A Fluid Dynamic Development Like None Other

Abstract

For more than 100 years, much uncertainty has surrounded fluid flow characteristics, both in open pipes and packed conduits. Not the least amongst this uncertainty has been the physics of the viscous boundary layer, in the former, and the so-called “wall-effect”, in the latter. Indeed, no fluid flow model has ever been able to reconcile both packed and empty conduits within the same theoretical framework, until now. In this paper, we describe the Quinn Fluid Flow Model (QFFM), which was first published in 2019 and represents the first model to capture, seamlessly, the physics of both empty and packed conduits, including all elements of wall-effects. This is not the only distinguishing feature of the model, which also includes, again, for the first time, a theoretical description of the so-called “constants” within the pressure flow relationship in closed conduits. Consequently, this model enables fluid dynamic validation over the entire fluid flow regime from creeping flow, at low Reynolds number values, to fully turbulent, at high Reynolds number values. This unique feature is possible because, on the one hand, in empty conduits, extremely large Reynolds number values are achievable at reasonable pressure drops but, very low Reynolds number values are not, due to the pressure drops being prohibitively low. In packed conduits, on the other hand, very low Reynolds number values are achievable at reasonable pressure drops but, large Reynolds number values are not, due to the pressure drops being prohibitively high. Accordingly, the QFFM enables simultaneous validation, at high Reynolds number values in the former and, at low Reynolds number values in the latter. This characteristic, therefore, to validate over the entire fluid flow regime using the same underlying physical and mathematical framework, sets this fluid flow model apart from all others. In addition to highlighting the many features of the QFFM in this paper, we will also demonstrate a comprehensive validation over ten orders of magnitude of the Reynolds number using published classical studies, as well as home grown experiments. To our knowledge, no extant fluid flow model comes even close to this comprehensive description of the fluid dynamics of fluid flow, not only in closed conduits, but also, by extrapolation, in other applications outside of this very narrow field of study.