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Wow, looks like I'm not the first person to come up with this analogy!
https://www.skepticalscience.com/graphics.php?g=103

Of course, this image alone doesn't fully illustrate a key point of the analogy... that the increased depth of water in the tank increases the pressure at the bottom so that the flow rate can again achieve an equilibrium.

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3 hours ago, Mallow said:

Wow, looks like I'm not the first person to come up with this analogy!
https://www.skepticalscience.com/graphics.php?g=103

Of course, this image alone doesn't fully illustrate a key point of the analogy... that the increased depth of water in the tank increases the pressure at the bottom so that the flow rate can again achieve an equilibrium.

This case that skeptical science shows would lead to water overflowing....is it not a good analogy for energy. because energy would increase in the entire system for a constant supply of energy...the sun. Its a rate problem. Energy comes to the Earth at a certain rate, the outflow of the energy must equal the rate of inflow of energy or the whole planet will warm indefinitely which we know will not happen. Like the tank would overflow in the example. You have to have higher emission above the warmer Earth+lower atmosphere for high temperatures which cools these upper layers. I don't think we are disagreeing here. You could increase the tropopsheric temperatures from GHGs(more absorption) but in order to conserve energy there must be compensating cooling (increased emissions) above....  You tank analogy would be faster flow out the base of the tank from higher pressure or else you overflow the tank from a constant rate of inflow.  Are we in agreement here?? 

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1 hour ago, blizzard1024 said:

This case that skeptical science shows would lead to water overflowing....is it not a good analogy for energy. because energy would increase in the entire system for a constant supply of energy...the sun. Its a rate problem. Energy comes to the Earth at a certain rate, the outflow of the energy must equal the rate of inflow of energy or the whole planet will warm indefinitely which we know will not happen. Like the tank would overflow in the example. You have to have higher emission above the warmer Earth+lower atmosphere for high temperatures which cools these upper layers. I don't think we are disagreeing here. You could increase the tropopsheric temperatures from GHGs(more absorption) but in order to conserve energy there must be compensating cooling (increased emissions) above....  You tank analogy would be faster flow out the base of the tank from higher pressure or else you overflow the tank from a constant rate of inflow.  Are we in agreement here?? 

As I see it, the aspects on which we agree are the following: that energy input and output must be equal or else there is an imbalance, and the temperatures will change; and that faster flow out of the base of the tank due to higher pressure (a higher water level, analogous with more total energy in the Earth system) can compensate for a smaller hole in the bottom of the tank (increased GHGs), leading to a new equilibrium. Where we disagree is on the following points: that 1) the described systems (the Earth system and the tank system) are in an unstable equilibrium, such that any imbalance between the rate of incoming energy/water and the rate of outgoing energy/water must necessarily lead to a runaway out of control warming/overflow; and that 2), given a constant input from the sun and warming near the surface, there must be a reduction in temperature in some layer of that atmosphere so that the average temperature of the Earth system remains constant.

With regard to 1), this is obviously not true, since the sun has variable output on long timescales. The simplest way to understand this is to realize that the decreased flow due to the smaller hole (the decreased outgoing radiative flux due to increased GHGs) is not permanent, and that, given time, the system will find a new equilibrium without any additional changes from outside forces (that is, the outflow rate/emission rate will increase again to match the inflow rate/incoming solar radiation rate). The mechanism by which the Earth reaches a new equilibrium (and then remains there) is the change in the average temperature of (total energy stored in) the Earth system, leading to a change in the rate of radiative energy flux leaving the Earth. In my experiment, this is analogous to the increase in flow due to the increased pressure when the tank fills up. This process occurs regardless of what caused the initial imbalance in the radiative energy flux/water flow into and out of the system. It can be caused by increased output from the sun, OR decreased output from the Earth. Increased GHGs lead to decreased radiative output from the Earth before the temperature has changed. Then the temperature must go up, as more energy is coming into the system than is leaving. This process continues until the temperature increase is sufficient that the increased radiative output compensates for the decrease due to GHGs.

