The Reynolds number (Re) is the fundamental dimensionless group that governs whether pipe flow is laminar, transitional, or turbulent. ChemCalc computes Re automatically inside the pipe pressure drop module (Darcy-Weisbach + Swamee-Jain turbulent friction factor) and displays the flow regime alongside the pressure drop result.
Formula
| Symbol | Quantity | SI Unit |
|---|---|---|
| ρ (rho) | Fluid density | kg/m³ |
| v | Mean flow velocity | m/s |
| D | Pipe internal diameter | m |
| μ (mu) | Dynamic viscosity | Pa·s |
| Re = ρvD/μ | Reynolds number | dimensionless |
Flow Regime Classification (Pipe Flow)
| Regime | Re range | Characteristic |
|---|---|---|
| Laminar | Re < 2300 | Streamlines parallel; f = 64/Re (Hagen-Poiseuille) |
| Transitional | 2300 ≤ Re < 4000 | Unstable; avoid in design |
| Turbulent | Re ≥ 4000 | Swamee-Jain explicit approximation to Colebrook-White |
Inputs (inside ChemCalc Pipe Pressure Drop)
| Parameter | Notes |
|---|---|
| Pipe length L (m) | Straight pipe only; add equivalent lengths for fittings |
| Internal diameter D (mm) | Nominal bore schedule selected from ASME B36.10 table |
| Roughness ε (mm) | Steel ≈ 0.046 mm; smooth PVC ≈ 0.0015 mm |
| Flow velocity v (m/s) | Or enter volumetric flow; velocity computed from bore |
| Density ρ (kg/m³) | Liquid or gas at operating conditions |
| Dynamic viscosity μ (cP) | 1 cP = 1 mPa·s |
Outputs
- Reynolds number Re with flow-regime label
- Darcy friction factor f using laminar, blended transition, or Swamee-Jain turbulent branch
- Pressure drop ΔP (Pa, kPa, bar) via Darcy-Weisbach: ΔP = f·(L/D)·(ρv²/2)
- Velocity head ρv²/2
Related Correlations Using Re
| Application | Correlation |
|---|---|
| Pipe friction factor (turbulent) | Swamee-Jain explicit approximation of Colebrook-White |
| Orifice plate discharge Cd | Reader-Harris/Gallagher (ISO 5167-2), function of Re and β |
| Forced convection Nusselt | Dittus-Boelter: Nu = 0.023 Re⁰·⁸ Pr⁰·⁴ (turbulent, Re > 10 000) |
| Hydraulic diameter (non-circular) | D_h = 4 · A / P_wetted; use in Re for channels |