Solving the Mystery: Which Tank Fills First?

[Dadface]

Ok...

No.

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.

I tried the question on a student this morning and his first response was the question: How big is the hole? I told him that it could be any size you like from the tiniest pin prick upwards. His response was that the bucket might fill up if the hole was small enough but not if it was a big hole. He spent just seconds thinking about the question. And he didn't use any physics but just general knowledge. I also tried it on my wife who has no interest in physics and she also came up with the same answer which is that it depends on the size of the hole. Of course there are other variables but we didn't discuss them.

It's a very simple question but for some reason some people here seem to accept the possibility that Tank A does not fill up but deny the possibility that it does fill up. With limited information the best that can be done is to describe possibilities ,not absolutes.

I can appreciate your concern about not confusing students but I can tell you that in the UK questions of the type discussed here do not come up in high school science exams. But I do think it can be helpful to tackle other style questions.
Anyway thank you very much for your response but as I said in a previous post I want out of this now. It's taking up too much time and It seems that I keep going over the same stuff.

 

[davenn]

Of course there are other variables but we didn't discuss them.

BUT that is exactly what you are trying to do here, instead of taking the diagram at face value

all I can say is thank god I'm not one of your students ...
it would be a wonder if any of them could pass an exam when you keep changing the position of the goal posts

you took a very simple puzzle and totally destroyed it

 

[sophiecentaur]

There's a hole in my bucket dear Liza dear Liza.

 

[Nidum]

Then mend it dear Henry dear Henry

 

[sophiecentaur]

But which one should I mend first?
Can I go home now?

 

[russ_watters]

I tried the question on a student this morning and his first response was the question: How big is the hole? I told him that it could be any size you like from the tiniest pin prick upwards. His response was that the bucket might fill up if the hole was small enough but not if it was a big hole. He spent just seconds thinking about the question. And he didn't use any physics but just general knowledge. I also tried it on my wife who has no interest in physics and she also came up with the same answer which is that it depends on the size of the hole.

Fair enough. Very surprising to me since none of the other dozen or so respondents in this thread see it that way. [Shrug]

 

[DrGreg]

I tried the question on a student this morning and his first response was the question: How big is the hole? I told him that it could be any size you like from the tiniest pin prick upwards. His response was that the bucket might fill up if the hole was small enough but not if it was a big hole. He spent just seconds thinking about the question. And he didn't use any physics but just general knowledge. I also tried it on my wife who has no interest in physics and she also came up with the same answer which is that it depends on the size of the hole.

Fair enough. Very surprising to me since none of the other dozen or so respondents in this thread see it that way. [Shrug]

Maybe not that surprising, since the bit I've highlighted in bold is steering the student towards an answer. That extra hint wasn't part of the published question.

 

[Dadface]

BUT that is exactly what you are trying to do here, instead of taking the diagram at face value

1. Taking the diagram at face value is exactly what I've been doing. Have you been taking the diagram at face value ? Do you think its a scale drawing? My best guess is that its a schematic but whatever it is the information it provides is limited.Do you not see that whatever the diagram is there is not enough information to prove emphatically that Tank A does not fill up nor that it does fill up?
It seems that we differ in that you insist that A does not fill up whereas I say that not filling up is indeed a possibility but filling up is another possibility There is insufficient evidence to conclude what really happens.

all I can say is thank god I'm not one of your students ...
it would be a wonder if any of them could pass an exam when you keep changing the position of the goal posts

2. My record shows that wonders happen.

you took a very simple puzzle and totally destroyed it

3.No I took a very simple puzzle and like other people on this forum tried to answer it. But for some reason you disagree with my reasoning that Tank A could be the first one to fill up.

 

[Dadface]

Maybe not that surprising, since the bit I've highlighted in bold is steering the student towards an answer. That extra hint wasn't part of the published question.

Yes DrGreg you are right. I didn't realize at the time that the highlighted sentence was steering the student but now you've mentioned it I see that it was. I will try the question again with other people but without the steering. Thanks for pointing it out.

