• Members 514 posts
    June 5, 2023, 6:37 a.m.

    I may be writing about pressure gradient but if so, only by accident. It's quite clear the "Greg" piece is about a density gradient. The whole argument rests on the idea that there is a density gradient present and the consequences of that is that there are more molecules at the bottom of the balloon than at the top and the consequence of that is even if each molecule hits the balloon with exactly the same force irrespective of its position, the the overall effect is more forces applied at the bottom than the top.

    My intuition today is that this can't be right. And many people over the years have queued up to say it isn't right. But I'm not sure why it isn't right, it sounds right, but none of them so far has gone beyond "that is not right". Nobody seems willing to able to explain exactly why it isn't right in terms of the behaviour of individual molecules. There must be an obvious error or an unspoken error or something is omitted but if that is the case, why can't people just explain it very simply: "Those 4 molecules at the bottom that provide the lift in this model don't exist, or their forces operate at right angles to the direction the model suggests", or something of this nature. My take away from this situation is that there are a lot of people who struggle to accurately describe physical situations, even those who believe they have a good understanding. Probably because physics is subtle.

    No doubt, when someone finally hits on the correct microscopic description, it will be face palm time and I'll be saying "Ah, of course, that's how it works. How obvious and how silly of me to think otherwise". I'm looking forward to that moment of enlightenment but I've been waiting 20 years so far, patience is a virtue...

  • June 5, 2023, 7:07 a.m.

    Exactly!
    I have theory - if one cannot explain what one knows well, then one doesn't know it so well, after all...

    If you have understood my drawings and explanations so far, let me know; then I'll continue later today with more complex situation.
    If not, then just ask over.

  • Members 514 posts
    June 6, 2023, 9:44 a.m.

    I hurt my back a couple of days ago which is limiting my ability to sit at the computer for long periods at the moment. But please carry on...

  • June 6, 2023, 5:09 p.m.

    I hope it is nothing serious!


    But well, let's continue.
    To recall most important claims and conclusions so far, for fluid or gaseous environment in static conditions:

    • our 'tiny forces' are caused by chaotic, non-directional movement and can thereby drawn as ✴, not ↗ or ↙ or something else with clear direction
    • without external forces (gravity) we can replace any part of our environment with some solid object, this does not change any forces in surrounding environment

    Now we will introduce gravity, first without any additional objects or real walls in our environment (boundaries between 'cells' are again purely imaginary).

    model-3.png

    As you can see, there appeared additional force to our tiny water droplet - bluish arrow on picture. Similar forces, caused by gravity, apply of course to all other 'cells' too.
    But we have condition that our model has to be static - this means that we must have some other force(s), balancing gravitational one. As there are no more 'big' forces, then apparently our 'tiny forces' need to be reconfigure itself in some way - in lower part of our droplet they need to be stronger (water molecules need to kick harder). As our forces are in form ✴ and symmetrical (otherwise water would start to flow into other directions, which is excluded by static nature of our model), then we can first conclude that they are equal at the same level (at same gravitational potential) and then that applying gravity creates 'tiny forces' gradient in entire environment, aligned in directon of gravity.
    As you can see on image, 'tiny' forces at lower level are drawn as longer arrows. Of course if our cell is tiny, then real forces differ much less - but they are certainly different.

    Although some words are explicitly forbidden here 🙃, I will anyway note that those non-directional ✴ forces are called pressure. Previous claim can also be reworded as "applying gravity to fluidous/gaseous environment creates pressure gradient".

    model-3.png

    PNG, 225.6 KB, uploaded by ArvoJ on June 6, 2023.

  • Members 514 posts
    June 8, 2023, 12:33 p.m.

    Just got back from seeing the physio at my GP's surgery. She has given me an exercise to treat my "trigger finger" problem (fingers lock in position and won't move) - likely caused by typing too much stuff about buoyancy 🙂, she's diagnosed my shoulder/arm problem and will send me an exercise programme to deal with that, but the back will have to wait for another appointment. Hopefully it will get a bit better on its own.

    My description of your scenario above:

    In the absence of gravity, we have a bunch of particles all vibrating randomly. Each particle moves randomly back and forth about a point. This movement causes there to be lots of random collisions with neighbouring forces. On average, these cancel out and thus we have a static situation.

    With gravity added, all the molecules also have the force of gravity pushing (pulling) them downwards towards their neighbours below (who push back equally and oppositely). The whole group of particles should fall as a block. No idea how the block remains in a static position.

  • June 8, 2023, 6:20 p.m.

    I should have guessed that 🙃
    You inverted my assumption - remember, we have static situation and we need to find out, what happens then.

    But well, let's confine our water somehow - like I said many postings ago, to hold water in place we have to put some walls somewhere. Like on next image:

    model-3-1.png

    Now we have perfectly bottled water, gravity is vertical, our tiny droplet is also located there (my previous model is just magnification of it).
    I did not draw forces at water-bottle surface, but they are reaction forces to water molecules, similar situation we have talked before.
    I won't explain what happens at the top surface of water - this is very different topic.

    By orange lines I have marked levels, where tiny ✴ forces (pressure) have to be equal.
    Can you explain, why? In few words, to not hurt your finger :)

    model-3-1.png

    PNG, 491.7 KB, uploaded by ArvoJ on June 8, 2023.

  • Members 514 posts
    June 12, 2023, 9:48 a.m.

    Assuming the blob of water is held in place by the walls of the bottle, and assuming your orange line goes through the centre, I guess forces half to balance to prevent the top half of the blob pushing the bottom half out of the way (or the reverse).

    But I doubt somehow that is what you meant....Please enlighten me 🙂

  • June 14, 2023, 8:42 p.m.

    For given tiny cell it is correct. A bit more generally - molecules below some water volume need to counteract to weight of 'upper' molecules; they would gladly move away - but there is nowhere to go, molecules in the neighbourhood have similar 'pressure' from upper ones and then we have walls, which don't go away. 'Lower' molecules thereby just need to kick harder (= exert bigger force) to keep situation stable.

    Then we claim that ✴ forces on same level are equal.
    Remember that the only external force (gravity) is vertical, there is no horizontal component of it - this implies that forces cancel out in horizontal direction or in other words, they are just equal. Or in prohibited :) words - pressure at the same level is equal.
    (Wikipedia calls related principle as 'Communicating vessels'.)

    This holds even in strange geometric forms, like our bottle above - pressure at a level, marked by orange line, is equal in all three areas.

    Can we use the word pressure for our tiny ✴ forces from now or should I continue to avoid that?
    I mean do you start seeing pressure as a result of omnidirectional (molecular) forces or not yet?
    Few posts ago you attempted to assign direction to pressure, this is not possible in our static fluid or gaseous environment - I hope you have changed your mind :)

    (I'm really not a teacher kind of person.)

  • Members 514 posts
    June 19, 2023, 2:46 p.m.

    Sorry about the slowness in replying. Minor medical problems have kept me away from the keyboard plus I've been ferrying my daughter around the country to university open days. Got more to do as well.