Question How does pressure increase with depth in water?

[rjack321]

I don't think this is correct.

For example, let's assume a 10m tall cylindrical tank the top of which is buried 30m below ground level. The tank is completely filled with water and is connected to the surface only by a very narrow pipe. If the pipe is full of air, then I think we can agree the absolute pressure at the bottom of the tank is very close to 2 atmosphere (surface pressure + 1 atmosphere of water).

Now if we fill the pipe with water, what happens to the absolute pressure at the bottom of the tank? Does it suddenly become 5 atmospheres? It seems more likely to me that it becomes 2 atmospheres + a little bit where the little bit is the weight of the water in the pipe divided by the surface area of the tank.

If I'm wrong about this, I can't wait to find out how.

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.

 

[steinbil]

This has been very enlightening! I was using the same thought process as @lowwall because intuitively that's how I understand the forces of gravity. Reading about Pascal's law has definitely helped my understanding. And now all of a sudden Hydraulics starts making sense as well...

 

[lowwall]

What if your 10m tall cylindrical tank were just the diameter of the little pipe connecting it to the surface. Would your conclusion about the pressure at the bottom of the tank once the pipe is full of water change?

It would still be 2atm + (the weight of the water in the pipe divided by the surface area of the tank).

In this case the total would be 5atm.

 

[tursiops]

It would still be 2atm + (the weight of the water in the pipe divided by the surface area of the tank).

In this case the total would be 5atm.

Maybe the confusion is that pressure is pounds per square inch......not just pounds? "Weight" is not the point. The area aspect has already been taken out.

 

[lowwall]

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.

 

[lowwall]

Maybe the confusion is that pressure is pounds per square inch......not just pounds? "Weight" is not the point. The area aspect has already been taken out.

Let's say the area of the tube is 1 square inch and the weight of the water in the tube is 14.7 pounds (so a bit under 2 gallons). Let's also say the surface area of our tank is 100 square miles.

Are you really suggesting that a tube with 2 gallons of water in it is going to increase the pressure 10m down in our tank by a full atmosphere?

I wonder how the desalinization engineers missed all this.

 

[lowwall]

I think this is confusing because of the way incompressible fluids can transmit force every which way, including up and down and around corners. What you need to keep in mind is that it can only transmit the forces that are acting on it. For something like a cave system that's open to the atmosphere (as opposed to something like a hydraulic system), the only net force is the net weight of the water above you. Sideways doesn't matter. Up gets subtracted. Surface area greater than you doesn't matter because the force is acting on something else.

Edit: this is for static systems. Flow will result in additional forces.

 

[tursiops]

Let's say the area of the tube is 1 square inch and the weight of the water in the tube is 14.7 pounds (so a bit under 2 gallons). Let's also say the surface area of our tank is 100 square miles.

Are you really suggesting that a tube with 2 gallons of water in it is going to increase the pressure 10m down in our tank by a full atmosphere?

I wonder how the desalinization engineers missed all this.

what holds the water up in in your 1 sq in pipe? Why doesn't it just flow down and fill up the container beneath it?

How does the water tank in your town manage to provide water to everybody?

 

[BRT]

Let's say the area of the tube is 1 square inch and the weight of the water in the tube is 14.7 pounds (so a bit under 2 gallons). Let's also say the surface area of our tank is 100 square miles.

Are you really suggesting that a tube with 2 gallons of water in it is going to increase the pressure 10m down in our tank by a full atmosphere?

I wonder how the desalinization engineers missed all this.

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.

 

[lowwall]

what holds the water up in in your 1 sq in pipe? Why doesn't it just flow down and fill up the container beneath it?

I said the tank is full.

You haven't answered how 14.7 pounds of water is going to increase the pressure at the bottom of a 100 square mile x 10m tank by 3 atmospheres.

How does the water tank in your town manage to provide water to everybody?

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?