Reynolds Number
The Reynolds Number, the non-dimensional velocity, is defined by the ratio of
· dynamic pressure (ρ u2) and
· shearing stress (μ u / L)
and can be expressed as
Re = (ρ u2) / (μ u / L)
= ρ u L / μ
= u L / ν (1)
where
Re = Reynolds Number (non-dimensional)
ρ = density (kg/m3, lbm/ft3 )
u = velocity based on the actual cross section area of the duct or pipe (m/s, ft/s)
μ = dynamic viscosity (Ns/m2, lbm/s ft)
L = characteristic length (m, ft)
ν = kinematic viscosity (m2/s, ft2/s)
Example - Calculating Reynolds Number
A Newtonian fluid with a dynamic or absolute viscosity of 0.38 Ns/m2 and a specific gravity of 0.91 flows through a 25 mm diameter pipe with a velocity of 2.6 m/s.
The density can be calculated using the specific gravity like
ρ = 0.91 (1000 kg/m3)
= 910 kg/m3
The Reynolds Number can then be calculated using equation (1) like
Re = (910 kg/m3) (2.6 m/s) (25 mm) (10-3 m/mm) / (0.38 Ns/m2)
= 156 (kg m / s2)/N
= 156 ~ Laminar flow (1 N = 1 kg m / s2)
Reference
The Engineering Toolbox
