Hagen-Poiseuille Fluid Resistance & Pipe Flow Calculator
Calculate laminar pipe flow rate (Q = πr⁴ΔP/8μL), fluid hydraulic resistance, 4th-power radius sensitivity, and vascular pressure drop.
Calculated Results
Frequently Asked Questions
What is the Hagen-Poiseuille law of laminar fluid flow?
Formulated independently by Gotthilf Hagen and Jean Léonard Marie Poiseuille, the law states that the volumetric flow rate of an incompressible laminar fluid through a cylindrical pipe is directly proportional to pressure drop and the fourth power of the radius: Q = (π × r^4 × ΔP) / (8 × μ × L).
Why does pipe radius have such an extreme impact on fluid flow?
Flow rate scales with radius to the 4th power (r^4). Increasing vessel radius by just 19% doubles the flow rate. Conversely, a 50% arterial stenosis (radius halved) cuts blood perfusion by a staggering 16-fold (93.75% reduction), forcing the heart to spike blood pressure.
What conditions are required for Poiseuille's equation to be valid?
The equation is valid ONLY when: (1) Flow is strictly laminar (Reynolds number Re < 2,300), (2) Fluid is Newtonian with constant viscosity, (3) Pipe walls are rigid and smooth with zero slip at boundaries, and (4) Pipe length is significantly larger than diameter.
What is hydrodynamic vascular peripheral resistance?
In physiology, total peripheral vascular resistance (SVR) is defined as R = ΔP / Q = (8 × μ × L) / (π × r^4). Arterial vasoconstriction and vasodilation are the body's primary mechanisms for regulating blood pressure.