Quinn’s Law of Fluid Dynamics: Supplement #1 Nikuradze’s Inflection Profile Revisited

Hubert Michael Quinn

doi:doi:10.11648/j.fm.20200601.11

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Quinn’s Law of Fluid Dynamics: Supplement #1 Nikuradze’s Inflection Profile Revisited

Hubert Michael Quinn

Published in Fluid Mechanics (Volume 6, Issue 1)

Received: 30 January 2020 Accepted: 11 February 2020 Published: 18 February 2020

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Abstract

This paper is directed at the important contribution to fluid dynamics made by Johan Nikuradze. His seminal paper published in 1933 represents the gold standard of empty conduit permeability, for the flow of water through roughened pipes, even to this very day. We revisit in some detail the “inflection profile” in Nikuradze’s plot, which appears in the curve for his roughened data found in Figure 9 in that publication. In so doing, we show that the data points at low Reynolds number values, and particularly those surrounding the value of 3.4 approximately on the x-axis of his plot, do not represent the reported experimental results found in his tables of data. Furthermore, we also demonstrate that this discrepancy in his original paper is very problematic because it forms the basis for many subsequent scholarly works. As a result, this inflection profile has become erroneously embedded in conventional folklore concerning fluid flow in closed conduits and has enjoyed widespread acceptance as being a legitimate feature of fluid dynamics dogma. With the advent recently of Quinn’s Law, a novel approach to the understanding of fluid flow in closed conduits, we are able to articulate in a manner not heretofore possible, the significance of this discrepancy which is far too important to ignore.

Published in	Fluid Mechanics (Volume 6, Issue 1)
DOI	10.11648/j.fm.20200601.11
Page(s)	1-14
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2020. Published by Science Publishing Group

Keywords

Inflection Profile, Nikuradze, Friction Factor, Transition Region, Turbulent Flow, Wall Effect, Boundary Layer

References

[1]	Nikuradze, J. NACA TM 1292, Laws of Flow in Rough Pipes, July/August 1933. Translation of “Stromungsgesetze in rauhen Rohren.” VDI-Forschungsheft 361. Beilage zu “ Forschung auf dem Gebiete des Ingenieurwesens” Ausgabe B Band 4, July/August 1933.
[2]	Blasius, H (1908). "Grenzschichten in Flüssigkeiten mit kleiner Reibung". Z. Angew. Math. Phys. 56: 1–37.
[3]	Quinn, H. M. Quinn’s Law of Fluid Dynamics Pressure-driven Fluid Flow Through Closed Conduits, Fluid Mechanics. Vol. 5, No. 2, 2019, pp. 39-71. doi: 10.11648/j.fm.20190502.12.
[4]	Farkas, T., Zhong, G., Guiochon G.,, Validity of Darcy’s Law at Low Flow Rates in Liquid Chromatography Journal of Chromatography A, 849, (1999) 35-43.
[5]	Mckeon, B. J., Zagarola, M. V. and Smits A. J. A new friction factor relationship for fully developed pipe flow; J. Fluid Mech. (2004), vol. 511, pp. 41-44. Cambridge University Press; DO1; 10.1017/S0022112004009796.
[6]	Mckeon, B. J., Swanson, C. J., Zagarola, M. V., Donnelly, R. J., and Smits, A. J., Friction factor for smooth pipe flow., J. Fluid Mech. (2005), vol. 238, pp. 429-443. Cambridge University Press; DO1; 10.1017/S0022112005005501.
[7]	Nikuradze, J., NASA TT F-10, 359, Laws of Turbulent Flow in Smooth Pipes. Translated from “Gesetzmassigkeiten der turbulenten Stromung in glatten Rohren” VDI (Verein Deutsher Ingenieure)-Forschungsheft 356.
[8]	Kozeny, J., "Uber kapillare Leitung des wassers in Boden," Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften, vol. 136, 1927.
[9]	Blake, F. E."The resistance of packing to fluid flow," Transactions of American Institute of Chemical Engineers, vol. 14, pp. 415-421, 1922.
[10]	Quinn, H. M., A Reconciliation of Packed Column Permeability Data: Deconvoluting the Ergun Papers. Journal of Materials Volume 2014 (2014), Article ID 548482, 24 pages http://dx.doi.org/10.1155/2014/548482.
[11]	Ergun, S. and Orning, A. A., Fluid Flow through Randomly Packed Columns and Fluidized Beds, Ind. Eng. Chem. vol. 41, pp. 1179, 1949.
[12]	Ergun, S., Determination of Particle Density of Crushed Porous Solids, Anal. Chem. vol. 23, 1951.
[13]	Ergun, S., Fluid Flow Through Packed Columns, Chem. Eng. Progr. vol. 48, pp. 89-94, 1952.
[14]	Poiseuille, J. L. M., Memoires des Savants Etrangers, Vol. IX pp. 435-544, (1846); BRILLOUIN, M. (1930) Jean Leonard Marie Poiseuille. Journal of Rheology, 1, 345.
[15]	Quinn, H. M., A Reconciliation of Packed Column Permeability Data: Column Permeability as a Function of Particle Porosity; Journal of Materials Volume 2014 (2014), Article ID 636507, 22 pages http://dx.doi.org/10.1155/2014/636507.
[16]	Giddings, J. C., Dynamics of Chromatography, Part I: Principles and Theory, Marcel Dekker, New York, NY, USA, 1965.
[17]	Brown, G., Henry Darcy and His Law, Biosystems and Agricultural Engineering, Ohlahome State University, 1999-2005.
[18]	Prandtl, L. in Verhandlungen des dritten internationalen Mathematiker-Kongresses in Heidelberg 1904, A. Kraser, ed., Teubner, Leipzig, germany (1905), p. 484. English trans. In Early Developments of Modern Aerodynamics, J. A. K. Ackroid, B. P. Axcell, A. I. Ruban, eds., Butterworks-Heinemann.
[19]	Brki´c, Dejan., and Praks Pavel,, Unified Friction Formulation from Laminar to Fully Rough Turbulent Flow; Appl. Sci. 2018, 8, 2036; doi: 10.3390/app8112036.