 

[Dadface]

sophicentaur and Nidum, thanks for the musical interlude. It was very melodic.

 

[jack action]

3.No I took a very simple puzzle and like other people on this forum tried to answer it. But for some reason you disagree with my reasoning that Tank A could be the first one to fill up.

Nobody is disagreeing with the physics you propose. We disagree with the interpretation of the problem, namely the assumptions that are or are not made.

You say that it is acceptable to assume the pipe are restrictive and, therefore, the answer «it depends» is an acceptable one. Listening to you, one can imagine that, as a teacher, you would give partial points for the answer «tank F» and give bonus points to the one student who give the answer «It depends on the pipe size and faucet flow, which are not mentioned: tank A if the flow is restricted or tank F if it's not.»

But with this kind of reasoning, if the problem would be «Which tank will fill up first, knowing the pipes do not restrict the flow?», one could answer «It depends on the type of fluid, which is not mentioned: tank A if it is a Bingham plastic (like toothpaste) or tank F for a Newtonian fluid.»

My answer is true and respect physics in every way. But with the question asked and the drawing shown, we all know water is the fluid even if it's not explicitly mentioned. I'm not wiser by assuming toothpaste is coming out of the faucet, I'm just a smarty-pants and I don't deserve points for that.

 

[Karen Moullet-Flores]

ok so us non-geniuses ( sorry i know i shouldn't even be on this site...help I am lost) without all the formulas and equations, arguments and headaches think its K. i do (believe it or not ) understand why F must be the answer i guess...but i think in a race at the county fair, K might win lol! So, I guess its wrong of me to have assumed the tanks and attached fill tubes are of equal size and capacity then huh?

 

[RonL]

ok so us non-geniuses ( sorry i know i shouldn't even be on this site...help I am lost) without all the formulas and equations, arguments and headaches think its K. i do (believe it or not ) understand why F must be the answer i guess...but i think in a race at the county fair, K might win lol! So, I guess its wrong of me to have assumed the tanks and attached fill tubes are of equal size and capacity then huh?

You are not wrong about the tank and tube size, they are all the same. Elevation is the only difference as to water flow and as one that has worked with water levels in many ways, for me the answer came quick and I believe the puzzle is not about intelligence but rather the ability to make mental observations.
Flipping the picture upside down and being able to mentally see the proper flow and elevations might require intelligence ??

 

[OCR]

Ok, as of right now, we need some distraction ... lol

So try this... About 493,000 results.

 

[Dadface]

Please bear in mind that my take is that there is a possibility that Tank A fills up first but additional information is needed to disprove that or to prove it. But the possibility remains. I'm going to try a different approach of defending my position by writing a series of statements and if anyone can be bothered, look at each statement and decide whether its true (T), false (F), possibly true/false (P) too vague to reach a decision(V) or whether it falls under any other category (C). If you do this It might help to clarify my position. But then again it probably wont. I will start with the tank being empty

1. Water drips into the tank.
2. As time proceeds the water level in the tank rises.
3. There is a tube sticking out of the side of the tank.
4. The internal radius of the tube seems to be smaller than the drop size.
5. It could be a capillary tube.
6. When the water level reaches the level of the tube the water starts to drain out of the tank.
7. It is relevant to consider the average volume per second of water entering the tank (Ve) and the average volume per second of water leaving the tank (Vl)
8. Vl and Vc both have very low values
9. As soon as the water starts to drain Vl becomes bigger than Ve and the average water level drops.
10. On second thoughts that won't happen. What might happen is that Vl becomes equal to Ve and the water level fluctuates at the height of the tube.
11. On third thoughts Vl becoming equal to Ve as soon as the tube height is reached seems to be a bit of a coincidence.
12. On fourth thoughts when the water starts to drain Vl might be smaller than Ve.
13. If Vl is smaller the water level continues to rise,but now more slowly.
14. If the water level rises the pressure difference at the two ends of the tube increases.
15. As the pressure increases Vl increases.
16. Eventually the water level will reach a height such that an equilibrium situation is reached where Vl becomes equal to Ve.
17. If equilibrium is reached the average water level will stay constant but will fluctuate.
18. If the tank is not tall enough equilibrium may not be reached and the tank will fill up and overflow as more drops are added.

