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 Type	Characteristic Dimension D	Velocity v
Circular Pipe	diameter	m_flow/ρ/crossArea
Rectangular Duct	4*crossArea/perimeter	m_flow/ρ/crossArea
Wide Duct	distance between narrow, parallel walls	m_flow/ρ/crossArea
Packed Bed	diameterOfSpericalParticles/(1-fluidFractionOfTotalVolume)	m_flow/ρ/crossArea (without particles)
Device with rotating agitator	diameterOfRotor	RotationalSpeed*diameterOfRotor

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

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)

Re	Type: ReynoldsNumber Description: Reynolds number