# Reynolds Number Calculator

Created by Dominik Czernia, PhD
Reviewed by Małgorzata Koperska, MD and Adena Benn
Last updated: Dec 22, 2022

With our Reynolds number calculator, you can quickly compute the Reynolds number that helps predict whether the flow of a liquid will be laminar or turbulent. This factor measures the ratio of inertial forces to viscous forces occurring during the fluid movement. Keep reading if you want to find the answers to these questions:

• What is Reynolds number?
• How to calculate it?
• What are its units?
• What is the laminar flow definition?
• What is the turbulent flow definition?

The Reynolds number has broad applications in real life. It can describe liquid flow in a pipe, flow around airfoils, or an object moving in a fluid. In the following text, we have provided the Reynolds number equation, units discussion, and a comparison of laminar and turbulent flows. Read on to find out what are the laminar flow and turbulent flow Reynolds numbers. Using this calculator, you will also find some examples of calculations that can be done with the Reynolds number formula.

Are you interested in fluid mechanics? You should also check our buoyancy calculator or Bernoulli equation calculator. They can be very useful in analyzing fluid motion.

## What is the Reynolds number? – Reynolds number units

Reynolds number is one of the characteristic numbers used in fluid dynamics to describe a character of the flow. For example, if you want to compare a small-scale model (e.g., a model of an airplane) with a real situation, you should keep the Reynolds number the same. The Reynolds number is the ratio of inertial forces to viscous forces exerted on a fluid that is in relative motion to a surface. On one hand, inertial forces generate fluid friction which is a factor in developing turbulent flow. On the other hand, viscous forces counteract this effect and progressively inhibit turbulence.

The Reynolds number definition generally includes the velocity of a fluid, the characteristic length (or characteristic dimension), and the properties of the fluid, such as density and viscosity. If you want to learn more about fluid viscosity, you should check out Stokes' law calculator, where you can find, among others, viscosity definition. Although the Reynolds number can be defined in several different ways, it remains a non-dimensional factor.

## Laminar vs turbulent flow (laminar flow Reynolds number, turbulent flow Reynolds number)

Now, you probably want to know what Reynolds number means. Reynolds number is used to predict whether the fluid flow will be laminar or turbulent.

1. What is laminar flow? It occurs when viscous forces are dominant and is characterized by smooth, constant fluid motion. Reynolds number for laminar flow is typically Re < 2100.

2. Turbulent flow definition is the opposite. It is dominated by inertial forces and is characterized by chaotic eddies, vortices, and other flow instabilities. Turbulent flow definition is usually employed when Re > 3000.

But what happens when 2100 < Re < 3000? In this situation, the flow will begin to change from laminar to turbulent flow and then back to laminar flow. It is the so-called intermittent or transitional flow. Therefore, the choice of laminar vs. turbulent flow isn't always easy and possible.

## How to calculate Reynolds number? – Reynolds number equation

The Reynolds number formula depends on viscosity. We generally distinguish two types of viscosity:

1. Dynamic viscosity $\mu$ is a quantity that measures the force needed to overcome internal friction in a fluid. The units of dynamic viscosity are: $\rm Pa/s$, $\rm N/(m² \cdot s)$ or $\rm kg/(m \cdot s)$.

2. Kinematic viscosity $ν$ is the dynamic viscosity divided by density $ν = \mu/\rho$. Therefore, it's a quantity that represents the dynamic viscosity of a fluid per unit density and is expressed in $\rm m²/s$. to learn more about density, visit our density calculator.

The Reynolds number calculator simultaneously uses two different Reynolds number equations, as below:

$\begin{split} {\rm Re} &= \rho × u × L / \mu; {\rm\quad and}\\ {\rm Re} &= u × L / \nu, \end{split}$

where:

• $\rm Re$ – Reynolds number;
• $\rho$ – Fluid density;
• $u$ – Velocity of fluid (with respect to the object);
• $L$ – Characteristic linear dimension;
• $\mu$ – Dynamic viscosity of a fluid; and
• $\nu$ – Kinematic viscosity of a fluid ($\nu = \mu / \rho$).

In this calculator, you can choose a particular substance from some examples we have prepared or enter your own fluid parameters. Characteristic linear dimension $L$ (or characteristic length) in the above formulas is a matter of convention. For example, to describe:

• A sphere, we can use either its radius or diameter;
• For An aircraft, we can use either the length and width of aerofoils; and
• For A flow in a pipe, we can use either its internal radius or diameter.

Other shapes usually have a defined equivalent diameter.

For example, let's calculate the Reynolds number for the water flow in an $L = 2.5\ \rm cm$ diameter pipe. The velocity of tap water is about $u = 1.7\ \rm m/s$. In our Reynolds number calculator, you can choose (as a substance) water at $\rm 10\ °C,$, and you obtain the Reynolds number $\rm Re = 32 483$. Hence, the water flow is turbulent.

Dominik Czernia, PhD
Flow parameters
Fluid velocity
ft/s
Characteristic linear dimension
ft
Fluid parameters
Substance
Custom ▾
Fluid density
lb/cu ft
Dynamic viscosity
lb/(ft⋅s)
Kinematic viscosity
ft²/s
Reynolds number
Reynolds number
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