Flow parameters
Fluid velocity
ft/s
Characteristic linear dimension
ft
Fluid parameters
Substance
Custom ▾
Fluid density
lb/cu ft
Dynamic viscosity
oz
/(m*s)
Kinematic viscosity
ft²
/s
Reynolds number
Reynolds number

# Reynolds Number Calculator

By Dominik Czernia, PhD candidate

With our Reynolds number calculator, you can quickly compute 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 the questions:

• what is Reynolds number?
• how to calculate it?
• what are its units?
• what is laminar flow definition?
• what is 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 Reynolds number equation, units discussion and comparison of laminar and turbulent flows. Read on to find out what are laminar flow and turbulent flow Reynolds numbers. You will also find some examples of calculations which can be done with Reynolds number formula using this calculator.

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., 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 which 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 at all. 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 with 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 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 `μ` is a quantity that measures the force needed to overcome internal friction in a fluid. The units of dynamic viscosity are: `Pa/s`, `N/(m²*s)` or `kg/(m*s)`.
2. Kinematic viscosity `ν` is the dynamic viscosity divided by density `ν = μ/ρ`. Therefore, it's a quantity that represents the dynamic viscosity of a fluid per unit density and is expressed in `m²/s`.

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

`Re = ρ * u * L / μ` and `Re = u * L / ν`

where

• `Re` is the Reynolds number,
• `ρ` is the fluid density (you might want to estimate the density of air at given temperature, just check our air density calculator),
• `u` is the velocity of a fluid (with respect to the object),
• `L` is the characteristic linear dimension,
• `μ` is the dynamic viscosity of a fluid,
• `ν` is the kinematic viscosity of a fluid (`ν = μ / ρ`).

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 and diameter,
• an aircraft, we can use either the length and width of aerofoils,
• 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 a `L = 2.5 cm` diameter pipe. The velocity of tap water is about `u = 1.7 m/s`. In our Reynolds number calculator, you can choose (as a substance) water at `10 °C` and you obtain Reynolds number `Re = 32 483`. Hence, the water flow is turbulent.

Dominik Czernia, PhD candidate