I Solving the Mystery: Which Tank Fills First?

[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.

 

[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.