Question How does pressure increase with depth in water?

[Brett Hatch]

Not quite right. If the diameter is 8" at the surface, at 10m/33ft the volume will halve, not the diameter. So when the pressure doubles, the diameter will actually be 6.35" (Using for the formula (4/3) × π × r³)

Good correction, thanks!

 

[rjack321]

Which argument

Let me restate my initial argument using a visual aid.

View attachment 808882

In the right bottom corner of each body of water is a depth gauge. One is labeled x, the other y.

My argument is that x will show a shallower depth than y.

Edit: I should note that the "roof" of the x chamber is magically self-supporting in this scenario and so adds no pressure to the water below it.

Sorry to say, and Tracy is correct

X = Y

 

[steinbil]

Here's a YouTube video will explains reasonably well.


The mind-bending concept here comes about when trying to apply the physics of a solid to a fluid. If you have an oddly shaped solid object, the entire mass of the object is concentrated on the surface on which it is resting.

With fluids, there is an additional dimension of pressure - the pressure keeping the fluid in the container, which is exerted on the sides of the container. And the in the narrow pipe scenario, the ceiling of the large chamber is what exerts the pressure against the water, which is needed to keep it in the container.

Great video! That really helped make sense of why it doesn‘t relate to the weight of the water.

Again, I’m clearly no engineer, but I guess that has major implication for the forces on any vertical pipe filled with fluid. I mean if the vertical drop is long enough, the pressure on the sides of the pipe would be massive. Not that I have any sort of understanding of the actual forces in play and the tensile strength of different materials. I was going to say: is this a consideration in let’s say plumbing in the world’s tallest buildings? But I guess it would only apply if there was standing water in the pipe…

 

[OTF]

Great thread. Several excellent posts, great to see such civil learning and debate.

The thing that really took me a while to wrap my head around was the phenomenon where pressure increases linearly with depth, but expansion/compression of submerged air is exponential. Maybe partially a semantic issue as it's often incorrectly phrased as something like "the biggest pressure change happens in the first 30 feet".

Next up, the tide bulge on the side opposite the moon...

 

[huwporter]

That is a very interesting question. My hypothesis is that the pressure would drop to just a bit more than 1 atmosphere as you moved the gauge just under the "roof".

Well OK, so, under your hypothesis here, where and and at what rate exactly does this pressure drop happen? Instantaneously the moment the pressure gauge moves below the level of the roof? Or gradually - in which case how far do you have to move the gauge for the drop to occur? Would it start to drop before you have even left the tube? Or not?

 

[Alekseolsen]

Which argument

Let me restate my initial argument using a visual aid.

View attachment 808882

In the right bottom corner of each body of water is a depth gauge. One is labeled x, the other y.

My argument is that x will show a shallower depth than y.

Edit: I should note that the "roof" of the x chamber is magically self-supporting in this scenario and so adds no pressure to the water below it.

They will have exactly the same pressure depth.
If you want some real world examples, more than a few times water tanks on sailing ships have bursted, as they've been pressurised by water level in the (very small, but vertical) vent lines

 

[OTF]

For the sake of severely complicating things unnecessarily, at some point the "vertical tube" could be thin enough that that capillary effects would be a consideration...

Capillary Action and Water | U.S. Geological Survey

Plants and trees couldn't thrive without capillary action. Capillary action helps bring water up into the roots. With the help of adhesion and cohesion, water can work its way all the way up to the branches and leaves. Read on to learn more about how this movement of water takes place.

www.usgs.gov

 

[berndo]

I could mock it all up, but I can save you the hassle and just tell you the depth gauges will read the same in that drawing.

There is gotta be a cutt-off point though. If the tube on the first container is only the diameter of a tiny straw or smaller you would see a lower pressure, I reckon. I don't think the downtube can be infinitely small. Is there a cut-off point when is comes to diameter of the downtube, @Angelo Farina?

 

[steinbil]

There is gotta be a cutt-off point though. If the tube on the first container is only the diameter of a tiny straw or smaller you would see a lower pressure, I reckon. I don't think the downtube can be infinitely small. Is there a cut-off point when is comes to diameter of the downtube, @Angelo Farina?

I guess this would go a long way towards answering that question:

For the sake of severely complicating things unnecessarily, at some point the "vertical tube" could be thin enough that that capillary effects would be a consideration...

Capillary Action and Water | U.S. Geological Survey

Plants and trees couldn't thrive without capillary action. Capillary action helps bring water up into the roots. With the help of adhesion and cohesion, water can work its way all the way up to the branches and leaves. Read on to learn more about how this movement of water takes place.

www.usgs.gov

Aside from that, if I understand what I've learned in this thread, the relation between the sizes otherwise will not matter. You can have the whole Atlantic connected to a thin pipe and the physics would be the same.

 

[Tanks A Lot]

There is gotta be a cutt-off point though. If the tube on the first container is only the diameter of a tiny straw or smaller you would see a lower pressure, I reckon. I don't think the downtube can be infinitely small. Is there a cut-off point when is comes to diameter of the downtube, @Angelo Farina?

As unintuitively as it may be, there is no cut-off point until capillary effects take over as OTF has hinted.

For the sake of severely complicating things unnecessarily, at some point the "vertical tube" could be thin enough that that capillary effects would be a consideration...

Capillary Action and Water | U.S. Geological Survey

Plants and trees couldn't thrive without capillary action. Capillary action helps bring water up into the roots. With the help of adhesion and cohesion, water can work its way all the way up to the branches and leaves. Read on to learn more about how this movement of water takes place.

www.usgs.gov