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Comment by jackdawed | Hacker News Reader

I imagined it has to do with how the water coming out of a faucet is affected by gravity, and gains velocity. If you imagine two cross section slices, one near the faucet, and the other near the sink, the bottom slice is going faster than the top due to gravity. Another insight is that the amount of water (flow rate) passing through these slices remain constant. To keep the flow rate the same, it has to be narrower. If you let the water fall far enough, it would hit terminal velocity and it would not narrower any further. I looked it up and found it was called the continuity equation.

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> If you let the water fall far enough, it would hit terminal velocity

Does it ever hit terminal velocity? There is no air in front of it, just more fast falling water.

It's well known that water gains velocity until it vaporizes. I assume it vaporizes because some small flow turbulence gets strong enough to atomize it once it reaches enough speed.

The water will break apart into raindrops which fall at terminal velocity. Depending on relative humidity, they evaporate as they go, making them cool and get smaller, which lowers the weight/surface area ratio, and they get slightly slower.

Surely it depends on the diameter of the water column. For diameters much less than a rain drop, surface tension will dominate, and perhaps no column is produced (unless initially at high velocity, like water cutting?). For larger diameters air pressure will keep the column in shape at initiation. For very large diameters I am fairly sure the column would very easily exceed the terminal velocity of a rain drop. That would be a fun experiment to do from the top of a tall building!

Most of our intuition is with columns that have turbulent flow and standing waves (e.g. taps), which affect how quickly the column disperses.

A non-turbulent column of water acts very differently, see https://google.com/search?q=laminar+water+jet

I like this way of looking at the problem, I wouldn't have thought of this! I think this relies implicitly, too, on incompressibility of the fluid, no? As well as surface tension? Otherwise, we might imagine the fluid having less density at the bottom, while occupying a circular cross-section of the same area.

It does rely on incompressibility, but, to this order, does not include surface tension.

The water faucet puzzle that interested me as a student was after the water had reached the sink and begun to spread out radially from the stream. Have you noticed that there is a circular boundary where the layer of water suddenly changes depth?

> Have you noticed that there is a circular boundary where the layer of water suddenly changes depth?

I stumbled upon an explanation for this a while ago: https://en.wikipedia.org/wiki/Hydraulic_jump

google "hydraulic jump"

Separately, when you model surface tension, you get an equation for when a stream breaks up into droplets - https://en.wikipedia.org/wiki/Plateau%E2%80%93Rayleigh_insta...

You mean the hydraulic termination shock?

Something like this: http://3.bp.blogspot.com/-ryzFfMYaEV4/TZist3z0dxI/AAAAAAAAAE...

Yup.

It turns out to be more complicated than one (or than I) would think at first.

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