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Hubert Michael Quinn. (2020). Quinn’s Law of Fluid Dynamics: Supplement #1 Nikuradze’s Inflection Profile Revisited. Fluid Mechanics, 6(1), 1-14. https://doi.org/10.11648/j.fm.20200601.11

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ACS Style

Hubert Michael Quinn. Quinn’s Law of Fluid Dynamics: Supplement #1 Nikuradze’s Inflection Profile Revisited. Fluid Mech. 2020, 6(1), 1-14. doi: 10.11648/j.fm.20200601.11

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AMA Style

Hubert Michael Quinn. Quinn’s Law of Fluid Dynamics: Supplement #1 Nikuradze’s Inflection Profile Revisited. Fluid Mech. 2020;6(1):1-14. doi: 10.11648/j.fm.20200601.11

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@article{10.11648/j.fm.20200601.11,
  author = {Hubert Michael Quinn},
  title = {Quinn’s Law of Fluid Dynamics: Supplement #1 Nikuradze’s Inflection Profile Revisited},
  journal = {Fluid Mechanics},
  volume = {6},
  number = {1},
  pages = {1-14},
  doi = {10.11648/j.fm.20200601.11},
  url = {https://doi.org/10.11648/j.fm.20200601.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.fm.20200601.11},
  abstract = {This paper is directed at the important contribution to fluid dynamics made by Johan Nikuradze. His seminal paper published in 1933 represents the gold standard of empty conduit permeability, for the flow of water through roughened pipes, even to this very day. We revisit in some detail the “inflection profile” in Nikuradze’s plot, which appears in the curve for his roughened data found in Figure 9 in that publication. In so doing, we show that the data points at low Reynolds number values, and particularly those surrounding the value of 3.4 approximately on the x-axis of his plot, do not represent the reported experimental results found in his tables of data. Furthermore, we also demonstrate that this discrepancy in his original paper is very problematic because it forms the basis for many subsequent scholarly works. As a result, this inflection profile has become erroneously embedded in conventional folklore concerning fluid flow in closed conduits and has enjoyed widespread acceptance as being a legitimate feature of fluid dynamics dogma. With the advent recently of Quinn’s Law, a novel approach to the understanding of fluid flow in closed conduits, we are able to articulate in a manner not heretofore possible, the significance of this discrepancy which is far too important to ignore.},
 year = {2020}
}

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TY  - JOUR
T1  - Quinn’s Law of Fluid Dynamics: Supplement #1 Nikuradze’s Inflection Profile Revisited
AU  - Hubert Michael Quinn
Y1  - 2020/02/18
PY  - 2020
N1  - https://doi.org/10.11648/j.fm.20200601.11
DO  - 10.11648/j.fm.20200601.11
T2  - Fluid Mechanics
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JO  - Fluid Mechanics
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EP  - 14
PB  - Science Publishing Group
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UR  - https://doi.org/10.11648/j.fm.20200601.11
AB  - This paper is directed at the important contribution to fluid dynamics made by Johan Nikuradze. His seminal paper published in 1933 represents the gold standard of empty conduit permeability, for the flow of water through roughened pipes, even to this very day. We revisit in some detail the “inflection profile” in Nikuradze’s plot, which appears in the curve for his roughened data found in Figure 9 in that publication. In so doing, we show that the data points at low Reynolds number values, and particularly those surrounding the value of 3.4 approximately on the x-axis of his plot, do not represent the reported experimental results found in his tables of data. Furthermore, we also demonstrate that this discrepancy in his original paper is very problematic because it forms the basis for many subsequent scholarly works. As a result, this inflection profile has become erroneously embedded in conventional folklore concerning fluid flow in closed conduits and has enjoyed widespread acceptance as being a legitimate feature of fluid dynamics dogma. With the advent recently of Quinn’s Law, a novel approach to the understanding of fluid flow in closed conduits, we are able to articulate in a manner not heretofore possible, the significance of this discrepancy which is far too important to ignore.
VL  - 6
IS  - 1
ER  -