 

[Karen Moullet-Flores]

You are not wrong about the tank and tube size, they are all the same. Elevation is the only difference as to water flow and as one that has worked with water levels in many ways, for me the answer came quick and I believe the puzzle is not about intelligence but rather the ability to make mental observations.
Flipping the picture upside down and being able to mentally see the proper flow and elevations might require intelligence ??

Hey! thanks for responding to my comment and NOT making me look and feel like a complete dummy. In my head, i see K starting to fill before fluid gets to F. There's only one way in or out of K and that's at the top, so like you said, from my own mental observation i think K. someone on here pointed out that there's too many unanswered facts to have a 100% cut and dry answer...i like that, makes me feel like I am up in the mix with you brainiacs lol...now...HOW DO I GET BACK HOME TO MY MINDLESS DRONES ON FACEBOOK ETC?

 

[Nidum]

Time to pull the plug ?

 

[Dadface]

Ok, as of right now, we need some distraction ... lol

So try this... About 493,000 results.

That's what I thought. But only when Belgium.

 

[sophiecentaur]

Maybe not that surprising, since the bit I've highlighted in bold is steering the student towards an answer. That extra hint wasn't part of the published question.

Exactly. The published question was not the one you wanted your student to answer. You changed it into a Physics question from a common sense one. If everyone gives their own version of the question then there is no answer unless the revised questions are formally specified - which they haven't been.

 

[Dadface]

Exactly. The published question was not the one you wanted your student to answer. You changed it into a Physics question from a common sense one. If everyone gives their own version of the question then there is no answer unless the revised questions are formally specified - which they haven't been.

I have been trying to show that there is a possibility that Tank A fills up first. What happens beyond Tank A -Tanks B,C,D etc is totally irrelevant to the point I'm trying to make because if Tank A does fill up first the original question has been answered. I have been having trouble convincing people here that the possibility exists. You may have noticed that. So in one of my attempts to explain my point I stripped away everything else that's irrelevant and presented the problem with the relevant parts only, tank A, the pipe poking out of it and the water dripping into it. I then changed it slightly with the assumption, possibly mistaken, that describing something more familiar would show, more clearly, that the analysis is not a difficult one. So the tank became a bucket the pipe became a hole and the the dripping water became, well, dripping water. So the situation I described was an analogy but it was a good enough analogy for the purpose I was trying to show.
Just as there is a possibility that Tank A does fill up first there is also a possibility that it doesn't fill up first and if that's the case different bits of the rest of the system can be relevant. But looking at it now even that can be simplified by stripping away the distracters such as.D,E,G and H.

 

[sophiecentaur]

I have been having trouble convincing people here that the possibility exists.

It wouldn't be hard to convince them that you could fill A from a fast enough source. The fact is that your addition to the discussion is just not interesting enough unless you introduce some actual Maths - with a suitable differential equation. But all that would merely spoil the fun of answering this question that can be solved by anybody.
You don't appear to have got the point of the original question. It wasn't about Physics.
Start another thread about filling a leaky bucket and there may be some takers. Alternatively, you could search those terms and find, I'm sure, loads of stuff that's already been said. I found this - top of my list of hits.

 

[Dadface]

It wouldn't be hard to convince them that you could fill A from a fast enough source. The fact is that your addition to the discussion is just not interesting enough unless you introduce some actual Maths - with a suitable differential equation. But all that would merely spoil the fun of answering this question that can be solved by anybody.
You don't appear to have got the point of the original question. It wasn't about Physics.
Start another thread about filling a leaky bucket and there may be some takers. Alternatively, you could search those terms and find, I'm sure, loads of stuff that's already been said. I found this - top of my list of hits.

