Question How does pressure increase with depth in water?

[feldomatic]

The "tiny gauge line" problem is counter-intuitive, you have to look at it in pieces.

On the left side of the guage, you've got this 0.5cm pipe going up 30m, on the right you've got the same size pipe connected horizontally to some massive 10m tall tank buried 30m under the ground.

The left side will read 4atm, and that makes sense because it's a vertical column.

The right side will read 2atm (nominally, neglecting increase in air pressure from the additional 20m) and that also makes sense.

Put them together and bypass the gauge and yes, that tank is now at 4atm on the bottom.

It feels like wacky sea-magic but it absolutely works, and it's why hydraulic pumps are able to deliver insane amounts of pressure while being surprisingly small.

If you really want to bake your noodle, think about how your insta-pot only needs a (bear with me on the non-metric units) weight of a couple of ounces to offset a full extra atmosphere of steam produced by the pressure cooker. why? because the stand-pipe it's blocking is only like 1/16" in diameter. Force over area for the win!

 

[lowwall]

Wouldn't matter if the tube filled with water was 1/8" diameter and only had a few ounces of water in it. The height of the water column is what matters. Don't believe this? Run a hose out of the side of an above ground swimming pool. It will expel water until you raise it up to the water level of the pool. Because the pressure at the inlet to the tube is at the same level as the outlet from the swimming pool.

Your example has nothing to do with what I said in my initial post. You have fallen into the exact error I discussed in post 17 above.

 

[Brett Hatch]

@lowwall, I think what you are getting stuck on is the Pascal principle. Not to wag a finger -- I get stuck on it too, that principle is counter-intuitive as hell. Have a look at this diagram from the Encyclopedia Britannica article on this principle:

What this diagram is showing is that you can apply a small force to a narrow area of liquid. If the other side of the container has a wider opening, the resulting force will be much larger. The increase in force is proportional to the difference in the two areas. So if one hole is 10 times smaller than the other hole, the force on the big-hole side is 10 times larger. Amazing, right?

If you turn your head sideways, this diagram is very similar to the wide cylinder that narrows down to a smaller cylinder at the top.

 

[tursiops]

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?

Because big pumps are expensive, so you store the water to meet the high-demand times and refill the tank with a smaller pump during low-demand times.

How Water Towers Work — Practical Engineering

Clean water is one of humanity’s most fundamental needs, and those of us who live in urban areas usually get our water from some kind of centralized public system. Operating a water system is a major responsibility that has implications for public health and safety. In dense urban areas, a clean and

practical.engineering

 

[rjack321]

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.

I don't think this is correct.

The surface area of the water has no effect on the pressure. If it did then 10m deep in the ocean would have a much higher(?) pressure than 10m deep in a vertical sewer pipe.

No. The only force that affects you is the water "above" you. Most of the ocean's force is exerted elsewhere.

I'm not sure what you read. But this is what I read.

And @steinbil is correct, the XY dimension of the water is irrelevant and only the Z (height) is the relevant metric

 

[lowwall]

It feels like wacky sea-magic but it absolutely works, and it's why hydraulic pumps are able to deliver insane amounts of pressure while being surprisingly small.

That's not how hydraulics work. Hydraulics are simple levers. Large movement at low pressure at one spot becomes small movement at high pressure at another. What's cool about hydraulics is the transmission of force via the fluid means you have huge freedom is how you can apply that lever.

Force over area for the win.

We agree here. But my example is a small force over a small area. It's going to do very, very little when applied to a vastly larger area.

 

[rjack321]

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?

In addition to what @tursiops said... because not all municipal wells produce water at rates which peak use can sustain. If you need to store water to accommodate peak flows then you might as well put it at a height which will deliver it at a suitable pressure without requiring power - or a massive pump.

 

[lowwall]

@lowwall, I think what you are getting stuck on is the Pascal principle. Not to wag a finger -- I get stuck on it too, that principle is counter-intuitive as hell. Have a look at this diagram from the Encyclopedia Britannica article on this principle:
View attachment 808867

What this diagram is showing is that you can apply a small force to a narrow area of liquid. If the other side of the container has a wider opening, the resulting force will be much larger. The increase in force is proportional to the difference in the two areas. So if one hole is 10 times smaller than the other hole, the force on the big-hole side is 10 times larger. Amazing, right?

If you turn your head sideways, this diagram is very similar to the wide cylinder that narrows down to a smaller cylinder at the top.

The diagram is not accurately depicting the relative size of the movement of the two pistons. It's not amazing when you realize the increase in force is inversely proportional to the distance over which it is applied.

 

[feldomatic]

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?

That's a matter of capacity/demand and the flow rate and duty cycle of the pumps involved. Also, the bigger the tank, the less the height of the water changes as water flows out of the bottom, so pressure stays more consistent.

Makes the control system for the pump that gets the water up there easier as well. (level low -> turn on, level high -> turn off, calibrated to not cycle too rapidly or slowly and prematurely wear the pump/motor)

 

[tursiops]

One caveat to all this.....
All the statements assume steady-state, static containers. If you take lowwall's large tank with the 10m air-filled tank on top of it, and then pour water into that pipe, the pressures equilibrate (at each depth) with the large tank but not instantaneously. Think of it like a sound wave bouncing around, it takes a while for the reverberation to fill the tank, and for all the pressures to settle out and equilibrate.