Quinn’s Law of Fluid Dynamics: Supplement #2 Reinventing the Ergun Equation

Hubert Michael Quinn

doi:doi:10.11648/j.fm.20200601.12

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Quinn’s Law of Fluid Dynamics: Supplement #2 Reinventing the Ergun Equation

Hubert Michael Quinn

Published in Fluid Mechanics (Volume 6, Issue 1)

Received: 17 March 2020 Accepted: 13 May 2020 Published: 15 June 2020

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Abstract

This paper is directed at the important contribution to fluid dynamics made by Sebri Ergun. In his three papers published in 1949, 1951 and 1952, using various gases as his percolating fluid, Ergun used his empirical permeability results of packing conduits with fractured coke (irregularly shaped particles), in combination with some theoretical concepts, to generate an equation which captured the viscous and kinetic contributions to packed conduit permeability in two separate terms in that equation, resulting in his now famous “Ergun Equation”. In addition, he identified a discrete “constant” for each of the terms which we label herein the “viscous” and “kinetic” constants, respectively. We demonstrate herein, however, that the values assigned by Ergun to both his constants are not certifiable and, thus, are problematic in predicting the permeability of packed conduits. Moreover, since the publication of his 1952 paper, in which he disclosed the values of 150 and 1.75 for the viscous and kinetic constants, respectively, many scholarly works have been published which claim to validate these values. As a result, these values have become erroneously embedded in conventional folklore concerning fluid flow in closed conduits and have 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 in Ergun’s values of the constants, which we demonstrate is far too important to ignore.

Published in	Fluid Mechanics (Volume 6, Issue 1)
DOI	10.11648/j.fm.20200601.12
Page(s)	15-29
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

Viscous Constant, Kinetic Constant, Ergun Equation, Friction Factor, Transition Region, Turbulent Flow, Wall Effect, Boundary Layer

References

[1]	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.
[2]	Ergun, S. and Orning, A. A., Fluid Flow through Randomly Packed Columns and Fluidized Beds, Ind. Eng. Chem. vol. 41, pp. 1179, 1949.
[3]	Ergun, S., Determination of Particle Density of Crushed Porous Solids, Anal. Chem. vol. 23, 1951.
[4]	Ergun, S., Fluid Flow Through Packed Columns, Chem. Eng. Progr. vol. 48, pp. 89-94, 1952.
[5]	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.
[6]	Quinn, H. M., Quinn’s Law of Fluid Dynamics: Supplement #1 Nikuradze’s Inflection Profile Revisited, Fluid Mechanics. Vol. 6, No. 1, 2020, pp. 1-14. doi: 10.11648/j.fm.20200601.11.
[7]	Quinn, H. M., Reconciliation of Conventional Wisdom with Reality. A Misconstrued Constant Used as a Tool to Manipulate Paying Customers. Lambert Academic Publishing (2019).
[8]	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.
[9]	Van Lopik, J. H., Snoeijers, R., Van Dooren, T. C. G., Raoof, A., Schotting, R. J., The Effect of Grain Size Distribution on Nonlinear Flow Behavior in Sandy Porous Media, Transp Porous Med (2017) 120: 37-66. DOT. 10.1007/s11242-017-0903-3.
[10]	Van Lopik, J. H., Zazai, L., Hartog, N., Schotting, R. J., Nonlinear Flow behavior in Packed Beds of Natural and Variably Graded Granular Materials, Transp Porous Med, https://dci.org/10.1007/s11242-019-01373-0 (2019).

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Hubert Michael Quinn. (2020). Quinn’s Law of Fluid Dynamics: Supplement #2 Reinventing the Ergun Equation. Fluid Mechanics, 6(1), 15-29. https://doi.org/10.11648/j.fm.20200601.12

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Hubert Michael Quinn. Quinn’s Law of Fluid Dynamics: Supplement #2 Reinventing the Ergun Equation. Fluid Mech. 2020, 6(1), 15-29. doi: 10.11648/j.fm.20200601.12

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Hubert Michael Quinn. Quinn’s Law of Fluid Dynamics: Supplement #2 Reinventing the Ergun Equation. Fluid Mech. 2020;6(1):15-29. doi: 10.11648/j.fm.20200601.12

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@article{10.11648/j.fm.20200601.12,
  author = {Hubert Michael Quinn},
  title = {Quinn’s Law of Fluid Dynamics: Supplement #2 Reinventing the Ergun Equation},
  journal = {Fluid Mechanics},
  volume = {6},
  number = {1},
  pages = {15-29},
  doi = {10.11648/j.fm.20200601.12},
  url = {https://doi.org/10.11648/j.fm.20200601.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.fm.20200601.12},
  abstract = {This paper is directed at the important contribution to fluid dynamics made by Sebri Ergun. In his three papers published in 1949, 1951 and 1952, using various gases as his percolating fluid, Ergun used his empirical permeability results of packing conduits with fractured coke (irregularly shaped particles), in combination with some theoretical concepts, to generate an equation which captured the viscous and kinetic contributions to packed conduit permeability in two separate terms in that equation, resulting in his now famous “Ergun Equation”. In addition, he identified a discrete “constant” for each of the terms which we label herein the “viscous” and “kinetic” constants, respectively. We demonstrate herein, however, that the values assigned by Ergun to both his constants are not certifiable and, thus, are problematic in predicting the permeability of packed conduits. Moreover, since the publication of his 1952 paper, in which he disclosed the values of 150 and 1.75 for the viscous and kinetic constants, respectively, many scholarly works have been published which claim to validate these values. As a result, these values have become erroneously embedded in conventional folklore concerning fluid flow in closed conduits and have 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 in Ergun’s values of the constants, which we demonstrate is far too important to ignore.},
 year = {2020}
}

