Bottomless Water Barrel: Observing the Falling Chasm

• joeco23
In summary, the conversation discusses the hypothetical scenario of an infinite barrel of water accelerating upward and the resulting chasm of water hitting the ground. The onlooker questions the behavior of the water and the experts mention factors such as surface tension, turbulence, and air friction that would cause the water to break into droplets. The Weber number is also mentioned as a determining factor in the size and behavior of the droplets.
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?

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

CWatters said:
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?

joeco23 said:
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.

Dale said:
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.

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.

jbriggs444
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...

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.

Dale
Dale said:
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.

Dale

1. How does the bottomless water barrel work?

The bottomless water barrel is a scientific demonstration that relies on the principles of air pressure and gravity. The barrel is filled with water, and when the bottom is opened, the water does not fall out. This is because the air pressure inside the barrel is equal to the air pressure outside, creating a balance that keeps the water in the barrel. However, when the barrel is tilted and the bottom is opened, the air pressure inside decreases, causing the water to flow out due to gravity.

2. What is the purpose of observing the falling chasm in this experiment?

The falling chasm in this experiment serves as a visual representation of the effects of air pressure and gravity. By observing the water falling out of the bottomless water barrel, we can better understand these scientific principles and their impact on everyday objects.

3. Can the bottomless water barrel be used for practical purposes?

While the bottomless water barrel may seem like a fun experiment, it does not have any practical applications. It is simply a demonstration of scientific principles and is not designed for everyday use.

4. How can the bottomless water barrel be modified to change the duration of the falling chasm?

The duration of the falling chasm can be modified by changing the size and shape of the barrel, as well as the amount of water inside. A smaller barrel or less water will result in a shorter falling chasm, while a larger barrel or more water will result in a longer falling chasm.

5. Are there any safety precautions to keep in mind when conducting this experiment?

Yes, it is important to take safety precautions when conducting this experiment. The falling chasm can create a slippery surface, so make sure to perform the experiment in a safe and open area. Also, be careful when handling the barrel and avoid tilting it too quickly to prevent any spills or accidents.

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