I Solving the Mystery: Which Tank Fills First?

[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.

 

[Pie Ban]

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.

Asking for a beer you would expect a full glass filled to the top. But your expectations will change when you order a whiskey "straight up".

 

[sophiecentaur]

when you order a whiskey "straight up".

I only drink 'proper whisky, neat or with a dash of water.
I sometimes offer a guest "two or three fingers?". They don't take offence!

 

[Low-Q]

F is the only one which will fill up. So F will not only fill up first, but be the only one.
All other remains empty or partially filled.
ABCJLF is the path.

Vidar

View attachment 208203

I originally thought tank K because the area in tank J is much larger than the area in the pipe connecting J to I
But then I realize Bernoulli's equation does not include volume but only includes height.
H_1, H_2 = height of water tank J, height of water in pipe between tanks J and I
P, p, V = pressure, density, velocity
$$P_1+pgH_1+\frac{1}{2}pV_1^2=P_2+pgH_2+\frac{1}{2}pV_2^2$$
Pressure terms are the same, so is density. Velocity = 0, gravity cancels out $H_1=H_2$
So even in the small pipe connecting J to I, the water level is going to be the same as the height of water in the tank J.

Is this correct?

Also note the pipe from C to D is blocked off.
Also I assume A would be trivial solution so water must exit pipe faster than the tap fills tank A

 

[Jon Richfield]

I say F will fill up (overflowing) first!

Same here; in fact it probably will be the only one to fill properly at all (depending on flow rate and whether someone opens the tap to cause A to overflow!)

 

[Ron Spencer]

My thought because of levels in and out: A to B to C to J to L to F. Funny how the mind can miss the blocks to D and H. I certainly missed the block at D :)

 

[Alt-Bringer]

sorry i only read first and last page here so if its been explained aldready forgive me

my thoughts is L would fill up and be the only one to do so due to the "pressure?"

cause watter will fill the botoms as needed then "bleed out" till certian capacities are met

F is lower but bottom filling
F would get only so full before the pressure starts equaling tween L and F
(pipe gets full then needs higher pressure from L to push water into F)
meaning L needs to get fuller for the pressure to push the water up into tank F

so in my thinking L would over flow before F, meaning L is full first
and overflow means F won't get any fuller, nor will watter continue to fill any previous tanks

also i know that the answer is some formulae of hydrolics, but please explain it in laymans terms

oh... i looked at the spoiler answer on first page, now it makes sense a bit more
how F fills, but would i be correct in my thinking if L and F were same height?
(cause L being placed higher means the water level dosent need to be higher to push into F
and its that placement of L that dictates the results in this setup)

 

[jack action]

also i know that the answer is some formulae of hydrolics, but please explain it in laymans terms

• Which tank fills first - post #19
• Which tank fills first - post #97

 

[vin300]

I've been given the solution. F fills first but what happens later is impossible.

https://drive.google.com/file/d/0B0O8pXjmFFrReVNCbkVlZU9DQ00/view?usp=drivesdk

 

[Jamison Lahman]

A or F depending how fast the water is flowing from the faucet and what it means to "fill up". Assuming dripping and completely filled, F. The latter definitions give A, but do not seem to be what OP is looking for.

EDIT: I am surprised no one has brought up the fact A is directly under the faucet hence the first water from the faucet will "fill" this bucket first.

 

[Jamison Lahman]

View attachment 208203
So even in the small pipe connecting J to I, the water level is going to be the same as the height of water in the tank J.

Is this correct?

Yes.

 

[jbriggs444]

EDIT: I am surprised no one has brought up the fact A is directly under the faucet hence the first water from the faucet will "fill" this bucket first.

No need for surprise. Read the thread to find the discussion you expect.

 

[sophiecentaur]

any waters goes to A first and 'fills it up' regardless of flow rate of A.

We have been there several times in this thread. "Filling up" was clearly(?) to do with a bucket becoming 'Full" - same as Boiling a Kettle does not happen within seconds of it being switched on.
Why can't this just lie down and die?

 

[Jamison Lahman]

We have been there several times in this thread. "Filling up" was clearly(?) to do with a bucket becoming 'Full" - same as Boiling a Kettle does not happen within seconds of it being switched on.
Why can't this just lie down and die?

It was asserted numerous times (never by OP), but never explicitly given.
Why not unwatch the thread if you want it to die?

 

[vin300]

The point is this was not supposed to be a science question in the first place. It was designed just to test how closely the candidate observes the setup and whether he manages to evade the trickery. In fact there is a real possibility that any tank except the ones that have been shut out: D, E, G and H can fill up and in any sequence depending upon dimensions, material properties, fluid properties, flow rates. Some may never fill up.

 

[vin300]

Think of the problem as a hydraulic open circuit pumped by pressure in tank A and all other tanks as accumulators along the line. Even if you assume all accumulators to be of similar construction and all pipes to be frictionless, you need some more details such as the lengths of the pipes and ratio of cross section area of the tank to the inflow rate to be able to comment on which accumulator gets most pressure. Then you can use some industrial software and simulate.

 

[Jamison Lahman]

The point is this was not supposed to be a science question in the first place. It was designed just to test how closely the candidate observes the setup and whether he manages to evade the trickery.

Is it not possible the trickery is the assumption that "fill up" does not necessarily imply filling up all of the way?

 

[Tom.G]

Why can't this just lie down and die?

After just running across this and reading the whole thread, there seems to be at least three answers.
1) Newcomers don't read the whole thread
2) Different people start off with slightly different assumptions
3) Some posters seem to feel that showing themselves to be 'right' is the main point of participation

As for the third observation, I am not pointing at those that brought up and supported other possible interpretations/starting assumptions. I point more to those that refused to consider that those other interpretations/starting assumptions could be valid. At the risk of being ostracized, there seems to be a few of us scattered throughout PF that are guilty. Unfortunately, we don't always recognize when we fall into that trap.

Well, that's my two cents worth.

Tom

 

[sophiecentaur]

@Tom.G That just about sums it up and we are all guilty of 1,2 and 3.
My problem is when people read the OP and failed to see it for what it is - a 'fun' / intelligence-test / common-sense type of question. It absolutely screams "Not Technical" at you and it is not a vehicle for being a smartypants and bringing in Physics to it. That's only really ok if the Full set of assumptions in a smartypants answer is made clear, from the start. This never happens, of course and we end up shouting at each other in quadrature.

 

[jack action]

Is it not possible the trickery is the assumption that "fill up" does not necessarily imply filling up all of the way?

Do you seriously think this problem is meant as a grammar exercise? Well, let's go with it. Here's what I found as relevant definitions:

fill (third-person singular simple present fills, present participle filling, simple past and past participle filled)

1. (transitive) To occupy fully, to take up all of.
2. (transitive) To add contents to (a container, cavity or the like) so that it is full.
3. To enter (something), making it full.
4. (intransitive) To become full. the bucket filled with rain; the sails fill with wind

 

[fresh_42]

Now that we have obviously and utterly discussed every aspect of this riddle, I will close this thread. Off-topic posts and jokes have recently become more likely than anything new to the problem. To all who are still interested in the debate, I suggest to post a new riddle of the kind (or a similar one), as I'm almost certain there can be found many on the internet (and even in our archive).

Thread closed.