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TY  - JOUR
T1  - Quinn’s Law of Fluid Dynamics: Supplement #2 Reinventing the Ergun Equation
AU  - Hubert Michael Quinn
Y1  - 2020/06/15
PY  - 2020
N1  - https://doi.org/10.11648/j.fm.20200601.12
DO  - 10.11648/j.fm.20200601.12
T2  - Fluid Mechanics
JF  - Fluid Mechanics
JO  - Fluid Mechanics
SP  - 15
EP  - 29
PB  - Science Publishing Group
SN  - 2575-1816
UR  - https://doi.org/10.11648/j.fm.20200601.12
AB  - This paper is directed at the important contribution to fluid dynamics made by Sebri Ergun. In his three papers published in 1949, 1951 and 1952, using various gases as his percolating fluid, Ergun used his empirical permeability results of packing conduits with fractured coke (irregularly shaped particles), in combination with some theoretical concepts, to generate an equation which captured the viscous and kinetic contributions to packed conduit permeability in two separate terms in that equation, resulting in his now famous “Ergun Equation”. In addition, he identified a discrete “constant” for each of the terms which we label herein the “viscous” and “kinetic” constants, respectively. We demonstrate herein, however, that the values assigned by Ergun to both his constants are not certifiable and, thus, are problematic in predicting the permeability of packed conduits. Moreover, since the publication of his 1952 paper, in which he disclosed the values of 150 and 1.75 for the viscous and kinetic constants, respectively, many scholarly works have been published which claim to validate these values. As a result, these values have become erroneously embedded in conventional folklore concerning fluid flow in closed conduits and have 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 in Ergun’s values of the constants, which we demonstrate 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 #2 Reinventing the Ergun Equation. Fluid Mechanics, 6(1), 15-29. https://doi.org/10.11648/j.fm.20200601.12

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ACS Style

Hubert Michael Quinn. Quinn’s Law of Fluid Dynamics: Supplement #2 Reinventing the Ergun Equation. Fluid Mech. 2020, 6(1), 15-29. doi: 10.11648/j.fm.20200601.12

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AMA Style

Hubert Michael Quinn. Quinn’s Law of Fluid Dynamics: Supplement #2 Reinventing the Ergun Equation. Fluid Mech. 2020;6(1):15-29. doi: 10.11648/j.fm.20200601.12

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@article{10.11648/j.fm.20200601.12,
  author = {Hubert Michael Quinn},
  title = {Quinn’s Law of Fluid Dynamics: Supplement #2 Reinventing the Ergun Equation},
  journal = {Fluid Mechanics},
  volume = {6},
  number = {1},
  pages = {15-29},
  doi = {10.11648/j.fm.20200601.12},
  url = {https://doi.org/10.11648/j.fm.20200601.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.fm.20200601.12},
  abstract = {This paper is directed at the important contribution to fluid dynamics made by Sebri Ergun. In his three papers published in 1949, 1951 and 1952, using various gases as his percolating fluid, Ergun used his empirical permeability results of packing conduits with fractured coke (irregularly shaped particles), in combination with some theoretical concepts, to generate an equation which captured the viscous and kinetic contributions to packed conduit permeability in two separate terms in that equation, resulting in his now famous “Ergun Equation”. In addition, he identified a discrete “constant” for each of the terms which we label herein the “viscous” and “kinetic” constants, respectively. We demonstrate herein, however, that the values assigned by Ergun to both his constants are not certifiable and, thus, are problematic in predicting the permeability of packed conduits. Moreover, since the publication of his 1952 paper, in which he disclosed the values of 150 and 1.75 for the viscous and kinetic constants, respectively, many scholarly works have been published which claim to validate these values. As a result, these values have become erroneously embedded in conventional folklore concerning fluid flow in closed conduits and have 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 in Ergun’s values of the constants, which we demonstrate is far too important to ignore.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Quinn’s Law of Fluid Dynamics: Supplement #2 Reinventing the Ergun Equation
AU  - Hubert Michael Quinn
Y1  - 2020/06/15
PY  - 2020
N1  - https://doi.org/10.11648/j.fm.20200601.12
DO  - 10.11648/j.fm.20200601.12
T2  - Fluid Mechanics
JF  - Fluid Mechanics
JO  - Fluid Mechanics
SP  - 15
EP  - 29
PB  - Science Publishing Group
SN  - 2575-1816
UR  - https://doi.org/10.11648/j.fm.20200601.12
AB  - This paper is directed at the important contribution to fluid dynamics made by Sebri Ergun. In his three papers published in 1949, 1951 and 1952, using various gases as his percolating fluid, Ergun used his empirical permeability results of packing conduits with fractured coke (irregularly shaped particles), in combination with some theoretical concepts, to generate an equation which captured the viscous and kinetic contributions to packed conduit permeability in two separate terms in that equation, resulting in his now famous “Ergun Equation”. In addition, he identified a discrete “constant” for each of the terms which we label herein the “viscous” and “kinetic” constants, respectively. We demonstrate herein, however, that the values assigned by Ergun to both his constants are not certifiable and, thus, are problematic in predicting the permeability of packed conduits. Moreover, since the publication of his 1952 paper, in which he disclosed the values of 150 and 1.75 for the viscous and kinetic constants, respectively, many scholarly works have been published which claim to validate these values. As a result, these values have become erroneously embedded in conventional folklore concerning fluid flow in closed conduits and have 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 in Ergun’s values of the constants, which we demonstrate is far too important to ignore.
VL  - 6
IS  - 1
ER  -

Copy | Download