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Level surface of a contained liquid

by BrainSalad
Tags: contained, liquid, surface
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BrainSalad
#1
Nov13-13, 07:06 PM
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It's interesting to me that a liquid, under the force of gravity, in a container has a flat surface. Tell me if my explanation is correct: if the surface of the liquid were uneven, the higher parts of it would be "sitting on top of" the liquid below. Necessarily, the liquid under these parts would have higher pressure than the rest. Pascal's principle says that this cannot be the case, so the pressure equalizes throughout, allowing the higher liquid to fall and raising the lower liquid, flattening out the surface.
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elegysix
#2
Nov13-13, 07:29 PM
P: 316
How could the earth be round if the oceans were flat? You have the right logic, but the wrong conclusion.
BrainSalad
#3
Nov13-13, 07:43 PM
P: 52
Ok, so in that case, a flat liquid surface over a round Earth, the pressure of the liquid would be greater as the planet curves away from the flat sutface, forcing the shallower section up and falling into a curved surface. Correct? So the real answer is that a contained liquid strives for the most even surface. One part of the surface will not be higher than another.

TumblingDice
#4
Nov13-13, 08:10 PM
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Level surface of a contained liquid

Quote Quote by BrainSalad View Post
Ok, so in that case, a flat liquid surface over a round Earth, the pressure of the liquid would be greater as the planet curves away from the flat sutface, forcing the shallower section up and falling into a curved surface. Correct?
Thinking in terms of pressure exerting a force gets you on a better track, and gravity plays a role in more than one way. It causes the liquid to stay in the container. :)

The pressure at the surface of the liquid needs to maintain an equilibrium across the area to stay 'flat'. Consider if you used a straw to gently blow on the surface, or inserted it and drew the liquid's surface 'up' inside the straw. How do these two scenarios relate to the position of the liquid's surface? Seriously. Can you describe a new answer to your original question?

The complete answer is going to involve pressure on both sides, and that's going to include temperature, mass/volume, and gravity, but the bottom line is it's the equilibrium from these factors that both sides are able to support.
elegysix
#5
Nov13-13, 08:12 PM
P: 316
What you said at first was correct, but the water isn't flat, it isn't even spherical. It arranges itself to the position toward equilibrium. If our moon was more massive, we might very well have a mountain of water pointed towards it. (We do have something similar, it causes the tides)
BrainSalad
#6
Nov13-13, 08:19 PM
P: 52
Very interesting. So gravity, fluid pressure due to the arrangement of the liquid, air pressure, etc all determine the final configuration of the liquid.
adjacent
#7
Nov14-13, 04:54 AM
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Quote Quote by BrainSalad View Post
Very interesting. So gravity, fluid pressure due to the arrangement of the liquid, air pressure, etc all determine the final configuration of the liquid.
Your original question was about a liquid in a container.So gravity of the moon or some massive body doesn't play a major role there.Yes gravity of the moon plays a major part in the tides,thats because we are considering a larger surface are of liquid.
Andy Resnick
#8
Nov14-13, 08:18 AM
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Quote Quote by BrainSalad View Post
It's interesting to me that a liquid, under the force of gravity, in a container has a flat surface. <snip>
Except it's not- google 'meniscus'.
BrainSalad
#9
Nov14-13, 10:49 AM
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Right. Add adhesion to the list.
BrainSalad
#10
Nov14-13, 10:54 AM
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Think water in a large bucket has a curved surface like the oceans? At a tiny angle of curvature? Not sure about that, but I think not.
Nugatory
#11
Nov14-13, 11:16 AM
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Quote Quote by BrainSalad View Post
Think water in a large bucket has a curved surface like the oceans? At a tiny angle of curvature? Not sure about that, but I think not.
It does, or at least it would if other effects (like some bit of residual sloshing, surface tension, whatever) didn't overwhelm the tiny curvature effect.
jbriggs444
#12
Nov14-13, 11:19 AM
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Quote Quote by BrainSalad View Post
Think water in a large bucket has a curved surface like the oceans? At a tiny angle of curvature? Not sure about that, but I think not.
Can you make that quantitative?

If we had a bucket the size of the Pacific Ocean, surely it would have a surface that is convex upwards over most of its extent. If we had a bucket the size of a test tube, surely it would have a surface that is concave upwards over all of its extent. By inspection, there ought to be a specific bucket size where there is a transition from "concave everywhere" to "convex somewhere".
BrainSalad
#13
Nov14-13, 12:22 PM
P: 52
What about a huge container, rectangular, laid tangent to the Earth? I see no reason for the liquid in it to curve upwards. In fact, it seems that outer portions, being farther from the Earth's COM, would have less attraction to the Earth and raise farther up the container than the center, closer portion. If this is true, couldn't the effect be present at a smaller scale? Thus, the only reason large bodies of water are convex upwards is that the Earth curves and gravity is pretty much even across the fluid at a given depth.
adjacent
#14
Nov14-13, 12:27 PM
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Quote Quote by BrainSalad View Post
What about a huge container, rectangular, laid tangent to the Earth? I see no reason for the liquid in it to curve upwards. In fact, it seems that outer portions, being farther from the Earth's COM, would have less attraction to the Earth and raise farther up the container than the center, closer portion.
Less gravity doesn't mean things should rise up.
BrainSalad
#15
Nov14-13, 12:29 PM
P: 52
No, but greater gravity pushes things down farther.
Nugatory
#16
Nov14-13, 12:42 PM
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Quote Quote by BrainSalad View Post
What about a huge container, rectangular, laid tangent to the Earth? I see no reason for the liquid in it to curve upwards. In fact, it seems that outer portions, being farther from the Earth's COM, would have less attraction to the Earth and raise farther up the container than the center, closer portion. If this is true, couldn't the effect be present at a smaller scale? Thus, the only reason large bodies of water are convex upwards is that the Earth curves and gravity is pretty much even across the fluid at a given depth.
Don't just go with intuition, calculate it! The surface of the water will follow a surface of equal potential... and that surface will be curved when you calculate where it is, such that all points on the surface are an equal distance from the center of the earth.

Although if you want an intuitive model, you might ask yourrself two questions:
1) Suppose the earth were completely water, just a giant drop of water 8000 miles across. What shape would it naturally assume, under the influence of its own gravity?
2) The earth's gravity is strong enough, over long distances, to pull solid rock into a spherical shape. If it can force solid rock into that shape, why wouldn't it pull water into that shape?
dauto
#17
Nov14-13, 12:48 PM
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Quote Quote by BrainSalad View Post
No, but greater gravity pushes things down farther.
No, it doesn't. The water will always find the configuration of lowest energy.


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