Have You Ever Photographed Something You Can't Explain?

Where does the pressure difference come from? Is it the height difference between the top and bottom of the block within the density gradient of the surrounding medium? I did try to explain hot air balloon flight once in terms of the forces on the top side and bottom side of the balloon arising from the differential energy of brownian motion on the low pressure side (top) vs high pressure side (bottom). I thought it promising but it never quite seemed to make complete sense. I was left with this nagging feeling I was omitting important stuff. A friend I tried this on implied I was slightly loopy to try and explain buoyancy with kinetic theory, and recommended reading up on the works of the guy in the bath. But the Archimedes picture always seemed a bit slippery to me in the sense that while it explains what happens in a practical sense it doesn't provide the step by step causal physical explanation I'm drawn to. Normally when you explain motion it comes back to Newton, but not with ballooning and sailing for some reason. My friend said "Different layers of explanation are appropriate for different purposes", you don't explain balloons with appeals to quantum field theory. I thought that a bit of a mischaricterisation of what I was trying to do, which was simply to understand something in terms of concepts I was already comfortable with. Sadly, I don't have what it takes to work it all out from first principles myself, hence the muddled attempts.

Without them, we would all float away....

This is a lunar eclipse photo I took, using HDR. Not easy to explain at first.

Gravity.

No.

In water, there is effectively no density difference between the surface and the deepest part of the ocean.

Pressure comes from gravity pulling down on the medium and the medium having to push up with equal force to remain in static equilibrium. Think of it as the air pressure on you is the weight of all the air above you between you and space or all the water above you between you and the surface of the ocean.

Now that that's clear, the pressure is higher the lower you go because there's more weight of medium (water, air, whatever) above you. That makes the pressure at the bottom higher than at the top which is what causes buoyancy - pressure on the bottom pushes up harder than pressure on the top pushes down.

While this is not a phenomena, it is phenomenal parking.

It was really hard to explain the vertical lines in this series, but I eventually figured it out:

Thanks for trying but your explanation doesn't clarify anything to me. How does the pressure at the bottom push harder if it's an equal and opposite force? And, if liquids are incompressible and gases compressible, does that means the mechanism of buoyancy in a liquid and in air are different ie balloons don't work the same way as boats?

You're way over-thinking this and confusing the issue with non-related concepts (such as "equal and opposite" forces.

If you're at a depth of about 1 foot in the ocean, you feel the weight of the atmosphere above plus the weight of the water at that depth pushing against you. It pushes equally from every direction. So what you feel is an overall pressure against your entire body.

At a depth of twenty feet, you feel the weight of the atmosphere above plus the weight of an additional 19 feet of water pressing everywhere against you. The pressure gets higher the deeper you go and it presses in every direction.

The deeper you go, the more weight of the medium you are in pressing against you from every direction.

Liquids are almost incompressible. But that has no bearing on this situation. The mechanism of buoyancy in air and in water is similar.

Rich

Who said it's equal? Equal to what? It's equal to the weight of all the fluid above it. More fluid = more pressure.

No. Forget density. It has nothing to do with anything in this context.

Pressure is force per unit of area. Draw a horizontal square meter. Add up all the weight of the fluid above it (if air, air out to space, if water, water to the surface plus air out to space) and you will get a weight in Newtons. A Pascal (the metric unit of pressure) is a Newton per square meter. That's it.

More stuff above you (because you are deeper) = more pressure. More pressure on the same object means more force. So, there's more force at the bottom than at the top, which gives you a net upward force we call "buoyancy".

Its not the density of, e.g. water, but the hydrostatic pressure that increases with depth.

A balloon filled with air will become compressed the further down it is placed from the surface.

The same applies to the atmosphere. At ground level there's approximately 1 tonne of pressure/square foot.
A balloon filled with hydrogen will float up & expand the higher it goes.

Perhaps this explains pressure differences better :

Archimedes Principal

Hydrostatic pressure

DavidMillier, they are right. There's no difference in buoyancy mechanism in air/gas than in water/liquid. Principle is exactly the same. The only difference is in change of it with altitude/depth, because gases are compresible, liquids almost not. But this has nothing to do with buoyancy/Archimedes law itself. That difference just influences changes of buoyancy with height/depth when You move the object significantly up&down. Large scale effect, not local as buoyancy itself.
The buoyancy itself is caused by very local pressure differences within height/depth just taken by floating object. For example, when You submerge totaly in water a cylinder of of 1 m height, the pressure on the top of it will be always lesser than on its bottom surface (hope You understand why). Thus the forces caused by this pressure do not cancel each out (otherwise to the forces on the sides of the cylinder) and You have the net force directed up (buoyancy force). Archimedes law just says that this force is equal to the weight of the volume of water (or other medium we float in) equal to the volume of submerged object. You may show it mathematicaly for objects of different model size easy to calculate (like cylinder or cube). Sorry, but this is (or should have been) done in school...
So when You want to float an object neutrally, it must have in total the same density than local medium when fully submerged (the case of a submarine or a baloon), or less if not fully submerged (case of any boat/ship or a piece of wood/styrofoam on the surface of water).
Regards,
-J.

I was absolutely with you until the bolded part. That just appeared out of thin air. Why is there more force at the bottom than the top? That's my core issue.