With regard to 2), it follows logically from 1), and can be illustrated with my analogy. Even though the rate of water entering the tank has remained constant, the total water stored in the tank has gone up. This is exactly analogous to the situation where the solar energy input rate remains constant, but the total energy in the Earth system increases.

Of course, there is cooling in the stratosphere associated with AGW, but the processes that control this cooling are complicated and not fully understood. Regardless, this cooling is not necessitated (nor driven) by conservation of energy.

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This case that skeptical science shows would lead to water overflowing....is it not a good analogy for energy. because energy would increase in the entire system for a constant supply of energy...the sun. Its a rate problem. Energy comes to the Earth at a certain rate, the outflow of the energy must equal the rate of inflow of energy or the whole planet will warm indefinitely which we know will not happen. Like the tank would overflow in the example. You have to have higher emission above the warmer Earth+lower atmosphere for high temperatures which cools these upper layers. I don't think we are disagreeing here. You could increase the tropopsheric temperatures from GHGs(more absorption) but in order to conserve energy there must be compensating cooling (increased emissions) above....  You tank analogy would be faster flow out the base of the tank from higher pressure or else you overflow the tank from a constant rate of inflow.  Are we in agreement here?? 

No the link is accurate and would not overflow. As has been explained a bunch.

1. Aperture is decreased and flow out bottom decreases because hydrostatic pressure is the same.

2. Tank fills up because delta in flow rates.

3. Flow out bottom increases as tank fills up, as hydro static pressure at bottom increases.

Until...

4. Flow rates go to same value and new equilibrium is reached. This equilibrium has more water in tank.

Do you follow?

Sent from my SM-G930V using Tapatalk

Edit:what he said^

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35 minutes ago, drstuess said:

No the link is accurate and would not overflow. As has been explained a bunch.

1. Aperture is decreased and flow out bottom decreases because hydrostatic pressure is the same.

2. Tank fills up because delta in flow rates.

3. Flow out bottom increases as tank fills up, as hydro static pressure at bottom increases.

Until...

4. Flow rates go to same value and new equilibrium is reached. This equilibrium has more water in tank.

Do you follow?

Sent from my SM-G930V using Tapatalk

Edit:what he said^

Very concise explanation, and exactly what I mean. Thank you! :)

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10 minutes ago, Mallow said:

Very concise explanation, and exactly what I mean. Thank you! :)

i do appreciate the civility in this discussion, but my opinion remains the pressure at the opening INCREASES the moment you make the aperture a tiny bit smaller maintaining the same flow rate out because of that pressure increase.........we differ in that your side is saying the pressure doesnt increase until the water inside the tank gets deeper.......it doesnt happen that way in a real life water hose, the hose has constant input and outflow(same amount entering one end and exiting the other), then you squeeze it a bit and clearly the water is under MORE pressure because of the altered aperture, it idoesnt wait for any build up in the hose, it immediately squirts the water further and faster.....again thanks to all posters for the civility.

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40 minutes ago, BillT said:

i do appreciate the civility in this discussion, but my opinion remains the pressure at the opening INCREASES the moment you make the aperture a tiny bit smaller maintaining the same flow rate out because of that pressure increase.........we differ in that your side is saying the pressure doesnt increase until the water inside the tank gets deeper.......it doesnt happen that way in a real life water hose, the hose has constant input and outflow(same amount entering one end and exiting the other), then you squeeze it a bit and clearly the water is under MORE pressure because of the altered aperture, it idoesnt wait for any build up in the hose, it immediately squirts the water further and faster.....again thanks to all posters for the civility.

