okay, so i’ve been meaning to post this for a while. and i just read the helium balloons and negative weight thread, so i am a man on a mission.
the question is this- what is pushing the balloon up? i understand about densities and all, but by what mechanism is the balloon thrust upward? what in blazes is doing the pushing?
the same force that keeps a ship afloat: the pressure of the fluid which is denser. The tiny molecules keep bumping into the object and pushing it.
I’ve answered this one before on the SDMB.
The force that pushes the balloon up is really the pressure gradient that the gravitational field induces. In other words, because gravity is pulling on the air, the weight of the air on top causes the pressure to increase the closer to the ground you get. It’s a hydrostatic pressue, meaning that it is equal in all directions at any one point.
Place your balloon in this, and assume for the sake of simplicity that t is perfectly spherical. The force due to pressure is directed orthogonal to the surface, s it’s pointing towards the center of the balloon everywhere. If here is no pressure gradient – on the Space Shuttle in orbit, for instance – then all of these forces cancel out and the balloon doesn’t move. Even though you have density differences between the helium-filled balloon and the normal air outside.
Here on earth, however, the air at the bottom pushes up harder than the air at the top presses down, because the pressure is greater at the bottom. So the balloon goes up. This really is the same as saying that because the density in the baloon is less, the balloon goes up. But in THIS explanation it’s easier to see where the upward force comes from that makes the balloon go up.
Finally, the cute thing about the situation as I’ve sketched it is that you can actually solve the problem. Assume that there is a linear pressure gradient from top to bottom (not a bad approximation to the exponentially-varying gradient over the size of the baloon) and integrate the forces over the surface of the balloon by resolving the inward-directed force vectors into vertical and radial cmponents, integrated over the srface of a spherical balloon.
The three major forces that act on the balloon are: gravity pulling it down, air pressure pushing down on the top surface of the balloon, and air pressure pushing up on the bottom surface of the balloon. If you add up those and the net force is upward, the balloon goes up. If the net force is downwards, it goes down.
Now, of these, the upward and downward pressures are only dependent on the size of the object and the air pressure. You would think they would cancel out completely, right? But the top surface of the object is at a higher altitude, where air is slightly less dense. Therefore the downward pressure is slightly smaller than the upward pressure. So if the weight of the object is equal to the difference in upward and downward pressures, it will just float there without going up or down. For this to happen, how dense does the material have to be? Well, air doesn’t go up or down, so it must be that anything with the same density as air will stay there. Anything denser than air (say, a brick) falls down, and anything less dense than air (like a helium balloon) will go up.
Don’t get me wrong, I’m not disputing just astounded.
You mean to say that there’s enough of a pressure gradient between the top and bottom of a small helium-filled balloon to cause it to rise? That’s amazing. What kind of numbers are we talking here? What is the pressure difference over, say, a 10 cm balloon?
I think the pressure gradient idea is a bit off base. Those differencs are imperceptable at the scale we’re talking about. It has impact on the altitude that the balloon may be neutrally bouyant but it isn’t the force that causes it to float.
It’s displacement. Use a tub full of water as a more quantifiable analogy. Your toy battle ship will displace a volume of water equal to its weight, pushing the level of water in the tub up slightly. Add some lead shot to the bilges of the ship and it will displace more water, raising the level in the tub more. The ocean of air we call the atmosphere isn’t all that different.
it seems like it’ll simplify matters. if i take my toy boat (watertight and hollow) and pull it down to the bottom of the tub, what PHYSICALLY is transmitting that force that pushes the boat up? where does it act, on the top, the bottom, inside or out?
it’s late and I was getting a little punchy so I cracked my college physics book and I was wrong about the pressure gradient thing. Sorry for shooting off my mouth.
OK, JB…here it comes. Your toy boat, watertight and full of air displaces an amount of water equal to it’s weight. If it weighs less than an equivalent volume of water (because it is full of air), it rises. Archimede’s principle is at work here. If you like, I will drag out my PADI instructor manual and give you the formulas for calculating bouyancy. Not tonight though, please. I am getting tired.
However, this same principle applies to balloons (and lungs), both in the water and in the air. If you descend to 33’underwater, fill a balloon with air and release it, it will explode before it gets to the surface. So will your lungs if you do not exhale during the ascent phase of the dive.
