Reynolds Number Calculator

Use the Reynolds number calculator to easily determine the Reynolds number of a fluid and identify if it's on a turbulent or laminar flow pattern.

If you'd like to learn more about the Reynolds number we invite you to keep reading and find out:

• What is the Reynolds number?;
• The Reynolds number equation;
• How to calculate the Reynolds number; and
• Reynolds number for laminar flow and turbulent flow.

Introduced in 1883 by the British engineer Osborne Reynolds, the Reynolds number is one of the most important dimensionless parameters used in fluid mechanics. This parameter describes the behavior of a Newtonian fluid by relating the inertial and viscous forces.

Inertial forces are related to the fluid's momentum. They resist changes in velocity and allow fluid motion to continue. Whereas viscous forces oppose to the motion and slow down the flow:

Are you unsure of what momentum is or how to calculate it? Then Omni's momentum calculator might come in handy.

The inertial forces are dominant in turbulent flows. However, when the viscous forces govern, the flow is said to be laminar. The parameters affecting the inertia and viscosity of a fluid in motion are included in the Reynolds number formula:

where:

• $\rho$ - Density of the fluid in kg/m³ or lb/cu ft;
• $V$ - Velocity of the flow in m/s or ft/s;
• $L$ - Characteristic length of the flow in m or ft;
• $\mu$ - Dynamic viscosity of the fluid in kg/(m⋅s), or lb/(ft⋅s) or cP; and
• $\nu$ - Kinematic viscosity m²/s, or ft²/s or cSt.

For flow in a pipe, the Reynolds number equation can be expressed in terms of the volumetric flow rate Q as:

where:

• $D_H$ - Hydraulic diameter of the pipe in m or ft; and
• $A$ - Cross-sectional area of the pipe in m² of ft².

The first step in studying a flow should be to calculate its Reynolds number. This value will define the flow pattern:

• Low values of Reynolds, $Re \leq 2100$ are associated with a laminar flow. This one is characterized by soft variations and slow and viscous flow. In this type of flow pattern, the predominant velocity and direction of the main flow coincide.

• High values of Reynolds number, $Re \geq 3000$, indicate turbulent flow. This flow type is dominated by inertial forces and is characterized by strong random fluctuations, vortices, eddies, and other instabilities.

• In between these two flow patterns, we find the transitional flow o, $2100 < Re < 3000$. This one combines laminar and turbulent flows. Turbulence in the center and laminar flow towards the pipe's edges.

The Reynolds number for laminar flow, transitional flow and turbulent flow are shown in the table below:

The Reynolds number calculator makes it simple to estimate the Reynolds number of a fluid and determines whether it is laminar or turbulent. To use this tool:

1. In the first section of the calculator, Flow parameters, input the fluid's velocity and characteristic length.
2. Below, you'll find the Fluid parameters section. Here you can choose from a list of different substances that already have charged their density and viscosities.
3. Once the flow and fluid parameters are defined, the calculator will display the Reynolds number and indicate the type of flow pattern, laminar, intermittent, or turbulent.