Solving the Mystery: Which Tank Fills First?

[Dadface]

this has also already been discussed and is irrelevant
The water is only dripping into the A tank

The fact that the water is "only dripping" into the tank does not make my point irrelevant and drip rate and drip size are yet other variables that determine what will happen.
Take another look at the diagram and compare the drop size to the radii of the tubes. I know the diagram is only a schematic but it is the main information we have to go on. And by comparing the sizes it seems that the tubes are capillaries with very small internal radii. If that's the case then the effect of surface tension on flow rate will be considerable.
The point I'm trying to make is that the question as presented is not specific enough.

 

[davenn]

The point I'm trying to make is that the question as presented is not specific enough.

it is presented well enough for a basic solving of the problem
all you are doing is turning it into something much more difficult
don't over think or over complicate it

 

[Dadface]

I know I'm probably over complicating it but I like to think of the problem in terms in terms of a real situation in addition to a situation where certain simplifying assumptions are made. Imagine water dripping into a bucket with a very narrow capillary tube sticking out the side, along with the question:
Will the bucket ever fill to the brim?
Without further information you couldn't give a definite answer but you could describe the conditions needed for it to fill to the brim.

 

[CWatters]

A reasonable assumption to make would be that the problem is intended to be solvable without additional info. It's unlikely the setter expected people to answer that is was "Unsolvable for the following 10⁶ reasons".

 

[davenn]

A reasonable assumption to make would be that the problem is intended to be solvable without additional info. It's unlikely the setter expected people to answer that is was "Unsolvable for the following 10⁶ reasons".

exactly :)

 

[sophiecentaur]

I know I'm probably over complicating it

Yep. The thread got out of hand after the point where we came up with the Obvious Answer. (But that's Physicists for you.)

 

[Dadface]

It seems that some people here think there's only one possible answer to the question. If that's the case what's the answer to the question below which illustrates the point I'm making and which illustrates what happens at tank A. Does the tank fill or does it not fill? The answer is not obvious and we can't tell what the answer is because what happens depends on the flow rates of water entering and leaving the tank. And we don't know what those flow rates are. So there are two possible answers and not just one. Similarly there are two possible answers to the original question.

 

[sophiecentaur]

It seems that some people here think there's only one possible answer to the question.

Of course there are dozens of answers, depending on the depth you want to discuss. But this puzzle is not a Physics Puzzle. You could find it in any old magazine or on Facebook. You could introduce string theory into it if you want but it would just exclude a vast number of people who might enjoy dealing with the initial problem - as presented.

 

[Dadface]

Of course there are dozens of answers, depending on the depth you want to discuss. But this puzzle is not a Physics Puzzle. You could find it in any old magazine or on Facebook. You could introduce string theory into it if you want but it would just exclude a vast number of people who might enjoy dealing with the initial problem - as presented.

Although the problem can be discussed in terms of physics a detailed knowledge of the subject is not necessary in order to understand it. It's simple and just needs a bit of common sense and general knowledge. It's something that people can experience in everyday life, for example leave a tap running and if the sink doesn't drain quickly enough you get an overflow. It happened my house recently the result being that there was a very wet bathroom floor to clean up.

Please look again at the question I posed in post 42. It describes a situation where there is no definite answer because the relevant flow rates are not known. So there are two possible answers to my question and by similar reasoning two possible answers to the original question. With the original question Tank F is one possible answer. But Tank A is the second possible answer.

I have been referring to physics in this thread because after all it is a physics forum. But that does not prevent any non physics person from tackling the question and seeing that Tank A is a possible answer. The main thing they need to know is that the water does not necessarily leave the tank at the same rate as it enters the tank.

 

[NTL2009]

Although the problem can be discussed in terms of physics a detailed knowledge of the subject is not necessary in order to understand it. It's simple and just needs a bit of common sense and general knowledge. It's something that people can experience in everyday life, for example leave a tap running and if the sink doesn't drain quickly enough you get an overflow. It happened my house recently the result being that there was a very wet bathroom floor to clean up. ... .

See post #2. The picture shows it dripping, not flowwing. You are overthinking it. It's already 'tricky' with levels and ports that are not obviously blocked. Plenty tricky for the intended audience w/o going into flow rates past the 'drip'.

