Quinn’s Law of Fluid Dynamics Pressure-driven Fluid Flow Through Closed Conduits

Hubert Michael Quinn

doi:doi:10.11648/j.fm.20190502.12

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Quinn’s Law of Fluid Dynamics Pressure-driven Fluid Flow Through Closed Conduits

Hubert Michael Quinn

Published in Fluid Mechanics (Volume 5, Issue 2)

Received: 12 October 2019 Accepted: 11 December 2019 Published: 6 January 2020

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Abstract

In this paper we develop from first principles a unique law pertaining to the flow of fluids through closed conduits. This law, which we call “Quinn’s Law”, may be described as follows: When fluids are forced to flow through closed conduits under the driving force of a pressure gradient, there is a linear relationship between the fluid-drag normalized dimensionless pressure gradient, P_Q, and the normalized dimensionless fluid current, C_Q. The relationship is expressed mathematically as: P_Q=k₁ +k₂C_Q. This linear relationship remains the same whether the conduit is filled with or devoid of solid obstacles. The law differentiates, however, between a packed and an empty conduit by virtue of the tortuosity of the fluid path, which is seamlessly accommodated within the normalization framework of the law itself. When movement of the fluid is very close to being at rest, i.e., very slow, this relationship has the unique minimum constant value of k₁, and as the fluid acceleration increases, it varies with a slope of k₂ as a function of normalized fluid current. Quinn’s Law is validated herein by applying it to the data from published classical studies of measured permeability in both packed and empty conduits, as well as to the data generated by home grown experiments performed in the author’s own laboratory.

Published in	Fluid Mechanics (Volume 5, Issue 2)
DOI	10.11648/j.fm.20190502.12
Page(s)	39-71
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

Closed Conduits, Conduit Permeability, Friction Factor, Wall Effect, Boundary Layer, Turbulent, Flow Profile, Chaos

References

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Hubert Michael Quinn. (2020). Quinn’s Law of Fluid Dynamics Pressure-driven Fluid Flow Through Closed Conduits. Fluid Mechanics, 5(2), 39-71. https://doi.org/10.11648/j.fm.20190502.12

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ACS Style

Hubert Michael Quinn. Quinn’s Law of Fluid Dynamics Pressure-driven Fluid Flow Through Closed Conduits. Fluid Mech. 2020, 5(2), 39-71. doi: 10.11648/j.fm.20190502.12

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AMA Style

Hubert Michael Quinn. Quinn’s Law of Fluid Dynamics Pressure-driven Fluid Flow Through Closed Conduits. Fluid Mech. 2020;5(2):39-71. doi: 10.11648/j.fm.20190502.12

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@article{10.11648/j.fm.20190502.12,
  author = {Hubert Michael Quinn},
  title = {Quinn’s Law of Fluid Dynamics Pressure-driven Fluid Flow Through Closed Conduits},
  journal = {Fluid Mechanics},
  volume = {5},
  number = {2},
  pages = {39-71},
  doi = {10.11648/j.fm.20190502.12},
  url = {https://doi.org/10.11648/j.fm.20190502.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.fm.20190502.12},
  abstract = {In this paper we develop from first principles a unique law pertaining to the flow of fluids through closed conduits. This law, which we call “Quinn’s Law”, may be described as follows: When fluids are forced to flow through closed conduits under the driving force of a pressure gradient, there is a linear relationship between the fluid-drag normalized dimensionless pressure gradient, PQ, and the normalized dimensionless fluid current, CQ. The relationship is expressed mathematically as: PQ=k1 +k2CQ. This linear relationship remains the same whether the conduit is filled with or devoid of solid obstacles. The law differentiates, however, between a packed and an empty conduit by virtue of the tortuosity of the fluid path, which is seamlessly accommodated within the normalization framework of the law itself. When movement of the fluid is very close to being at rest, i.e., very slow, this relationship has the unique minimum constant value of k1, and as the fluid acceleration increases, it varies with a slope of k2 as a function of normalized fluid current. Quinn’s Law is validated herein by applying it to the data from published classical studies of measured permeability in both packed and empty conduits, as well as to the data generated by home grown experiments performed in the author’s own laboratory.},
 year = {2020}
}

