Reynolds Number

An introduction and definition of the dimensionless Reynolds Number

A dimensionless combination of variables that is important in the study of viscous flow is called the Reynolds Number.

The Reynolds Number is important in analyzing any type of flow when there is substantial velocity gradient - shear. The Reynolds Number indicates the relative significance of the viscous effect compared to the inertia effect. The Reynolds number is proportional to inertial force divided by viscous force.

Reynolds Number can be expressed as:

The viscosity above is dynamic viscosity also called absolute viscosity. For a pipe or duct the the characteristic length is the pipe or duct diameter.

• What is Hydraulic and what is Equivalent Diameter?

Reynolds number may also be calculated using kinematic viscosity. The first formula (1) above must then be modified to (2) by removing the density because the kinematic viscosity is simply the absolute viscosity divided by the density of the liquid.

• Absolute, dynamic and Kinematic Viscosity An introduction and explanation of dynamic, absolute and kinematic viscosity and how to convert between CentiStokes, CentiPoises, SSU and degree Engler

The flow is

• laminar if Re < 2300
• transient if 2300 < Re < 4000
• turbulent if Re > 4000

• Laminar, Transitional or Turbulent Flow? It is important to know if the fluid flow is laminar, transitional or turbulent when calculating heat transfer or pressure and head loss.

Example - Calculating the Reynolds Number - SI Units

A Newtonian fluid having 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 fluid density is calculated from the specific gravity:

density = 0.91 x 1000 kg/m³ = 910 kg/m³

The Reynolds Number can be calculated from equation (1) above:

Re = ( 910 kg/m³ 2.6 m/s 25 mm 10^-3 m/mm ) / 0.38 Ns/m² = 156 (kgm/s²)/N = 156 ~ Laminar flow

since 1 N = 1 kgm/s²

• Reynold's Number in Water Tubes Reynolds Number in tubes at different dimensions transporting clean cold water
• An Online Reynolds Number Calculator Calculate laminar or turbulent flow with the Reynolds number online calculator
• Absolute Viscosity of Several Fluids Absolute or dynamic viscosity of fluids as motor oil, diesel fuel, peanut oil and many more.
• Absolute or Dynamic Viscosity of Water Absolute or dynamic viscosity of water depends on the temperature
• Laminar, Transitional or Turbulent Flow? It is important to know if the fluid flow is laminar, transitional or turbulent when calculating heat transfer or pressure and head loss

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