Poiseuille’s Law describes how an incompressible, Newtonian fluid flows in a laminar (smooth and orderly) manner through a long, straight, cylindrical pipe. It establishes a relationship between the flow rate and the physical properties of the fluid and pipe.
According to Poiseuille’s Law, the flow rate increases with the fourth power of the pipe’s radius, the pressure difference between the ends, and is inversely proportional to the fluid’s viscosity and the pipe’s length. This means even a small increase in the pipe’s radius can dramatically increase the flow.
Key Conditions:
- The flow must be laminar (not turbulent).
- The fluid must be incompressible and have constant viscosity.
- The pipe must be rigid and circular in cross-section.
Examples:
- Blood flow in capillaries and arteries is often modeled using Poiseuille’s Law, helping understand circulatory conditions.
- Industrial fluid transport through pipelines is designed considering this law to ensure efficiency.
- Medical devices like IV drips use principles of Poiseuille’s flow to regulate fluid delivery.
Poiseuille’s Law is crucial in fluid mechanics, biomedical engineering, and any application involving controlled laminar fluid movement through narrow tubes.