# What is the characterisitc length of the flow in this case?

We can compute Reynolds number to determine if the flow is laminar or turbulent, therfore we need a characteristic length; for example, In the case of external flow around an airfoil, we can consider $$L =c$$ the chord of the airfoil. For internal flows, the characteristic length is the hydraulic diameter

My question is: in the case of a cigarette smoke, what is the characteristic length? How can we evaluate the nature of the flow in this case?

EDIT: Can we evaluate the nature of a flow without relating it to an object?

The smoke emanates from a certain area of the cigarette - namely the tip. The column of smoke is roughly the size of the top initially but as the hot air picks up speed the column quickly becomes narrower.

Note that is you spewed (cigarette) smoke from a large chimney, the aperture of the chimney would set the characteristic length. For the cigarette it is the size of the tip.

In all cases, these things only set an approximate scale of the problem.

The only thing that provides scale to the problem: The size (edit: diameter) of the cigarette.

Always keep in mind that 'characteristic lengths' are generally poorly defined (e.g. why the cord of the airfoil instead of the height? the maximum cord or ... ?). The type of answer you get will generally be an order of magnitude one.

• thank you, but can we determine the nature of the flow without relating it to an object ? Oct 16, 2016 at 1:17
• More specifically, the diameter of the cigarette. The length is not a deciding factor here. Oct 16, 2016 at 1:48
• @Navaro you need something to determine the characteristic length scale of the flow. That basically needs to be a source (i.e. object) of some sort... I suppose you could construct a situation where the flow was started by a different type of external force (e.g. electromagnetic field driving a plasma) but that would still produce a characteristic length in a similar way. Oct 16, 2016 at 2:40
• I think the question and answer may be much more complicated than it first appears. If we don't think the length has not much to do with it just hold it upside down. How is it packed? Tough question. Oct 16, 2016 at 2:41
• Take the object away and evaluate smoke only. Tough question. Oct 16, 2016 at 2:50