Hagen–Poiseuille equation
Law for pressure drop in laminar pipe flow.
The Hagen–Poiseuille equation is a physical law in fluid dynamics that describes the pressure drop of an incompressible and Newtonian fluid in laminar flow through a long cylindrical pipe of constant cross section.
- field
- Fluid dynamics
- known_for
- Hagen–Poiseuille equation (pressure drop in laminar pipe flow)
- key_contributors
- Jean Léonard Marie Poiseuille, Gotthilf Heinrich Ludwig Hagen, George Stokes
Lore & Background
R. Wilberforce extended the law to turbulent flow based on Hagenbach's work.
Reader's Guide
The Hagen–Poiseuille equation is significant because it provides a fundamental relationship for pressure drop in laminar flow through pipes, with applications ranging from airflow in lung airways to flow through drinking straws and hypodermic needles. It is derived from the Navier–Stokes equations under assumptions of steady, laminar flow of an incompressible Newtonian fluid through a long cylindrical pipe. The equation fails for turbulent flow, low viscosity, wide or short pipes, and near the pipe entrance. It relates to the Darcy–Weisbach equation through the friction factor, where for laminar flow the Darcy friction factor Λ equals 64/Re. The law is important in hemorheology and hemodynamics, fields of physiology. Its legacy includes providing the basis for understanding viscous flow in pipes and influencing later work on turbulent flow.
Did You Know?
- The law can be applied to air flow in the airways of the lungs, flow through a drinking straw, or through a hypodermic needle.
- For laminar flow in a circular pipe, the Darcy friction factor Λ equals 64 divided by the Reynolds number.
More in Mechanics And Fluid Dynamics 1-24
Elsewhere in the Mechanics And Fluid Dynamics universe
Spotted an error? Know more?
This is a living reference — every entry is fact-audited, and reader corrections feed straight into our audit queue. Suggest an edit · See this site's audit record