The paper presents a mathematical formulation of an incompressible two-dimensional groundwater creeping flow past a fully constrained impermeable obstacle. The physical boundary of this obstacle is modeled as a smooth surface having negligible roughness. Referring to the impact of boundary roughness, it is known that from Hydrodynamics point of view, a solid surface is called “smooth” when the average depth of the surface irregularities is less than the thickness of the laminar sublayer over the surface. In this framework, a theoretical evaluation of the piezometric head is exhibited and concurrently the position of velocity distribution local extrema is determined.

piezometric head, creeping flow, Darcy’s law, conformal mapping, Schwarz-Christoffel transformation.

Received: March 2, 2022; Accepted: April 25, 2022; Published: May 11, 2022

How to cite this article: J. Venetis, Analytic evaluation of piezometric head for a creeping flow past a fully constrained obstacle, Advances in Differential Equations and Control Processes 27 (2022), 163-179. http://dx.doi.org/10.17654/0974324322019

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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