# I Which tank fills first

1. Aug 2, 2017

### fahraynk

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

2. Aug 2, 2017

### jbriggs444

The water is dripping in. Flow velocity will be negligible.

3. Aug 2, 2017

### Regla

It really depends on what point do you consider the tank is 'full', let's say that the point full is when the tank is overfilling. I think the tank H would get filled first because the connection JI goes higher than connection JL.

4. Aug 2, 2017

### jerromyjon

I say F will fill up (overflowing) first!

5. Aug 2, 2017

### jbriggs444

There is no path into tank H.

6. Aug 2, 2017

### Regla

whoops that's true. Then my guess is F. Thanks.

7. Aug 2, 2017

### CWatters

Tank G fills up first. The water flows A B C D G. No water goes into J. No water goes into E.

Darn I didn't spot the blocked pipe. Ok so yes it's F.

8. Aug 2, 2017

It's G

9. Aug 2, 2017

### Staff: Mentor

You've missed the blocked pipe C to D.

10. Aug 2, 2017

### Staff: Mentor

A and B fill to the level of their outputs; C fills to the level of its outlet into J; J fills to the level of its outlet into L; L fills to the level of the top of F; and F fills and overflows. Once F is full, every drop of water into A causes another drop to overflow from F and the system is in steady state.

11. Aug 2, 2017

### phinds

Damn ! Thanks.

CWaters even SAID it was there and I still couldn't see it.

12. Aug 2, 2017

### fahraynk

So, basically, the area doesn't matter of tank J, it wont push the water through the pipe higher than its own water level? Tank J is roughly 27 times the cross sectional area then the pipe... but it doesn't matter right?

13. Aug 2, 2017

### Staff: Mentor

Not as long as the rate at which water enters the tank is small compared with the rate at which a single pipe can carry the water out - the water level will not rise above the height of the lowest flowing pipe. The illustration suggests that we're dealing with a dripping faucet which will easily be handled by a single pipe - think about an air conditioning unit's condensate drain tray.

14. Aug 2, 2017

### Gurjeet210

It's K

15. Aug 3, 2017

### Staff: Mentor

Can't be - nothing flows from J to I because the level in J doesn't rise above the outlet from J to L.

16. Aug 5, 2017

### Stressil

I choose L due to pressure and flow

17. Aug 5, 2017

### RonL

I agree with you, F will overflow before any others

18. Aug 5, 2017

### davenn

no ... look again .... F is at a lower level than L which fills F

Like phinds and a couple of others, I originally was going for G as I didn't see the block between C and D

19. Aug 5, 2017

### DrGreg

Here's the picture for the slow-drip steady-state solution:

20. Aug 8, 2017

### Dr_Zinj

Tank F will fill up first