Reynolds Number Calculator Formula

Understand the math behind the reynolds number calculator. Each variable explained with a worked example.

Formulas Used

Reynolds Number

re = velocity * diameter / kinematic_visc

Laminar Threshold (Re < 2300)

regime = 2300

Variables

VariableDescriptionDefault
velocityFlow Velocity (V)(m/s)2
diameterPipe Diameter (D)(m)0.1
kinematic_viscKinematic Viscosity (nu)(m^2/s)0.000001

How It Works

Reynolds Number

The Reynolds number is a dimensionless quantity that predicts whether fluid flow will be laminar or turbulent.

Formula

Re = V D / nu

where V is the mean velocity, D is the pipe inner diameter, and nu is the kinematic viscosity. For pipe flow: Re < 2300 is laminar, 2300 < Re < 4000 is transitional, and Re > 4000 is turbulent.

Worked Example

Water at 20 deg C (nu = 1e-6 m^2/s) flowing at 2 m/s through a 100 mm pipe.

velocity = 2diameter = 0.1kinematic_visc = 0.000001
  1. 01Re = 2 x 0.1 / 1e-6 = 0.2 / 1e-6 = 200,000
  2. 02Since 200,000 >> 4000, flow is fully turbulent.

Frequently Asked Questions

What is kinematic viscosity for common fluids?

Water at 20 deg C: 1.0e-6 m^2/s. Air at 20 deg C: 1.5e-5 m^2/s. SAE 30 oil at 38 deg C: about 1.0e-4 m^2/s. Glycerin: about 1.2e-3 m^2/s.

Why does the Reynolds number matter?

It determines the flow regime, which affects friction losses, heat transfer rates, and mixing. Turbulent flow has higher friction but better heat transfer and mixing than laminar flow.

Can Reynolds number be used for non-circular ducts?

Yes, replace diameter D with the hydraulic diameter Dh = 4A/P, where A is the cross-sectional area and P is the wetted perimeter.

Learn More

Guide

Understanding Fluid Mechanics Basics: A Practical Introduction

Master the fundamentals of fluid mechanics including pressure, viscosity, Bernoulli's equation, Reynolds number, and flow types. Essential knowledge for engineers working with pipes, pumps, and hydraulic systems.

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