Definition of Poiseuille's Law
Poiseuille's Law, also known as the Hagen-Poiseuille equation, quantifies the volumetric flow rate of an incompressible, Newtonian fluid through a long, cylindrical pipe under laminar flow conditions. It states that the flow rate is directly proportional to the pressure difference across the pipe and the fourth power of the pipe's radius, and inversely proportional to the fluid's viscosity and the pipe's length.
Key Variables and Relationship
The law's equation is typically expressed as Q = (ΔP * π * r^4) / (8 * η * L), where Q is the volumetric flow rate, ΔP is the pressure difference, r is the pipe's internal radius, η (eta) is the dynamic viscosity of the fluid, and L is the pipe's length. This demonstrates a strong dependence on radius, meaning even a small change significantly impacts flow.
Practical Applications
Poiseuille's Law is crucial in various fields. In biomedical engineering, it helps model blood flow through arteries and veins. In chemical engineering, it's used to design piping systems for transporting liquids. It also applies to understanding fluid transport in geological formations and microfluidic devices where laminar flow dominates.
Underlying Principles and Limitations
The law assumes laminar flow (smooth, layered flow) and a Newtonian fluid (viscosity is constant regardless of shear rate). It also requires a fully developed flow profile, a constant radius, and steady, incompressible flow. When flow becomes turbulent or these conditions are not met, more complex fluid dynamics equations are needed.