This example demonstrates a simple application for fluid dynamics in a straight\
\ cylindrical pipe.
\n\n<h2 id=\"law-of-hagen-poiseuille\">Law\
\ of Hagen-Poiseuille\n
The <a href=\"https://en.wikipedia.org/wiki/Hagen\u2013\
Poiseuille_equation\">law of Hagen-Poiseuille is a physical law that gives the\
\ pressure drop <span class=\"math inline\">\(\Delta p\) for an incompressible\
\ Newtonian fluid in the laminar regime flowing through a long cylindrical pipe\
\ of constant cross section. This geometric setup is depicted in figure <code class=\"\
interpreted-text\" role=\"numref\">fig-pouseille-setup.
\n<div id=\"fig-pouseille-setup\"\
\n\n<img src=\"02_pressuredrop_instationary/HagenPouseilleSetup.png\" class=\"\
align-center\" width=\"556\" alt=\"\" />Geometry for the Hagen-Poiseuille\
\ law.\n\n\n
The law states that
\n
<span class=\"\
math display\">\[\Delta p = \frac{8\mu LQ}{\pi R^4}\]
\n
where
\n\
\n
\\(\\Delta p\\) is the pressure drop\
\ (in Pascal)
\n
\\(L\\) is the length\
\ of the pipe (in meter)
\n
\\(\\mu\\)\
\ is the dynamic viscosity of the fluid (in Pascal seconds)
\n
\\(Q\\) is the volumetric flow rate (in cubic meter per seconds)