Laminar Flow

  • An explanation of laminar flow and where can it be observed
  • A brief history of laminar flow’s study and the experiments that led to its discovery
  • An explanation of the Reynolds number and how it can be calculated
  • An analysis of the different types of flow and the transition regime between them

Laminar flow is a phenomenon observed in flowing fluids that manifests during the study of fluid dynamics. In general, fluid flow can be described in two ways: laminar flow and turbulent flow. This article will describe laminar flow, how and when it was first observed, and its relationship to the Reynolds number.

What is Laminar Flow?

Laminar flow is often referred to informally as a “streamline” flow, as it describes a flow that contains parallel streamlines that don’t cross each other. In other words, adjacent layers of fluid molecules pass alongside each other smoothly, without any mixing or interference.

luminar flow vs turbulent flow diagram

The absence of any eddy currents, cross-currents, or swirls means that the flow is perfectly laminar. The laminar state of the flow leads to relatively high momentum diffusion with reduced momentum convection.

Laminar flow can only be maintained at lower velocities. As the velocity increases, it reaches a threshold at which the flow begins to act turbulently.

Both types of flow can be seen in some waterfalls. The smooth, clear flow of some of the slower-moving water (laminar flow) can be seen as large sheets of clear water flowing over the top of the waterfall. As the water flow accelerates due to gravity the contrast shows up as rough, foamy, choppy flow (turbulent flow).

History of Laminar Flow

19th-century scientist Osborne Reynolds specialised in the study of fluid dynamics. He first noticed the distinction between turbulent and laminar flows in the latter half of the 1800s.

In 1883, his first publication on the properties of water motion through parallel channels appeared in the proceedings of the Royal Society of London.

The experiment involved measuring and observing water flow in a large glass pipe. Reynolds added a small amount of dyed water to the flow and observed the action of the water at various flow rates.

At low flow speeds, the dyed layer could be seen as a straight, uninterrupted line through the glass pipe. As the velocity increased, the line of dyed water quickly broke up and diffused into the volume of the tube.

In this experiment, Reynolds demonstrated that there are two types of flow – turbulent and laminar – and that there is a transition period between them.

Reynolds Number

The Reynolds number (Re) is a dimensionless value for the ratio between viscous and inertial forces. Although the concept was originally introduced by George Gabriel Stokes in 1851, it was Osborne Reynolds who applied it to the transition phase between the laminar and turbulent flow.

The Reynolds number is defined mathematically as:

reynolds number formula

link to reynolds number calculator

 

 

 

Where:

  • ρ is the density
  • u is the macroscopic velocity
  • d is the characteristic dimension (such as pipe diameter) chosen for the measurement
  • μ is the dynamic viscosity
  • 𝑣 is the kinematic viscosity

At low Re values the fluid flow is laminar. At a certain range of Re values, the flow enters a transition period between the laminar and turbulent flow. When the Re value exceeds a level known as the “critical Reynolds number,” the flow becomes fully turbulent.

Transition Regime

The transition regime describes the transition period or phase between laminar and turbulent flow. It occurs between a specific range of Re values within the same flow. Outside parameters may also affect the turbulence of the flow.

For example, flow in a closed pipe (famously analysed in Moody’s chart – see below) is dependent on both the Reynolds number and the roughness of the pipe’s inner surface. The relative roughness of the pipe is a local parameter which varies depending on how close the flow is to the rough curved edge of the pipe.

Image credit: JoKalliauer

For an entertaining explanation and demonstration of laminar and turbulent flow, check out this video.

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