 

[Dadface]

See post #2. The picture shows it dripping, not flowwing. You are overthinking it. It's already 'tricky' with levels and ports that are not obviously blocked. Plenty tricky for the intended audience w/o going into flow rates past the 'drip'.

I have seen post 2 and I ask you to please see my question in post fourty two where the water is dripping. The question mimics the situation at Tank A in the original question where in both cases water moves in and water moves out.
When a question is posted in a physics forum its reasonable to assume that the intended audience is a group of people many of whom have an interest in physics. Therefore it's reasonable to refer to some physics which has been done in this thread. But the question can also be tackled in terms of general knowledge.
Try to forget physics and please look again at my question in post fourty two. What would your answer be if you were told:
1. The hole is extremely big?
2. The hole is extremely small?
3. The size of the hole is unknown?

 

[fahraynk]

I have seen post 2 and I ask you to please see my question in post fourty two where the water is dripping. The question mimics the situation at Tank A in the original question where in both cases water moves in and water moves out.
When a question is posted in a physics forum its reasonable to assume that the intended audience is a group of people many of whom have an interest in physics. Therefore it's reasonable to refer to some physics which has been done in this thread. But the question can also be tackled in terms of general knowledge.
Try to forget physics and please look again at my question in post fourty two. What would your answer be if you were told:
1. The hole is extremely big?
2. The hole is extremely small?
3. The size of the hole is unknown?

2 situations are possible for the first tank. 1) the water is entering faster than it can exit through the pipe. Then the first tank wins and it is a trivial solution.
Case 2) the pipe can pass water faster than it is entered into the system. In this case, the obvious solution will win.

Am I wrong?

 

[Dadface]

2 situations are possible for the first tank. 1) the water is entering faster than it can exit through the pipe. Then the first tank wins and it is a trivial solution.
Case 2) the pipe can pass water faster than it is entered into the system. In this case, the obvious solution will win.

Am I wrong?

Yes, tank F wins but if water enters tank A faster than it leaves then tank A wins.

 

[shihab-kol]

I don't know much of this but shouldn't all of them (except blocked ones) have the same amount of water to maintain equilibrium ?
Most probably though I am wrong.

 

[jbriggs444]

I don't know much of this but shouldn't all of them (except blocked ones) have the same amount of water to maintain equilibrium ?
Most probably though I am wrong.

An "equlibrium" would not imply that all tanks have the same amount of water. Instead, it would mean that the situation remains the same from one moment to the next. In the problem at hand, we have an evolving situation that does not remain the same from one moment to the next. This is the opposite of equilibrium.

When one tank overflows, we will have an equilibrium situation. That equilibrium state is nicely portrayed in the spoiler by @DrGreg in response #19.

[Provided that we do not concern ourselves with the possibility of pipes narrow enough to restrict the flow unexpectedly]

 

[shihab-kol]

Ok,
Thanks!

 

[NTL2009]

I have seen post 2 and I ask you to please see my question in post fourty two where the water is dripping. The question mimics the situation at Tank A in the original question where in both cases water moves in and water moves out.
When a question is posted in a physics forum its reasonable to assume that the intended audience is a group of people many of whom have an interest in physics. Therefore it's reasonable to refer to some physics which has been done in this thread. But the question can also be tackled in terms of general knowledge.
Try to forget physics and please look again at my question in post fourty two. What would your answer be if you were told:
1. The hole is extremely big?
2. The hole is extremely small?
3. The size of the hole is unknown?

But we were not "told" any of those things directly.

We were shown a single drip, not a constant flow. And a single drip over that distance (assume a typical faucet for scale), means the inlet rate appears far slower than the limit of what those pipes could handle.

There is no need to take it further. Again, consider the intended audience.

Now, if they included an actual flow number, and pipe sizes, then we could go down your path. But there is no reason to do that, given the information presented.

I could also say "none of them overflows". Maybe that drop signifies the last drop - the water was shut off just prior to the image. But no reason to go there either.

 

[jack action]

There are so many variables to consider and it would help at the outset to be told what simplifying assumptions can be made.

The point I'm trying to make is that the question as presented is not specific enough.

I like to think of the problem in terms in terms of a real situation in addition to a situation where certain simplifying assumptions are made.

But the question can also be tackled in terms of general knowledge.

