The 12 Principles of Fluid Dynamics in Closed Conduits Aerodynamic Analysis of a Golf Ball in Flight

Abstract

In the real world, fluid flow in closed conduits manifests in both empty conduits, i.e., conduits devoid of solid obstacles and conduits packed with solid particles. The majority of packed beds reported in the literature over the last 100 years, approximately, contain spheroidal particles, for the most part. However, the particles within the packed conduits can vary over a very broad range of shapes and diameter values and when coupled with a wide choice of both conduits and available fluids, this ensemble of experimental variables complicates the study matter, immensely. Empirical studies covering this very broad dynamic range of choices has created many difficulties which has, unfortunately, contributed to a compromised data base of published results. In fact, it is not an exaggeration to suggest that more than 50% of published articles in this field are fraught with errors, misinformation and contradictions. For instance, the use of gases as the fluid of choice, in any experiment, always presents a problem because it is a compressible fluid which means that its’ density varies as a function of pressure drop. In addition, because the viscosity also varies with density, the turbulent tipping point of the packed conduit under study cannot be predicted a priori which means that when a compressible fluid is chosen as the fluid of choice in permeability studies, all fluid variables must be measured simultaneously, i.e., viscosity, density, pressure drop and velocity. This is a significant experimentation undertaking for any particular study which many times in the published literature is omitted from the experimental protocol. There is the added difficulty of managing pressure drop, since small particles render large pressure drops while large particles render small pressure drops. If one also considers the additional important variables of packed bed porosity and boundary layer (wall-effects), it becomes very clear that such empirical studies are anything but simple experiments. In fact, there are a total of seven discrete variables and one universal constant embedded in the validated mathematical expression for the pressure flow relationship of packed conduits. A dimpled golf ball, therefore, is a very interesting candidate as a choice for the study of packed beds because it is large in diameter, has a roughened surface, and its’ aerodynamic flight takes place through a compressible fluid medium (air), which stands at standard temperature and pressure (STP) in the path of the golf ball flight. Accordingly, a commercial golf ball represents an ideal study candidate and, therefore, the gold standard candidate, albeit of the most difficult variety from an empirical standpoint, to evaluate the performance claims of any fluid flow model which purports to describe the hydrodynamics of packed conduits. In this paper, a relatively new fluid flow model (QFFM) will be used to do exactly that. The aerodynamics of a golf ball in flight will be documented by taking measurements using water, an incompressible fluid, in a packed conduit containing many golf balls, something that has never been accomplished, as far as we know. The teaching of this unique fluid flow model will be used to demonstrate an experimental technique which circumvents/ solves many of the aforementioned issues for studies in packed beds. In short, this paper defines the gold standard of how an experimental protocol should be carried out for permeability in closed conduits, even when the particles are irregular (non- spherical) in shape, compressible (non-rigid), very small in diameter and/or have a roughened surface morphology and, even when the fluid of choice is compressible, such as air.