Laminar flow of Newtonian liquids in ducts of rectangular cross-section a model for both physics and mathematics

Abstract

In this paper, we considered the laminar fully developed flow, of a Newtonian fluid, in ducts of rectangular cross-section. Poisson's partial differential equation Saint-Venant solution was used, to calculate Poiseuille number values whatever is rectangles aspect ratio. From these results, we considered limit cases of square duct and plane Poiseuille flow (infinite parallel plates). We showed there exists a rectangle equivalent to a circular cross-section for energy dissipation through viscous friction. Finally, we gave some mathematical consequences of this approach for odd integers zeta function calculations and Catalan's constant.