[SARCASM]I think you're on to something. What about acceleration? It's not mention anywhere what is the direction of the acceleration of the system; Or even if there is one! What if this system is on a roller coaster, you know, one that goes into a loop? Then we need to know the actual path and the velocity of the moving frame to be able to get the full picture. Combined with the flow velocity of the water (who says it is water? Again an assumption!), we will have to take into account the Coriolis acceleration.

What about ambient pressure? If it is below the boiling point of the liquid, no tanks will ever get filled because the liquid will evaporate! I'm not going to fell into that trap. no sir!

At first, I was also fooled by the diagram, thinking water was coming out of the faucet under gravity in a fixed frame. You opened up my eyes, physics is much more complicated than that.

Don't be tricked by the lack of information. The REAL answer is: It depends.[/SARCASM]

 

[Rajini]

Hello,
It depends on the flow velocity (from tap) of blue liquid! If the blue liquid's flow velocity if very high then tank A will be first filled and over flows.
If the liquid falls drop by drop then F will fills first.
If the tank material is high porous & permeable (at connections) then G tank fills first.
Cheers, Rajini

 

[RonL]

And now the reason why I am so misunderstood in most cases, becomes very clear

 

[Dadface]

But we were not "told" any of those things directly.

1 .Precisely and that's the point I've been making with my variation of the question.We cannot describe exactly what would happen without further information but if you read further into my reply it doesn't matter.

We were shown a single drip, not a constant flow. And a single drip over that distance (assume a typical faucet for scale), means the inlet rate appears far slower than the limit of what those pipes could handle.

2. It seems that you're extracting information from the diagram and if that diagram is to scale and not just a schematic then you should also notice that the pipe diameter seems narrower than the drop size. If that's the case what does it tell you?

There is no need to take it further. Again, consider the intended audience.

3. The question was posed here, on a forum to do with physics so you tell me who you think the intended audience is?

Now, if they included an actual flow number, and pipe sizes, then we could go down your path. But there is no reason to do that, given the information presented.

4.You don't need that information to "go down my path". Please read my posts carefully

I could also say "none of them overflows". Maybe that drop signifies the last drop - the water was shut off just prior to the image. But no reason to go there either.

5. The question implies that a tank will fill so your comment is not really relevant.

 

[Dadface]

[SARCASM]I think you're on to something. What about acceleration? It's not mention anywhere what is the direction of the acceleration of the system; Or even if there is one! What if this system is on a roller coaster, you know, one that goes into a loop? Then we need to know the actual path and the velocity of the moving frame to be able to get the full picture. Combined with the flow velocity of the water (who says it is water? Again an assumption!), we will have to take into account the Coriolis acceleration.

What about ambient pressure? If it is below the boiling point of the liquid, no tanks will ever get filled because the liquid will evaporate! I'm not going to fell into that trap. no sir!

At first, I was also fooled by the diagram, thinking water was coming out of the faucet under gravity in a fixed frame. You opened up my eyes, physics is much more complicated than that.

Don't be tricked by the lack of information. The REAL answer is: It depends.[/SARCASM]

I'm just wondering if you have anything non sarcastic and constructive to add.

 

[Dadface]

I think that there are some people who have not been reading my posts properly or perhaps not reading them at all so let me put it another way:
1. Please look again at the diagram and look at tank A and its outlet. For the time being forget all the other tanks.
2. Now ask yourself the following question:

Does tank A fill to the top?

As far as the original question goes there are three answers of relevance:

• Yes it does fill to the top
• No it doesn't fill to the top
• There is no definite answer

Most people here seem to be of the opinion that the second answer is the correct answer. But can they justify that answer?
Some people may be of the opinion that the first answer is the correct answer. But can they justify their answer?
In both cases the answer is no. The two answers cannot be justified because the question, as presented, does not give enough information.
The best response is the third one. In other words it may fill to the top or it may not. If it fills to the top then obviously tank A fills up first. If it doesn't fill to the top then tank F fills up first. It's easy.

 

[NTL2009]

I think that there are some people who have not been reading my posts properly or perhaps not reading them at all ... .

And some of us may be wondering that about you! :)

It is simple - you are viewing the puzzle from a different set of limits/assumptions than some others. Given the simplicity of the diagram, and lack of specific technical info, and the insertion of a enough 'tricks' to already make it non-obvious to a majority of people (even the assumed 'above average' people on this forum missed some of those tricks), most of us see no reason to go to further complications for this sort of puzzle.

