Reynolds Number Calculator

The Reynolds Number Calculator calculates the ratio between the inertia and the viscosity of the liquid.

The Reynolds Number:

The  Reynolds Number is the dimensionless value and the ratio between the inertia and viscosity of the liquid. It describes the degree of the laminar and turbulent flow rate. The Reynolds Number remains constant and has the same characteristics if the liquid speed and length vary.

The Reynolds Number Formula:

The Reynolds number calculation is the same for all the liquids, you need to enter the specific parameter for each liquid.

You can calculate Reynolds number by the following formula:

Re = [(ρ * u * L) / μ]

Now,

The Kinematics viscosity of a liquid ν = μ / ρ

Re = [( u * L) /ν]

Where:

• Re is the Reynolds Number
• ρ is the density of liquid(Check the density of air at a given temperature by air density calculator)
• u is the velocity of the object with respect to the object
• L is the Characteristics Linear Dimension of liquid.
• μ is the dynamics of the viscosity of the fluid
• v is the Kinematic Viscosity of a fluid (ν = μ / ρ)

How to Calculate Reynolds Number Online?

When calculating Reynolds Number by using the online Reynolds Number Calculator, there can be two possibilities. Once you enter a new substance, you need to enter all the parameters like density, viscosity etc. Second, if you are selecting the substances like air, water, ethanol etc. You would see a specific viscosity and density at a given temperature. 

•  For example, the Reynolds number of water at 10 degrees centigrade is 764297, if you are taking fluid velocity and characteristic dimension as unity. All the remaining values are pre-measured. 
• The water Reynolds number at 50 degrees centigrade is 1805886, keeping the same values as above.

The Viscosity and Reynolds Number: 

The Reynolds number formula depends upon two different types of viscosity. You need to distinguish types the two types of viscosity.

Dynamics Viscosity (μ):

The Dynamics Viscosity (μ) is the quantity that measures the internal friction in a fluid. The unit of the dynamic viscosity is Pa/s, N/(m²*s) or kg/(m*s).

Kinematics Viscosity (v):

The Kinematics Viscosity (v) can be measured by dividing the Dynamics Viscosity (μ) by the density (ρ). So Kinematics Viscosity is equal to the ν = μ/ρ. The quantity represents the dynamic viscosity of fluid per unit density and is expressed in m²/s.

Reynolds Number Example:

Find the  Reynolds number water and consider the water flow dimension as L = 2.5 cm Pipe. The velocity of the tap water is around u = 1.7 m/s and the temperature is  10 °C.

Given: 

Water flow dimension L = 2.5 cm

Characteristics Linear Dimension  u = 1.7 m/s

Temperature T= 10 °C

Solution:

The water viscosity at 10 °C = 999.7 kg/m3 (constant)

Dynamics Viscosity  μ = 0.001308 Kg/m-s

Kinematics viscosity ν = μ/ρ = 0.0000013084

The Reynolds number formula is:

                                     Re = [(ρ * u * L) / μ] or

                                     Re = [( u * L) /ν]

Water Reynolds number = 32483

How Does the Reynolds Number Calculator Work?

This calculator can be operated easily you need to follow the steps given below:

Input:

• Add the Fluid Velocity and Linear Dimensions
• Enter the fluid parameters for liquid(Common substances have fixed parameters)
• Hit the calculate Button 

Output:

• The Kinematics Viscosity 
• Reynolds Number of Liquid

References:

From the source of Wikipedia: Reynolds Number, Definition

From the source of Vedantu.com: Reynolds NumberFormula, What is Reynolds Number?