Unless I completely misunderstand how this works, I think 5 is the only one that will fill up. It then overflows, preventing any of the taller ones from filling. 7 is shallower but won't start filling until 3 gets fuller than 5, which it never will. This would be true whether the blockage between 2 and 3 is a mistake or not.
Please help. I have nightmares of being in a room where everyone else is just waiting patiently for me to remember the thing I forgot/figure out what is happening.
That's assuming the valve is open all the way and that there's a bunch of water pressure behind the spigot. It should be entirely possible to create a very slow trickle by having a massive body of water behind the spigot (making it functionally infinite) but having only a small part of the entrance beneath the surface.
5, but it also depends on the circumstances. What liquid is used, temperature, viscosity, etc. There's some material science stuff that's far beyond the intended scope of this question.
5 and 4 are the only ones getting water other than 1 and 2. 3 has a solid line blocking the flow into it, and even if that wasn't there, since 4 has a hole/drain in the bottom and 5 can overflow, 3 can't fill enough to reach the outflow. 5 is the only one that can fill up.
Depends on diameter of the pipes leading out too. They look small in the image, but if they're big enough to handle the max flow out of the faucet, 5 will still fill up first.
Wouldn't scale and viscosity play a role? Seriously, imagine a river vs a capillary tube. Also how many dimensions? And forces involved? Is that a blockage between 2 and 3? Are the walls breakable? How will the fluid hold air? Are the lines into structure 5 lower than the walls? Is this in a vacuum?
There is no mention of any fluid involved, just a faucet. So lets think inside of the box and assume we have some form of 2d-gravity and it is going to rain a newtonian fluid? I think most surface area on the top is draining into 5. If it snows the whole sheet can turn white and the problem is gone, too.
5 will be the only one that will ever fill up unless you really crank up the pressure in which case 7 will also fill but very slowly. 5 and 7 are open containers and there's a hole in the bottom of 4. But if it's water coming out of a tap then only 5 will fill .
Even if you assume that it is not blocked, it is still 5. The pipe from 2 to 3 is never reached because 4 leaks out the hole in the bottom. Assume that the hole in the bottom is a flaw and 4 still leaks out the top before the pipe to 3 is reached.
I got it! First, the free floating faucet will drop into bucket one. The impact will certainly break its connecting tube and broken 1 + faucet collapse into 4. Therefore 4 will be broken but full of shards.
The number of people in these comments who already understand the self-siphoning nature of water with zero explanation required makes me so proud to be here among them.
Ha. Trick question! All of them are already full of air, and niether the flow rate nor the direction (or lack) of gravity was specified anyway. You lose. :)