Reynolds Number
Introduction and definition of the dimensionless Reynolds Number  online calculators.
Reynolds Number  the nondimensional velocity  can be defined as the ratio
 inertia force (ρ u L) to viscous or friction force (μ)
and interpreted as the ratio
 dynamic pressure (ρ u^{2}) to shearing stress (μ u / L)
Reynolds Number can therefore be expressed as
Re = ρ u L / μ
= ρ u^{2} / (μ u / L)
= u L / ν (1)
where
Re = Reynolds Number (nondimensional)
ρ = density (kg/m^{3}, lb_{m}/ft^{3})
u = velocity based on the actual cross section area of the duct or pipe (m/s, ft/s)
μ = dynamic viscosity (Ns/m^{2}, lb_{m}/s ft)
L = characteristic length (m, ft)
ν = μ / ρ = kinematic viscosity (m^{2}/s, ft^{2}/s)
Reynolds Number for Flow in Pipe or Duct
For a pipe or duct the characteristic length is the hydraulic diameter.
L = d_{h}
where
d_{h} = hydraulic diameter (m, ft)
The Reynolds Number for the flow in a duct or pipe can with the hydraulic diameter be expressed as
Re = ρ u d_{h} / μ
= u d_{h} / ν (2)
where
d_{h} = hydraulic diameter (m, ft)
Reynolds Number for a Pipe or Duct in Imperial Units
The Reynolds number for a pipe or duct expressed in Imperial units
Re = 7745.8 u d_{h} / ν (2a)
where
Re = Reynolds Number (non dimensional)
u = velocity (ft/s)
d_{h} = hydraulic diameter (in)
ν = kinematic viscosity (cSt) (1 cSt = 10^{6} m^{2}/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
In practice laminar flow is only actual for viscous fluids  like crude oil, fuel oil and other oils.
Example  Calculate Reynolds Number
A Newtonian fluid with a dynamic or absolute viscosity of 0.38 Ns/m^{2} and a specific gravity of 0.91 flows through a 25 mm diameter pipe with a velocity of 2.6 m/s.
Density can be calculated from the specific gravity of the fluid and the density of the specific gravity reference water 1000 kg/m^{3}  as
ρ = 0.91 (1000 kg/m^{3})
= 910 kg/m^{3}
Reynolds Number can then be calculated using equation (1) like
Re = (910 kg/m^{3}) (2.6 m/s) (25 mm) (10^{3} m/mm) / (0.38 Ns/m^{2})
= 156 ((kg m / s^{2})/N)
= 156 ~ Laminar flow
1 (N) = 1 (kg m / s^{2})
Related Mobile Apps from The Engineering ToolBox
 free apps for offline use on mobile devices.
Online Reynolds Calculator
Density and absolute (dynamic) viscosity is Known
This calculator can be used if density and absolute (dynamic) viscosity of the fluid is known. The calculator is valid for incompressible flow  flow with fluids or gases without compression  as typical for air flows in HVAC systems or similar. The calculator is generic and can be used for metric and imperial units as long as the use of units are consistent.
Default values are for air at 60 ^{o}F, 2 atm pressure and density 0.146 lb_{m}/ft^{3}, flowing 20 ft/s between two metal sheets with characteristic length 0.5 ft. Dynamic (absolute) viscosity is 1.22 10^{5} lb_{m}/s ft.
Kinematic viscosity is known
The calculator below can be used when kinematic viscosity of the fluid is known. The calculator is generic and can be used for metric and imperial units as long as the use of units are consistent.
Default values are for water at 20^{o}C with kinematic viscosity 1.004 10^{6} m^{2}/s in a schedule 40 steel pipe. The characteristic length (or hydraulic diameter) of the pipe is 0.102 m.
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