 31, Moscow, 119991, Russia

    V. V. Dil’man

Authors
  1. A. D. Polyanin
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  2. E. A. Vyazmina
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  3. V. V. Dil’man
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Correspondence to A. D. Polyanin.

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Original Russian Text © A.D. Polyanin, E.A. Vyaz’mina, V.V. Dilman, 2009, published in Teoreticheskie Osnovy Khimicheskoi Tekhnologii, 2009, Vol. 43, No. 2, pp. 131–140.

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Polyanin, A.D., Vyazmina, E.A. & Dil’man, V.V. Applicability tests for empirical formulas: Analysis of turbulent flows and general comments. Theor Found Chem Eng 43, 119–128 (2009). https://doi.org/10.1134/S0040579509020018

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