Solving the Mystery: Which Tank Fills First?

[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...

 

[Dadface]

If this discussion in this thread was to continue I didn't want to be part of it but a few minutes ago and out of curiosity I did a search and found this .It shows that the answer depends on flow rates. Similar results would be obtained if the flow rate in was kept constant ,for example water dripping in and the flow rate out reduced sufficiently for example by using thinner pipes.

 

[RonL]

If this discussion in this thread was to continue I didn't want to be part of it but a few minutes ago and out of curiosity I did a search and found this .It shows that the answer depends on flow rates. Similar results would be obtained if the flow rate in was kept constant ,for example water dripping in and the flow rate out reduced sufficiently for example by using thinner pipes.

I don't know how to describe it but there seems to be something wrong with how water flows out of C into J and at the same time into L ? overall I think the video confuses the real lesson of flow rate.

 

[Dadface]

I don't know how to describe it but there seems to be something wrong with how water flows out of C into J and at the same time into L ? overall I think the video confuses the real lesson of flow rate.

I agree, it goes at a speed such that it's difficult to see it in detail.

 

[FactChecker]

Flow rate should not be a factor. Obviously if you dump water in, A will fill up immediately. But the picture shows a slow drip into A and the instructions say to pay attention to the details of the drawing. The slow drip and the closed paths need to be accounted for in the answer.

 

[Jacqueline]

I think F will fill up first.

 

[Jacqueline]

The picture.

 

[Dadface]

Flow rate should not be a factor. Obviously if you dump water in, A will fill up immediately. But the picture shows a slow drip into A and the instructions say to pay attention to the details of the drawing. The slow drip and the closed paths need to be accounted for in the answer.

I know the video is not a particularly good representation of the situation shown by the original question but it's the best I can find. I posted it here because it shows that the answer depends on the difference between the flow rate into the tank and the flow rate out of the tank.
The video shows that the tank fills up first when the water flows in quicker than it leaves The same applies no matter how quickly the water flows in because it's the difference in flow rates that matters. When the water level in the tank rises the rate at which water leaves increases. Equilibrium is reached if the level reaches a value such that water leaves as quickly as it enters. If that level is not reached, for example if the tank is not tall enough, the tank will fill up and then overflow.

 

[BL4CKB0X97]

I think g. The water from c will go to d first, before j.

But that's just an educated guess.

Edit: scratch that, didnt notice that it was blocked.

Go k!

 

[FactChecker]

Go k!

See @Jacqueline 's attachment in post #111 and notice how high the exit of the line from J to I is.

 

[BL4CKB0X97]

See @Jacqueline 's attachment in post #111 and notice how high the exit of the line from J to I is.

Got it[emoji106]

 

[fahraynk]

If this discussion in this thread was to continue I didn't want to be part of it but a few minutes ago and out of curiosity I did a search and found this .It shows that the answer depends on flow rates. Similar results would be obtained if the flow rate in was kept constant ,for example water dripping in and the flow rate out reduced sufficiently for example by using thinner pipes.

The tanks in this video are definitely tilted which is messing up the results. In tank A all the water flows out at the rate it enters (mostly). Yet in other pipes/tanks it flows at a different rate. Is this just a bad set up with the bottom pipes not being identical in area?

 

[sophiecentaur]

Yet in other pipes/tanks it flows at a different rate. Is this just a bad set up with the bottom pipes not being identical in area?

That and several other things go to demonstrate that the only way to deal with this problem is at the simplest level - with a slow water supply and everything 'ideal'. We just finished a marathon about a 747 taking off on a conveyor belt. As with this thread, it only required a single reply but both threads would just no lie down.

 

[Pie Ban]

Read the question with no assumptions. The FIRST tank to be filled up is A. Nowhere does it specify how full the tank needs to be.

 

[IanBro]

Firstly you have to assume the water is flowing into A slower than it is exiting to B otherwise the whole question is pointless as A fills first. With that F must fill first: Water will exit J-L before J-I and so K cannot fill, therefore L and F will self-level and F will fill before L.

 

[sophiecentaur]

Read the question with no assumptions. The FIRST tank to be filled up is A. Nowhere does it specify how full the tank needs to be.

Hmm. That same argument applies to when you 'boil' a kettle of water. Is it boiling as soon as you switch it on? Our language is not really precise enough for this. If you asked the barman to "fill your glass", you wouldn't be happy if he handed it back to you with a splash of beer in the bottom.