Reynolds Number Calculator (Flow Rate)
Calculate the Reynolds number based on volumetric flow rate in a circular pipe.
Unit: Cubic Meters per Hour (m³/h)
Unit: Millimeters (mm)
Unit: kg/m³ (Water ≈ 1000)
Unit: Centipoise (cP) (Water ≈ 1.0)
Calculated Reynolds Number (Re)
0
Laminar
Understanding Reynolds Number and Flow Rate
The Reynolds Number (Re) is a dimensionless quantity in fluid mechanics that helps predict flow patterns in different fluid flow situations. When calculating Reynolds number from flow rate, engineers can determine whether the fluid moving through a pipe is exhibiting laminar, transitional, or turbulent flow. This is crucial for sizing pumps, designing piping systems, and calculating pressure drops.
The Formula
While the standard definition uses velocity, practical engineering often starts with the volumetric flow rate ($Q$). The formula to calculate Reynolds number for a full circular pipe using flow rate is:
Re = (4 × ρ × Q) / (π × μ × D)
Where:
- ρ (Rho): Fluid Density (kg/m³)
- Q: Volumetric Flow Rate (m³/s)
- μ (Mu): Dynamic Viscosity (Pa·s)
- D: Pipe Internal Diameter (m)
Note: Our calculator above automatically handles unit conversions (like m³/h to m³/s and mm to m) for your convenience.
Flow Regimes Explained
The magnitude of the Reynolds number defines the flow regime:
- Laminar Flow (Re < 2000): The fluid flows in parallel layers, with no disruption between the layers. It is smooth and orderly.
- Transitional Flow (2000 ≤ Re ≤ 4000): The flow is unstable and may fluctuate between laminar and turbulent states.
- Turbulent Flow (Re > 4000): The flow is characterized by chaotic changes in pressure and flow velocity. This is common in industrial process piping.
Practical Example
Consider water flowing through a 50mm pipe at 10 m³/h:
- Density: 1000 kg/m³
- Viscosity: 1 cP (0.001 Pa·s)
- Diameter: 0.05 m
- Flow Rate: 10 m³/h ≈ 0.00278 m³/s
Using the calculator, this yields a Reynolds number of approximately 70,735, indicating highly Turbulent Flow.