Reynolds number calculator

Description

q - volumetric flow rate

Fluid flow rate in terms of units of volume per unit of time

ṁ - mass flow rate

Fluid flow rate in terms of units of mass per unit of time

V - velocity

Flow velocity in terms of units of distance per unit of time

D - pipe diameter

Internal circular pipe diameter

H - channel height

The height of channel for rectangle shaped pipe

W - channel width

The width of channel for rectangle shape pipe

A - area

Internal pipe cross section area

ρ - fluid density

Mass per unit of volume

T - temperature

Fluid temperature for gas density calculation based on the ideal gas state equation

p - pressure

Fluid pressure at the start of the pipe for gas density calculation based on the ideal gas state equation

R - gas constant

Gas constant in terms of energy per unit of mass and temperature, for gas density calculation using ideal gas state equation

ν - kinematic viscosity

Result of fluid particles colliding to each other and moving at different velocities in terms of area per square unit of time

μ - dynamic viscosity

Result of fluid particles colliding to each other and moving at different velocities in terms of mass per square unit of distance and time

Re - Reynolds number

Dimensionless number representing viscous versus inertial forces ratio

Calculation setup

Select value to input. You should enter selected one. The other two will be calculated

q

volumetric flow rate

ṁ

mass flow rate

V

flow velocity

Select value to input. You should enter selected one. The other one will be calculated. Available only if the gas is selected fluid

ρ

fluid density

T

temperature

Select value to input. You should enter selected one. The other one will be calculated

ν

kinematic viscosity

μ

dynamic viscosity

Select fluid type

liquid

for incompressible fluids

gas

for fluids where ideal gas state equation is used. Enables selection between density and temperature to input.

Select pipe shape

round pipe

full cross section fluid flow

rectangular duct

for rectangle channels and full cross section flow

When is This Reynolds Number Calculator Suitable?

The Reynolds number calculator can be used for all types of fluids and flow rates without restriction. It applies to fluid mixtures, requiring the density and viscosity of the mixture.

Whether analyzing flow in a pipe as laminar or turbulent, this tool helps engineers determine the flow regime by evaluating the ratio of inertial forces to viscous forces. Using characteristic length, it assesses how inertial forces to viscous forces influence fluid behavior in pipelines and closed systems.

What is Reynolds Number?

The Reynolds number, named after Osborne Reynolds (1842–1912), represents the relationship between inertial and viscous forces in fluid flow.

• If the Reynolds number is greater than 2320 (Re > 2320), the flow is turbulent.
• If the Reynolds number is less than 2320 (Re < 2320), the flow is laminar.

The transition between laminar and turbulent flow occurs at Reynolds numbers near 2000–4000, depending on the system conditions.

Images below illustrates laminar and turbulent flow in the closed round pipe. On the left side of the image is laminar and on the right side is turbulent flow. Please note the laminar boundary layer in the image for turbulent flow. A laminar boundary layer always forms within a turbulent flow.

How Does the Reynolds Number Calculator Work?

To calculate the Reynolds number, the following parameters are required:

• Fluid velocity (V) – The average velocity of the fluid.
• Pipe diameter (D) – The internal diameter of the pipe.
• Fluid viscosity (μ) – The dynamic viscosity of the fluid.
• Fluid density (ρ) – If needed, kinematic viscosity (ν = μ/ρ) can be used instead of dynamic viscosity.

The formula for Reynolds number is:

Re = (ρ × V × D) / μ    or    Re = (V × D) / ν

Example Calculation

For a pipeline with:

• Fluid velocity: 2 m/s
• Pipe diameter: 0.05 m
• Dynamic viscosity: 0.001 Pa·s
• Fluid density: 1000 kg/m³

The Reynolds number is calculated as:

Re = (1000 × 2 × 0.05) / 0.001 = 100,000

Since Re > 2320, the flow is turbulent.

Why is Reynolds Number Important?

The Reynolds number is a key parameter in fluid dynamics because it helps predict how fluids behave in different conditions:

• In small-diameter pipes, laminar flow is more likely, even with low-viscosity fluids.
• With temperature changes, viscosity varies, causing the flow regime to shift between laminar and turbulent.
• Understanding flow regime is critical in engineering applications like pipe design, heat exchangers, and fluid transport systems.

How to Use the Reynolds Number Calculator?

Follow these simple steps to determine the flow regime using our Reynolds number calculator:

1. Enter the fluid velocity in meters per second (m/s).
2. Input the internal pipe diameter in meters (m).
3. Provide the fluid viscosity (either dynamic or kinematic viscosity).
4. Click the calculate button to get the Reynolds number.
5. Compare the result with the critical Reynolds number (2320) to determine if the flow is laminar or turbulent.

Key Takeaways

• The Reynolds number helps classify fluid flow as laminar (smooth) or turbulent (chaotic).
• It is influenced by fluid velocity, pipe diameter, and viscosity.
• Use the Reynolds number calculator to predict flow behavior in pipelines and fluid systems.

With this Reynolds number calculator, you can quickly analyze flow characteristics and make informed decisions in engineering applications.

• Read more about Reynolds number
• Read more on Osborne Reynolds
• Read more on turbulence