Agreed.

Agreed.

But none of this helps.

So:
1. We have gravity exerting a downwards force on the body
2. We have gravity exerting a downwards force on any air/water above the body and this in turn pushes on the body increasing the downwards force
3. This sums to a lot of downward force. The body will sink

Then
4. We have upwards forces operating on the body that opposes the sinking of the body.
5. If the opposing forces sum to less than the total downwards forces (3. above), the body will sink, but at a slowed rate
6. If the opposing forces sum to more than the total downward forces (3. above) the body will rise.

Now to the real problem with my understanding:

The body does not have a built in rocket motor to propel it upwards.

My question, therefore is: can you provide a list of all the upward forces that act on the body and what causes them? (I presume newton 3rd law plays a part, but what else is there. Little pushes from Brownian motion perhaps?).

This doesn't explain anything to me. I appreciate all the attempts at explanation but what no one is directly grappling with is this:

For a balloon to rise it must feel a net upwards force that exceeds the downwards force of gravity on the balloon itself, and the gravity of all the air pressing down on the top of the balloon. The balloon has no rocket engine firing downwards to provide an uplift force to counter all the downward forces of gravity.

Where does all these upwards forces come from? What exactly is exerting an upwards force on the bottom of the balloon to push it upwards.

We know those upwards forces must exist else balloons wouldn't work.

What I'm looking for is both a list of those upward forces and an explanation of what causes them.

I'm 61 years old. I studied O-level physics when I was 16. I passed the exam with a grade B which suggests 45 years ago I was capable of manipulating Archimedes principle. But that is not the same as understanding something - rather it is performing a set of rote actions to answer a question.

I have, of course, forgotten the details of Archimedes in the intervening time, but no doubt I could relearn it in 15 minutes if I had to.

But this would be ignoring my problem. I don't find Archimedes a satisfactory level of explanation. It's not the done thing, but what I want to do is to translate Archimedes into an equivalent explanation using Newtonian net forces as if we we talking about accelerating and decelerating cars along a road. My brain just seems to find that level of explanation easier to grasp than comparing volumes of displaced liquid.

I absolutely believe it should be straight forward to re-cast the explanation in those terms. But so far, I haven't managed it and nor has anyone I have asked. Most of the time people reject my request completely, telling me Archimedes figured it out, be content with that. But I never will be. The rest of the time, they try but the attempt doesn't make sense. What no one has done yet it simply list out all the upwards forces and explain what causes them. I don't need a complete explanation laid out, I have grasped most of it, it is simply the list of upwards forces and their causes that is baffling me.

You said:

This bit is my issue. Forget the rest. I do not understand why the pressure on the top is always less than on the bottom surface.

What I need to understand is what the forces are that operate on the bottom pushing upwards. A list of those forces and their causes would be very welcome!

First, let's agree that the hydrostatic pressure at a point on a vessel is normal to to any surface thereon. That makes it a vector, i.e. a force of course but also having a direction.

Then let's agree that the degree of hydrostatic pressure at the point is directly proportional to the depth of the point below the surface (ignore the fluids' surface pressure which does not vary much). Now take any point on the upper surface and figure the hydrostatic pressure. Now take the "same" point on the lower surface and figure the hydrostatic pressure. The vectorial pressures will not be the same.

Assume for example a perfect sphere. Separating the vector quantities into horizontal and vertical values gives the vertical force at a point. And the difference between the two points gives the net vertical force for those two points.

Integrating the vertical force for all points gives the net vertical force acting on the sphere due to hydrostatic pressure.

If the net upward force is less than the local force due to local gravity on the sphere, it will accelerate upwards until the acceleration becomes zero due to drag and thereby makes the velocity constant.

As to the degree of force versus depth, deeper = more energy = more molecules banging against the vessel wall per unit area = mo' pressure.

This is the part that hints at an answer to my question "what are the forces acting on the bottom of the body" and "what is the cause of those forces" but it is only a hint...

Here's a website: asset.pitsco.com/c/forces-balloon.pdf This is absolutely typical of the level of explanation you find on the internet and it threatens to drive me insane.

Look at the picture. It neatly shows a downward force. It explains the cause of this force: gravity. Beautiful, clear, clean, perfect.

Then it shows an upwards force (labelled lift) with the following "explanation":

This is a complete non-explanation. There is zero explanation of why the less dense air floats on the denser air. It's an unexplained, unevidenced assertion with no mechanical justification of why this happens. You can find a thousand similar "explanations" on the web.

I want to understand one thing and one thing only, and it is proving agonisingly impossible to acquire that understanding: what are the forces that create this imaginary quantity called "lift" and what causes them?

I know for a fact it's not anti-gravity and the balloon does not have a launch booster. Those forces have to be something to do with pressure differences, something to do with the density of the air at the top and bottom of the balloon, maybe something to do with the velocity of air particles at the top and at the bottom but I seem completely unable to find any adequate description of how it actually works.

This a great frustration that I have thought about on and off for 20 years with no satisfaction. And rather fascinatingly, I find that people who claim they understand it all perfectly and it is very straight forward are no better than explaining it than my 10 year old nephew I first tasked with solving it 20 years ago. And he's an engineer now as well and he still hasn't solved it!