# Riddle with flowing water

Staff Emeritus
Homework Helper

Assume the water flows from the faucet sufficiently slow.

Gold Member
3 and 4 at the same time.

DaveC426913
Gold Member
To be perfectly pedantic, 3 will be full fractions of a second before 4, but yeah, 3 and 4.

looks like 3 would be full before it starts overflowing into 4

Electron Spin
3

These little puzzles are fun.. Tx micromass!

Mentor
Depends on how you define "full". I am assuming it means "overflowing". Then, it is still a function of how fast water is added from the tap. Or, more precisely, it depends on whether the water is added faster than it can flow through the tubes connecting tanks.

If it is added slow enough, 3 and 4 with overflow at almost the same time. If it is added pretty fast, it will overflow the first tank first.

BillTre and 256bits
Staff Emeritus
Homework Helper
Depends on how you define "full". I am assuming it means "overflowing". Then, it is still a function of how fast water is added from the tap. Or, more precisely, it depends on whether the water is added faster than it can flow through the tubes connecting tanks.

If it is added slow enough, 3 and 4 with overflow at almost the same time. If it is added pretty fast, it will overflow the first tank first.

The speed of the water was specified in the OP.

Mentor
ROFL, completely missed the description below the image.

i-like-maths
Three?
Four?
Has got to be one of those 2

Gold Member
Four. Water pressure from tank #3 will make the level of tank 4 slightly higher than the level of tank 3.

Gold Member
Four. Water pressure from tank #3 will make the level of tank 4 slightly higher than the level of tank 3.
I disagree. The only way there would be positive pressure from 3 into 4 (once they're at the same height) is if 3 is slightly more full. The water still has to get to 4 by going from high water level to low water level - even if it's one drop at a time. It ain't going to flow uphill.

And remember, it states the water is filling sufficiently slow.

Gold Member
I disagree. The only way there would be positive pressure from 3 into 4 (once they're at the same height) is if 3 is slightly more full. The water still has to get to 4 by going from high water level to low water level - even if it's one drop at a time. It ain't going to flow uphill.

And remember, it states the water is filling sufficiently slow.
Consider the force balance for water in the tube connecting tanks 3 and 4. If tanks 3 and 4 have the same height of water (above the inlet to tank 4), how much water is pushing on the outlet from tank 3? Is this more or less than the amount of water pushing on the inlet to tank 4?

Gold Member
3 will fill first. As flow approaches zero the difference in time between the filling of 3 and 4 will approach zero.

BoB

Gold Member
Is this more or less than the amount of water pushing on the inlet to tank 4?

There is actually more water pushing into tank 4. You have the volume of tank 2 as well. This is irrelevant.

If you turn off the tap where you have tank 4 filled nearly to the top you have 3 filled to the same level. When you turn your tap on you need the level of tank 3 to rise slightly to cause a pressure imbalance in the pipe to have flow. Tank 3 will always have to be higher in order to fill 4 more.

BoB

Gold Member
Is this more or less than the amount of water pushing on the inlet to tank 4?
It's the same. Otherwise there would be flow.

There can never be more water in 4 than in 3.

At some point, when 3 and 4 are equal, a subsequent drop will enter 3, making it one drop higher. Only then will water flow from 3 to 4.

See rebellis post, above.

Gold Member
It's the same. Otherwise there would be flow.

There can never be more water in 4 than in 3.

At some point, when 3 and 4 are equal, a subsequent drop will enter 3, making it one drop higher. Only then will water flow from 3 to 4.

See rebellis post, above.

Ok, on second thought, you and @rbelli1 are correct.

Gold Member
Hard water forms a mineral deposit in the outlet from 1 to 2, thus, one is the answer.

mfb, 256bits, billy_joule and 1 other person
Mentor
Consider the force balance for water in the tube connecting tanks 3 and 4. If tanks 3 and 4 have the same height of water (above the inlet to tank 4), how much water is pushing on the outlet from tank 3? Is this more or less than the amount of water pushing on the inlet to tank 4?

What about water in the tube? It pushes back as well, it is not just about tanks.

Gold Member
It looks as if 3 will fill a moment before 4. I don't see 2 being able to completely fill, as 3 is spilling water received from it. If that is the case, then 1 cannot be filled either.

Gold Member
ROFL, completely missed the description below the image.
you were right the other time.¨
Another word definition game problem.
"sufficiently slow" sets a baseline for the flow, and direction to the baseline, and that can be set at any level for a desired result.

Example:
In your Lambougini traveling down the highway, a police car flashes and pulls you over.
The policeman says that you were going sufficiently slow so as to acquire a speeding ticket.
He explains that the speed limit is 65 mph, the car will do at least 300 mph, but you at 66 mph, were sufficiently slow to still register on radar.
You were going slower than the maximum speed of the car but not slow enough.

Most policemen use the same baseline, but the approach is from the bottom up - sufficiently slow is anything 65 mph and under.
They would say you were driving sufficiently fast to warrant a ticket.

So 1 can fill before 2,3, or 4.

Gold Member
Hard water forms a mineral deposit in the outlet from 1 to 2, thus, one is the answer.
For engineering, there really is "insufficient" description. We also could add viscosity together with L/d of the tubes connections,, capillary and surface tension if the tubes are small and/or long. A real world engineering challenge.

Gold Member
If all 4 cups are identical in weight while empty, then rapidly filling 1 or 2 before 3 & 4 can support the weight will cause the entire apparatus to topple over.
I don't think that the water level in cup 2 will be able to rise to be level with the pipe connecting to 1. I think that once the water level in 2 reaches in line with the bottom of 1 and is slightly above the top level of 3, then that added pressure will force 3 to slowly leak from the sides- there are no tops on the cups to create enough pressure to force it all the way back UP to 2 & 1 after it fills 3 then 4. Maybe, 4 will resist any extra water after filled level to 3, the pipe is too low for changes near the top of 3 to affect it. Not that I know anything about plumbing, really. Where could I be wrong?
I forgot to do the spoiler insert earlier! Sorry!

Has anyone tried doing this experiment to see what really happens?

Gold Member
If the water flows "sufficiently slowly", it could evaporate faster than it arrives, in which case none of them would fill up. Or if it's hard water, number 1 would eventually fill up with a stalagmite.

fresh_42