I may have misunderstood your post earlier--are you talking about a hose hooked up to a city water system? If so, that situation is far more complicated than my simple analogy. Water pressure may build up behind the aperture of a squeezed garden hose attached to a city water system, though it's unclear to me that that is necessary. What is clear is that, even in this example, the flow rate coming out the end of the hose must not be constant, because if it were (i.e. if there was always an increase in water pressure to compensate for the decreased aperture size), then completely cutting off the flow would result in infinite water pressure, which it clearly does not. Regardless, that system is not what I'm talking about at all. The city water pressure is a variable I have no control over, and I cannot tell you how it reacts to changes in the system. There is no constant "input" into a "tank" in that case, and thus it is not obvious how this particular analogy relates to the one I am talking about. And the hose itself adds another physical dimension that I think is far too complicated and unnecessary for my analogy. I intentionally made my analogy as simple as possible, with as few variables as are necessary to get across my point (that initial and final flow into and out of the system can remain the same while total storage has changed, with no violation of conservation laws invoked). I remain unclear as to why my experimental setup is being perceived as controversial--it's very straightforward and relies on only a minimal few parameters.

Again, it is easily demonstrable that the water pressure of the fluid coming out of a hole in the bottom of a tank is almost completely dependent on the depth of the water in the tank. The only minor caveats have to do with friction and turbulence at the aperture (these caveats potentially being much less minor if you introduce a hose instead of a hole, which is why I prefer not to overcomplicate my system in that way). If, as you suggest, the water pressure immediately compensated for the change in the size of the hole keeping the outflow rate constant, then that would imply that two holes in the bottom of a tank should have the same outflow rate regardless of size. That is clearly untrue.

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how is the water getting into your tank please since using the city water pipes presents some problem when i use them?   and how in reality is the hose not just a much smaller "tank"?

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17 minutes ago, BillT said:

how is the water getting into your tank please since using the city water pipes presents some problem when i use them?   and how in reality is the hose not just a much smaller "tank"?

In my analogy, the constant flow coming into the top of the tank can be from any water source. This is preferably a well-controlled source with a constant flow rate. I don't know what the best method of doing this would be, but using a tap would probably be a decent approximation. Of course, it's still impossible to know that the water flow is constant in that case. However, I think it's clear that the situation is significantly more complicated when the water pressure in the tank depends on more than just the depth of the water in the tank. If all of the water is contained in the walls of the hose/tank system, with zero exposure to the air, then the water pressure is heavily dependent on how changes in the water flow interact with the pressure coming from the city water supply. This is exactly the situation I would like to avoid. This also addresses your second question.

And I'd like to again reiterate that my experimental setup is simple, with only two adjustable variables (only one of which needs actually be adjusted) and no extraneous complications. If you have a specific problem with my setup, please state what it is. Otherwise, I fail to see how discussing these unrelated, more complicated experiments contributes to the discussion of my experiment.

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doesnt we both accepting that we can consider the city source to be a constant flow seem reasonable?....i ask because to do this already requires we assume the earth gets a constant input to the surface from the sun(which it clearly DOES NOT)........the pressure either in the tank or the hose comes from the source of the input water....also adding a second hole and changing nothing else would drain the "tank" because it would slowly empty to the point the input is flowing straight out the bottom.

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25 minutes ago, BillT said:

doesnt we both accepting that we can consider the city source to be a constant flow seem reasonable?....i ask because to do this already requires we assume the earth gets a constant input to the surface from the sun(which it clearly DOES NOT)........the pressure either in the tank or the hose comes from the source of the input water....also adding a second hole and changing nothing else would drain the "tank" because it would slowly empty to the point the input is flowing straight out the bottom.

I'd like to start by again asking why we're discussing your more complicated setup when my more simple setup suffices.

We know that the energy rate coming from the sun is not constant, although it is very close. This is not the point my analogy is addressing. As I have said numerous times before, this experiment addresses the question of whether conservation laws are violated when storage of a quantity increases while flow rate before and after some change are equal. It is not meant to address every aspect of the climate system.

