Reynolds Number Scale
Laminar <2300
Transitional 2300–4000
Turbulent >4000
010002300400060008000+
Live Visualization
Streamline Behavior
Flow Velocity (v)
30 cm/s
Mean velocity in the vessel
Vessel Diameter (D)
2.0 mm
Inner diameter of catheter or vessel
Fluid Density (ρ)
1,060 kg/m³
Blood ≈ 1,060 · NS ≈ 1,005 · Contrast ≈ 1,200
Dynamic Viscosity (μ)
3.5 cP
Blood ≈ 3–4 · NS ≈ 1 · Contrast ≈ 5–8 cP
Clinical Scenarios
Why Turbulence Matters Clinically
Turbulent flow increases energy loss (more pressure needed for same flow), creates vessel wall vibration (audible bruit), increases hemolysis risk in narrow-lumen catheters, and promotes thrombus formation through platelet activation.
Contrast Agents are High-Risk
CT contrast at 4–5 mL/s through a small peripheral IV carries genuine turbulence risk. The combination of high velocity, high density (1200 kg/m³), and moderate viscosity pushes Re well above 4000 in the catheter hub.
Diameter Has Linear Effect
Unlike flow rate (where radius has fourth-power effect), Re scales linearly with diameter. Doubling the catheter diameter doubles Re for the same mean velocity — larger catheters actually tolerate less relative flow before going turbulent.
Blood is Protective
Blood's high viscosity (3–4 cP vs saline's 1 cP) means Re is 3–4× lower at the same flow velocity. This is why normal cardiovascular flows stay laminar despite relatively high velocities in the aorta.
Historical Origin · 1883
Osborne Reynolds
Reynolds injected dye threads into flowing water in glass tubes. Below the critical threshold, the thread stayed straight; above it, the thread dissolved into chaos. He proved that the transition from order to chaos follows a predictable, universal law — the same number applies to blood in an IV catheter and oil in a pipeline.
Mental Model
The Traffic Flow Model
Laminar
→
Highway at 65 mph
Transitional
→
Merge lane chaos
Turbulent
→
Traffic jam gridlock
Energy that should carry fluid forward instead spins it sideways — wasted as heat and wall shear. The jam is the injury mechanism.
Intracav Opportunity
Risk Heatmap Overlay
Overlay turbulence risk directly on the ultrasound image — before needle insertion. Using vessel diameter (measured by US) and planned flow rate (set by clinical context), compute Re in real time.
🟢 Green — Laminar, optimal access
🟡 Amber — Transitional, proceed with care
🔴 Red — Turbulence likely, reconsider gauge
🟡 Amber — Transitional, proceed with care
🔴 Red — Turbulence likely, reconsider gauge