The Poiseuille flow demonstrations is the profound influence of pipe geometry on fluid dynamics: The volumetric flow rate ( $Q$ ) is critically dependent on the pipe's internal radius ( $R$ ) raised to the fourth power ( $R^4$ ). This means that while factors like the pressure gradient ( $\Delta P / L$ ) and fluid viscosity ( $\mu$ ) exhibit a linear relationship with flow, even minor changes in the radius-such as those caused by plaque buildup in arteries or subtle variations in manufactured pipe size-result in disproportionately large impacts on the resulting flow, demanding significantly greater pumping power to compensate for reduced capacity.
Hagen-Poiseuille flow-or called Poiseuille flow through a circular pipe-L.mp4
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