Reader Questions

Reader Question: Faucet Physics

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jessecaps-blog-deactivated20170 asks:

With respect to the laminar/turbulent flow in the faucet, at the end he explains that the diameter is smaller inside the valve compared to the nozzle and therefore the velocity is greater and turbulence is achieved there before it leaves the nozzle. But turbulence is characterized by the Reynolds number not the velocity, so a larger velocity with a smaller diameter will yield the same Reynolds number, why would we expect turbulence in the nozzle before the stream?

ETA: As pointed out in the comments, I made a very silly mistake when calculating the Reynolds number last night. While most of what I say below is still true in general, it’s not in the case in the faucet, and so I’ve edited the entry to reflect that.

Great question! A quick control volume analysis of an incompressible fluid shows that, while the flow speed is higher through the faucet’s valve, the Reynolds number (based on diameter) at the valve is the same as higher than the Reynolds number at the nozzle by a factor of (nozzle diameter)/(valve diameter). Thus transition can occur at the valve before the nozzle. A word of caution, though: although we often use Reynolds number as a method of characterizing when a flow becomes turbulent, it is not a hard and fast rule.

As undergraduates we learn that pipe flow transitions to turbulence at a Reynolds number of 2,300 based on the pipe’s diameter. However, under the right laboratory conditions, it’s possible to maintain laminar flow in a pipe to a Reynolds number an order of magnitude larger. (#) It all depends on the initial conditions of the flow and the influence of factors like surface roughness. What this means in the case of the faucet is that the same Reynolds number (based on diameter) may not correctly indicate whether the flow is laminar or turbulent at a given point.

Now, while it may be possible that the contraction at the valve introduces some small turbulence that decays prior to the flow’s exit from the nozzle, that does not seem overly likely to me. Even though, by Reynolds number, transition can occur at the valve before the nozzle, I suspect most of the sound we hear comes from the increased flow rate caused by turning the faucet. It may also be that the sound is associated with the onset of turbulence at the valve but the turbulence is still slight enough that we do not notice it by eye in the external flow.

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