HagenPoiseuilleyhtälöä

The Hagen-Poiseuille equation, also known as the Poiseuille law, describes the pressure drop of a viscous fluid flowing through a cylindrical pipe of constant cross-section. It is a fundamental equation in fluid dynamics, particularly relevant in fields such as hydrodynamics, rheology, and biomechanics.

The equation states that the flow rate (Q) of a Newtonian fluid through a pipe is directly proportional to the pressure difference (ΔP) across the pipe and the fourth power of the pipe's radius (r), and inversely proportional to the pipe's length (L) and the fluid's dynamic viscosity (η). Mathematically, it is expressed as: Q = (π * ΔP * r^4) / (8 * η * L).

This relationship highlights how sensitive the flow rate is to changes in pipe radius. A small increase in radius can lead to a significant increase in flow, while a decrease in radius drastically reduces it. The equation assumes laminar flow, meaning the fluid moves in smooth, parallel layers without significant mixing, and that the pipe is rigid and of uniform diameter.

The Hagen-Poiseuille equation finds applications in various scenarios, including calculating blood flow in arteries, the flow of oil through pipelines, and the dispensing of liquids in laboratory settings. It provides a quantitative understanding of how physical parameters influence fluid transport in confined spaces.