“Plan your dive and dive your plan”.
Even better, try this. It is well known that objects tend to be forced to the outside of the curve as a car rounds a corner. Put a helium balloon in the car. It will move to the inside of the curve. The air inside the car moves to the outside of the curve, as usual, which means that the lighter balloon will be displaced to the inside of the curve.
Well, the pressure difference across a 10cm height difference is created by the weight of a 10cm column of air. Air weighs about 0.001 gram/cm[sup]3[/sup]. A 10-cm thick layer of air weighs 0.01 gram/cm[sup]2[/sup]. Or about 0.002 oz per square inch. So if you had a 10x10x10cm (4x4x4 inch) cube, the force on it due to the pressure gradient (a.k.a. buoyant force) is 1 gram, or 0.04 oz. Not much, but a 10x10x10cm helium balloon weighs less than 1 gram, so it goes up.
Yes I know gram is a unit of mass and not weight/force, but you know what I mean…
There has been a lot of amazement expressed that the pressure difference can be so large from the top of a balloon to the bottom of a balloon–I guess folks are thinking of the great variations in air pressure due to weather and wind and the like.
But wait, a draft in a room can push a helium balloon around. The balloon reacts just to its local environment, the air immediately around it.
What is the pressure difference from the top of the balloon to the bottom of the balloon? It’s due to the weight of the air that would be the same size as the balloon! Since the helium balloon weighs less, it goes up.
Calmeacham is right on, padeye is mistaken. Padeye, think about it, there is no other explanation
It is the pressure gradient that causes a net force. If you had a room not subject to gravity and filled with air at any pressure, a body suspended in mid air would not move regardless of its density precisely because the pressure is exactly equal in all directions.
As has been pointed out the pressure difference can be caused by gravity or by acceleration (like in a car) which need not be vertical.
yeah, but what the HELL is moving the balloon? if i were that balloon, would i feel an ever so slight breeze pressing against my bottom? what is transmitting the force? or rather, by what mechanism is that force traveled?
perhaps pretend we are all newtonians and explain it ala billiard balls.
Um, OK. What the HELL is moving the balloon is the fact that there is more pressure on the bottom than on the top. If you understand what pressure is (i.e. a force applied over an area) then you’ll see that the force is proportional to the area pushed upon. Where does the pressure come from? From air molecules bouncing off the balloon. There are slightly more molecules hitting the bottom of the balloon than there are hitting the top.
Since there is pressure on the top of the balloon, and on all sides, you need to do a bunch of math to figure out the exact amount (and as described above it reduces to the weight of the fluid displaced), but the simple answer is there is more pushing up on the balloon than is pushing down on the balloon.
If you are a newtonian, whatever that is, and want to see a bunch of billiard balls, OK. Imagine a gazillion billiard balls bouncing around in a room. Now imaging you have put a ‘balloon’ of some size much greater than a billiard ball in that room. What you would see if the balls correspond to air molecules is that there is a very slightly larger number of billiard balls hitting the bottom of the balloon than are hitting the top of the balloon. The balls bouncing off the balloon tend to make it move up. It is up to the balloon’s weight to determine if it moves up or down.
It’s like earthball, if you’ve ever seen that game. A gazillion people get under a 10 foot wide ball and try to move it around - if there are slightly more people pushing it in one direction, that’s the way it goes. If you add some kind of gravity to earthball, say by playing it on a hill, then you’d need a larger difference of people to make the ball go up, and you could make the ball go down with a minority of the people.
Did this help at all?
douglips, thank you for explaining.
one more quick question- the closer to the surface of the earth one gets, the thicker (more dense) the air is, correct? so there are more molecules to press against the bottom then at the top, and the molecules are moving every which way so some of them happen to bounce against the balloon. since there is statistically more contact on the bottom, the balloon gets pushed up?
danke schoen, all of you.
You got it. Give that man a cigar!
moderator, please close this thread. to all who contributed, much obliged.
why close it? what if someone feels they have something to add?
mainly so my delicate psyche doesn’t get bombarded with “Geez I’m dumb” more than absolutely necessary.
but on the other hand, keep the damn thing open.
on a related topic (see title of thread) here’s another force which bothers me. magnetism
when i put two magnets near eachother, north to south, they jump together. what in blazes did the moving (and please don’t say ‘magnetism’)