The Reynolds number is the single most important dimensionless group in fluid mechanics — it predicts whether flow is laminar or turbulent. Enter the fluid density, velocity, characteristic length (pipe diameter), and dynamic viscosity to get Re and the resulting flow regime.
The Reynolds number (Re) is a dimensionless ratio of inertial forces to viscous forces in a flowing fluid. Introduced by Osborne Reynolds in 1883, it is the master parameter that tells an engineer whether flow will be smooth and layered (laminar) or chaotic and mixed (turbulent) — a distinction that changes pressure drop, heat transfer, and mixing behavior by orders of magnitude.
Re = ρ·v·D / μ = v·D / ν.
Where ρ is the fluid density (kg/m³), v is the average velocity (m/s), D is the characteristic length — pipe inside diameter for internal flow (m), μ is the dynamic viscosity (Pa·s), and ν = μ/ρ is the kinematic viscosity (m²/s). Because the units cancel, Re is dimensionless: it represents the ratio of inertial forces (ρv²) to viscous shear forces (μv/D).
Example: water (ρ = 1000 kg/m³, μ = 0.001 Pa·s) at 2 m/s in a 50 mm pipe gives Re = (1000 × 2 × 0.05) / 0.001 = 100,000 — firmly turbulent.
For flow in a round pipe the accepted transition points are: Re < 2300 laminar, 2300 ≤ Re ≤ 4000 transitional, and Re > 4000 turbulent. In laminar flow the fluid moves in smooth parallel layers and the velocity profile is parabolic; in turbulent flow eddies mix the fluid and the profile is flatter and fuller. The transitional band is unstable and unpredictable, so good designs avoid sitting a pipe velocity right in that range.
Note that the critical Reynolds number depends on geometry: flow over a flat plate transitions around Re ≈ 5×10⁵, and flow around a sphere or in an open channel uses different thresholds. Always use the right characteristic length for the geometry.
The flow regime controls almost everything downstream. The friction factor — and therefore pressure drop and pumping power — follows f = 64/Re in laminar flow but a weak function of Re (via the Colebrook or Swamee-Jain correlation) in turbulent flow. Heat- and mass-transfer coefficients are far higher in turbulent flow because the eddies carry energy and species across the boundary layer. Mixing, residence-time distribution, and even whether a tracer disperses as a plug or spreads out all hinge on Re.
That is why the Reynolds number is the first thing a process engineer computes before sizing a pipe, a heat exchanger, or a reactor.
Use consistent SI units. Density and viscosity are temperature-dependent — water viscosity drops by half between 20 °C and 50 °C, which can move you from one regime toward another, so use properties at the actual operating temperature. For non-circular ducts, replace D with the hydraulic diameter Dₕ = 4·(cross-sectional area)/(wetted perimeter). For non-Newtonian fluids the simple Reynolds number does not apply and a generalized Reynolds number is needed.
For flow inside a round pipe, Re below 2300 is laminar (smooth, layered flow), Re above 4000 is turbulent (chaotic, well-mixed flow), and the 2300–4000 band is transitional and unstable. Other geometries use different critical values — for example, flow over a flat plate transitions near Re ≈ 500,000.
None — it is dimensionless. As long as you use a consistent unit system (SI: density in kg/m³, velocity in m/s, diameter in m, dynamic viscosity in Pa·s), all the units cancel and you get a pure number. The most common mistake is mixing centipoise with Pa·s; 1 cP = 0.001 Pa·s.
For full internal pipe flow it is the inside diameter D. For non-circular ducts use the hydraulic diameter Dₕ = 4A/P (four times the flow area divided by the wetted perimeter). For external flows it is a geometry-specific length, such as plate length for a flat plate or particle diameter for flow around a sphere.
Because the Darcy friction factor depends on it. In laminar flow f = 64/Re exactly, so pressure drop is directly proportional to velocity. In turbulent flow the friction factor comes from the Colebrook/Moody chart and pressure drop scales closer to velocity squared. Knowing Re is the first step in any pressure-drop or pump-sizing calculation.
Yes, strongly, because both density and especially viscosity change with temperature. Liquid viscosity falls sharply as temperature rises (raising Re), while gas viscosity rises slightly. Always evaluate the fluid properties at the actual operating temperature, since a temperature swing can shift a borderline design from laminar to turbulent.