Reynolds Number Calculator

This calculator determines Reynolds number, which is the ratio of the inertia forces to the friction forces in flow. Reynolds number is used to determine the transition from laminar flow to turbulent flow in pipes. 
To help solve Reynold's Number, two extra calculators are provided for conversion purposes.
CalculationReynolds Number Calculator
Inputs
﻿﻿ρ
:1,000kg/m3​
﻿
﻿﻿u
:1.00m/s​
﻿
﻿﻿L
:1.00m​
﻿
﻿﻿μ
:1.00Pa s​
﻿
Output
﻿﻿Re
:1000​
﻿
﻿
Laminar: ﻿Re<2300
﻿
Transitional: ﻿2300<Re<4000
﻿
Turbulent: ﻿Re>4000
﻿
The equation for Reynolds number is given by:
﻿
Re=ρ × u × Lμ\large {Re =\dfrac {\rho \ \times\ u \ \times\ L}{\mu}}Re=μρ × u × L​
Where:
﻿﻿ρ
 is the density of the fluid ﻿(kg/m3)
﻿
﻿﻿u
 is the mean velocity of flow ﻿(m/s)
﻿
﻿﻿l
 is the characteristic linear length, such as the diameter of a pipe or the chord length of an airfoil ﻿(m)
﻿
﻿﻿μ
 is the dynamic viscosity, which is a fluid property that describes the fluid's resistance to flow ﻿(m⋅skg​,Pa⋅s)
. A higher ﻿μ
 means the fluid will flow more slowly for a given applied force.
﻿﻿Re
 is Reynolds number (dimensionless)
﻿
Characteristic Length of a Non-circular Tube
If your tube is non-circular, use this calculator below to convert your tube into a characteristic length which is an input in Reynolds number calculator.
Inputs
﻿﻿Cross-sectional area
:1.50m2​
﻿
﻿﻿Wetted perimeter
:3.00m​
﻿
Output
﻿﻿Hydraulic diameter, Dh
:2.00m​
﻿
The equation for the hydraulic diameter is given by:
﻿
Dh=4×cross-sectional areawetted perimeterD_h= \dfrac{4\times \text{cross-sectional area}}{\text{wetted perimeter}}Dh​=wetted perimeter4×cross-sectional area​
Where:
Cross-sectional area, is the area of a non-circular tube
Wetted perimeter is the perimeter of a non-circular tube for closed channels, while on open channels it is the perimeter of the surface that comes in contact with the fluid.
﻿﻿Dh​
 is the hydraulic diameter, which can be used as your characteristic length in the Reynolds number equation
﻿
Kinematic Velocity to Dynamic Viscosity Convertor
Use the convertor below to determine the dynamic viscosity, which is an input in Reynolds number calculator.
﻿﻿Kinematic viscosity, v
:1.0e-6m2/s​
﻿
﻿﻿Density, ρ (1)
:1,000kg/m3​
﻿
﻿﻿Dynamic viscosity, μ (1)
:0.00Pa s​
﻿
﻿
μ=ρν​\mu= \dfrac{ρ}{\nu}​μ=νρ​​
ExplanationWhat is Reynolds Number?Reynold's number, denoted by ﻿Re
, is a dimensionless number that describes the flow of a fluid. In aerospace engineering, aircraft design can be based on Reynolds number.
💡Who was Osborne Reynolds?
Laminar vs Turbulent FlowReynold's number can be defined as the ratio of internal forces to the viscous forces within a fluid experiencing relative internal movement due to different fluid velocities. 
﻿
Re=inertial forcesviscous force=fluid and flow propertiesfluid propertiesRe=\dfrac{inertial \: forces}{viscous \: force} = \dfrac{fluid \: and \: flow \: properties}{fluid \: properties}Re=viscousforceinertialforces​=fluidpropertiesfluidandflowproperties​
For most practical purposes concerning pipes, if the Reynolds number is:
﻿﻿Re<2300
 the flow is considered laminar. However, for flat plates the flow is considered laminar if the Reynolds number is below 2000.
﻿﻿2300<Re<4000
 the flow is considered transitional
﻿﻿Re>4000
 the flow is considered turbulent
﻿
Find out more about laminar vs turbulent flow in the toggle below.
 💡Laminar vs Turbulent Flow
Assumptions of Reynolds Number EquationThe Reynolds number of fluid is calculated using the following equation;
﻿
Re=ρ × v × Lu\large {Re =\dfrac {\rho \ \times\ v \ \times\ L}{u}}Re=uρ × v × L​
While the equation is convenient, several assumptions and limitations are observed, such as: 
the fluid is a Newtonian fluid
compressibility is disregarded
surface roughness is disregarded
Also, an adjustment is required to the characteristic length ﻿L
 if the fluid flows in a non-circular tube or open channel, wherein the new parameter is used and is called the wetted perimeter. 
Related ResourcesReynolds Number Calculator (for motion of a viscous fluid)
Bernoulli Mass Flow Rate Calculator
Froude Number Calculator: Open Channel Flow
Check out our full library of CalcTree templates here!
﻿
﻿
﻿