Last updated: Jul 25, 2024

Reynolds Number Calculator

Q: What is the Reynolds number?

The Reynolds number is a fundamental parameter of fluid mechanics . It's an adimensional parameter that quantifies the behavior of a fluid, characterizing if a flow is laminar or turbulent . This indication comes from comparing a fluid's inertial and viscous forces . For dominant viscous forces, the flow would be "calm"; we say laminar . If inertial forces dominate, vortices and other currents cause chaotic behaviors to arise, giving the fluid a turbulent connotation.

Q: At what Reynolds number does a flow become turbulent?

For a cylindrical pipe, the transition between laminar and turbulent flow happens between Re D 2300 and Re D = 2900 . Below the first threshold, the fluid is likely laminar in behavior. Above 2900 , the fluid completes its transition to turbulent fluid. Between these two values, we can find a transition region , where the behaviors are mixed in complex ways.

Q: How do you calculate the Reynolds number?

To compute the Reynolds number Re D , we use a simple formula: Re D = ρ × u × L/µ where: ρ — Fluid density ; u — Flow velocity ; L — A geometric parameter (it can be the diameter of the pipe crossed by the flow); and µ — Dynamic viscosity of the fluid .

Q: What is the Reynolds number for water flowing in a 25 cm pipe at 1 m/s?

The Reynolds number for a water flow at u = 1 m/s in an L = 0.25 m pipe is: 191,074 . To find this result: Find the density of water at 10 °C: ρ = 999.7 kg/m³ Find the dynamic viscosity : µ = 0.001308 kg/(m · s) Compute the product of the density of water, the velocity of the flow, and L : ρ × u × L = 249.925 (m · s)/kg Divide the result by the dynamic viscosity to find the Reynolds number: Re D = 249.925/0.001308 = 191,074 The flow is likely turbulent.

Created by Dominik Czernia, PhD

Dominik Czernia

PhD, Institute of Nuclear Physics PAN

LinkedInWebsiteResearch Gate

Physicist at the Institute of Nuclear Physics in Kraków interested in magnetism and always ready to explain everything to everyone in simple terms. He is currently working on adding more scientific papers to his collection, accompanied by his son and another baby on its way. A perfectionist with an acute eye for detail, he has a unit converter in his brain and uses it to compare prices at the supermarket. Loves peace and quiet, especially during hiking. See full profile

Check our editorial policy

Reviewed by Małgorzata Koperska, MD and Adena Benn

Adena Benn

LinkedInWebsite

Adena Benn is an Information Technology teacher with a degree in Computer Science. She has been teaching high schoolers since 1996 and loves everything computers. She loves problem-solving, so creating calculators to solve real-world problems is her idea of fun. She writes children's stories, is a seamstress, and is an avid reader. In her spare time, she travels and enjoys nature. See full profile

Check our editorial policy

New

Table of contents

What is the Reynolds number? — Reynolds number units Laminar vs turbulent flow (laminar flow Reynolds number, turbulent flow Reynolds number)How to calculate Reynolds number? — Reynolds number equation FAQs

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.

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.
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:

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 $\rm kg/(m \cdot s)$ .
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.

FAQs

What is the Reynolds number?

The Reynolds number is a fundamental parameter of fluid mechanics. It's an adimensional parameter that quantifies the behavior of a fluid, characterizing if a flow is laminar or turbulent. This indication comes from comparing a fluid's inertial and viscous forces.

For dominant viscous forces, the flow would be "calm"; we say laminar. If inertial forces dominate, vortices and other currents cause chaotic behaviors to arise, giving the fluid a turbulent connotation.

At what Reynolds number does a flow become turbulent?

For a cylindrical pipe, the transition between laminar and turbulent flow happens between Re_D 2300 and Re_D = 2900. Below the first threshold, the fluid is likely laminar in behavior. Above 2900, the fluid completes its transition to turbulent fluid. Between these two values, we can find a transition region, where the behaviors are mixed in complex ways.

How do you calculate the Reynolds number?

To compute the Reynolds number Re_D, we use a simple formula:

Re_D = ρ × u × L/µ

where:

ρ — Fluid density;
u — Flow velocity;
L — A geometric parameter (it can be the diameter of the pipe crossed by the flow); and
µ — Dynamic viscosity of the fluid.

What is the Reynolds number for water flowing in a 25 cm pipe at 1 m/s?

The Reynolds number for a water flow at u = 1 m/s in an L = 0.25 m pipe is: 191,074.

To find this result:

Find the density of water at 10 °C:

ρ = 999.7 kg/m³
Find the dynamic viscosity:

µ = 0.001308 kg/(m · s)
Compute the product of the density of water, the velocity of the flow, and L:

ρ × u × L = 249.925 (m · s)/kg
Divide the result by the dynamic viscosity to find the Reynolds number: Re_D = 249.925/0.001308 = 191,074 The flow is likely turbulent.