A droplet of water falling from height experiences terminal velocity. What about a case of a continuous vertical stream of water? For the purpose of discussion, I assume a continuous vertical stream of water typically has no breaks in between that might generate a water “front”.
Does it mean that the stream would not have terminal velocity whereas droplets would be very slow (relatively)?
Assume that there are no crosswinds, up/down drafts.
If the stream were to stay together it would have a higher terminal velocity because the only drag would be skin-friction drag. It won't stay together, though. It will break up into droplets.
Exactly! The tendency of a stream to break into droplets is the Plateau-Rayleigh instability, described here: https://en.wikipedia.org/wiki/Plateau–Rayleigh_instability
thanks! that is an interesting read, didn't realise a field exist just to investigate the formation of droplets. I can now see why it is so important to ink-jet printers.
Ok but hear me out, what if we model the stream as an infinite long cylinder of water with radius r, and then take the limit r-> infinity.
Throw it in a random chapter of Jackson and see if some poor sleep deprived student notices how out of place it is.
Honestly, the stream would probably fall slower. As the stream falls, sure, there is no lower pressure behind it to help slow it down, but due to the front-facing air resistance, the "bottom-most sheet" of water would be pulled back harder.
This would, over time, result in the water spreading out like an umbrella. This would probably end up worsening the fall time.
This is only if they have the same volume of water though. If they're completely different volumes, then it's a lot more complicated.
i don't that would be the case though. The "front-facing air resistance" would not be happening because it is a continuous stream (i.e. we are not referring to the initial instance when the stream first falls). And according to what u/John_Hasler said, then the only resistance will come from skin-friction drag.
For the droplets, each drop encounters a front-facing air resistance and the skin-friction drag. So it seems the droplet would have a lower terminal velocity.