funny balloon thought experiment

Q_Goest

Empty space? If it's empty, it's vacuum. But a vacuum can't be in equilibrium with water, it will boil. For the case of a liquid that can't boil, that's a slightly different issue. It doesn't really matter as long as the surface of the water doesn't boil.

Regardless; let's change the liquid for the sake of discussion. I think this should help shed some light on things.

Thus far we’ve discussed water which has some vapor pressure at ambient temperature that’s well above a perfect vacuum. It’s around 0.3 to 0.4 psia at 70 F.

What if we used a liquid that could not convert to a gas? Vacuum pump oils for example are highly refined, long chain hydrocarbons with a vapor pressure in the micron range. For the sake of argument, let’s just consider a hypothetical liquid such as hypothetical vacuum pump oil that does not boil/does not vaporize at any low pressure. We'll aslo hypothesize that this liquid is completely incompressible so it rules out any bulk modulus affects. I think these affects are probably getting in the way of understanding what's going on anyway, so let's just ignore them.

For our experiment, we use the balloon and this non-boiling liquid. Let’s start at atmospheric pressure at the upper surface, say 15 psia for the sake of argument, and the balloon is at the top of the container. Let’s also assume the liquid is roughly the same as water, so for every 2 feet of head we get 1 psi. So 30 feet down in this liquid, the pressure is 30 psia (ie: rho*g*h +P_s where P_s is the pressure at the surface = 15 psia at the surface, plus 15 psi head).

As we pull the balloon down 2 feet, we might think the balloon shrinks due to increased head. But if it did, we’d need to come up with that volume somewhere else in our system (ie: We may think there's an additional volume = V_v (vacuum volume)).

-> If a vacuum space formed above the liquid, and assuming Bernoulli’s still holds (which it does) then the surface pressure would be 0 psia, so the pressure 2 feet down (per rho*g*h + P_s where P_s =0 for vacuum) would be only 1 psia. But the balloon had 15 psia in it to begin with, hence it won’t be at 1 psia if it shrinks. Pressure has to be greater than 15 psia and the conclusion is it hasn’t shrunk.

In other words, if the surface pressure drops instantly from 15 psia to 0 psia, because there's a vacuum there, we have a sudden change in pressure ALL THE WAY DOWN to the bottom of the container.

So we are left with the balloon not shrinking and not expanding. We are left with the surface pressure decreasing by 1 psi, not suddenly going into vacuum. There is no sudden step change in pressure at the upper surface.

When the balloon gets down to 30 feet, the pressure at the top of the column finally reaches 0 psia (rho*g*h = 15 psi). At this point, a vacuum just starts to form, and the pressure 30 feet down is only 15 psia instead of the 30 psia originally. Everything is still in equilibrium, and the balloon hasn't changed volume yet.

As the balloon goes deeper, a vacuum space finally begins to form above the liquid as the depth of the balloon goes down more than 30 feet and pressure in the balloon exceeds 15 psia. Now, as the balloon goes deeper and contracts, the volume that it decreases by can be made up by the volume of the vacuum at the top of the container.

What everyone is missing is the Bernoulli equation for a static column of liquid, P(at some point below the surface) = P_s + rho*g*h

Doc Al

I agree 100%! In fact I started to make the same point--somewhat obliquely--in post #55. (All the talk about vapor formation must have obscured the issue.) The first thing that happens as the balloon lowers is that the overpressure (the 1 atmosphere at the top of the water) must be reduced throughout the fluid. As I was imagining the balloon being lowered 1000 m, that bit was minimized in my mind as it was resolved in the first 10 m.

So I think we agree after all. And thanks for your patience and clarification. (Whew!)

belliott4488

Okay, that was a pretty good set-up - well thought-through - but I see a critical step where I think your reasoning goes astray. Not surprisingly, it's right where you say "the surface pressure drops instantly from 15 psia to 0 psia". Discontinuous changes like that are usually a sign that something needs be looked at carefully, in case you're side-stepping a process that must be considered in more detail (sometimes it's okay, and the change is just due to a simplifying assumption that does not affect the issue being investigated).

First, where does the 15 psi pressure come from at the start? We might consider that there's a tiny amount of gas at this pressure above the fluid (I know you didn't, but just bear with me for a moment). In that case, it's clear what happens when the balloon is drawn down - the level of the fluid drops, causing the volume of the tiny amount of gas to increase, its pressure decreases, Bernoulli applies, and the rest is as you've described. The final state is such that the pressure of the tiny amount of gas has been reduced to whatever value is necessary to balance all the equations.

Now, what if there is no gas at all, other than what's inside the balloon, as I believe you had in mind? Well, if there is 15 psi of pressure on the surface of the fluid, the only thing that can be exerting this pressure is the top of the container where it contacts the fluid. It cannot exert such a pressure unless it is less than perfectly rigid, which means that as the balloon is lowered and the level of the surface of the fluid drops, the top of the container will flex downward, exerting less pressure (think of it as an extremely stiff spring). It will do this until it reaches its mechanical equilibrium point, i.e. it is exerting zero pressure, after which time the vacuum appears.

