Trying to understand hydrostatic pressure

[abrek]

TL;DR Summary

Water pressure when closing the bottom of the cylinder.

Imagine we have a cylinder filled with water with a closing mechanism, the height of the cylinder is quite large to create increased pressure at the very bottom. If the mechanism closes a small part at the bottom of the cylinder, will the pressure decrease or not?
Thanks in advance for the answer

 

[jbriggs444]

If the mechanism closes a small part at the bottom of the cylinder, will the pressure decrease or not?

What thoughts do you have?

And have you ever encountered the phrase "statically indeterminate"?

 

[Lnewqban]

If the mechanism closes a small part at the bottom of the cylinder, will the pressure decrease or not?

What point are you referring to?
The pressure right above the gate valve should remain the same it was at that level when the valve was open.

 

[abrek]

What point are you referring to?
The pressure right above the gate valve should remain the same it was at that level when the valve was o

I mean, the pressure at the bottom of the cylinder itself, it seems to me that the pressure at the very bottom will be less because of the valve, is that so?

 

[abrek]

What thoughts do you have?

And have you ever encountered the phrase "statically indeterminate"?

no, I have not encountered this, thanks for the comment from what you sent, I will study it

 

[kuruman]

Consider answering the following four questions.

1. As you slowly slide the partition in place, is the pressure at the bottom of the cylinder going to change?
2. Slowly slide the partition out. As you do that, is the pressure at the bottom of the cylinder going to change?
3. Now slide the partition back in place and pump out the liquid from the top part of the tube. Is the pressure at the bottom of the cylinder going to change?
4. When the liquid above the partition is gone, slide the partition out. Is the pressure at the bottom of the cylinder going to change?

 

[Lnewqban]

I mean, the pressure at the bottom of the cylinder itself, it seems to me that the pressure at the very bottom will be less because of the valve, is that so?

I may be wrong, but this is how I see it:

If we have a liquid in an open recipient, we have atmospheric pressure above the liquid surface and atmospheric plus hydrostatic pressures at the bottom of the recipient.

If we then close tight the lid of that recipient, we still have the same pressures inside it.

If we then relocate that recipient to the exosphere, or to the bottom of the ocean, the low or high external pressure should not make any change in the inferior pressures of our recipient (assuming that the lid and recipient are strong enough to support the in-out pressure differential and perfectly rigid).

 

[jbriggs444]

If we then relocate that recipient to the exosphere, or to the bottom of the ocean, the low or high external pressure should not make any change in the inferior pressures of our recipient (assuming that the lid and recipient are strong enough to support the in-out pressure differential and perfectly rigid).

If we also assume that the fluid is an incompressible ideal liquid then we have good reason for concern.

The pressure in the enclosed space can take on any value at all. The laws of physics that we hope to employ to predict a pressure make no prediction. If this makes us uneasy, that is a good thing. Our idealizations are wrong.

There is no such thing as a perfectly rigid container. Or a perfectly incompressible fluid. If we want to make a prediction about the actual behavior of a physical system, we will have to dig into the details and explore how the actual behavior deviates from the ideal.

As engineers, we should be thinking about head space and pressure relief valves.

 

[russ_watters]

The OP doesn't say anything about relocating the cylinder. There's nothing indeterminate here as long as the volume of the gate is negligible: the pressures don't change.

Sure, a real application with safety concerns due to changing conditions needs a safety relief valve, but that's not an answer to the OP's question.

 

[kuruman]

Here is an interesting variation. This is an experiment that you can do at home.

1. You insert a straw in a glass all the way to the bottom and then cap it with your finger (figure below left). What is the pressure at the bottom of the straw?
2. You lift the straw with the finger in place (figure below right). What is the pressure at the bottom of the straw?
3. You lift the straw with its bottom end completely out of the glass (not shown) such that no water leaks out the straw. What is the pressure at the bottom of the straw? What is the pressure at the top of the straw just below the finger?

 

[abrek]

Consider answering the following four questions.

1. As you slowly slide the partition in place, is the pressure at the bottom of the cylinder going to change?
2. Slowly slide the partition out. As you do that, is the pressure at the bottom of the cylinder going to change?
3. Now slide the partition back in place and pump out the liquid from the top part of the tube. Is the pressure at the bottom of the cylinder going to change?
4. When the liquid above the partition is gone, slide the partition out. Is the pressure at the bottom of the cylinder going to change?