As for your statement that "the pressure either in the tank or the hose comes from the source of the input water," it is not correct. Hydrostatic water pressure increases with depth of water, just as air pressure increases towards the Earth's surface. Any tank of water, even one with no flow, has higher water pressure in the bottom of the tank than at the top. This is a simple physical fact. In my experimental design, the point is to avoid having to deal with other sources of water pressure. A hose hooked directly up to a city water supply not only does not avoid this complication, but it actually imposes it directly to the system. This is why it's an invalid comparison. As an aside, many city water supplies actually get their water pressure from the same physical concept that makes the water pressure at the bottom of the tank higher than at the top--they lift water to a higher level so that the effective water "depth" is deeper. This, however, requires a completely closed system of water pipes. This is exactly why we don't have control in the hose scenario--the water pressure is still dependent on the water "in the tank," but the "tank" includes the entire city water supply, and I cannot tell you how a change in aperture size will interact with the pressure of the city water supply. It is an unnecessary complication, and is just not the right way to design this experiment.

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10 minutes ago, BillT said:

without the constant input you have no water in the tank and no pressure at all.......

I do not understand the relevance of this statement. We can agree that you can store water in a bucket or open tank, no? In your words, how would you describe the distribution of water pressure in this still tank? Does it depend on the water pressure of the source that added water to the tank?

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22 hours ago, BillT said:

without the constant input you have no water in the tank and no pressure at all.......

That's not true in his analogy. Fill a bucket with water. Turn off the hose so that there is a static amount of water in the bucket. 

Now, poke a hole in the bottom of the bucket. Does the water flow out of the hole?

Yes, it does. It does so because of the pressure of the water in the bucket. The pressure at the surface of the water is less that the pressure at the bottom of the bucket. The amount of pressure is determined by the height of the water. 

sanitarry%20tri-camp%20centrifugal%20pum

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22 minutes ago, FloridaJohn said:

That's not true in his analogy. Fill a bucket with water. Turn off the hose so that there is a static amount of water in the bucket. 

Now, poke a hole in the bottom of the bucket. Does the water flow out of the hole?

Yes, it does. It does so because of the pressure of the water in the bucket. The pressure at the surface of the water is less that the pressure at the bottom of the bucket. The amount of pressure is determined by the height of the water. 

sanitarry%20tri-camp%20centrifugal%20pum

and SOON the bucket is empty and there is zero pressure or water.......for their claim to work REQUIRES constant input.....this had been civil until now......your question is utterly insulting to the concept of civility....and the "pressure" can indeed come from a city water system OR a tall column of water, it reacts the same way.
 

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2 hours ago, BillT said:

and SOON the bucket is empty and there is zero pressure or water.......for their claim to work REQUIRES constant input.....this had been civil until now......your question is utterly insulting to the concept of civility....and the "pressure" can indeed come from a city water system OR a tall column of water, it reacts the same way.
 

I did not see his response as insulting at all. In fact, it is exactly the point I was trying to make with my previous post. I am trying to understand where you think pressure in the system comes from. In my experiment, the water pressure is 100% dependent on the depth of the water in the tank.
 

So I'd like to try to understand what it is that you disagree with about my experiment. And to understand what you're describing better, I would like to know your answer to the simpler question:  In your words, how would you describe the distribution of water pressure in a still tank? Does it depend on the water pressure of the source that added water to the tank?

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1 minute ago, Mallow said:

I did not see his response as insulting at all. In fact, it is exactly the point I was trying to make with my previous post. I am trying to understand where you think pressure in the system comes from. In my experiment, the water pressure is 100% dependent on the depth of the water in the tank.
 