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Author Information

Hubert Michael Quinn

Department of Research and Development, the Wrangler Group LLC, Brighton, USA

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Plain Text BibTeX RIS

APA Style

Hubert Michael Quinn. (2020). Quinn’s Law of Fluid Dynamics: Supplement #1 Nikuradze’s Inflection Profile Revisited. Fluid Mechanics, 6(1), 1-14. https://doi.org/10.11648/j.fm.20200601.11

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ACS Style

Hubert Michael Quinn. Quinn’s Law of Fluid Dynamics: Supplement #1 Nikuradze’s Inflection Profile Revisited. Fluid Mech. 2020, 6(1), 1-14. doi: 10.11648/j.fm.20200601.11

Copy | Download

AMA Style

Hubert Michael Quinn. Quinn’s Law of Fluid Dynamics: Supplement #1 Nikuradze’s Inflection Profile Revisited. Fluid Mech. 2020;6(1):1-14. doi: 10.11648/j.fm.20200601.11

Copy | Download

@article{10.11648/j.fm.20200601.11,
  author = {Hubert Michael Quinn},
  title = {Quinn’s Law of Fluid Dynamics: Supplement #1 Nikuradze’s Inflection Profile Revisited},
  journal = {Fluid Mechanics},
  volume = {6},
  number = {1},
  pages = {1-14},
  doi = {10.11648/j.fm.20200601.11},
  url = {https://doi.org/10.11648/j.fm.20200601.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.fm.20200601.11},
  abstract = {This paper is directed at the important contribution to fluid dynamics made by Johan Nikuradze. His seminal paper published in 1933 represents the gold standard of empty conduit permeability, for the flow of water through roughened pipes, even to this very day. We revisit in some detail the “inflection profile” in Nikuradze’s plot, which appears in the curve for his roughened data found in Figure 9 in that publication. In so doing, we show that the data points at low Reynolds number values, and particularly those surrounding the value of 3.4 approximately on the x-axis of his plot, do not represent the reported experimental results found in his tables of data. Furthermore, we also demonstrate that this discrepancy in his original paper is very problematic because it forms the basis for many subsequent scholarly works. As a result, this inflection profile has become erroneously embedded in conventional folklore concerning fluid flow in closed conduits and has enjoyed widespread acceptance as being a legitimate feature of fluid dynamics dogma. With the advent recently of Quinn’s Law, a novel approach to the understanding of fluid flow in closed conduits, we are able to articulate in a manner not heretofore possible, the significance of this discrepancy which is far too important to ignore.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Quinn’s Law of Fluid Dynamics: Supplement #1 Nikuradze’s Inflection Profile Revisited
AU  - Hubert Michael Quinn
Y1  - 2020/02/18
PY  - 2020
N1  - https://doi.org/10.11648/j.fm.20200601.11
DO  - 10.11648/j.fm.20200601.11
T2  - Fluid Mechanics
JF  - Fluid Mechanics
JO  - Fluid Mechanics
SP  - 1
EP  - 14
PB  - Science Publishing Group
SN  - 2575-1816
UR  - https://doi.org/10.11648/j.fm.20200601.11
AB  - This paper is directed at the important contribution to fluid dynamics made by Johan Nikuradze. His seminal paper published in 1933 represents the gold standard of empty conduit permeability, for the flow of water through roughened pipes, even to this very day. We revisit in some detail the “inflection profile” in Nikuradze’s plot, which appears in the curve for his roughened data found in Figure 9 in that publication. In so doing, we show that the data points at low Reynolds number values, and particularly those surrounding the value of 3.4 approximately on the x-axis of his plot, do not represent the reported experimental results found in his tables of data. Furthermore, we also demonstrate that this discrepancy in his original paper is very problematic because it forms the basis for many subsequent scholarly works. As a result, this inflection profile has become erroneously embedded in conventional folklore concerning fluid flow in closed conduits and has enjoyed widespread acceptance as being a legitimate feature of fluid dynamics dogma. With the advent recently of Quinn’s Law, a novel approach to the understanding of fluid flow in closed conduits, we are able to articulate in a manner not heretofore possible, the significance of this discrepancy which is far too important to ignore.
VL  - 6
IS  - 1
ER  -

Copy | Download