Reynolds Number Calculator - Free Fluid Mechanics Calculator
Free Reynolds number calculator for fluid mechanics. Calculate Reynolds number to determine flow regime (laminar, transitional, or turbulent) using density, velocity, diameter, and viscosity. Our calculator uses the Reynolds number formula Re = (ρ × v × D) / μ to predict flow patterns in pipes, channels, and other fluid systems.
Last updated: October 19, 2025
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Reynolds Number Result
Flow Regime:
Turbulent Flow
Flow is turbulent (Re > 4000). Fluid moves in irregular patterns with mixing and eddies.
Density
1000.00 kg/m³
Velocity
1.00 m/s
Diameter
0.10 m
Viscosity
0.00 Pa·s
Formula:
Re = (ρ × v × D) / μ = (1000.00 kg/m³ × 1.00 m/s × 0.10 m) / 0.00 Pa·s = 100000.00
The Reynolds number for fluid with density 1000 kg/m³, velocity 1 m/s, diameter 0.1 m, and viscosity 0.001 Pa·s is 100000.00. This indicates turbulent flow.
Step-by-Step Solution
- Step 1: Convert all units to SI base units (kg/m³, m/s, m, Pa·s)
- Density: 1000 kg/m³ (already in SI units)
- Velocity: 1 m/s (already in SI units)
- Diameter: 0.1 m (already in SI units)
- Viscosity: 0.001 Pa·s (already in SI units)
- Step 2: Apply the Reynolds number formula
- Re = (ρ × v × D) / μ
- Re = (1000.00 kg/m³ × 1.00 m/s × 0.10 m) / 0.00 Pa·s
- Re = 100.00 / 0.00
- Re = 100000.00
- Step 3: Determine flow regime
- Re = 100000.00 > 4000 → Turbulent flow
Reynolds Number Calculator Types & Applications
Characteristic length
D = pipe diameter
Most common application for pipes and conduits
Characteristic length
Dₕ = hydraulic diameter
Uses hydraulic diameter for non-circular geometries
Flow regime
Re < 2300
Smooth, orderly flow in parallel layers
Flow regime
Re > 4000
Chaotic, irregular flow with mixing
Flow regime
2300 < Re < 4000
Unstable flow that may switch regimes
Applications
Engineering, Physics
Essential for fluid system design and analysis
Quick Example Result
For water at 20°C (ρ = 1000 kg/m³, μ = 0.001 Pa·s) flowing in a 0.1 m diameter pipe at 1 m/s:
Reynolds Number
Re = 100,000
Flow Regime
Turbulent
How Our Reynolds Number Calculator Works
Our Reynolds number calculator uses the fundamental fluid mechanics formula Re = (ρ × v × D) / μ to determine flow regime. The calculation applies dimensional analysis principles to predict whether flow is laminar, transitional, or turbulent based on the ratio of inertial to viscous forces.
The Reynolds Number Formula
Re = (ρ × v × D) / μ (Reynolds number)Re < 2300 (laminar flow)2300 ≤ Re ≤ 4000 (transitional flow)Re > 4000 (turbulent flow)Where ρ (rho) is density, v is velocity, D is characteristic length (pipe diameter), and μ (mu) is dynamic viscosity. The Reynolds number is dimensionless, meaning all units cancel out.
Shows laminar, transitional, and turbulent flow patterns
Fluid Mechanics Foundation
The Reynolds number was introduced by Osborne Reynolds in 1883 to characterize flow patterns. It represents the ratio of inertial forces (which tend to keep fluid moving) to viscous forces (which resist motion). Low Re indicates viscosity-dominated flow (laminar), while high Re indicates inertia-dominated flow (turbulent).
- Reynolds number is dimensionless - all units cancel out
- Flow regime depends on geometry, fluid properties, and velocity
- Critical values (2300, 4000) apply specifically to pipe flow
- Temperature affects viscosity, thus changing Re significantly
- Laminar flow has lower friction but poor mixing
- Turbulent flow has higher friction but excellent heat/mass transfer
Sources & References
- Fluid Mechanics: Fundamentals and Applications - Yunus A. Çengel, John M. Cimbala (4th Edition)Comprehensive textbook covering Reynolds number and flow regime analysis
- Introduction to Fluid Mechanics - Robert W. Fox, Alan T. McDonald, Philip J. PritchardStandard reference for dimensionless numbers and flow characterization
- Khan Academy - Fluid Dynamics and Reynolds NumberEducational resources for understanding Reynolds number concepts
Need help with other physics calculations? Check out our free fall calculator and acceleration calculator.
Get Custom Calculator for Your PlatformReynolds Number Calculator Examples
Given Values:
- Density (ρ): 1000 kg/m³
- Velocity (v): 2 m/s
- Diameter (D): 0.05 m
- Viscosity (μ): 0.001 Pa·s
Calculation Steps:
- Convert all units to SI base units (already in SI)
- Apply formula: Re = (ρ × v × D) / μ
- Calculate: Re = (1000 × 2 × 0.05) / 0.001
- Compute: Re = 100 / 0.001 = 100,000
- Determine regime: Re > 4000 → Turbulent flow
Result: Re = 100,000 (Turbulent Flow)
The flow is turbulent, indicating significant mixing and eddies. Energy losses will be proportional to velocity squared.
Laminar Flow Example
Water: ρ = 1000 kg/m³, v = 0.1 m/s, D = 0.02 m, μ = 0.001 Pa·s
Re = 2,000 (Laminar)
Smooth, parallel streamlines
Transitional Flow Example
Water: ρ = 1000 kg/m³, v = 0.15 m/s, D = 0.02 m, μ = 0.001 Pa·s
Re = 3,000 (Transitional)
Unstable, may switch regimes
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