Pressure-driven flow in a thin pipe with rough boundary

Abstract

Stationary incompressible Newtonian fluid flow governed by external force and external pressure is considered in a thin rough pipe. The transversal size of the pipe is assumed to be of the order $$\varepsilon $$ ε , i.e., cross-sectional area is about $$\varepsilon ^{2}$$ ε 2 , and the wavelength in longitudinal direction is modeled by a small parameter $$\mu $$ μ . Under general assumption $$\varepsilon ,\mu \rightarrow 0$$ ε , μ → 0 , the Poiseuille law is obtained. Depending on $$\varepsilon ,\mu $$ ε , μ -relation ($$\varepsilon \ll \mu $$ ε ≪ μ , $$\varepsilon /\mu \sim \mathrm {constant}$$ ε / μ ∼ constant , $$\varepsilon \gg \mu $$ ε ≫ μ ), different cell problems describing the local behavior of the fluid are deduced and analyzed. Error estimates are presented.

Exact solutions of flow and pressure variation inside a horizontalfilter chamber using Lie symmetry analysis

“…In the past and recent, various research works have been done to understand flow, mass and heat transfer in different channels to obtain scientific evidence which improves real-world phenomena. Experimental studies of the pipe flow go back to the 1840s when Poiseuille established the relationship between the volumetric efflux rate of fluid from the tube, the driving pressure differential, the tube length and the tube diameter, see the following references [1][2][3] for more information. The distinction between laminar, transitional and turbulent regimes for fluid flows was done by Stokes [4] and later was popularised by Reynolds [5].…”