🌊 Hydrodynamics & Dimensionless Numbers
Reynolds Number & Flow Regime Calculator
Compute the dimensionless Reynolds number ($Re = \frac{\rho v D}{\mu}$), classify flow regimes (Laminar vs Turbulent), and estimate Darcy friction factors for fluid conduits.
💧 Water (1,000 kg/m³, 1.0 mPa·s)
💨 Air (1.20 kg/m³, 0.018 mPa·s)
🩸 Blood (1,060 kg/m³, 3.5 mPa·s)
🛢️ Motor Oil (880 kg/m³, 290 mPa·s)
🍯 Glycerin (1,260 kg/m³, 1.41 Pa·s)
Flow Parameters
m/s
kg/m³
Pa·s (kg/m·s)
Reynolds Number (Re)
74,715
Kinematic Viscosity ($\nu$)
1.004 × 10⁻⁶ m²/s
Laminar Darcy Friction ($f$)
0.019 (Turbulent)
Inertial / Viscous Ratio
74,715 : 1
💡 Dimensionless Calculation:
$$Re = \frac{998.2 \times 1.5 \times 0.050}{0.001002} = 74,715 \quad (\text{Inertial forces dominate})$$
The Reynolds Number Explained
Osborne Reynolds introduced the ratio of inertial forces to viscous forces in 1883:
$$Re = \frac{\rho v D}{\mu} = \frac{v D}{\nu}$$
- Laminar Flow ($Re < 2300$): Smooth, parallel streamlines with minimal mixing. Darcy friction factor $f = 64 / Re$.
- Transitional Flow ($2300 \le Re \le 4000$): Unstable mix of laminar and localized eddy vortices.
- Turbulent Flow ($Re > 4000$): Chaotic, turbulent mixing and boundary-layer shear stress.