So I'd like to try to understand what it is that you disagree with about my experiment.

you see no insult is being asked if a bucket full of water gets a hole in the bottom will the water drain out????     that is insulting.....and when i first confronted your premise i pointed out the mere changing of the aperture ALTERS the pressure rendering this "the water pressure is 100% dependent on the depth of the water in the tank." FALSE

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1 hour ago, BillT said:

you see no insult is being asked if a bucket full of water gets a hole in the bottom will the water drain out????     that is insulting.....and when i first confronted your premise i pointed out the mere changing of the aperture ALTERS the pressure rendering this "the water pressure is 100% dependent on the depth of the water in the tank." FALSE

By what physical mechanism does altering the aperture change the water pressure at the bottom of the tank? And what is the "source" of water pressure in a still tank?

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Since it appears that the explanation of my analogous experiment was not as easy to comprehend as I had intended, I'll ask another, related question.

Start with an empty tank, with a small hole in the bottom. Let water flow into the top of the tank via a tap at a (near-) constant rate, such that the rate at which the water flows into the top is a little faster at first than the rate at which it exits the bottom of the tank. I think we can all agree that the tank would begin to fill with water, as the inflow rate is greater than the outflow rate. But what will happen after that? Will the tank continue to fill at the same rate perpetually? Or will something else happen? To me, it is clear that, as the water level increases, the water pressure in the bottom of the tank increases, increasing the outflow rate. Eventually, the outflow rate will match the inflow rate. At that point, the water level has reached an "equilibrium" level. Can we agree that this is what would happen in this experiment?

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3 minutes ago, Mallow said:

Since it appears that the explanation of my analogous experiment was not as easy to comprehend as I had intended, I'll ask another, related question.

Start with an empty tank, with a small hole in the bottom. Let water flow into the top of the tank via a tap at a (near-) constant rate, such that the rate at which the water flows into the top is a little faster at first than the rate at which it exits the bottom of the tank. I think we can all agree that the tank would begin to fill with water, as the inflow rate is greater than the outflow rate. But what will happen after that? Will the tank continue to fill at the same rate perpetually? Or will something else happen? To me, it is clear that, as the water level increases, the water pressure in the bottom of the tank increases, increasing the outflow rate. Eventually, the outflow rate will match the inflow rate. At that point, the water level has reached an "equilibrium" level. Can we agree that this is what would happen in this experiment?

i have no difficulty understanding your experiment please dont talk down to me.....you have failed to answer to the simple reality i posted with the water hose, the moment you close the aperture a tiny bit the pressure at the opening goes UP(no need for any buildup) and the flow rate remains the same just squirting further and moving faster.

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6 minutes ago, BillT said:

i have no difficulty understanding your experiment please dont talk down to me.....you have failed to answer to the simple reality i posted with the water hose, the moment you close the aperture a tiny bit the pressure at the opening goes UP(no need for any buildup) and the flow rate remains the same just squirting further and moving faster.

I am sorry, but I do not wish to discuss the scenario with the hose attached directly to the city water system anymore. It is far too complicated a system and not relevant to my experiment, as the physical mechanisms at play are different. I have addressed my concerns with it to the best of my ability, and I would like to focus on the experiment that I proposed. I am sure you will understand if I do not address this side-topic in the future.

If you feel that I am talking down to you, I apologize. However, I would like to know if you agree with my assertion in the post you quoted, as I am trying to understand what is unclear about my experiment. Do you agree?

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5 minutes ago, Mallow said:

I am sorry, but I do not wish to discuss the scenario with the hose attached directly to the city water system anymore. It is far too complicated a system and not relevant to my experiment, as the physical mechanisms at play are different. I have addressed my concerns with it to the best of my ability, and I would like to focus on the experiment that I proposed. I am sure you will understand if I do not address this side-topic in the future.

If you feel that I am talking down to you, I apologize. However, I would like to know if you agree with my assertion in the post you quoted, as I am trying to understand what is unclear about my experiment. Do you agree?

what is unclear is your source of even flowing water....you wont accept my city pipe source, so i dont get where you have a source with fewer complications as you put it?......i think were we differ is i am using a real world example of what happens.....and you are trying to dvise an experiment showing that isnt what happens.....by simply closing the aperture a tiny bit accepting all input water sources are equal, pretty sure i asked that we both accept there has to be an accepted water source because you do need to have that for your experiment.

