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BigDon
2015-Jul-17, 07:21 PM
Take two thick balloons.

Fill one with air and one with hydrogen to the same PSI at sea level.

Drag both 100 meters underwater and let them go.

Would the hydrogen balloon reach the surface first?

grapes
2015-Jul-17, 08:51 PM
What's that? 10 atmospheres?

The hydrogen balloon is lighter, so more buoyant.

Jeff Root
2015-Jul-17, 09:18 PM
No question that the hydrogen balloon is lighter, more buoyant,
has more lift, and rises faster than the air-filled balloon.

But I'm flabbergasted to realize yet again that I can't explain
why a hydrogen-filled balloon rises. I know it is a result of the
air or water around the balloon being fluid, and being denser
and heavier than the balloon and its contents, and thus falling
around the balloon. But how does that push the balloon up?
Why is the force of the surrounding medium pushing up on the
bottom of the balloon greater than the force of the surrounding
medium pushing down on the top of the balloon? Are balloons
pushed up just by the very, very, very tiny difference between
the column depth of the air or water on the bottom versus the
top of the balloon? If so, that is astonishing. I wouldn't expect
to ever see an instrument sensitive enough to detect such a tiny
difference in pressure for the size of an ordinary balloon, yet we
can all easily feel and see the upward tug of such balloons.

Is it just the difference in pressure on the outside of the bottom
of the balloon versus that on the top?

What about a balloon with a flat bottom that air or water can't
get under? I'm certain it still tries to rise.

-- Jeff, in Minneapolis

Trebuchet
2015-Jul-17, 10:09 PM
Take two thick balloons.

Fill one with air and one with hydrogen to the same PSI at sea level.

Drag both 100 meters underwater and let them go.

Would the hydrogen balloon reach the surface first?

My guess is that they'd both reach the bottom at about the same time, having been crushed to the point of bursting. Unless the material they are made of floats, in which case they'll reach the surface together.

Jeff Root
2015-Jul-17, 10:33 PM
They have to reach the bottom at the same time since they
are both tied to Don's ears.

They can't be crushed to the point of bursting unless they're
made of completely inappropriate materials. Ordinary rubber
or mylar balloons would work fine. Lead balloons might be
crushed and might not re-expand.

-- Jeff, in Minneapolis

Trebuchet
2015-Jul-17, 11:21 PM
But it's 10 atmospheres of pressure! They can't withstand that! Unless it's the same pressure inside and out.... d'oh! :doh:

The hydrogen MIGHT have more of a tendency to leak out, however.

swampyankee
2015-Jul-17, 11:24 PM
....
Is it just the difference in pressure on the outside of the bottom
of the balloon versus that on the top?

Yes.

What about a balloon with a flat bottom that air or water can't
get under? I'm certain it still tries to rise.

-- Jeff, in Minneapolis

That's how a suction cup works.

Ken G
2015-Jul-17, 11:52 PM
Yes, what you are feeling when you feel the tug of a helium balloon is the weight of the air that would fill a balloon. It doesn't seem like air would weigh that much, but think of how much a balloon filled with water would weigh-- air weighs 1/1000 that amount, it's enough to feel.

VQkr
2015-Jul-18, 12:34 AM
100m = ~1 MPa = ~10 atmospheres. We assume that the balloons remain spherical throughout the ordeal, and that their "thick" wall does not contribute significantly to their strength or volume, or mass. Let's assume each balloon has a volume of 1m3 at the surface (1 atmosphere). The compressibility of air stays within 1% of that of an ideal gas all the way up to ~150 atmospheres, so it should be a pretty good assumption to assume both balloons are filled with an ideal gas. Since water is a good conductor of heat, we also assume isothermal conditions - the gas in the balloons will warm up when brought to depth and cool as it expands again, but the heat will flow in and out of the surrounding water to keep the gas at a constant temperature.

At 100 m, they will be compressed by 10 atmospheres of water plus the 1 atmosphere of air. As an ideal gas they will both be at 9.1% of their 1-atm volume, or 91 L. Because both gasses are equally compressible, the balloons will displace the same volume and have the same shape at depth. This means they will have the same drag coefficient. 1m3 of air at STP has a mass of 1.29 kg, while hydrogen has a mass of 0.0899 kg. Since mass is conserved, the balloons will have the same mass at depth. As we noted above, they will displace 0.091 m3 of water at depth - 91 kg of water. The gross buoyant force on each balloon is the mass of water displaced * g = 893 N. The net buoyant force is the gross force minus the balloon's weight (which is 12.7 N for the air balloon and 0.882 N for the hydrogen balloon). So the net force for air is 880 N, and the net force for hydrogen is 892 N - a 1% difference.

