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

Hubert Michael Quinn

doi: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.

Highlights

The history of attempts to quantify a relationship between fluid flow in closed conduits and the relevant variables governing that relationship dates back at least to the work of Darcy in 1856 [1]
This field of study is in such disarray that there is no currently accepted theory of fluid dynamics from which one could derive an analytical solution to the supposed governing equation of fluid dynamics, the Navier-Stokes equation [4]
The Navier-Stokes equation for fluid flow stands without analytical solution

Summary

Introduction

The history of attempts to quantify a relationship between fluid flow in closed conduits (whether it be in a packed conduit or in an empty conduit) and the relevant variables governing that relationship dates back at least to the work of Darcy in 1856 [1]. The scientific literature is replete with reports of experimental results aimed at trying to resolve the many discrepancies which litter the fluid dynamics landscape [3] This field of study is in such disarray that there is no currently accepted theory of fluid dynamics from which one could derive an analytical solution to the supposed governing equation of fluid dynamics, the Navier-Stokes equation [4]. The subsequent model, which we refer to as the Quinn Fluid Flow Model (QFFM) took approximately 20 years to formulate, was developed from first principles, and is different from any other model currently extant Most importantly, it is a universal theory which applies to all fluid flow embodiments, regardless of whether they contain particles and regardless of the regime of flow in which they are operated. It has been validated by testing it against a host of generally accepted experimental data reported in the literature, as well as this author’s own measurements

Methods

Results

Discussion

Conclusion