1. To clarify, whether A fills or not depends on the rate at which water leaves the tank as well as the rate at which water enters the tank. Do you agree with that? Do you agree that there's not enough information To determine which of the two average rates is the bigger?
2. I don't understand your point. I've been saying that the problem can be solved by anyone. All that's needed is general knowledge. It's an easy problem.
3. You say it's not about physics but my introduction to the problem was here, on a physics forum. So it can be about physics as well as about anything else. And there's nothing wrong in applying a little basic physics in a physics forum. Or should physics be excluded? In fact the relevant physics I used is so basic that it can be suitably rephrased to come under the heading of general knowledge.

It seems that certain people here don't like my claim that it is possible that A fills up first and it seems that I am being knocked left right and centre. But I can't remember a post which shows that my claim is wrong. I will, however, take another look

 

[russ_watters]

1. To clarify, whether A fills or not depends on the rate at which water leaves the tank as well as the rate at which water enters the tank. Do you agree with that? Do you agree that there's not enough information To determine which of the two average rates is the bigger?

I think it should be clear enough by now that we agree with the first questionstatement and disagree with the second.

My concern with your approach is that it encourages analysis paralysis(not to mention knowitallism), which doesn't serve students or professionals well: https://en.m.wikipedia.org/wiki/Analysis_paralysis

 

[Clausen]

The top of tank F is the lowest top of any of the tanks that the water can get to, so it is tank F. I don't think it takes a genius to see that, just good eyesight.

 

[sophiecentaur]

So it can be about physics as well as about anything else.

I guess, if you haven't caught on to the spirit of such questions then you will never be able to enjoy such amusements. Millions of people enjoy cryptic crosswords and other such puzzles which could never be solved in a linear way. There are other ways of approaching life and I would recommend you try some. It brightens your day.

 

[russ_watters]

The top of tank F is the lowest top of any of the tanks that the water can get to, so it is tank F. I don't think it takes a genius to see that, just good eyesight.

Perhaps not, but I didn't pay enough attention (per the instructions) and missed that a couple of the pipes were dead ends.

 

[jack action]

Nothing beats the real thing (note that the water is not dripping):

​

Tank F fills up first. This is the intended answer.

Now to satisfy @Dadface , at 0:20, the input flow is high enough that the level rises in tank A. The flow is obliviously stopped until the water level goes back to the pipe level again. Note that this higher level transfers back to tank J and tank L afterward to a point where tank L almost spills out first (I suspect there is a larger restriction in pipe J-L).

 

[russ_watters]

Nothing beats the real thing (note that the water is not dripping):

​

Tank F fills up first. This is the intended answer.

Nice! For fun, they should merge it with this:

 

[Dadface]

I think it should be clear enough by now that we agree with the first questionstatement and disagree with the second.

My concern with your approach is that it encourages analysis paralysis(not to mention knowitallism), which doesn't serve students or professionals well: https://en.m.wikipedia.org/wiki/Analysis_paralysis

Thank you so much. You have actually addressed points relevant to my argument.. .

 

[Dadface]

Nothing beats the real thing (note that the water is not dripping):

​

Tank F fills up first. This is the intended answer.

Now to satisfy @Dadface , at 0:20, the input flow is high enough that the level rises in tank A. The flow is obliviously stopped until the water level goes back to the pipe level again. Note that this higher level transfers back to tank J and tank L afterward to a point where tank L almost spills out first (I suspect there is a larger restriction in pipe J-L).

Thank you very much. I really appreciate it when people take this discussion seriously and try to be constructive. The demonstration is brilliant except for... I will get back to you and explain what i mean by "except for", hopefully this evening but more likely tomorrow. It's been a rather hectic day and I've been tied up with matters of a medical nature. When I get a moment I will try to find a Utube video to back up the point I've been trying to make. Ideally i will find one like yours but with extras. In the meantime you might wish to look at the posts I have made here. The first post is post 34 and this is followed by something like twenty other posts.I guess you won't look at them all but please look at a few of them. Anyway I've taken up too much time on this already so I must go off now. But I'll be back as the big man said.

