The Reynolds Number is a non dimensional parameter 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 (m/s, ft/s)
μ = dynamic viscosity (Ns/m2, lbm/s ft)
L = characteristic length (m, ft)
ν = kinematic viscosity (m2/s, ft2/s)
Reynolds Number for a Pipe or Duct
For a pipe or duct the characteristic length is the hydraulic diameter. The Reynolds Number for a duct or pipe can be expressed as
Re = ρ u dh / μ
= u dh / ν (2)
where
dh = hydraulic diameter (m, ft)
Reynolds Number for a Pipe or Duct in common Imperial Units
The Reynolds number for a pipe or duct can also be expressed in common Imperial units like
Re = 7745.8 u dh / ν (2a)
where
Re = Reynolds Number (non dimensional)
u = velocity (ft/s)
dh = hydraulic diameter (in)
ν = kinematic viscosity (cSt) (1 cSt = 10-6 m2/s )
The Reynolds Number can be used to determine if flow is laminar, transient or turbulent. The flow is
laminar when Re < 2300
transient when 2300 < Re < 4000
turbulent when Re > 4000
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)