Reynolds Number and Flow Regime simulation
What's on screen
A recreation of Osborne Reynolds' 1883 dye experiment. A horizontal glass tube filled with fluid. A purple dye injector nozzle on the left continuously releases dye into the center of the flow. At low Re the dye stays as a clean straight streak.
At high Re it breaks apart into chaotic swirls. Flow particles (blue dots) and dye particles animate in real time. A velocity profile outline on the right edge shows parabolic (laminar) or flat (turbulent) shape.
Below the tube, a color-coded Re scale bar with a sliding marker shows where you are on the laminar/transition/turbulent spectrum.
How the dye visualization works:
Each dye particle tracks its position (x, y) and age. The behavior changes with regime:
Laminar (Re < 2300): Dye y-position stays almost exactly at the centerline. Tiny 0.5px sinusoidal wobble. The streak is razor-thin and perfectly parallel. No mixing.
Transition (2300 < Re < 4000): Wobble amplitude increases. Dye wanders up to 4px from center. Occasional breakaway. The streak looks "nervous" but mostly holds together.
Turbulent (Re > 4000): Dye y-position follows aggressive random walk plus large-amplitude sinusoidal wandering. The oy (original y) itself drifts randomly over time. Dye particles spread across the full pipe diameter within a short distance. Complete mixing.
The turbulence intensity scales continuously: turbulence = 0 at Re < 2300, ramps linearly through transition, and keeps increasing logarithmically into the turbulent regime.
Flow particles use proper velocity profiles:
Laminar: v(r) = Vmax × (1 - r²/R²). Center particles move fastest, wall particles barely move. Classic parabolic.
Turbulent: v(r) = Vmax × (1 - r/R)^(1/7). Much flatter profile. Wall particles move relatively faster. This is visible as the profile overlay on the right edge of the tube.
2 sliders:
Velocity V (0.01 to 2.0 m/s): The primary control. Slowly drag right and watch the dye streak go from straight line to wobble to full chaos. The Re pill, scale marker, and regime label all update live.
Diameter D (5 to 200 mm): Larger pipe = higher Re at the same velocity. A 200mm pipe with water at 0.05 m/s is already Re = 10,000 (turbulent), while a 5mm pipe at the same speed is Re = 250 (laminar).
Info bar changes per regime, per fluid:
Each fluid has three unique descriptions (laminar, transition, turbulent) explaining what that regime means for that specific fluid. For example:
Water turbulent: "The dye streak breaks apart instantly into chaotic swirls. Most real-world pipe flows are turbulent."
Honey laminar: "Re stays in single digits even at moderate speeds. Turbulent honey does not exist in any practical scenario."
Oil transition: "You need V > 30 m/s in a 25mm pipe to hit Re = 2300. In practice, oil flow is almost always laminar."
Key slider experiments::
Start with water, V = 0.05 m/s, D = 25 mm. Re = 1250. Dye is a perfect straight line. Now slowly drag V up. At V ≈ 0.09, Re crosses 2300 and the dye starts wobbling. By V = 0.20, Re = 5000 and the dye is fully mixed. That transition is the entire lesson.
Switch to honey at the same V = 0.20 m/s. Re drops to 0.7. The dye is frozen solid. Viscosity dominates everything.
Switch to air at V = 0.20. Re = 333. Still laminar in air. But drag V to 1.0 and Re = 1667. Drag to 2.0 and Re = 3333, transition zone. Air reaches turbulence fast.
Set water, V = 0.05, then drag D from 25 to 200 mm. Re jumps from 1250 to 10,000 without changing velocity. Pipe size matters as much as speed.
The formula bar at the bottom shows the full calculation: Re = VD/ν = 0.50 × 0.025 / 1.0e-6 = 12500. Every variable plugged in, visible.