Anaes · Measurement & monitoring physics

Fluid flow: laminar, turbulent and the Reynolds number

Also known as Laminar flow · Turbulent flow · Reynolds number · Hagen-Poiseuille equation · Poiseuille's law · Flow physics

Whether a fluid flows smoothly (laminar) or chaotically (turbulent) determines how much pressure it takes to push it through a tube — and the answer governs the design of IV cannulae, breathing systems, endotracheal tubes and vascular grafts. The framework rests on six exam-critical ideas. First, in LAMINAR flow the fluid moves in smooth parallel layers (streamlines) with no mixing between them; the velocity profile is parabolic (fastest in the centre, zero at the wall), and the flow obeys the HAGEN-POISEUILLE EQUATION: flow equals the pressure gradient times pi times the radius to the fourth power divided by eight times the viscosity times the length (Q equals delta-P times pi times r to the four divided by 8 times eta times L). Second, the radius-to-the-fourth-power term means that HALVING the radius reduces flow by a factor of SIXTEEN — which is why a small IV cannula delivers far less fluid than a large one, why a small endotracheal tube raises airway resistance so steeply, and why vasoconstriction (narrowing the arteriole) is such an effective way of regulating blood flow. Third, in TURBULENT flow the fluid moves in chaotic eddies and vortices with mixing across the tube; the velocity profile is flat across the cross-section, the resistance is much higher than laminar (pressure proportional to flow SQUARED rather than to flow), and a stethoscope over a turbulent segment (a bruit) hears it. Fourth, the transition from laminar to turbulent is predicted by the REYNOLDS NUMBER (Re), a dimensionless ratio of inertial to viscous forces: Re equals density times velocity times diameter divided by viscosity (rho times v times d divided by eta); values below about 2000 are laminar, above about 4000 turbulent, and between 2000 and 4000 transitional. Fifth, turbulence is favoured by HIGH velocity, LARGE diameter, LOW viscosity, HIGH density and surface roughness or bends in the tube — which is why anaemia (low viscosity) makes a murmur, a high-flow IV line turns turbulent, and kinking a circuit or narrowing a vessel creates turbulent jet flow. Sixth, in clinical practice: blood flow in the normal vascular tree is mostly LAMINAR (Poiseuille applies), becoming TURBULENT in the aortic root, across stenotic or regurgitant valves, in aneurysms and at vascular bifurcations; gas flow in the large airways (trachea and bronchi during peak flow) is TURBULENT (favoring mixing and humidification), while in the small airways it is laminar. Built on the hemodynamics-induced aneurysm-progression study (Li 2026), the posterior-aneurysm hemodynamics study (Du 2026), the CTA-CFD flow-diverter study (Zhang 2026), the collateral-circulation hemodynamics study (Hu 2026), the coronary fractional-flow-reserve study (Yang 2026), the cervical-hemodynamics study (Zheng 2026), the resistance-respiratory-training study (Ivisic 2026), and the difficult-airway-management study (Ghaffar 2026).