Poiseuille’s law for resistance

Definition

Poiseuille's law for resistance quantifies the resistance to flow in a cylindrical pipe due to viscosity. It states that the resistance is directly proportional to the length of the pipe and the viscosity of the fluid, and inversely proportional to the fourth power of the radius of the pipe.

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 $R$ is resistance, $\eta$ is dynamic viscosity, $L$ is length, and $r$ is radius.
2. A small change in the radius of a pipe results in a large change in resistance due to the fourth power dependence on radius.
3. This law applies strictly to laminar flow, where fluid flows in parallel layers without disruption between them.
4. In biological systems, Poiseuille's law helps understand blood flow through arteries and veins.
5. The unit for measuring fluid resistance using Poiseuille's law is typically pascal-seconds per cubic meter ($Pa \cdot s/m^3$).

Review Questions

Related terms

Viscosity:

A measure of a fluid's resistance to deformation or flow.

Laminar Flow:

A type of fluid flow where layers do not mix and move smoothly, often described as streamlined.

Reynolds Number:

A dimensionless number used to predict flow patterns in different fluid flow situations; it indicates whether flow will be laminar or turbulent.