Poiseuille’s law

Definition

Poiseuille's law describes the volumetric flow rate of a fluid through a cylindrical pipe based on the fluid's viscosity, the pressure difference, and the dimensions of the pipe. It is particularly applicable to laminar flow conditions.

5 Must Know Facts For Your Next Test

1. Poiseuille's law is expressed mathematically as $$Q = \dfrac{\pi r^4 \Delta P}{8 \eta L}$$, where $Q$ is the volumetric flow rate, $r$ is the radius of the pipe, $\Delta P$ is the pressure difference, $\eta$ is the dynamic viscosity, and $L$ is the length of the pipe.
2. The flow rate increases dramatically with an increase in the radius of the pipe due to its fourth-power relationship ($r^4$).
3. It applies only to incompressible, Newtonian fluids under steady-state and laminar flow conditions.
4. An increase in fluid viscosity or pipe length results in a decrease in flow rate, assuming other variables remain constant.
5. Poiseuille’s law becomes invalid when turbulent flow occurs; Reynold’s number can help determine whether flow will be laminar or turbulent.

Review Questions

• What are the key variables that Poiseuille's law depends on?
• How does an increase in pipe radius affect volumetric flow rate according to Poiseuille's law?
• Why does Poiseuille’s law not apply to turbulent flows?

Related terms

Laminar Flow:

A type of fluid motion characterized by smooth parallel layers with minimal mixing between them.

Viscosity:

A measure of a fluid’s resistance to deformation or flow; higher viscosity means higher resistance.

Reynolds Number:

$$\text{Re} = \dfrac{\rho v L}{\eta}$$. A dimensionless number used to predict flow patterns in different fluid flow situations; helps determine if flow will be laminar or turbulent.