This might seem like an unnecessarily arcane detail - we don't usually worry about the sides of a sealed vessel flexing - but if you insist that there was 15 psi on the surface of the fluid at the start, then I believe you must take this into consideration.

Doc Al

The way I see it is that the pressure applied by the top (and sides) of the container compresses the water ever so slightly. But the assumptions that the container is rigid and the water is incompressible mean that the change in volume is microscopic and can be ignored. So "for all practical purposes" the water level (and balloon volume) won't change until that top pressure is reduced to zero. (It doesn't happen instantly.)

Q_Goest

An air bubble or gasseous volume of any sort is not needed at the top of the container. Consider for example, a perfectly rigid container filled with a perfectly incompressible liquid. Now we put this 15 psia balloon in, just under the surface and cap it so there's no air or gas of any kind inside. What's creating the 15 psia at the surface? Well, the balloon is! If we imagine taking out 1 molecule of liquid, the balloon volume increases by some infintesimal amount along with a corresponding infintesimal decrease in pressure. The entire system is completely stable for minor changes in the container's volume. There's no need to hypothesize about an extremely stiff spring. We can make the container infinitly rigid and the liquid infinitely incompressible. There's no details here that need clarification because of the rigidity of the container nor the incompressibility of the liquid. The balloon's ability to accomodate small changes in volume can account for that. As the balloon is pushed down, the pressure at the upper surface changes gradually because the balloon's volume is able to take up any hypothesized miniscule variations in pressure at the upper surface.

Phrak

A very interesting phenomena. It would be nice to see a simple experimental arrangement As a ballon in a sealed, constant volume container is pulled downward, the pressure in the ballon remains nominally constant and the pressure of the container drops.

As long as the pressure at the top of the container remains above vapor pressure, is this correct by you, Q Goest?

Phrak

Nice probelm Physical1, to keep so many (myself included) scratching their heads!

The result is very counterintuitive. How could a little bubble pushed to the bottom of a container cause a large change in pressure?

It might be more intuitive to consider the following. You have a large rigid container 32 feet deep. It's filled with pure water and caped, without any air, at one atmosphere of pressure. Someone kicks the container loosening a bubble loose from a crack in the bottom. It rises, but doesn't significantly expand. The pressure rises to twice atmospheric pressure to keep the bubble at it's original volume. I find this scenario more fathomable.

Very small bubbles shouldn't have the same effect, due to the compressibility of water and expansion of the container.

Q_Goest

Yes, that's correct. There are other phenomena that will affect this however, such as disolved gas and the liquid's bulk modulus, but what you're saying here is essentially correct.

Q_Goest

Very nice! You're quite right, the bubble at the bottom of an incompressible liquid inside an infinitely rigid container rises in that container at a constant volume. Regardless of how high the container is (it can be infinitely tall) then assuming there's no vacuum space at the top of the container, the bubble will not increase in volume as it rises.

Phrak

Somebody oughta tell Cyrus. He left on an early flight.

Dadface

So let us now consider the dissolved gases, the bulk modulus, the hysteresis properties of the rubber,the speed of descent, etc etc.Just kidding.

pallidin

So, a bowling ball dropped into a swimming pool will cause the water level to rise.

However, is the water-level rise slightly less when the bowling-ball is just 1-ft underneath the surface versus the ball being at, say, 12-ft underneath the surface?

physical1

I would start out with a system under 34 feet so I can build something on my stairways in my first home I just got (mortgage free, baby!). Well I may be able to make a system over 34 feet by going out windows with some tubes or pipes.

It is interesting to consider systems 500, 1000, or even 10,000 metres high too, even if the experiment can not be done right away - it would be nice to predict what would happen in those cases.

If water started boiling then it will also take up lots of space - causing... the balloon to collapse even more, and maybe even causing a sterling engine to spin since water needs to extract something in order to boil and gain that molecular movement.......

Ultimately what would be interesting is if someone, maybe even myself, could invent a device based on this experiment.

I suspect I was having troubles getting water to boil in a syringe due to lacking a trigger air bubble or a mineral/impurity. I have now read that to get water boiling in a syringe, one needs to snap back the syringe and let things move around a bit, or let a dissolved air bubble pop out of place. Maybe water can therefore be "super steam" before it boils, similar how water can be super cooled and not turn into ice!

I got reading about how water surface actually has a sort of vapor existing above it (water liquid is therefore not just a liquid, to be anal retentive about it - it is a bit both a gas and a liquid in liquid state - therefore it is not a binary 0 or 1). Then I started looking into mercury barometers and they refreshed my memory that in fact even mercury has vapor sitting above it. I can see why some of the quacks are worried about mercury fillings in teeth so much.

I am going to try the balloon experiment with some simple materials. From the day I thought this up, I had planned to take a trip to the dollar store and purchase the materials required.