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16 minutes ago, BillT said:

what is unclear is your source of even flowing water....you wont accept my city pipe source, so i dont get where you have a source with fewer complications as you put it?......i think were we differ is i am using a real world example of what happens.....and you are trying to dvise an experiment showing that isnt what happens.....by simply closing the aperture a tiny bit accepting all input water sources are equal, pretty sure i asked that we both accept there has to be an accepted water source because you do need to have that for your experiment.

I have explained to the best of my ability why I do not believe the experiments are equivalent. The problem is with water pressure, not water flow rate, which should be constant enough for my experiment. In other words, in my experiment, the water pressure in the tank does not depend on the city water pressure. The water pressure in the hose is almost completely determined by the city water pressure. This is why I am not interested in the hose design. So please in the future, let us discuss my design. If you believe the two designs are equivalent, then please couch your argument in the terms of my design rather than that of the hose example, since I do not agree that they are equivalent, and the hose example is thus irrelevant to me.

In order to understand where we disagree, I am trying to ascertain what parts of my experiment you agree with and what parts you don't agree with. So I will repeat the questions I asked above. Start with an empty tank, with a small hole in the bottom. Let water flow into the top of the tank via a tap at a (near-) constant rate, such that the rate at which the water flows into the top is a little faster at first than the rate at which it exits the bottom of the tank. I think we can all agree that the tank would begin to fill with water, as the inflow rate is greater than the outflow rate. But what will happen after that? Will the tank continue to fill at the same rate perpetually? Or will something else happen? To me, it is clear that, as the water level increases, the water pressure in the bottom of the tank increases, increasing the outflow rate. Eventually, the outflow rate will match the inflow rate. At that point, the water level has reached an "equilibrium" level. Can we agree that this is what would happen in this experiment?

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how do you get an input source PLEASE?    i have asked repeatedly for your experiment to be valid in the real world you need an steady input source, not subject to any complications......

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3 minutes ago, BillT said:

how do you get an input source PLEASE?    i have asked repeatedly for your experiment to be valid in the real world you need an steady input source, not subject to any complications......

A tap is sufficiently steady. But there are many other ways if you want a more precise flow rate. For one, you can use a very large tank as a source, with an output (that would serve as an input for my experiment) at a given level in the tank, such that the level in the very large tank doesn't change substantially through the course of the experiment. This would provide a very steady flow.

However, again, a tap should be sufficiently steady for the flow rate in my experiment.

Will you please tell me whether you agree or disagree with my above questions?

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i already have answered your questions and now we can agree we differ in the size of the TANK my hose versus your tank to maintain pressure BOTH are dependent upon the TAP and in the real life use of the hose it immediately squirts the same flow rate faster and further when closing the aperture a bit....that happens with a bit smaller aperture with a constant state of pressure........

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15 minutes ago, BillT said:

i already have answered your questions and now we can agree we differ in the size of the TANK my hose versus your tank to maintain pressure BOTH are dependent upon the TAP and in the real life use of the hose it immediately squirts the same flow rate faster and further when closing the aperture a bit....that happens with a bit smaller aperture with a constant state of pressure........

I do not think you have answered my questions at all. Did you agree that the water would reach an equilibrium level in the experiment I described above where you start with an empty tank and keep the hole size constant (yes or no)?

I do not understand the rest of your comment. As far as I can tell, you are arguing that the water pressure in my tank depends on the city water pressure? If so, that is simply incorrect. Water pressure is not a conserved variable, the water does not somehow "remember" the pressure level from whence it originated. And there is no physical mechanism by which water pressure must change to keep flow rate constant--if that were the case, than a change to an infinitesimally small hole would cause the hole to be under an infinitesimally large pressure to maintain a constant flow rate. There is no physical basis by which this could or should occur.

