Reynolds Number

Overview

The Reynolds number is a dimensionless quantity that expresses the ratio of inertial forces to viscous forces within a fluid. It is the primary parameter for predicting whether flow through a pipe, duct, or around a body is laminar, transitional, or turbulent.

For internal flow the characteristic length is the hydraulic diameter $D_h$, which equals the pipe inner diameter for circular cross-sections.

Key Formulas

Reynolds Number (SI)

$Re = \frac{\rho \, v \, D}{\mu}$

Equivalently, using kinematic viscosity $\nu = \mu / \rho$:

$Re = \frac{v \, D}{\nu}$

Reynolds Number (Imperial — pipe flow)

$Re = 7745.8 \;\frac{u \; d_h}{\nu}$

where $u$ is in ft/s, $d_h$ is in inches, and $\nu$ is in centistokes (cSt).

Variables

Flow Regimes

Calculator

Unit Converter

Schedule 40 Water Flow Chart

The source chart for water flow in Schedule 40 steel pipe is represented below as an interactive calculated chart. Values use water at approximately 20 °C with kinematic viscosity 1.004 cSt and typical Schedule 40 internal diameters.

Example Calculation

Given: A fluid with specific gravity 0.91 and dynamic viscosity 0.38 Pa·s flows at 2.6 m/s through a 25 mm diameter pipe.

1. Density: $\rho = 0.91 \times 1000 = 910 \;\text{kg/m}^3$
2. Reynolds number:

$Re = \frac{910 \times 2.6 \times 0.025}{0.38} \approx 156$

Since $Re \approx 156 \ll 2300$, the flow is clearly laminar.

Restored Original Source Tables

The following tables are restored from the original source page to preserve the complete reference data. The cached source tables outside the engineering chart are shared search/layout artifacts, not Reynolds-number data tables, and are intentionally not copied as reference data.

Related Mobile Apps

The source page references a Reynolds Number Calculator App for offline mobile use. The calculators above preserve the same core calculations directly in the page.

Original Source Images

The following original source images are preserved to avoid losing visual reference material. When an image contains chart or tabular data, its extracted values are represented in the page tables, calculators, or interactive charts; remaining images are retained as visual source references.

Engineering Notes

• Turbulent flow is the norm in most water, air, and process piping systems. Laminar conditions are typically limited to heavy oils, polymer melts, or very small-diameter / low-velocity flows.
• The transitional range (2300–4000) is sensitive to entrance conditions, pipe roughness, and vibration. Design conservatively by assuming turbulent behaviour above Re ≈ 2300.
• For non-circular ducts always use the hydraulic diameter $D_h = 4A / P$, where $A$ is the flow area and $P$ is the wetted perimeter.
• The Imperial shortcut ($Re = 7745.8 \; u \; d_h / \nu$) embeds the unit conversion from inches and centistokes. Verify that viscosity is given in cSt before applying it.
• The Reynolds number also governs external flows (around cylinders, spheres, airfoils) but the critical Re values for transition differ from the pipe-flow thresholds listed above.

References

• Original Source — Engineering ToolBox