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03 // Bidirectional STEM Calculators // ENGINEERINGRe = (ρ × v × D) / μ

Reynolds Number & Fluid Flow Regime Calculator

The Reynolds number Re is a dimensionless similarity parameter in fluid mechanics comparing inertial momentum forces against viscous shear forces: Re = (ρ × v × D) / μ.

Re = (ρ × v × D) / μ
Pick which value you want to calculate (or type into any field):Solving for: Re — Reynolds Number
Calculated

Dimensionless ratio of inertial to viscous forces

110,000,000.00
unit

Mass per unit volume (Water @ 20°C ≈ 998.2 kg/m³)

0.115,000.00
unit

Bulk fluid velocity inside pipe or duct in m/s

0.01100

Internal pipe diameter or characteristic length in meters

0.00110

Absolute viscosity in Pa·s (Water @ 20°C = 0.001 Pa·s)

1.0000e-6100
unit
Calculated Result · Reynolds Number (Re)
100,000.00

Step-by-Step Calculation

01Canonical Law: Re = (ρ × v × D) / μ
02Given Inputs (Base Units): ρ (kg/m³) = 1,000, v = 2 m/s, D = 0.05 m, μ (Pa·s) = 0.001
03Solve for Re (Reynolds Number): Re = 100,000

The Reynolds number Re is a dimensionless similarity parameter in fluid mechanics comparing inertial momentum forces against viscous shear forces: Re = (ρ × v × D) / μ.

Real-World Reference Values

Laminar Pipe Flow RegimeRe < 2,300

Smooth parabolic Poiseuille velocity profile

Transitional Pipe Flow2,300 ≤ Re ≤ 4,000

Intermittent turbulent bursts

Fully Turbulent Pipe FlowRe > 4,000

Moody chart friction factor depends on roughness ε/D

20-Row Comparison Table

Reynolds Number (Re) · Fluid Density (ρ (kg/m³))

Reynolds Number & Fluid Flow Regime Calculator — Fluid Density → Reynolds Number
#Fluid Density (ρ (kg/m³))Reynolds Number (Re)Δ %
010.1 10 -99.99%
02161.2782 16,127.82 -83.87%
03322.4564 32,245.64 -67.75%
04483.6347 48,363.47 -51.64%
05644.8129 64,481.29 -35.52%
06805.9911 80,599.11 -19.40%
071,000.00 Current100,000.00 0.00%
081,128.35 112,834.76 +12.83%
091,289.53 128,952.58 +28.95%
101,450.70 145,070.40 +45.07%
111,611.88 161,188.22 +61.19%
121,773.06 177,306.05 +77.31%
131,934.24 193,423.87 +93.42%
142,095.42 209,541.69 +109.54%
152,256.60 225,659.51 +125.66%
162,417.77 241,777.34 +141.78%
172,578.95 257,895.16 +157.90%
182,740.13 274,012.98 +174.01%
192,901.31 290,130.80 +190.13%
203,062.49 306,248.63 +206.25%
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Frequently Asked Questions

How do I find the maximum pipe velocity to keep flow laminar?+

Click SOLVE FOR on v (Mean Flow Velocity) and set Re = 2300 alongside your fluid density ρ, diameter D, and viscosity μ.

How do I convert centipoise (cP) to Pa·s?+

1 centipoise (cP) = 1 mPa·s = 0.001 Pa·s. Water at 20 °C has a viscosity of 1.00 cP = 0.001 Pa·s.

What is kinematic viscosity ν?+

Kinematic viscosity ν (m²/s) equals dynamic viscosity divided by density (ν = μ / ρ), simplifying Reynolds number to Re = vD / ν.