# Discontinuity in fluid friction as a function of Reynolds number

I have observed a discontinuity in the Fanning friction factor chart, at around Reynold's number of 2000.

I know that this is the region where laminar flow changes to turbulent flow, but a discontinuity seems rather weird to me. I could accept a non-differentiability or a sharp turn in the graph as plausible, but a discontinuity doesnt make sense to me. It seems as if a small change in Re around 2000 could result in a large change in the friction factor, which is absurd.

Am I missing something here? Any help would be appreciated.

• Please edit your question to give some background on what this graph represents and the meaning of the notation. E.g., we don't know what is meant by $\Delta P$. – Ben Crowell Jul 4 at 17:18
• @BenCrowell $\Delta P$ is change in pressure. Usually one works out a friction factor and calculates the pressure loss or drop for a given set of conditions, but for that chart the friction factor is given as the result of that expression... – user207455 Jul 4 at 17:46

## 1 Answer

The change from laminar to turbulent is called critical and can happen in the range of 1700 to 2200. That said laminar flows have been achieved above 2200 but can be very unstable (the slightest disturbance causing the change).

The critical region can be very difficult to deal with as the conditions can change rapidly, which is why the diagram shows that discontinuity.

If the flow is laminar and staying laminar then the conditions can be calculated ie a friction factor of 64/Re etc

If the flow is turbulent and staying there, again the conditions can be calculated, with various expressions available Colebrook-White etc

• Ahh, so basically a steady-laminar and a steady-turbulent states approach different friction factor values for the same Reynold's number, is that correct? – Pritt Balagopal Jul 4 at 14:05