But there is probably no way to objectively defend either position, so I will do what I should have done several posts back, and move on!

 

[Dadface]

And some of us may be wondering that about you! :)

It is simple - you are viewing the puzzle from a different set of limits/assumptions than some others. Given the simplicity of the diagram, and lack of specific technical info, and the insertion of a enough 'tricks' to already make it non-obvious to a majority of people (even the assumed 'above average' people on this forum missed some of those tricks), most of us see no reason to go to further complications for this sort of puzzle.

But there is probably no way to objectively defend either position, so I will do what I should have done several posts back, and move on!

I have not introduced further complications and everything I have referred to is inherent in the question. I'm assuming that many people think A will not fill to the top but they will find it just as hard to justify that as people who think it will fill to the top. I'm saying that with the limited information given one scenario is just as likely as the other (What really happens depends on factors such as flow rates into and out of the tank)

 

[jack action]

If it fills to the top then obviously tank A fills up first. If it doesn't fill to the top then tank F fills up first

According to your own interpretation, tank F will not necessarily fill up first if tank A doesn't fill to the top.

If the input & output flows in tank A are the same when, say, the tank is ¾-filled, then tank J might be the one to fill up first. Assuming the pipes give the same restriction to the flow everywhere (Again, an assumption), the pipe J-K will also need the equivalent of a ¾ of the tank height to reach the input flow. That will never happen since the pipe J-K is about halfway into tank J.

This reasoning could also apply to tank C.

And given the proper flow and restriction, if tank C level gets higher than the input pipe, but not enough to reach the top, it could restrict further more the flow in tank B which may rise to the top first.

Is that constructive enough?

The point is that assuming there are no assumptions is not a valid argument as it clearly leads nowhere. The single drop dripping from the faucet is the information that stipulate the flow is slow enough that we can assume no pipe restriction, which answers your question:

Most people here seem to be of the opinion that the second answer is the correct answer. But can they justify that answer?

A question that was already answered in post #2 and was also pointed out to you in post #45. But you still refused to admit defeat in post #46 by ignoring the justification given to you. The droplet symbol means «no matter how small are the pipes, they will never be a restriction».

 

[russ_watters]

It seems that some people here think there's only one possible answer to the question. If that's the case what's the answer to the question below which illustrates the point I'm making and which illustrates what happens at tank A. Does the tank fill or does it not fill? The answer is not obvious and we can't tell what the answer is because what happens depends on the flow rates of water entering and leaving the tank. And we don't know what those flow rates are. So there are two possible answers and not just one. Similarly there are two possible answers to the original question.View attachment 208915

As someone else said, I think you are muddling the provided constraints to generate this nebulosity where there doesn't need to be any.

Or perhaps more straightforward; sometimes we get trolled by unanswerable questions. This does not appear to be such a case. And even if it were, then it is just unanswerable, so there is STILL nothing to argue about!

 

[NTL2009]

Given one of those puzzles about two trains leaving such and such cities at such and such time at such and such speed, I wonder if some of those debating here would ask:

How much fuel does each train have? What condition are the tracks in? When was each train last maintained? How competent are the engineers, do they have any medical conditions that could affect their ability to guide the train? Are there any other conditions which would cause one or both trains to stop or slow (earthquake, flood, landslide, etc)?

It's a puzzle. For entertainment. If we don't assume some reasonable limits, there's really no point. OK, now I'm done! ;)

 

[Dadface]

According to your own interpretation, tank F will not necessarily fill up first if tank A doesn't fill to the top.If the input & output flows in tank A are the same when, say, the tank is ¾-filled, then tank J might be the one to fill up first. Assuming the pipes give the same restriction to the flow everywhere (Again, an assumption), the pipe J-K will also need the equivalent of a ¾ of the tank height to reach the input flow. That will never happen since the pipe J-K is about halfway into tank J.

This reasoning could also apply to tank C.

And given the proper flow and restriction, if tank C level gets higher than the input pipe, but not enough to reach the top, it could restrict further more the flow in tank B which may rise to the top first.

Is that constructive enough?

1. According to my interpretation if A doesn't fill up first then F will fill up first. Not B or C or any of the other tanks. Please look at my previous posts

The point is that assuming there are no assumptions is not a valid argument as it clearly leads nowhere.

