# Reynolds number determines turbulent or laminar but Moody Chart has different interpretation

One can calculate the Reynolds number to determine whether or not flow is turbulent or not inside a pipe with circulating water. The formula is:

$$Re = \frac{\rho VD}{\mu}$$

Let's say one gets $$Re = 10,000$$. This means that the flow is turbulent (so $$Re >4000$$, according to some sources). Now, if one looks at the Moody Charge for $$\ Re = 10,000$$ or $$10^4$$, one can see that depending on the roughness, it can be both in transitional or in a fully turbulent flow. My question is... Is Reynolds number enough to determine whether a flow is turbulent or laminar or one needs extra information about the roughness to get the correct flow type?

Yes, Reynolds number is enough. In circular pipes:

$$Re = \frac{\rho V D}{\mu} = \frac{V D}{\nu}$$

As you pointed out, the flow becomes turbulent at about $$Re = 4000$$. For values lower than $$2100$$ it is laminar. For values in between is transitional. This is seen in the typical experience in a stream of dye injected in the direction of the pipe flow. If the flow is laminar, you will see a straight line of dye. If it is transitional, the line of dye will have fluctuations (in space and time) and will start showing eventual bursts of irregular behaviour. If the flow is turbulent, you will see the dye being spread and blurred randomly in space and time.

Let's say that we are now in turbulent regime.

Now we can look into the dashed line called in that figure "Complete Turbulence".

What happens if the Reynolds number is small enough (but still turbulent $$> 4000$$) and roughness is also small enough is that, in a thin layer next to the wall, the flow is dominated by viscous effects (viscous sublayer).

When Reynolds increases, the thickness of this layer decreases. So, if the Reynolds is high enough (layer getting very thin) and the roughness gets very large (big microscopic features), there is no thin viscous layer anymore and the near wall region is dominated by the surface roughness features. This corresponds to the "Complete Turbulence" in the Moody chart (horizontal lines in the plot - independence from $$Re$$ - region to the right of the dashed line).

So, as pointed out in other comments, there are two "transitions". One is between the transitional flow and turbulent flow (just ignoring laminar for this discussion) and it occurs roughly at $$Re = 4000$$. The other occurs within the domains of the turbulent regime, and has to do with the transition between a near wall region dominated or not by viscous effects.

Note that, at $$Re = 10000$$ (your example), whether you are to the left or to the right of the dashed line, you are still in turbulent regime.

• This a very nice answer. Thank you! Commented Jul 26, 2020 at 18:54

There are actually two "transitions," one from laminar to turbulent flow, and the other from "smooth wall turbulence" to "full turbulence." So there is actually no ambiguity with regard to the transition from laminar to turbulent flow.

• But Reynolds gives Turbulent, Transitional, or Laminar correct? So if Re = 10,000 it is turbulent. Why can it be Transitional or Turbulent in the diagram? Commented Jul 21, 2020 at 17:03
• @Physther, the small "bumps" that determine relative roughness obviously influence where the flow transitions to turbulence. And note - the Moody diagram was obtained from measured data, not theory. Commented Jul 21, 2020 at 17:17
• So you are saying (taking this diagram) that at Re = 10,000 and eps/D = 10e-5 means that flow is in transition and at Re = 10,000 and eps/D = 0.05 it is fully turbulent? Commented Jul 21, 2020 at 17:24
• It's true that there are two transitions and it is very important to make a distinction between smooth and full turbulence, that's why I upvoted you. However, I can't agree that there's no ambiguity, because every person stablishes different limits haha. Actually, it depends quite much in "how much turbulence you're willing to tolerate" Commented Jul 21, 2020 at 17:48
• Transition from laminar to turbulent flow typically occurs suddenly at a critical Reynolds number in the range 2000 to 4000; it is characterized by the transition from a steady time-independent flow to a flow featuring significant transient velocity fluctuations. The change to "complete rough wall turbulence," on the other hand occurs gradually, and is characterized at the end by a constant friction factor (dog coefficient) and a wall shear stress that varies with the square of the velocity. Commented Jul 21, 2020 at 18:20