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YES to keep a constant pressure in your tank requires the input water.....the only thing that gets altered is the aperture by a tiny bit...when done in the real world that constant pressure forces the same flow rate through to smaller opening with no build up of pressure needed.

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10 minutes ago, BillT said:

YES to keep a constant pressure in your tank requires the input water.....the only thing that gets altered is the aperture by a tiny bit...when done in the real world that constant pressure forces the same flow rate through to smaller opening with no build up of pressure needed.

Again, I don't understand this. I never constrained my experiment to maintain a constant pressure in the tank. And I have since simplified my experiment to not include changing the size of the hole. You have not yet addressed whether you agree with my conception of the new experiment yet. I had hoped that removing the need to change the size of the hole during the experiment would remove that source of your concern. Please let me know if you agree with my statements about my simpler experiment.

And again, when done in the real world, there is absolutely no physical mechanism or reason to suspect that the flow rate through two different sized holes at constant pressure would be the same. In fact, physically speaking, it is guaranteed that the flow rate under equal pressure through a larger hole would be greater. And that, I feel, is also intuitive. A large hole in the bottom of a tank would be associated with a greater water flow rate than a smaller hole in the same tank. I don't understand what could lead someone to conclude otherwise.

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11 hours ago, BillT said:

you see no insult is being asked if a bucket full of water gets a hole in the bottom will the water drain out????     that is insulting.....and when i first confronted your premise i pointed out the mere changing of the aperture ALTERS the pressure rendering this "the water pressure is 100% dependent on the depth of the water in the tank." FALSE

First, let me apologize if my response was insulting to you. That was not the intent. I was not trying to point out that water will flow out of a hole in a bucket, but WHY that is the case. More specifically, I was trying to illustrate the physics behind it. Clearly I did not communicate that effectively.

However, after reading some of your responses, I think I have figured out where the disconnect is. The difference between your hose example and the bucket example is that the hose is a constant pressure system, and the bucket is a variable pressure system.

Due to Bernoulli's Law, in a closed system, pressure is equal against all surfaces. That means that when you have your thumb completely covering the end of the hose, the pressure is the same against your thumb, against the walls of the hose, and against all the plumbing in your house. When you remove your thumb from the end of the hose, the pressure inside the hose is still the same.

As the water leaves the hose, it is no longer constrained by the walls of the hose, and the pressure drops to zero (Bernoulli's Law again). The pressure differential between the water in the hose and the water leaving the hose causes the water to flow out of the hose (moving from a high pressure area to a low pressure area).

When you partially block the end of the hose, you are creating a restriction in the system. The pressure inside the hose is still 45 psi (or whatever the city water pressure is in your house) and the water outside of the hose is still 0 psi. Since the pressure differential is still the same, the water still flows at the same rate (probably around 2.5 gallons per minute (gpm) or so).

Since the pressure differential is still the same, and the flow rate is still the same, then the only thing that can change to account for the restriction on the hose (your thumb) is the velocity of the water. It speeds up to get around your thumb. Since the water is now going at a faster velocity, it shoots further out into the lawn.

That is what you are seeing when you partially cover the end of the hose with your thumb. The more you cover up the hose, the faster the velocity of the water, the farther it goes. The less you cover the end of the hose, the slower the velocity, the closer the stream of water comes to your shoes. The pressure inside the hose never changed. If that was not the case, then, as pointed out earlier, if pressure increased as you added more restriction, there would be ever increasing pressure inside the hose and the hose would burst when you completely stopped the flow.

Also, this is why the pressure in the faucet does not add to the pressure of the water in the bucket. Once the water leaves the confines of the faucet, the pressure drops to zero. This completely separates the pressure inside the faucet from the pressure at the bottom of the bucket. They are not additive because the water enters the bucket at zero pressure.

Sorry for the wall of text. I hope this clarifies the physics behind what we are discussing.

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