the relationship between numerical modeling and analytical solutions Poiseuille's Law in fluid mecha
Автор: Cross-Disciplinary Perspective(CDP)
Загружено: 2025-11-29
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Name: the relationship between numerical modeling and analytical solutions-Poiseuille's Law in fluid mechanics
Notes: https://viadean.notion.site/Fluid-Mom...
Summary: Both the static plot and the dynamic animation of Hagen-Poiseuille flow illustrate the same fundamental principle: the laminar, parabolic velocity profile, $v(r)=V_{\text {max }}\left(1-(r / R)^2\right)$, is the governing characteristic of fluid transport in a capillary viscometer. The static visualization confirms the accuracy of numerical methods (FDM) by showing its convergence to the analytical parabolic curve, thereby establishing FDM's reliability for solving the underlying Navier-Stokes equations, even in its simplest form. The dynamic animation reinforces this insight by showing tracer particles moving fastest at the pipe's center ( $V_{\text {max }}$ ) and exhibiting zero velocity at the wall due to the no-slip condition, visually confirming that flow speed depends only on the radial position, which directly leads to the critical volumetric flow scaling $Q \propto \Delta P \cdot R^4$.
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