Poiseuille’s Law Calculator
Enter the pipe radius, length, fluid viscosity, and pressure difference to calculate the laminar volumetric flow rate using the Hagen-Poiseuille equation.
What This Calculator Does
Poiseuille’s Law (the Hagen-Poiseuille equation) describes the volumetric flow rate of a viscous, incompressible fluid in steady laminar flow through a straight cylindrical pipe. It’s widely used in fluid mechanics, engineering, and physiology (e.g. blood flow modeling) for general educational purposes.
The Formula
The equation is Q = (π × r⁴ × ΔP) ÷ (8 × μ × L), where Q is volumetric flow rate, r is the pipe’s inside radius, ΔP is the pressure difference between the two ends, μ is the fluid’s dynamic viscosity, and L is the pipe length. Because flow depends on radius to the fourth power, small changes in radius cause very large changes in flow rate.
- This law applies strictly to laminar (non-turbulent) flow of a Newtonian fluid in a rigid, straight cylindrical tube.
- The average velocity across the pipe is half the maximum (centerline) velocity in laminar flow, since the velocity profile is parabolic.
This is the standard Hagen-Poiseuille formula used for general physics, engineering, and educational reference; it is not intended as clinical or diagnostic guidance for biological systems.