# In What Order Will These Fill?

So, my hamsters get wonderful places in which to live and play; things like this:

But what about my poor fish? They just get a basic bowl.
Well, NO MORE. I decided to do something about that, and make something epic for them, too!

A bit of work later and I put together a wonderful design of interconnected fish bowls that let Nemo and Dory swim all about different places as they desire. It's night here and they don't much like flash photography, so I didn't really want to take a photo of them in their fancy new digs, but I've got this mockup I made while I was planning the layout:

When it came time to fill the whole thing up with water, the neighbor's kids wondered what I was doing so I explained what it all was. On a whim, I asked the two of them to tell me in what order they thought the 5 bowls would become full. They each gave me a different answer, and it was different still from what I thought.

So we all watched as it filled, to see who, if any of us, would be right.
And now, we know.

I'm not going to spoil the fun by telling you; instead, you tell me!
In what order will the bowls fill?



### Bonus Question:

Does it make a difference if the small outlet at the top of $E$ is plugged?
Why or why not?

• Bowl A will fill first if you are pouring water enough quickly. – user11153 Dec 22 '16 at 10:03
• How does the pouring flux compare to the max flow rate through the thicker connecting pipes? How about compared to the thinner pipes? Do we assume a drip or a gush? That makes a big difference. Also, how full E gets when plugged (and possibly C&D) is dependent on the ambient air pressure because the water will compress the air somewhat but can't push it all out. – Engineer Toast Dec 22 '16 at 13:05
• Where it matters, you can assume a steady incoming flow rate less than what the thicker connecting pipes can handle, but more than what the thinner pipes can. (And max air flow rate through any pipe well exceeds incoming flow rate.) You can also assume typical room temperature in a typical room of a typical home; as my profile indicates, I'm in Chicago, roughly 730ft above sea level, and ambient air pressure is what you'd expect. – Rubio Dec 22 '16 at 16:47
• @EngineerToast The amount of pressure the trapped air exerts on the water is a function of its level of compression, whereas the amount of pressure the water exerts on the air is a function of the height of the water above it. The larger the tubs are, the more the air will compress to get out of the water's way. – Sconibulus Dec 22 '16 at 22:07
• @Sconibulus: Thanks; it’s reassuring to know that an even number of us are crazy.      :-)     ⁠ – Peregrine Rook Dec 23 '16 at 5:54

My prediction:

D and C fill simultaneously. Then B, then E and A simultanously.

My knowledge of water is that it fills evenly, not by volume, but by height.
Let's see what some other answers will say!

EDIT: Since this question is framed to have been performed IRL, if I had to order them, I would suggest:

C, D, B, A, E, as there will be some delay in waterflow from the boxes closer to the watersource to the boxes further away of the same height.]

BONUS QUESTION:

It makes a hell of a difference. Your thing won't even fill up! You'll end up filling most of D and C, all of B and A, and none of E at all :P

Why?

Air will get trapped in E and the upper parts of C and D. It has nowhere to go, so water can't just go into that area and compress air! So, instead, the water will start overflowing from A instead of filling the chambers full of air.

• I would give you a +1 for the main question, but I believe that you missed the bonus question. Can you explain this (hover here) or revise that part of your answer? – Peregrine Rook Dec 22 '16 at 3:15
• you could also make a point about the flow rate, if the amount of added water is higher than the tubes can handle the order is going to change (at least for A/B fo fill before C/D) – Rod Dec 22 '16 at 12:34
• @PeregrineRook TIL how to hide spoiler text in a comment. – Engineer Toast Dec 22 '16 at 13:07
• @PeregrineRook Please don't do that. It's completely unreadable on mobile. – ffao Dec 22 '16 at 17:54
• @ffao How would you suggest I post hidden text (e.g., quote a spoiler-text answer) in a comment? – Peregrine Rook Dec 22 '16 at 20:44

My Prediction:

A fills to the lower pipe to B, B fills to the pipe to C, C fills to the pipe to B/Exit of the pipe in D, D fills to catch C, C,D,and B fill together, including up into E once the water level reaches high enough (through D-E pipe) At this point the filling is purely horizontal, so finishing order is likely C&D, B, A&E.

If you plug the gap at the top of E

Once the pipe from B to C is covered (after C and D are almost full) no more air will be able to escape from the left-hand side of the device. The additional water pressure may compress the air slightly, so D and C might possibly fill completely, but guaranteed is only B, followed by A.

• +1 for the comment on the compressibility of air! We need a scale to know how significant this effect will be. :) Though I assume the fish tank probably isn't hundreds of meters tall or anything like that... :) – Chris Dec 22 '16 at 10:15

As the lowest two, D&C will fill together (unless pipe from C->D is larger than B->C, in which case D will fill first), then B then A. Since the top was taken off A to allow for filling, the spill level for A is lower than the fill level for E, so E will never fill. So D, C, B, A

Bonus question:

Since there is no air escape once the level in C has covered the pipe from B, C& will be filled to higher than the pipe and E will have nothing. Some air compression will occur, so level will be slightly above the B to C pipe. Air from B can escape to A, so B and A will fill. So B then A

• +1 - First answer to actually notice that A's rim is below the full level of E. – Rubio Dec 22 '16 at 23:46

None of them will fill up. There isn't enough water in the jug.
Bonus: Therefore, it also doesn't affect the result if the top of E is plugged.

However, looking at how full tank A is, and how much empty space there is in the jug, I can assume that the jug must be far away, and that amount of water has came out of it because of perspective. Without a 3D image it would be impossible to see how far. If I assume that the water in tank A is just a mistake of the mockup, the first part of my answer is correct.

• I don't see the "lateral-thinking" tag there.. – oleslaw Dec 22 '16 at 14:27
• The picture is, as it says, a mockup. Nowhere is it even vaguely hinted that exactly one jug is used; in fact, it doesn't say how it was filled at all, only that "we all watched as it filled." No lateral-thinking applies here, and this answer is manifestly incorrect. – Rubio Dec 22 '16 at 16:52
• "How much empty space"... How much empty space, pray tell, do you see in this 2-D image? Haha. Your lateral thinking is no match for mine :) These containers may only be a single inch wide for very small fish. – Neal Davis Dec 22 '16 at 18:25
• Ha well I'm sorry, @oleslaw. Just because it has the tag visual: this doesn't specify the type of question, and since it doesn't say not to think laterally, I see no reason why I shouldn't. – Jacob Garby Dec 22 '16 at 23:27
• It doesn't have riddle either, but that doesn't mean I can thus be free to interpret it as a riddle and insist that my answer of "Fish" is correct. Again, this answer is wrong. -1 – Rubio Dec 23 '16 at 20:41

C > D > B > E and A

If the top of E is plugged

E remains empty

• I suggest reading other answers before posting your own. – oleslaw Dec 22 '16 at 10:03