Now, does it matter? The "at depth" radii of our 91 L balloons is about 0.28 m; cross sectional area is about 0.25 m2. Plugging these values into the drag force equation solved for velocity, \mu = \sqrt{(Fd*2/A/\rho/Cd)}, and using the spherical drag coefficient (0.47) we get a terminal velocity of \sqrt{(880*2/0.25/1000/0.47)} = 3.87 m/s for air and \sqrt{(892*2/0.25/1000/0.47)} = 3.90 m/s for hydrogen. If these rates were constant over 100 m the difference in time would be about 0.2 s, but the volume, buoyant force, and cross sectional area all increase as the balloons rise. I will let someone else jump in to integrate the terminal balloon velocity over the rise from 100 m to the surface, but I suspect the result will remain that the difference in time to reach the surface is insignificant.

grapes
2015-Jul-18, 03:36 AM
At 100 m, they will be compressed by 10 atmospheres of water plus the 1 atmosphere of air. As an ideal gas they will both be at 9.1% of their 1-atm volume, or 91 L.

Plus? The pressure at that depth is 10 atm, the air in the balloon is not going to change that! :)

Robert Tulip
2015-Jul-18, 03:50 AM
Plus? The pressure at that depth is 10 atm, the air in the balloon is not going to change that! :)

The plus means the balloon containing a unit of air at the surface gains one atmosphere of pressure for every ten metres of depth, so at 100m has pressure of 11 atm, meaning it is one eleventh of its surface volume.

VQkr
2015-Jul-18, 06:17 AM
Plus? The pressure at that depth is 10 atm, the air in the balloon is not going to change that! :)

The atmosphere pushing on the surface of the water does contribute to the total force on the balloon. The ideal gas equation requires use of absolute pressure and temperature scales.

grapes
2015-Jul-18, 11:33 AM
The plus means the balloon containing a unit of air at the surface gains one atmosphere of pressure for every ten metres of depth, so at 100m has pressure of 11 atm, meaning it is one eleventh of its surface volume.
Doh!

Carry on :)

profloater
2015-Jul-18, 05:34 PM
The buoyancy is explained thus, the air or gas in the balloon is at constant pressure whereas the pressure in the water is greater at the bottom of the balloon due to the column of water height in a liquid. So whatever shape the balloon takes the pressure at the bottom is always greater than the top so the balloon rises. The difference in pressure is then represented by tension forces in the skin of the balloon on its top side. These could indeed burst the balloon but remain constant with depth except for the balloon shape changing.

Jeff Root
2015-Jul-19, 03:14 AM
Are you saying that the pressure is the same throughout the
balloon, even though the pressure on the balloon from outside
varies enough from the bottom to the top to push it upward?

If so, wouldn't that only be true of a superpressure balloon?
(A superpressure balloon is one so full that adding any more
gas increases the internal pressure. It is a balloon that is
not limp and resists further increase in volume.)

If the balloon is less than completely full, I would expect the
pressure inside the balloon to match the pressure outside.
Specifically, to have the same gradient from bottom to top.

-- Jeff, in Minneapolis

VQkr
2015-Jul-19, 07:54 AM
Ignoring the weight of the gas in the balloon on the gas below it, the pressure in the balloon is constant with height. Since there is a net force on the balloon from the hydraulic differential, one of three things (or a combination) happens:

1. The balloon accelerates upwards. The buoyant force is balanced per f=m*a.
2. An external force (ie a string) holds the balloon still.
3. The balloon is moving at constant velocity upwards, and the drag force force balances the buoyant force (terminal velocity).

For a thin-walled balloon that can resist force only in tension, any case involving 2 or 3 pushes the balloon out of a spherical shape. In all cases the internal pressure is nearly constant at all points in the balloon (technically, again the weight of the gas and in case 1 the acceleration of the gas cause a slight pressure differential).

Ken G
2015-Jul-19, 02:26 PM
Yes that's true, if we give the balloon, or some other form of surface tension, the power to keep the air bubble from elongating vertically, then the air pressure in the bubble must be nearly constant. So the surface tension would need to support pressure differences between the air and water that are on the scale of the weight of the displaced water. Note this also means that the air pressure is higher than the surrounding water pressure by the scale of the pressure difference in the water over that height. This also means the shape of the balloon should be rather domelike, because the water pressure at the top of the balloon needs help from the balloon tension to balance the air pressure, but the water pressure at the bottom of the balloon does not.

BigDon
2015-Jul-24, 04:11 PM
You know, I do occasionally feel like Mickey in the Sorcerer's Apprentice when I ask a question and the discussion spins out of my level of education.

:)

Ken G
2015-Jul-24, 06:24 PM
It's just hard without pictures with little arrows and all that jazz!

profloater
2015-Jul-24, 09:53 PM
If the ballon were perfectly elastic it would have to flatten to a pancake horizontally to resolve the pressure effect. Or it can accelerate upwards as mentioned.

A moving balloon or bubble causes pressure changes because of velocity of the fluid to let it pass and these must affect the shape too.

A rigid ballon of course rises due to the same pressure difference caused by the height of the water column. It's skin suffers compressive loads to resist the pressure forces, greater on the bottom.