Bottomless Water Barrel: Observing the Falling Chasm

[joeco23]

Conceptual question that's seemingly abstract:
There is a barrel of water that is bottomless, or has an infinite amount of water in it. It is upside down and thus releasing water from rest at Earth's acceleration. The barrel is suspended in the air and there is an onlooker on the ground observing this cylindrical chasm of water hit the ground. If the barrel of water were to begin to rise and accelerate upwards an infinite distance, what would the chasm of water hitting the ground look like to the onlooker as the barrel rises over time?

 

[CWatters]

Sounds similar to the "Ball dropped from a helicopter" problem.

 

[joeco23]

Sounds similar to the "Ball dropped from a helicopter" problem.

Yes true, I was stumped however on the constant chasm of water that is observed. Is there a point where the water separates?

 

[Dale]

Is there a point where the water separates?

Due to surface tension it will start separating into drops immediately upon leaving the barrel. The size of the drops will be a balance between the surface tension trying to make drops larger and turbulence trying to break them apart.

 

[joeco23]

Due to surface tension it will start separating into drops immediately upon leaving the barrel. The size of the drops will be a balance between the surface tension trying to make drops larger and turbulence trying to break them apart.

Ok, I see now. So the increase in acceleration will eventually bring it to a chasm of infinitesimally small water molecules, like mist.

 

[Dale]

My fluid dynamics isn't strong enough to give a definite answer, but from a gut feeling perspective I would expect a terminal velocity at a point where it is falling like rain rather than drifting like mist.

 

[ogg]

You seem to assume that the Earth's atmosphere pervades all of space. Realistically, there isn't much atmosphere above 60 mi. So, gravity, temperature and pressure are NOT being held constant. And then there's your implicit assumption that there's no wind. None of these are even close to accurate. But, OTOH, I lack the fluid/aero dynamics background to answer your question. I agree with the answer already given (but it's not based on solid calculation and theory) that the water stream will become turbulent (note that it will be subject to air friction at its surface, but in free fall (except for viscous (drag) effects) in its interior) and break apart. I believe it will reach (given sufficient height) the same state as any other type of water falling from the sky: droplets (or if cold enough crystals and pellets). Of course another variable is the relative humidity (evaporation) as it falls (which will only be important for droplets with large surface to volume ratios). I should add that there are waterfalls that are pretty close to falling from a great height and turning into a mist. Is it Angel Falls in S. America? I'm not sure...

 

[bigfooted]

The Weber number is the ratio of aerodynamic forces over surface tension and it determines if the droplet will break up into smaller droplets.

$\textrm{We}=\frac{\rho V^2 D}{\sigma}$

If the droplet falls and breaks up, the Weber number decreases (the diameter as well as the terminal velocity decreases), and there will be a droplet diameter for which the Weber number is so small that it is below the breakup threshold.

 

[jbriggs444]

Due to surface tension it will start separating into drops immediately upon leaving the barrel. The size of the drops will be a balance between the surface tension trying to make drops larger and turbulence trying to break them apart.

A quick trip to Google finds https://en.wikipedia.org/wiki/Plateau–Rayleigh_instability which gives some insight into the initial breakup of the stream into drops.

Of course, this has no impact on the final equilibrium state with surface tension favoring small drops assembling into larger while turbulence favors the reverse.