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Reynolds Number
An introduction and definition of the dimensionless Reynolds Number - with online calculators
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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)
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)
Related Mobile Apps from The Engineering ToolBox 
- free apps for offline use on mobile devices.
Online Reynolds Calculator
The calculator below can be used if the density and the absolute (dynamic) viscosity of a fluid is known. The calculator is valid for incompressible flow - flow with fluids or gases without compression - as typical for air flow in HVAC systems or similar.
The default values are based on an air at 60 oF, 2 atm and density 0.146 lbm/ft3, flowing 20 ft/s between two metal sheets with characteristic length 0.5 ft. Dynamic (absolute) viscosity is 1.22 10-5 lbm/s ft.
The calculator below can be used when the kinematic viscosity of a fluid is known. The default values are for water at 60oC with a kinematic viscosity of 1.13 10-6 m2/s in a schedule 40 steel pipe. The characteristic length (hydraulic diameter) of the pipe is 0.102 m.
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