Question

Discuss the significance of Reynold number for the classification of the type of fluid flow.

Answer 1

The dimensionless Reynolds number plays a prominent role in foreseeing the patterns in a fluid’s behavior. The Reynolds number, referred to as Re, is used to determine whether the fluid flow is laminar or turbulent.The Reynolds number is the ratio of the inertial forces and the viscous forces.

If the inertial forces, which resist a change in velocity of an object and are the cause of the fluid movement, are dominant, the flow is turbulent. Otherwise, if the viscous forces, defined as the resistance to flow, are dominant – the flow is laminar.

When calculating heat transfer or pressure and head loss it is important to know if a fluid flow is laminar, transitional or turbulent.

There are in general three types of fluid flow in pipes

laminar
turbulent
transient

Laminar flow :

Laminar flow generally happens when dealing with small pipes and low flow velocities. Laminar flow can be regarded as a series of liquid cylinders in the pipe, where the innermost parts flow the fastest, and the cylinder touching the pipe isn't moving at all.

Shear stress in a laminar flow depends almost only on viscosity - μ - and is independent of density - ρ.

Turbulent flow :
In turbulent flow vortices, eddies and wakes make the flow unpredictable. Turbulent flow happens in general at high flow rates and with larger pipes.

Shear stress in a turbulent flow is a function of density - ρ.

Transitional flow :
Transitional flow is a mixture of laminar and turbulent flow, with turbulence in the center of the pipe, and laminar flow near the edges. Each of these flows behave in different manners in terms of their frictional energy loss while flowing and have different equations that predict their behavior.

Turbulent or laminar flow is determined by the dimensionless Reynolds Number.

The flow is

laminar when Re < 2300
transient when 2300 < Re < 4000
turbulent when 4000 < Re

The Reynolds number is defined as

• ρ is the density of the fluid (kg/m³)
• u is the flow speed (m/s)
• D is the diameter of the tube (m)
• μ is the dynamic viscosity of the fluid (Pa·s or N·s/m² or kg/(m·s))
• ν is the kinematic viscosity of the fluid (m²/s).