Question How does pressure increase with depth in water?

[berndo]

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

Yes, but than there is a cut-off point when it comes to the diameter of the tube. I'm saying when the tube on lowwalls picture is small enough, you'd see a different reading on the spg. If you had a 1000 l closed tank and stuck a 5 meter long straw with water on top of the closed tank, I don't think the reading on the spg would jump by 0.5 bar.

 

[Angelo Farina]

That does help my understanding somewhat. It is not so much the path of water that confuses me. What I'm struggling to understand is that the actual amount of water above doesn't affect the force of pressure below - only the vertical distance.

@Angelo Farina
Thank you for the step by step explanation. I will look up the Pascal principle and read through your explanation again. By the way, what happens when there is flow? Is the water pressure at depth different in the spring caves of Florida than the caves of Mexico?

Yes, flow changes the pressure distribution in many different ways.
That's hydrodynamics, a part of science truly complex!
The two main phoenomena are governed by two scientists, Bernoulli and Navier.
Bernoully studies the flow inside a pipe of variable section, neglecting friction and losses. For example a Venturi tube, which is a conical restriction followed by a more gentle conical expansion.
Inside the throat of the venturi, velocity is increased significantly, and pressure drops dramatically. Energy is preserved, but converted from potential energy (pressure) to kinetic energy (velocity)..
After the throat, the flow slows down, and you come back with the same velocity and pressure as before the venturi.
Navier adds the evaluation of friction and losses, which become explicit in the Navier-Stokes differential equation.
Losses are due to viscosity, a property of water (and other fluids) which generetes tangential forces in presence of velocity gradients.
These tangential forces always oppose to the motion, resulting in a pressure loss along the pipe, even if its cross section is constant.
There are other phoenomena inside a fluid flow.
For example a submerged body is not subjected to an uniform pressure over its surface: in some parts the pressure will be higher, in some parts it will be smaller. The total resulting force will not be zero, it will be a vector pointing usually in the direction of flow.
But if the body has an asymmetric shape (like a wing), also a significant force in the transverse direction appears In case of a wing, the force in the direction of flow is called drag, the much larger force in transverse direction is called lift.
I tried to concentrate in a short post what requires a big book for being explained properly, so excuse me for the over-simplification and lack of rigour.

 

[huwporter]

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.

Noting that you can't actually raise the pressure in the Atlantic by sticking a thin tube in it and filling it up with water because the water would just flow out of the bottom of the tube due to not being in hydrostatic equilibrium.

 

[steinbil]

Yes, but than there is a cut-off point when it comes to the diameter of the tube. I'm saying when the tube on lowwalls picture is small enough, you'd see a different reading on the spg. If you had a 1000 l closed tank and stuck a 5 meter long straw with water on top of the closed tank, I don't think the reading on the spg would jump by 0.5 bar.

If I understand the capillary effect correctly, that would depend on the material of the straw, as well as the diameter. But disregarding the capillary effect, it would indeed jump by 0.5 bar.

Noting that you can't actually raise the pressure in the Atlantic by sticking a thin tube in it and filling it up with water because the water would just flow out of the bottom of the tube due to not being in hydrostatic equilibrium.

Of course! But if you were to drill a thin 20m deep hole in a landmass and connect it to the Atlantic Ocean, the pressure would be the same at the bottom of that thin hole and at 20m in the ocean. I was thinking the tube would be at the same level as the ocean, not above.

 

[phoque]

OK, don't have too much time to write a detailed answer, but to get back to @lowwall 's point and question with his 2 gauges x and y, the 2 gauges will read the same pressure regardless of their position under the roof or the thin tube, as long as they are at the same depth. What you need to visualize, is the fact that when the gauge is under the roof, and not the tube, there is a seemingly shorter water column directly above the gauge, which creates the confusion. The same pressure as at the bottom of the thin tube is applied by the bottom of your rock wall onto the water column directly above that gauge. The water at the contact point with the roof is pressurizing that roof upwards, and the rock roof is applying an equal reaction force downwards, otherwise, the water in the thin tube would just flow down into the chamber.
If you increase the water column height in the thin tube, you increase the pressure of the water at the roof level, the roof applies a corresponding increased reaction force, which will transfer to that gauge placed below it.

I hope that makes more sense in visualizing how increasing the water level in the thin tube increases the pressure of the water column which does not sit directly below it.

 

[berndo]

But disregarding the capillary effect, it would indeed jump by 0.5 bar.

You can't disregard it though.

 

[tursiops]

You can't disregard it though.

The tiny tiny pipe is a red herring, easily and properly disregarded in the context of the thread.

 

[BRT]

I think the pressure will settle between the initial readings of x and y.

I'm sending the drawing my with son to his high school physics class tomorrow.

Eventually I'm going to have to do this experimentally. Unless @Tracy wants to do it first (like How does moisture enter tanks? ).

Tell us what the physics teacher says. I have dealt with this for a lifetime so I already know.

 

[OTF]

Yes, but than there is a cut-off point when it comes to the diameter of the tube. I'm saying when the tube on lowwalls picture is small enough, you'd see a different reading on the spg. If you had a 1000 l closed tank and stuck a 5 meter long straw with water on top of the closed tank, I don't think the reading on the spg would jump by 0.5 bar.

It actually would.

As for the capillary red herring - now I'm actually not sure if water sucked up in a tall capillary would or wouldn't contribute normally to hydrostitic pressure. But it does NOT matter for the main question. The diameter of a capillary in this context would be on the order of microns to be significant in height. Very different from a pipe or cave, different forces and effects come into play at those tiny scales. So if there is a "cutoff" at all (which there might not be) it's probably submilliliter.

 

[EmotionalSupportTrevally]

My town only uses pumps, but I assume you are talking about a community water tower. That actually illustrates my point nicely. The job of the towers is not primarily to provide water, it's to pressurize the distribution of water from the municipal water treatment plant. Following your argument, all that would be needed to provide this pressure is a small column of water of the correct height (most towers are 40-50m above grade) and a fast enough pump to keep it topped off. Yet actual water towers typically contain 1 million gallons of water. Why would they source so much money to hang all this weight in the sky if they didn't need to?

The older standpipe water towers worked just like your description. Just a narrow tube to pressurize the whole system. There's a very famous one in downtown Chicago. St Louis has a few left.

Henry Palmer used a similar technique to measure stages of the Thames in the 1830s. A protected onshore standpipe, hydraulically connected to the river by a horizontal pipe. The level in the standpipe was always the same as the level of the river, but unaffected by waves, currents, boats, etc.