Some other simpler experiments I have done in the mean time:

1. fill up a 2 litre plastic p.e.t. pop bottle with water
2. squeeze pop bottle and let some water go out the top. Hold the squeeze still.
3. put hand palm tightly on the bottle opening, sealing it off
4. release the "squeeze"
5. bottle stays deformed in the squeezed state

Why wouldn't there be a vacuum space at the top of the container that is formed. Because the bottle "gives way" first before the vacuum space even has a chance to form. The vacuum is transmitted throughout the bottle, and takes the least path of resistance - which is holding the most flexible part of the bottle in deformed imploded state. If there was a balloon in the bottle, I suspect it would latch on to the balloon and pull it. Actually, this is all incorrect technically - since vacuum does not "suck". But you understand what I mean - suction is just an abstraction anyway. (Actually I could try and educate housewives that vacuums do not suck up dirt... forget it ;-) first I need to find one to prey on)

That is why I had trouble seeing how a balloon would just collapse under hydrostatic pressure in a sealed system - because the balloon can expand and contract according to how much vacuum is in the entire system. I think the balloon would more easily expand back to its original size than say a vacuum space being created of vapor/nothing. Why? For the same reason that a plastic pop bottle deforms under vacuum. So the balloon, to me just couldn't change size due to battling itself. I could be wrong and I am not happy until the experiments are completed!

What if we considered the balloon as "part of the container". I.e. consider it an "easily deformable portion of the container", similar to how a p.e.t. plastic bottle is deformable under vacuum. Different way of thinking about it. In the p.e.t pop bottle the container gives way fairly easily to any sort of vacuum. A balloon is even more sensitive and gives way easily.

Is it a matter of a fight for the path of least resistance. In a non rigid container, pop bottle "gives way" easier than water vaporizes/boils into a vacuum. In a rigid container a balloon trapped inside does what? Similar? Is the intra molecular bond strength quite strong, more strong than another path of lesser resistance (deforming something sitting in the container.. and if we can transmit throughout the container according to Pascal, what gives way first?)

Honestly, I am about to stop making any more hypothesis(es). I have had enough! I must experiment now. Experiments to me are a generally a waste of time. I would much prefer to have it done in the mind. But in this experiment the mind only seems to lie, cheat, and mislead. Begin the experiments ASAP.

I try to add some humor to my posts so I do not come off as a total jerk. Sorry for any flames/heat that this post has caused. Cheers to your p.e.t. pop and sparkling water bottles. Bonk!

physical1

If one places a turbine in the system, then he could extract power from the change of pressure? How does a conservation of energy apply? Something cools down? Temperature? Stealing energy from the atmosphere with the help of gravity, giving Tesla a big spin in his grave?

Disprove what I say - I encourage it.

It takes energy to push the balloon down - but sorry folks - I have a valve in mind. A valve can switch the hydrostatic pressure off and on, controlling the "height" of the system immediately. The balloon does not need to be drawn down with energy. It can be placed at a low level, and the water above it can be connected to this lower level container through a valve. The valve lets massive amounts of hydrostatic pressure be applied to the balloon immediately on an instant. To "recharge" the depressurized water, one might open the container to the atmosphere. The valve that connects to the lower portion of the system where the balloon is sitting is closed off before recharging. This isolates the balloon area from the recharging portion of the container: the upper water (hundreds of litres).

When recharging the low pressure water, the atmosphere pressure finds its way into a low pressure zone. Water and atmosphere find equilibrium. The upper portion container is sealed after recharging, and the valve is opened again to let the hydrostatics contact the balloon in the lower portion of the system.

The balloon is tied on a short string to a weight, to not float up, yet exposing its edges to hydrostatic pressure as much as possible. (does a balloon have edges? hehehe)

Above could be missing some important science that causes this system to fail, form icicles and frost, overheat, or simply "not work at all". On the other hand, refridgerators, heaters, pressure driven turbines, weather changing tools, and an endless amount of items for humanity could be created if this has any potential at all (a few puns on potential here).

Pressure is stolen from atmosphere potential? Any temperature changes or environmental effects?

Tesla where are you? Roll 3 times if you heard me, and get a few humans to prove me wrong please.

Cyrus

I'll read through Q_Goest's reply when I get some time later in the week or two.

physical1

What makes nature choose the container to become lower pressure, and not the balloon become higher pressure? Does pressure naturally want to decrease rather than increase?

For the balloon to become higher pressure in the constant volume, it would have to become hotter. Does nature not heat balloon because heat would have to be added by some external source, and cannot be just extracted spontaneously from the surrounding water? Does it not have any reason to want to heat up, or it simply can't due to thermodynamics laws?

The high pressure water molecules are ramming against the balloon which is transmitting through rubber, which rams against the air molecules. Are the air molecules affected at all by this ramming of water molecules against the balloon shell.

EEstudentNAU

Could you draw a diagram of this?