A Comparison of Sir Osborne Reynold’s 1883 Seminal Paper and the QFFM: A Hand in Glove Reconciliation

Abstract

Since Sir Osborne Reynolds wrote his seminal paper in 1883 in which he unveiled, for the first time, the elements of what would become the governing equation for fluid flow in closed conduits and which bears his name to this day, much confusion has surrounded the explanation for the phenomenon typically referred to as the fluid flow regime. In a follow up development circa 1904, Ludwig Prandtl and his students developed a concept known today as the viscous boundary layer which has to do with fluid flow adjacent to a solid boundary. Many consider this concept as a vital underpinning for modern day aerodynamics. In addition to these two fundamental developments, Johann Nikuradze who, incidentally, was one of Prandtl’s students, circa 1933 published his critical experiments in which he glued sand particles to the inner walls of conduits forming what stands as the gold standard, even to this day, for permeability measurements in roughened pipes. In the parallel field of study involving packed beds, John Calvin Giddings in 1965 outlined a teaching of permeability unprecedented in the published literature for conduits packed with solid obstacles. This appeared in the first of his two classic text books on this subject matter. These teachings and concepts for both packed and empty conduits have dominated the conversation of fluid flow in closed conduits for the best part of the last 150 years but without any coherent explanation of how they all combine, within the dictates of the Laws of Nature, to produce the complicated flow patterns we currently associate with the change in flow profile, from laminar to turbulent flow. The advent of the Quinn Fluid Flow Model (QFFM), however, first published in 2019, provides the missing understanding of how these concepts come together. In this paper, we will demonstrate how this is accomplished by using the original publications of these fluid dynamic icons to validate the teaching of the QFFM, over 13 orders of magnitude of the Reynolds number. Additionally, we will show that fluid flow in an empty conduit is merely a special case of fluid flow in a conduit packed with solid obstacles. Moreover, we will demonstrate that turbulent flow is a highly structured form of fluid motion, driven by forces easily quantified within the context of the QFFM and is represented, within the Hypothetical Q Channel (HQC), as a form of damped simple harmonic motion, wherein the two damping mechanisms are, (1) wall friction, and (2) fluid internal friction. Finally, we will demonstrate that Reynold’s observations regarding the transition from laminar to turbulent flow, in which he noticed a straight line of dye in the middle of the tube representing laminar flow, followed by a succession of eddies, representing the transition to turbulent flow, are replicated, virtually identically, in the QFFM teaching of damped curvy-linear simple harmonic motion in the HQC.