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In this paper, we considered the laminar fully developed flow, of a Newtonian fluid, inducts 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.

Summary Composite manufacturing processes usually proceed from preimpregnated preforms that are consolidated by simultaneously applying heat and pressure, so as to ensure a perfect contact compulsory for making molecular diffusion possible. However, in practice, the contact is rarely perfect. This results in a rough interface where air could remain entrapped, thus affecting the effective thermal conductivity. Moreover, the interfacial melted polymer is squeezed flowing in the rough gap created by the fibers located on the prepreg surfaces. Because of the typical dimensions of a composite prepreg, with thickness orders of magnitude smaller than its other in‐plane dimensions, and its surface roughness having a characteristic size orders of magnitude smaller than the prepreg thickness, high‐fidelity numerical simulations for elucidating the impact of surface and interface roughness remain today, despite the impressive advances in computational availabilities, unattainable. This work aims at elucidating roughness impact on heat conduction and the effective viscosity of the interfacial polymer squeeze flow by using an advanced numerical strategy able to reach resolutions never attained until now, a sort of numerical microscope able to attain the scale of the smallest geometrical detail.

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In this paper, following results obtained at cosmological scale, we tried to use fluid mechanics concepts at atomic scale. A model based on mixing systems mechanics was developed in order to calculate an electron rotational speed. Space-time transport properties i.e., density and dynamic viscosity were needed and their values were carefully chosen in literature. Moreover, we found that gravity acceleration at atomic scale has to be largely greater than the well known Newtonian value. Final results gave a rotational speed in fair agreement with Bohr model value for hydrogen atom indicating that, a fluid mechanics based approach, could be useful in building a physics model available whatever the scale and a quantum gravity theory.