Which one will fill up first puzzle

[DucatiWiz]

Hi all, I'd like as many opinions as possible please as this seemingly simple question has caused quite some discussion on Facebook.

Very grateful for any contributions.

http://www.bikersoracle.com/pics/fillquiz.jpg

 

[phinds]

First you need to say what YOU think will happen and why

 

[Student100]

What does it mean to fill up first? Which one is around 90% capacity first? Or which one overflows first? If the flow rate is as high as the image makes it out to be than 1.

 

[malemdk]

The 2 tank first to fill-up

 

[DucatiWiz]

What does it mean to fill up first? Which one is around 90% capacity first? Or which one overflows first? If the flow rate is as high as the image makes it out to be than 1.

It means to fill, i.e. fill to the brim; 90% isn't full

Ok I didn't know I was supposed to give my opinion. I think the answer is 3

This is merely an extension of an old water-level puzzle that has been done to death on the internet. The puzzle usually stops after the first 4 tanks and the answer is that the third and forth tanks in the sequence fill simultaneously (tanks 2 & 4 in the 6 tank version). See here:



However, in the new variant, tank 4 will not fill as it drains into 3, therefore, tank 3 will fill first. In fact, no other tank will ever fill as the liquid will continue to spill over the rim of tank 3 and the level will never rise above that.

 

[phinds]

I think the answer is 3 ... tank 4 will not fill as it drains into 3, therefore, tank 3 will fill first. In fact, no other tank will ever fill as the liquid will continue to spill over the rim of tank 3 and the level will never rise above that.

I agree and I don't even see why anyone would think this was much of a problem. Are we missing something?

 

[DucatiWiz]

Well, the argument is that that if the flow from the tap is fast enough to keep 1 full, the additional head of pressure will fill 5 faster and then 2 faster than the water can escape from 2 into 4, therefore 2 will fill first.

pgy1+1/2pv1^2=pgy2+1/2pv2^2

I don't agree, I think the guy arguing that case (who does have a physics degree) is not taking account of the following:
1. The flow from the tap is unknown. If it were high enough, it could fill 1 before it fills 5
2. The exit tube from 2 into 4 will remain at zero pressure because 4 will never fill past the entry point, so the extra speed of flow into 2 would have to be very much higher for it to fill faster than it could exit into 4.
3. There are no specific measurements to calculate an accurate flow rate. The puzzle is designed to demonstrate how water finds a level in any shape vessel or arrangement of tubing, not the dynamics of water flow rate, given pressure, diameter and viscosity. Whilst the tube from 2 to 4 does look thinner, it is not a scale drawing and without any specific measurements, there is no way to know if it would be small enough to cause 2 to fill first.

 

[phinds]

Again, I agree w/ you. Positing an extra fast water flow does not seem to me to be part of the problem as stated.

 

[Student100]

Again, I agree w/ you. Positing an extra fast water flow does not seem to me to be part of the problem as stated.

The problem stated is in the picture, in which we clearly see a high rate of flow from the nozzle.

Other iterations normally show a drip, in which case flow out of 1 is balanced with the flow in from the nozzle. Whereas I'm making the assumption here that the flow in >> than flow out of one. It's a problem with the graphics designer if that wasn't meant to be considered.

My assumption is as good as any other. One fills first.