Pharmaceutical Engineering
Reynolds Number Calculator
Works out Re = ρvD/μ for pipe flow, names the flow regime and gives the Darcy friction factor for that regime.
Reynolds number (Re)
Enter density, velocity, diameter and viscosity (all above 0) to find the flow regime.
Flow parameters
Fluid properties and the pipe conditions.
Water at 20 °C is 998 kg/m³.
Mean velocity across the pipe cross-section.
Internal diameter. 50 mm pipe = 0.05 m.
Water at 20 °C is about 0.001 Pa·s.
Flow regime guide
| Regime | Reynolds number | Friction factor used |
|---|---|---|
| Laminar | Re < 2000 | f = 64 / Re |
| Transitional | 2000 – 4000 | f = 0.316 / Re^0.25 |
| Turbulent | Re ≥ 4000 | f = 0.316 / Re^0.25 |
Re = (ρ × v × D) / μ
ρ density (kg/m³), v mean velocity (m/s), D internal diameter (m), μ dynamic viscosity (Pa·s). The units cancel, so Re is dimensionless.
The friction factor is the Darcy f. In laminar flow it is exact: f = 64/Re. Above Re 2000 this tool uses the Blasius correlation f = 0.316·Re^−0.25, which was fitted for smooth pipes in turbulent flow (roughly Re 4000 to 10⁵) — so treat the value in the transitional band, and far above 10⁵, as indicative only.
Common questions
Divide by 1000. Water is about 1 cP = 0.001 Pa·s. If you have kinematic viscosity in centistokes, convert to m²/s (÷10⁶) and multiply by the density to get Pa·s.
Because the correlation changes there. f = 64/Re is exact for laminar flow; Blasius is an empirical turbulent fit. The two do not meet smoothly, which mirrors the physical instability of the transition region.
No. A mixing vessel uses the impeller Reynolds number, Re = ND²ρ/μ, with N the impeller speed and D the impeller diameter. Use the Mixing Time Estimator for that.
Divide the volumetric flow rate (m³/s) by the pipe's cross-sectional area, πD²/4. A 0.1 m pipe has an area of 0.00785 m².
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