# Smoke and fluid mechanics

While lighting up a cigarette (I don't encourage smoking) I noticed that the flow of the smoke coming out of it, initially goes in a straight up direction, in a laminar flow, then about 10 cms above, the movement becomes chaotic. My questions are why does that happen? (In the simplest way possible) And what's the name of that phenomena?

• Dude, that's a textbook example of turbulence.
– Tofi
Mar 12, 2022 at 19:23

what's the name of that phenomena?

The phenomenon is called a turbulence.

why does that happen? (In the simplest way possible)

The surrounding air is colder and more dense than the smoke, so buoyant force on the smoke is larger than its weight. Hence, the net acceleration points upwards and its speed is increasing. The hot smoke rises in the cold air by the same principle as a balloon with hot helium.

The middle part of the smoke is hotter than the outer part so it has more acceleration and gains speed faster. As you go towards the edges of the smoke, the speed becomes equal to that of the surrounding air. This relative movement generates fluid friction, and viscosity of the fluid is counteracting the effect which can inhibit a turbulence in a fluid flow.

There is a dimensionless number (indicator) called the Reynolds number which can predict whether fluid flow will be laminar (steady) or turbulent

$$Re = \rho u L / \mu = u L / \nu$$

where $$\rho$$ is fluid density, $$u$$ is flow speed, $$\mu$$ and $$\nu$$ are dynamic and kinematic viscosity, respectively, and $$L$$ is characteristic linear dimension. At low values of $$Re$$ the flow tends to be laminar, and at high numbers it tends to be turbulent.

Note that the Reynolds number is not exact science in predicting fluid flow. Fluid flow is generally chaotic and very small changes to conditions can result in very different flow. Nevertheless, it is widely used as an important guide to predicting fluid flow.