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.
Related Topics

Fluid Flow and Pressure Loss in Pipes and Tubes
Fluid flow and pressure loss in pipe lines. Water and sewer systems. Steel pipes, pvc pipes, copper tubes and more. 
Fluid Mechanics
The study of fluids  liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time. 
Piping Systems
Calculate dimensions of pipes and tubes. Pressure drop calculations and head loss charts. Use of different piping materials. Insulation of pipes and tubes and heat loss diagrams. 
Water Systems
Design of hot and cold water service and utility systems with properties, capacities, sizing of pipe lines and more.
Related Documents

Butane  Dynamic and Kinematic Viscosity vs. Temperature and Pressure
Online calculators, figures and tables with dynamic and kinematic viscosity of liquid and gaseous butane, C_{4}H_{10}, at varying temperarure and pressure, SI and Imperial units. 
Colebrook Equation
Friction loss coefficients in pipes, tubes and ducts. 
DarcyWeisbach Equation  Major Pressure and Head Loss due to Friction
The DarcyWeisbach equation can be used to calculate the major pressure and head loss due to friction in ducts, pipes or tubes. 
Dimensionless Numbers
Physical and chemical dimensionless quantities  Reynolds number, Euler, Nusselt, and Prandtl number  and many more. 
Energy Equation  Pressure Loss vs. Head Loss
Calculate pressure loss  or head loss  in ducts, pipes or tubes. 
Ethylene  Dynamic and Kinematic Viscosity vs. Temperature and Pressure
Online calculator, figures and tables showing dynamic and kinematic viscosity of ethylene, C_{2}H_{4}, also called ethene or acetene, at varying temperature and pressure  Imperial and SI Units. 
Fluid Flow  Entrance Length and Developed Flow
The entrance length is the length in a tube or duct after an obstruction  until the flow velocity profile is fully developed. 
Fluid Flow  Hydraulic Diameter
Calculate hydraulic diameter for pipes and ducts. 
Laminar Flow  Friction Coefficients
Calculate friction coefficients for laminar fluid flow. 
Laminar, Transitional and Turbulent Flow
Heat transfer, pressure and head loss in a fluid varies with laminar, transitional or turbulent flow. 
Liquids  Kinematic Viscosities
Kinematic viscosities of some common liquids like motor oil, diesel fuel, peanut oil and many more. 
Methanol  Dynamic and Kinematic Viscosity vs. Temperature and Pressure
Online calculator, figures and tables showing dynamic and kinematic viscosity of liquid methanol,CH_{3}OH, at varying temperature  Imperial and SI Units. 
Moody Diagram
Calculate fluid flow friction coefficients from a Moody diagram. 
Oxygen  Dynamic and Kinematic Viscosity vs. Temperature and Pressure
Online calculator, figures and tables showing dynamic and kinematic viscosity of oxygen, O_{2}, at varying temperature and pressure  Imperial and SI Units. 
Prandtl Number
A dimensionless number approximating the ratio of momentum diffusivity to thermal diffusivity. 
Viscosity  Absolute (Dynamic) vs. Kinematic
Vicosity is a fluid's resistance to flow and can be valued as dynamic (absolute) or kinematic. 
Viscous Liquids  Friction Loss vs. Viscosity and Flow
Friction loss in steel pipes for fluids with viscosities ranging 32  80000 SSU. 
Volume Flow  Online Unit Converter
Convert between volume flow units like gpm, liter/sec, cfm, m^{3}/h. 
Water  Absolute (Dynamic) Viscosity vs. Temperature and Pressure
Absolute viscosity for water in centipoises for temperatures between 32  200^{o}F. 
Water Flow in Tubes  Reynolds Number
Reynolds number for clean cold water flow.