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Laminar and turbulent

Air and fluids · level 8, lesson 2 of 6

A question to start

Smoke from a candle rises in a smooth thread, then suddenly breaks into swirls. Why does a flow change from smooth to chaotic?

The idea

At low Reynolds number, a flow is laminar: the fluid slides in smooth layers, and a disturbance dies away. At high Reynolds number, small disturbances grow into eddies, and the flow becomes turbulent: chaotic and full of mixing.

For flow in a round pipe, with \(L\) the diameter:

\(Re\) in a pipe Flow
below about 2,000 laminar
about 2,000 to 4,000 in between
above about 4,000 turbulent

Turbulence mixes things fast: heat, dust, gases. It also raises drag in pipes, because the eddies waste energy.

laminar: low Returbulent: high Re

On a planet, the sizes are huge, so the Reynolds number of the wind is huge too, even on Mars.

Wind of 5 m/s Mars Earth
Past a 1 m rock \(Re \approx 7{,}300\) \(Re \approx 340{,}000\)
Over a 100 m hill \(Re \approx 730{,}000\) \(Re \approx 3.4\times10^7\)

So Mars's winds are turbulent at the scale of hills and craters, just like Earth's. Mars's thin air only feels syrupy at small scales: dust grains, rotor blades, small sensors.

Worked examples

1. A water pipe in a base. Diameter 0.02 m, water at 1 m/s, \(\mu = 1.0\times10^{-3}\) Pa s: \(Re = 1000 \times 1 \times 0.02/0.001 = 20{,}000\). Turbulent.

2. Honey in the same pipe, with \(\mu \approx 10\) Pa s and \(\rho = 1400\) kg/m³: \(Re = 1400 \times 1 \times 0.02/10 = 2.8\). Laminar.

3. The fastest laminar water. For \(Re = 2000\) in the 0.02 m pipe: \(v = 2000 \times 0.001/(1000 \times 0.02) = 0.1\) m/s.

Try it

  1. What is the difference between laminar and turbulent flow?
  2. Air in a habitat duct 0.2 m wide moves at 2 m/s, with \(\rho = 1.0\) kg/m³ and \(\mu = 1.8\times10^{-5}\) Pa s. Laminar or turbulent?
  3. Why is Mars's wind turbulent over hills, even though its air is so thin?
  4. Why does turbulence matter for how fast dust and heat spread in a planet's air?
Answers
  1. Laminar flow moves in smooth layers; turbulent flow is chaotic, with eddies.
  2. \(Re = 1.0 \times 2 \times 0.2/(1.8\times10^{-5}) \approx 22{,}000\): turbulent.
  3. The sizes are so large that \(Re\) is still very high.
  4. Eddies mix the air much faster than smooth flow can.

Common mistake

"Thin air flows smoothly." Whether a flow is turbulent depends on \(Re\), which also grows with speed and size. Over hills and plains, Mars winds are fully turbulent.

Where it leads