1. I will assume that the pressure on the bottom after closing the valve will still become less.

2. Accordingly, with my first assumption, when opening the valve, the pressure will increase due to a column of water

3.after closing the valve in place, a certain pressure will be created and after pumping out the water, it will remain the same

4.Similarly, after opening the flap, the pressure should remain the same as after pumping water with the flap closed

I answered because I imagine it in my head, probably wrong somewhere, I will be grateful if you correct me if I am wrong in the answers.

 

[jbriggs444]

The OP doesn't say anything about relocating the cylinder. There's nothing indeterminate here as long as the volume of the gate is negligible: the pressures don't change.

That is an assertion without evidence. Further, there can be no experimental evidence for that proposition.

To be clear, for any finite compressibility of the fluid or for any finite flexibility of the container then the pressure indeed does not change.

 

[kuruman]

1. I will assume that the pressure on the bottom after closing the valve will still become less.

Consider that you are sliding a very thin but very strong and stiff piece of metal across the tube as shown on the right.
In (A) the partition is all the way out.
In (B) the partition is halfway in.
In (C) it's almost all the way in.
Does the pressure at the bottom decrease slowly as the partition is moving closer and closer or does it drop abruptly as soon as the last micron of a gap is bridged?

 

[PeterDonis]

I will assume

You should not assume. You should use the laws of physics to determine the answer.

 

[PeterDonis]

it seems to me that the pressure at the very bottom will be less because of the valve

Why?

The pressure at the bottom is due to the weight of whatever is above it. The same weight is there whether the gate is open or closed (assuming the weight of the gate itself is negligible).

 

[Lnewqban]

I answered because I imagine it in my head, probably wrong somewhere

Will your responses change if we replace that sliding gate with a shutoff valve?

 

[PeterDonis]

replace that sliding gate with a shutoff valve?

I don't see the correspondence between the two cases.

 

[Lnewqban]

I don't see the correspondence between the two cases.

We are trying to visualize the lack of dependence between the condition of a valve (closed or open) and the values of the hydrostatic pressures in the points of the fluid located on both sides of that valve, and next to it.

... it seems to me that the pressure at the very bottom will be less because of the valve, is that so?

In this case, the only function of any type of valve is to isolate that volume located at the very bottom of the cylinder filled with water.

It seems to me that @abrek incorrectly believes that, once closed, that valve also reduces the hydrostatic influence that the rest of the water located above that volume had previously exerted on the bottom one.

 

[kuruman]

It seems to me that @abrek incorrectly believes that, once closed, that valve also reduces the hydrostatic influence that the rest of the water located above that volume had previously exerted on the bottom one.

I agree. That’s why I posted #13. The basic question is if the pressure at the bottom is indeed reduced, at what point during the partitioning does this happen?

 

[russ_watters]

That is an assertion without evidence. Further, there can be no experimental evidence for that proposition.

To be clear, for any finite compressibility of the fluid or for any finite flexibility of the container then the pressure indeed does not change.

?? Huh? Doesn't your second part contradict the first?

The OP doesn't understand the basic scenario, which people execute every day when filling a hydronic system. We should not be adding assumptions or complications to break it unnecessarily.

 

[russ_watters]

Consider answering the following four questions.

1. As you slowly slide the partition in place, is the pressure at the bottom of the cylinder going to change?
2. Slowly slide the partition out. As you do that, is the pressure at the bottom of the cylinder going to change?
3. Now slide the partition back in place and pump out the liquid from the top part of the tube. Is the pressure at the bottom of the cylinder going to change?
4. When the liquid above the partition is gone, slide the partition out. Is the pressure at the bottom of the cylinder going to change?

1. I will assume that the pressure on the bottom after closing the valve will still become less.

2. Accordingly, with my first assumption, when opening the valve, the pressure will increase due to a column of water

3.after closing the valve in place, a certain pressure will be created and after pumping out the water, it will remain the same

4.Similarly, after opening the flap, the pressure should remain the same as after pumping water with the flap closed

I answered because I imagine it in my head, probably wrong somewhere, I will be grateful if you correct me if I am wrong in the answers.

The key here is that hydrostatic pressure is a function of the height of the column of water, only. That's the fundamental point of hydrostatic pressure. And frequently misunderstood.

So in this case, as the valve is partly closed, you have changed the shape of the column slightly, but not its height. So the pressure at the bottom (or anywhere else) does not change. This principle (no pressures change) continues to apply all the way until the valve is fully closed. Still, no pressures have changed.

That's it. That's all there is to this scenario.

...of course if you make other changes to the system after you close the valve something might change, but that would be a different scenario.