When smooth flow breaks into turbulence
Push 5 mL/s of water through a 3 mm straw and the flow stays barely orderly. Halve the diameter, keep the same flow, and the layers break into mixing — because Reynolds number doubles.
dye injected at centre
Qualitative dye trace — not a CFD calculation
Fluiddensity ρ and viscosity μ
Volume flow rate Qmore flow → higher Re
1 mL/s10100300 mL/s
Inside diameter Dat fixed Q, narrower → higher Re
1.5 mm30 mm
Reynolds number
2,300
laminar limit
4,000
turbulent
Re 0.1Re 1,000,000
Try
Reynolds number is a dimensionless comparison of inertia with viscosity. For a round pipe, Re = ρvD/μ; substituting v = 4Q/(πD²) gives the control-friendly form shown above, Re = 4ρQ/(πμD). This page uses the same representative 20°C properties and baseline flows as the straw page: water (ρ = 1,000 kg/m³, μ = 0.001 Pa·s), milkshake (1,030; 0.3), honey (1,420; 5), plus ambient air (1.204; 1.81×10−5). Milkshake and honey are treated as Newtonian with one effective viscosity, a simplification because real food rheology depends on shear rate and temperature. In smooth round pipes, this site uses Re ≤ 2,300 as laminar, Re ≥ 4,000 as turbulent, and labels the intermittent region between them transitional; those are engineering boundaries, not a switch that every disturbed pipe obeys exactly. The dye-stream idea follows Osborne Reynolds’ 1883 experiment; the force-ratio interpretation is also summarized by NASA. For air, this page calculates local Re only: the compressible, high-speed pressure-flow behaviour it feeds into is solved on the straw page itself.
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