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# Reynolds Number

Reynolds Number - the non-dimensional 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 u2) to shearing stress (μ u / L)

Reynolds Number can therefore be expressed as

Re = ρ u L / μ

= ρ u2/ (μ u / L)

= 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 = μ / ρ = kinematic viscosity (m2/s, ft2/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 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

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/m2 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/m3 - as

ρ = 0.91 (1000 kg/m3 )

= 910 kg/m3

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

#### 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 oF , 2 atm pressure 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.

#### 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 oC with kinematic viscosity 1.004 10-6 m2/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, C4H10, at varying temperarure and pressure, SI and Imperial units.

### Colebrook Equation

Friction loss coefficients in pipes, tubes and ducts.

### Darcy-Weisbach Equation - Major Pressure and Head Loss due to Friction

The Darcy-Weisbach 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, C2H4, 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,CH3OH, 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, O2, 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, m3/h.

### Water - Absolute (Dynamic) Viscosity vs. Temperature and Pressure

Absolute viscosity for water in centipoises for temperatures between 32 - 200oF.

### Water Flow in Tubes - Reynolds Number

Reynolds number for clean cold water flow.

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