Laminar and turbulent flow

Inject a thin dye streak into a pipe at low speed and it remains narrow: the flow is laminar. Increase the speed and the streak begins to fluctuate, then spreads across the pipe as the flow becomes turbulent [1,2].

The distinction changes more than appearance. Velocity profiles, mixing, wall friction and pressure loss all change, directly affecting the design of pipes, heat exchangers and flow meters.

Fluid particles still move downstream in laminar flow, but have little average motion across neighbouring layers. Cross-stream transport relies mainly on molecular diffusion, so heat and species mix relatively slowly.

In turbulence, velocity fluctuates in space and time around the mean flow. Eddies carry parcels across the pipe and greatly enhance the transport of momentum, heat and mass [4]. The instantaneous motion is irregular, yet time-averaged velocity and pressure have repeatable distributions.

Laminar

Small velocity fluctuations; particles move downstream in broadly ordered layers.

Turbulent

Three-dimensional fluctuations and eddies create strong cross-stream mixing.

Transitional

Laminar and turbulent regions alternate in space and time and respond strongly to disturbances.

Reynolds injected a thin streak of dye into a transparent circular pipe. At low speed the streak remained narrow; at higher speed it fluctuated and dispersed across the section [2].

Dye spreading is an observation, not the definition of turbulence. The essential mechanism is fluctuating velocity transporting dye across the mean flow. Molecular diffusion also spreads dye, but much more slowly than turbulent mixing.

For pipe flow, calculate $\mathrm{Re}_D$ from internal diameter $D$, cross-sectional mean velocity $V$, density $\rho$ and dynamic viscosity $\mu$. For a long smooth circular pipe, $\mathrm{Re}_D<2300$ is a common laminar guide, roughly 2300–4000 is transitional and $\mathrm{Re}_D>4000$ is a turbulent guide [1].

The limits do not mean that the whole flow suddenly becomes turbulent one count above 2300. Pipe transition is triggered by finite disturbances, and carefully controlled flows can remain laminar at higher $\mathrm{Re}_D$ [3].

Fully developed laminar pipe flow has a parabolic velocity profile. No slip makes velocity zero at the wall, while the centreline velocity reaches twice the cross-sectional mean $V$.

The time-mean turbulent profile is flatter across the core and falls steeply near the wall. Eddies exchange high- and low-momentum fluid and carry core momentum towards the wall.

Turbulent mixing enhances heat and mass transfer in heat exchangers and reactors. It also transports more momentum towards the wall, so at the same pipe and mean speed turbulence generally produces greater wall shear and pressure loss.

The Darcy friction factor $f$ for developed laminar pipe flow is given exactly by Equation (3). Turbulent $f$ also depends on relative roughness and is obtained from correlations such as the Moody chart or Colebrook equation.

Reynolds number and friction factor are dimensionless. The SI unit of dynamic viscosity $\mu$ is $\mathrm{Pa{\cdot}s}$ and that of kinematic viscosity $\nu$ is $\mathrm{m^2/s}$ [5].

Water at 20 °C flows through a smooth pipe of internal diameter $D=0.020\ \mathrm{m}$. Use $\rho=998\ \mathrm{kg/m^3}$ and $\mu=1.002\times10^{-3}\ \mathrm{Pa{\cdot}s}$ to find the mean velocities corresponding to the laminar guide $\mathrm{Re}_D=2300$ and turbulent guide $\mathrm{Re}_D=4000$.

Rearrange Equation (1) for $V$ in Equation (4). Substitution gives Equation (5). Therefore $V=0.08\ \mathrm{m/s}$ lies in the laminar range, $V=0.16\ \mathrm{m/s}$ in the transitional range and $V=0.30\ \mathrm{m/s}$ in the turbulent range.

The 2300 and 4000 guides apply to $\mathrm{Re}_D$ defined with circular-pipe internal diameter and mean velocity. Boundary layers, jets, open channels and rotating flows use different scales and transition mechanisms.

A non-Newtonian fluid may require a modified Reynolds number because viscosity depends on shear rate. Pulsating flow, rapid acceleration and short entrance regions also fall outside the steady, fully developed pipe-flow assumptions.

Record the system, characteristic length, mean velocity and property temperature together with the classification.

Turbulent means fast

Speed alone is insufficient; size, density and viscosity enter through $\mathrm{Re}$.

Calling every transitional case turbulent

Transitional flow is disturbance-sensitive and may contain both laminar and turbulent regions.

Assuming averages are meaningless

Instantaneous values fluctuate, but time-mean velocity, pressure and loss remain useful engineering quantities.

Neglecting viscosity in turbulence

Viscosity remains essential to wall shear and dissipation.

Classify the flow before calculating pipe pressure loss, selecting a flow meter, sizing a heat exchanger, assessing reactor mixing, designing clean-room airflow, analysing lubrication films or working with microchannels.

Laminar flow is predictable and gentle but mixes slowly. Turbulence can improve mixing and heat transfer while increasing pressure loss, vibration and noise. Engineering chooses the state that serves the objective.

First review Reynolds number and the choice of characteristic scales. Continue to internal pipe flow and pipe losses to use the distinction in design calculations.

Prerequisites

Reynolds number; density, pressure & viscosity

Next

Internal pipe flow; Darcy–Weisbach equation; Moody chart; boundary layers