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I Why do denser objects sink?

  1. Oct 12, 2016 #1
    Column A: Let's assume we have a column of water of height 2m. And also assume water density is 1kg/m^3. Then the pressure at the depth of 1m is pgh = 1*g*1 = g, which means the top 1m of water is pushing down with pressure g, and the water right past 1m mark is pushing up with pressure g. Also, at the end of the 2m, the pressure is pgh = 1*g*2 = 2g.

    Column B: Ok, and then say we remove the top 1m of water and replace it with oil of density 1.01 kg/m^3. Now, the oil is supposed to sink to the bottom of the whole column because it's denser, so it should eventually become 1m of oil at the bottom. But let's assume for the sake of argument that the oil doesn't sink, and so the pressure at 1m is pgh = 1.01*g*1 = 1.01g.

    At height 1m, the oil in Column B pushes down with pressure 1.01g. In real life, this wouldn't happen, but the question is why, in real life, doesn't the water right past the 1m mark also push up with pressure 1.01g? We've shown that water is capable of pushing up to 2g of pressure at least, so why doesn't the water right below the 1m mark just push up 1.01g? Why does water care about the density of whatever is on top of it?

    Or another way to ask is: The water at height 2m has pressure 2g. The pressure at 1m is 1g. But is the water at 2g physically any different than the water at 1g? If both waters are the same material, and if one water is capable of sustaining 2g pressure, then why would the other water not be able to also sustain 2g of pressure?
    Last edited: Oct 12, 2016
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  3. Oct 12, 2016 #2


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  4. Oct 13, 2016 #3
    Oil is usually less dense than water and will sit on top anyway.

    I think you are trying to over complicate things. Denser materials push down more than less dense materials, at the end of the day all materials are being pulled downwards
  5. Oct 13, 2016 #4


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    It doesn't. It cares only about the displaced water volume, which determines the buoyant force.
  6. Oct 13, 2016 #5
    But how would the column know if water was even displaced in the first place?
    I could have a water column of height 1m, of which I then add some higher density oil. This addition of oil would displace some water, say 0.5m, so the buoyant force would be equal to the force exerted from that displaced water.

    Ok, but if I know the oil will displace 0.5m of water in the first place, couldn't I just make a column of water starting out with 0.5m, and then just fill the rest of the column with oil? This way, the buoyant force should be the same, right? Amount of water is same in both, and so is the oil. And in this case, no water was displaced.

    The displaced water I'm thinking about is overflowing over the walls, so it actually exits the column. Maybe this is the wrong assumption?

    And why can't water just exert some pressure at any height it wants? The water below the ocean can support more than 1000 psi, so why can't the water nearer the surface also support 1000 psi pressure?
  7. Oct 13, 2016 #6


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  8. Oct 13, 2016 #7


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    I don't understand your thinking. What makes you think the water at the surface can't. Can't is not the same as doesn't.
  9. Oct 13, 2016 #8
    When you have a situation with a denser fluid on top of a less dense one, we call this a Rayleigh-Taylor instability.

    If the layer between the top and bottom fluids is perfectly flat, then the bottom fluid can hold up the top fluid indefinitely. Water can sustain large pressures without a problem. But in any real fluid, you have some small imperfections in the layer between the top and bottom. The model says that these imperfections will grow because they are unstable. It's like trying to balance a pencil on its point. It's in equilibrium, but it is an unstable equilibrium.
  10. Oct 13, 2016 #9


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    Buoyancy occurs by displacing a fluid. You are confusing yourself by trying to set up a situation where the fluid is being mechanically constrained from being displaced.

    Yes, it is possible to set up a set of mechanical constraints that prevent fluid from displacing and then the simple model of buoyancy via displaced volume would not apply, or at least not tell the whole story.

    That said, I think in a column the fluids would slip past each other, as @Khashishi is noting.

    If you toss a penny into a fountain it will sink. If you put a penny into a hypothetical tube that is so well fit water cannot move past the penny, it won't sink. Understand the reason the penny sinks in open water before adding the complexity of preventing fluid displacement.
  11. Oct 14, 2016 #10
    Yeah, I was thinking that if both waters are the same, then the water on top should also be able to support large pressures, too. But why doesn't it do it?

    I'm not understanding the hydrostatic paradox. A column of water can be made to support any pressure by varying the height of the column. Why is this a paradox?

    Ok, so say we have a penny and a fountain. As Khashishi said, we know that water can withstand large pressures well. Then, initially, when the penny touches the water surface, why doesn't the surface of the water exert a pressure to support the penny?
  12. Oct 14, 2016 #11


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    Liquid water is a fluid, and you are mixing up your thinking by applying aspects of a solid material to it. The water in the fountain does not support the penny because its molecules move more or less sideways out of the way of the penny. Were you throw the penny onto a solid surface, the molecules of the solid surface are (compared to molecules in a fluid) much more tightly bound to each other and prevent each other from moving and they would support the penny.

    The force acting to move the fluid molecules aside is the mass of the object times gravity.

    The force acting to resist the moving out of the way that a fluid (gas or liquid) does is buoyancy, and it is equal to the mass of the displaced fluid times gravity.

    If you have ever experienced smoke from a campfire, you can see this happening. You walk into the smoke, it does not resist you like a wall, the smoke molecules move aside as you push into it. Gas is a fluid - it does not behave as a solid does. Liquid is also a fluid.
  13. Oct 14, 2016 #12


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    We'll, what is the pressure at the surface of the fountain? The water can only apply the pressure it has!
  14. Oct 14, 2016 #13
    There is pressure on all sides of the penny. The difference in pressure between the bottom and top of the penny is insufficient to hold the penny. The pressure can't "build up" under the penny because water is a fluid and will move around the penny, unless the penny seals the entire surface of the water (in a small tube).
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