2. If you make no assumptions at all about flow rates into or out of the tank then, in the context of this discussion, there are two outcomes that are relevant:

• Tank A does fill up
• Tank A doesn't fill up.

A lot of people here seem to be assuming,without justification, that what actually happens is described by the second outcome. I'm agreeing that the second outcome is a possibility but adding that the first outcome is also a possibility. And I take that opinion because there is not enough information to decide which of the two outcomes, or any other outcome, will actually occur. But I think I can confidently claim that just as there is a possibility that it may not fill up there is also a possibility that it may fill up.

The single drop dripping from the faucet is the information that stipulate the flow is slow enough that we can assume no pipe
restriction, which answers your question:

3. Really? That's new to me. Can you describe or point me to a reference giving the exact meaning of the drop symbol because it may have a big bearing on my argument.

A question that was already answered in post #2 and was also pointed out to you in post #45. But you still refuse to admit defeat in post #46 by ignoring the justification given to you. The droplet symbol means «no matter how small are the pipes, they will never be a restriction»

4. Are you saying that I should "admit defeat" if I don't agree with the points raised?
.

 

[haushofer]

I don't see any amount of spatial dimensions or particular compactification specified in this problem.

 

[Dadface]

I can't understand why some people here are finding the point I am making difficult to grasp. It doesn't make unjustified assumptions. It is simple, it is obvious. It can be answered in terms of physics and it can be answered in terms of pure straightforward common sense and general knowledge.
I have tried in many different ways to put my point across and now I'm going to try again by reiteration of a question I posed earlier in this thread. Here goes:

WATER CONTINUES TO DRIP INTO A BUCKET WHICH HAS A HOLE IN THE SIDE. WILL THE BUCKET FILL UP?

That's it, I have described a situation which is analogous to the water dripping into Tank A as in the original question set by fahraynk. So will the bucket fill up or won't it? The best response would be that there is no definite answer to the question because not enough information has been given.
Similarly if I ask whether tank A in the original question fills up or not, the best response again would be that there is no definite answer because not enough information has been given. Despite that some people assume that tank A will not fill up. Where's the proof for that? And where's the proof for the assumption that may be made that Tank A will fill up? There is no proof to back up either assumption or any other assumptions.
My answer to the questions would be that I don't know the answers but just as there is a possibility that the bucket or tank won't fill up there is also a possibility that they will fill up. So Tank A might fill up first and to paraphrase fahrank if it does so it's a trivial solution. I'm not sure that I agree with the word trivial but even if it is trivial it is still a possible solution.
That's it, like NTL 2009 I'm done. I don't have the inclination to keep going over the same ground. On top of everything else I'm getting things like looping the loop, the Coriolis effect and particular compactification entering the discussion.

 

[jbriggs444]

I can't understand why some people here are finding the point I am making difficult to grasp.

We understand your point. Many of us are gritting our teeth, waiting for the discussion to stop already.

 

[Dadface]

Thank you. I'm a fellow tooth gritter.

 

[RonL]

Thank you. I'm a fellow tooth gritter.

The surface condition of the faucet will determine the size of the drop, if the drawing represents the problem, then no math is required, tank size and drain tubes are scaled to reflect that no accumulation will occur and water level will be exactly like the spoiler presented by DrGreg indicates, an endless array of other possibilities can be conjured up to reflect other results.

 

[russ_watters]

I can't understand why some people here are finding the point I am making difficult to grasp. It doesn't make unjustified assumptions. It is simple, it is obvious. It can be answered in terms of physics and it can be answered in terms of pure straightforward common sense and general knowledge.

Ok...

WATER CONTINUES TO DRIP INTO A BUCKET WHICH HAS A HOLE IN THE SIDE. WILL THE BUCKET FILL UP?

No.

The best response would be that there is no definite answer to the question because not enough information has been given.

Why? Because you don't know the flow rate of a drip? Ok, fine. I don't think that's reasonable, but it isn't an absolute, so so be it - you can have it. If that's your objection, then I get what you are saying and I think most others do as well. That said, if someone sees a question like this on a test, they should answer it and not punt. I wouldn't want our students to get into the habit of diving so deep they can no longer see the surface, causing them to waste time and get wrong answers on tests unnecessarily.