 

[The Wizard]

As I stated in my previous post "F" is the correct answer based on the details depicted in the original question. All tanks are of equal size being linked by equal sized pipes and fed by a dripping water tap.

All the various posts relating to different bore sizes, speed of flow and even different diverse fluids (I believe somebody even mentioned toothpaste !) are totally irrelevant to the question posed.

 

[Dadface]

Hello jack action it's a nice video but I wish it went a bit further to demonstrate the point I have been making. To see what this is I'll firstly summarise, what has been my contribution to this thread.

From post 34 and onwards my main stance has been that Tank A filling up first is not necessarily the answer but is a possible answer. fahraynk gave it as a possible answer in the opening post. Take a look.

Whether A is the answer or not depends on average flow rates. It can be explained in terms of physics or in terms of general knowledge. In a nutshell If water flows in faster than it leaves A will fill up first. If not F will fill up first. It's easy and its obvious. But does water flow in faster than it leaves? The question can be answered only if the relevant information is known. Without the information the best that can be done is to make assumptions. And I think assumptions should be justified.

I don't know what the question compiler had in mind when setting the question but I made an assumption that I later realized couldn't be justified. By looking at the diagram and comparing the drop size to the outlet pipe radius I assumed that the outlet pipes were capillary tubes. But then I realized that the diagram, which I assume to be a schematic diagram.may not be drawn to any sort of scale. The best I can now say about the tubes is that they might be capillaries.

The structure of the tubes is relevant and I pointed out that pipe radius is a factor that affects the flow rate. But a general opinion seemed to be that pipe radius is irrelevant. If it is irrelevant are the other factors that affect flow rate irrelevant as well? Can I ignore pressure for example? Or can I be selective in what I ignore and forget about pipe radius etc but consider pressure because pressure is needed to move the water along. I'm not being nit picky but trying to highlight the fact that care needs to be taken when making assumptions that cannot be justified in terms of the information that is known. I have been using a bit of basic physics here and I know I'll probably get criticised again for using it, but I'm just pointing out some of the thoughts that came to me when I first looked at the problem.

In later comments it was pointed out that the puzzle was not a physics puzzle. But I didn't know that. After all I came across it in a physics forum. But I took the advice and afterwards avoided the tricky stuff and tried to keep everything in terms of general knowledge only. I tried to prove something which should be obvious.

I tried different ways to get my point across and thankfully received some feedback that addressed the points I was making. That includes from yourself. I particularly like the video you found and I think it gives a convincing demonstration that for a fast enough flow rate through the pipes F is the answer. But I would love to get my hands on the equipment and demonstrate the effects of varying the flow rates and in particular I would reduce the flow rates through the pipes eg by using a series of pipes of reducing radii. Then you will see that for a slow enough flow rate A is the answer.

As you said "nothing beats the real thing" and hopefully I may be able to find a video or something that backs up my analysis. I think I may be able to find details of experiments that used to be carried out in UK high schools when viscosity was on the syllabus. Such experiments are relevant to the puzzle discussed here.
In the meantime you may see the significance of the picture I found. And just to add a little physics,(sorry) if the radius of the tube is halved the flow rate reduces to one sixteenth of its original value. That's assuming laminar flow and Poiseuilles formula.

 

[Dadface]

http://academia.hixie.ch/bath/poiseuille/home.html

The situation described in the experiments carried out here is analogous to what happens with Tank A in the puzzle.
Looking at the bibliography etc it seems that the project was carried out by a UK A/S or A level student.In other words somebody probably in the age group 16-18.

 

[VuIcan]

Tank F.

Edited: missed a tiny detail.

 

[jerromyjon]

The top of tank F is the lowest top of any of the tanks that the water can get to, so it is tank F. I don't think it takes a genius to see that, just good eyesight.

The "lowest top" part is what takes intelligence to understand the significance of.

Most of the last 3 pages is about "but what if" and that is another branch of intelligence as well, except it leads to unnecessary questioning of assumptions in this case...