Poiseuille’s law for resistance

Definition

Poiseuille's law for resistance quantifies the resistance to flow in a cylindrical pipe due to viscosity. It is primarily used to describe laminar flow of incompressible fluids.

5 Must Know Facts For Your Next Test

1. The formula for Poiseuille's law for resistance is $R = \frac{8 \eta L}{\pi r^4}$, where $\eta$ is the fluid viscosity, $L$ is the length of the pipe, and $r$ is the radius of the pipe.
2. Resistance is inversely proportional to the fourth power of the radius ($r^4$), meaning small changes in radius have a large effect on resistance.
3. Poiseuille’s law applies strictly to laminar flow; it does not apply to turbulent flow.
4. The law assumes that the fluid is incompressible and Newtonian, meaning its viscosity remains constant regardless of stress.
5. In medical contexts, Poiseuille’s law can explain blood flow through arteries and veins.

Review Questions

• What factors influence the resistance in Poiseuille’s law?
• How does changing the radius of a pipe affect its resistance according to Poiseuille’s law?
• Why does Poiseuille's law not apply to turbulent flow?

Related terms

Laminar Flow: A type of fluid flow where layers do not mix; characterized by smooth paths or streamlines.

Viscosity: A measure of a fluid's resistance to deformation or flow; often perceived as 'thickness' or 'stickiness.'

Reynolds Number: A dimensionless number used to predict flow patterns in different fluid flow situations; low values indicate laminar flow, high values indicate turbulent flow.