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 $Q \propto \Delta P \cdot R^4$.
the relationship between numerical modeling and analytical solutions Poiseuille's Law in fluid mecha
‣
<aside> <img src="/icons/report_pink.svg" alt="/icons/report_pink.svg" width="40px" />
Copyright Notice
All content and images on this page are the property of Sayako Dean, unless otherwise stated. They are protected by United States and international copyright laws. Any unauthorized use, reproduction, or distribution is strictly prohibited. For permission requests, please contact [email protected]
© 2025 Sayako Dean
</aside>