College Physics II – Mechanics, Sound, Oscillations, and Waves
Definition
Poiseuille's Law describes the volumetric flow rate of a liquid through a pipe as a function of the fluid's viscosity, the pressure difference across the pipe, and the pipe's dimensions. It is particularly applicable to laminar flow in long, cylindrical pipes.
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Poiseuille's Law is given by $Q = \frac{\Delta P \pi r^4}{8 \eta L}$, where $Q$ is the volumetric flow rate, $\Delta P$ is the pressure difference, $r$ is the radius of the pipe, $\eta$ is the dynamic viscosity, and $L$ is the length of the pipe.
The law assumes laminar flow, meaning it does not apply to turbulent flow conditions.
Flow rate increases with the fourth power of the radius; doubling the radius results in a 16-fold increase in flow rate.
Flow rate decreases linearly with increasing viscosity and pipe length.
Poiseuille’s Law can be used to determine blood flow in capillaries and other small vessels in biological systems.
Review Questions
What are the variables that affect volumetric flow rate according to Poiseuille's Law?
Why does Poiseuille's Law only apply to laminar flow?
How does changing the radius of a tube impact flow rate according to Poiseuille’s Law?
Related terms
Viscosity: A measure of a fluid's resistance to deformation or flow. Higher viscosity means greater resistance.
Laminar Flow: A type of fluid motion characterized by smooth parallel layers that do not mix. Opposite of turbulent flow.
Reynolds Number: $Re = \frac{\rho v L}{\eta}$; a dimensionless number used to predict whether a fluid will exhibit laminar or turbulent flow based on its properties.