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 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.

In this paper, the experimental protocol which we disclose is designed to identify the values for both the constant in the Kozeny/Carman model, which relates to the linear component of permeability, and the variable kinetic coefficient in the newly minted Q- modified Ergun model, which relates to the non-linear components of permeability, without involving any new theoretical development. Moreover, kinetic contributions to measured pressure gradient, which are not accounted for in some currently accepted empirical fluid flow equations, such as Poiseuille’s for flow in empty conduits and Kozeny/Carman for flow in packed conduits, but which nevertheless contribute to measured pressure drop and thus hamper the identification of the value of the constant relative to the laminar component, are captured and lumped together into a single variable kinetic parameter-the kinetic coefficient.