Reynolds' Dye Streak

Plate 6 speaks for itself: “Same water. Faster. Then chaos.”

The Physics

Reynolds injected a thin dye streak into water flowing through a glass tube. At low speed the streak stayed straight (laminar); past a critical value of one dimensionless number it broke up into eddies (turbulent).

Re = ρ u D / μ

• Re: Reynolds number, dimensionless
• ρ: fluid density, kg m⁻³
• u: mean flow speed, m s⁻¹
• D: pipe diameter, m
• μ: dynamic viscosity, Pa s

Lower critical value ≈ 2000; engineering onset ≈ 2300. Manchester, 1883.

Honest caveat: Transition is not a sharp line: with very smooth inlets laminar flow has been kept far above 2000.

Sources

• O. Reynolds, Phil. Trans. R. Soc. 174, 935 (1883).

On the poster

Plate 006, “Reynolds' Dye Streak”: the pixel-art plate with its slogan “Same water. Faster. Then chaos.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.