Investigating Poiseuille Flows in Rotating Inclined Pipes: An Analytical Approach

Abstract

The study of Poiseuille flow, particularly relevant in diverse scenarios such as human blood circulation, crude oil transport, and industrial fluid dynamics, forms the crux of this research. Specifically, it delves into the analysis of fluid flow within a channel inclined at an angle relative to the horizontal axis, a scenario commonly encountered in rotating frames like bioreactors and drilling rigs, where the Coriolis force plays a crucial role. Employing the Navier-Stokes equations, this research formulates the governing equations for the flow and presents an analytical solution. It has been observed that an increase in the pressure gradient correlates with a rise in flow velocity. Furthermore, an escalation in rotational speed tends to flatten and elevate the velocity profiles. Additionally, an increase in the angle of inclination of the channel is found to boost the flow velocity. These findings have significant implications for optimizing the design and operational efficiency of systems involving inclined channels, with potential applications across various industries, including biotechnology and oil extraction.