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TY  - JOUR
T1  - Quinn’s Law of Fluid Dynamics Pressure-driven Fluid Flow Through Closed Conduits
AU  - Hubert Michael Quinn
Y1  - 2020/01/06
PY  - 2020
N1  - https://doi.org/10.11648/j.fm.20190502.12
DO  - 10.11648/j.fm.20190502.12
T2  - Fluid Mechanics
JF  - Fluid Mechanics
JO  - Fluid Mechanics
SP  - 39
EP  - 71
PB  - Science Publishing Group
SN  - 2575-1816
UR  - https://doi.org/10.11648/j.fm.20190502.12
AB  - In this paper we develop from first principles a unique law pertaining to the flow of fluids through closed conduits. This law, which we call “Quinn’s Law”, may be described as follows: When fluids are forced to flow through closed conduits under the driving force of a pressure gradient, there is a linear relationship between the fluid-drag normalized dimensionless pressure gradient, PQ, and the normalized dimensionless fluid current, CQ. The relationship is expressed mathematically as: PQ=k1 +k2CQ. This linear relationship remains the same whether the conduit is filled with or devoid of solid obstacles. The law differentiates, however, between a packed and an empty conduit by virtue of the tortuosity of the fluid path, which is seamlessly accommodated within the normalization framework of the law itself. When movement of the fluid is very close to being at rest, i.e., very slow, this relationship has the unique minimum constant value of k1, and as the fluid acceleration increases, it varies with a slope of k2 as a function of normalized fluid current. Quinn’s Law is validated herein by applying it to the data from published classical studies of measured permeability in both packed and empty conduits, as well as to the data generated by home grown experiments performed in the author’s own laboratory.
VL  - 5
IS  - 2
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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APA Style

Hubert Michael Quinn. (2020). Quinn’s Law of Fluid Dynamics Pressure-driven Fluid Flow Through Closed Conduits. Fluid Mechanics, 5(2), 39-71. https://doi.org/10.11648/j.fm.20190502.12

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ACS Style

Hubert Michael Quinn. Quinn’s Law of Fluid Dynamics Pressure-driven Fluid Flow Through Closed Conduits. Fluid Mech. 2020, 5(2), 39-71. doi: 10.11648/j.fm.20190502.12

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AMA Style

Hubert Michael Quinn. Quinn’s Law of Fluid Dynamics Pressure-driven Fluid Flow Through Closed Conduits. Fluid Mech. 2020;5(2):39-71. doi: 10.11648/j.fm.20190502.12

Copy | Download

@article{10.11648/j.fm.20190502.12,
  author = {Hubert Michael Quinn},
  title = {Quinn’s Law of Fluid Dynamics Pressure-driven Fluid Flow Through Closed Conduits},
  journal = {Fluid Mechanics},
  volume = {5},
  number = {2},
  pages = {39-71},
  doi = {10.11648/j.fm.20190502.12},
  url = {https://doi.org/10.11648/j.fm.20190502.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.fm.20190502.12},
  abstract = {In this paper we develop from first principles a unique law pertaining to the flow of fluids through closed conduits. This law, which we call “Quinn’s Law”, may be described as follows: When fluids are forced to flow through closed conduits under the driving force of a pressure gradient, there is a linear relationship between the fluid-drag normalized dimensionless pressure gradient, PQ, and the normalized dimensionless fluid current, CQ. The relationship is expressed mathematically as: PQ=k1 +k2CQ. This linear relationship remains the same whether the conduit is filled with or devoid of solid obstacles. The law differentiates, however, between a packed and an empty conduit by virtue of the tortuosity of the fluid path, which is seamlessly accommodated within the normalization framework of the law itself. When movement of the fluid is very close to being at rest, i.e., very slow, this relationship has the unique minimum constant value of k1, and as the fluid acceleration increases, it varies with a slope of k2 as a function of normalized fluid current. Quinn’s Law is validated herein by applying it to the data from published classical studies of measured permeability in both packed and empty conduits, as well as to the data generated by home grown experiments performed in the author’s own laboratory.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Quinn’s Law of Fluid Dynamics Pressure-driven Fluid Flow Through Closed Conduits
AU  - Hubert Michael Quinn
Y1  - 2020/01/06
PY  - 2020
N1  - https://doi.org/10.11648/j.fm.20190502.12
DO  - 10.11648/j.fm.20190502.12
T2  - Fluid Mechanics
JF  - Fluid Mechanics
JO  - Fluid Mechanics
SP  - 39
EP  - 71
PB  - Science Publishing Group
SN  - 2575-1816
UR  - https://doi.org/10.11648/j.fm.20190502.12
AB  - In this paper we develop from first principles a unique law pertaining to the flow of fluids through closed conduits. This law, which we call “Quinn’s Law”, may be described as follows: When fluids are forced to flow through closed conduits under the driving force of a pressure gradient, there is a linear relationship between the fluid-drag normalized dimensionless pressure gradient, PQ, and the normalized dimensionless fluid current, CQ. The relationship is expressed mathematically as: PQ=k1 +k2CQ. This linear relationship remains the same whether the conduit is filled with or devoid of solid obstacles. The law differentiates, however, between a packed and an empty conduit by virtue of the tortuosity of the fluid path, which is seamlessly accommodated within the normalization framework of the law itself. When movement of the fluid is very close to being at rest, i.e., very slow, this relationship has the unique minimum constant value of k1, and as the fluid acceleration increases, it varies with a slope of k2 as a function of normalized fluid current. Quinn’s Law is validated herein by applying it to the data from published classical studies of measured permeability in both packed and empty conduits, as well as to the data generated by home grown experiments performed in the author’s own laboratory.
VL  - 5
IS  - 2
ER  -

Copy | Download