WOLFRAM SYSTEM MODELER

ReynoldsNumber

Return Reynolds number from v, rho, mu, D

Wolfram Language

In[1]:=
SystemModel["Modelica.Fluid.Pipes.BaseClasses.CharacteristicNumbers.ReynoldsNumber"]
Out[1]:=

Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

Calculation of Reynolds Number 

Re = |v|ρD/μ

a measure of the relationship between inertial forces (vρ) and viscous forces (D/μ).

The following table gives examples for the characteristic dimension D and the velocity v for different fluid flow devices:

Device TypeCharacteristic Dimension DVelocity v
Circular Pipediameter m_flow/ρ/crossArea
Rectangular Duct4*crossArea/perimeter m_flow/ρ/crossArea
Wide Ductdistance between narrow, parallel walls m_flow/ρ/crossArea
Packed BeddiameterOfSpericalParticles/(1-fluidFractionOfTotalVolume) m_flow/ρ/crossArea (without particles)
Device with rotating agitatordiameterOfRotor RotationalSpeed*diameterOfRotor

Syntax

Re = ReynoldsNumber(v, rho, mu, D)

Inputs (4)

v

Type: Velocity (m/s)

Description: Mean velocity of fluid flow
rho

Type: Density (kg/m³)

Description: Fluid density
mu

Type: DynamicViscosity (Pa⋅s)

Description: Dynamic (absolute) viscosity
D

Type: Length (m)

Description: Characteristic dimension (hydraulic diameter of pipes)

Outputs (1)

Re

Type: ReynoldsNumber

Description: Reynolds number