Liquid Level in two tanks connected by a very long pipe

rahulpsharma

Joined Sep 5, 2010
55

Assume two tanks connected by a very very very long pipe...!!

Second tank is empty... Open to atmosphere...!!

Once we open the interconnecting valve, will the level of the liquid in two tanks become equal, eventually?

What if the liquid is more viscous OR pipeline diameter is small (thereby offering more friction)... Will the level in both tanks would still equalize eventually..??

Thanks & Regards,
Rahul

ericgibbs

Joined Jan 29, 2010
16,789
hi Rahul,
Is this a College question.?
What are the range of Viscosities and Pipe diameters you are designing for.?

I would say the two tanks would register the same level given sufficient time.
E

rahulpsharma

Joined Sep 5, 2010
55
hi Rahul,
Is this a College question.?
What are the range of Viscosities and Pipe diameters you are designing for.?

I would say the two tanks would register the same level given sufficient time.
E

It was a simple discussion between friends here and started getting confusing when more and more factors were brought in...!! So its only a hypothetical question...!!

What will happen if the pipe dia is made extremely small...!! What will happen if liquid viscosity is made very high...!!!

Some felt that due to friction in pipe and viscosity, there would be a point of time when the tank with high level wont be able to push the liquid enuf to raise it in the second tank... Hence there would always be a difference between the heights of the liquid in two tanks...!!

So just thot to ask for more expert views here...

Thanks and regards,
Rahul

ericgibbs

Joined Jan 29, 2010
16,789
What will happen if the pipe dia is made extremely small...!! What will happen if liquid viscosity is made very high...!!!
hi R,
At these 'extremes' I would say the liquid would not flow, the liquid would 'clog' the pipe.
E

AlbertHall

Joined Jun 4, 2014
12,187
So does it imply that after an astronomically long time, the level in two tanks would indeed equalize...??
I can imagine a pipe with a diameter smaller than the molecules of the substance and then presumably there would be no flow.

Alec_t

Joined Sep 17, 2013
13,229
Even glass, which is a super-cooled liquid, can flow (albeit extremely slowly) under gravity at room temperature.

Edit:
In general, the volume rate of flow V of a liquid of viscosity coefficient η through a narrow pipe of length L and radius r under a pressure difference p is given by Poiseuille's formula V=πpr^4/8ηL

Last edited:

ericgibbs

Joined Jan 29, 2010
16,789
hi,
Yes, But the TS, is including extremely small diameter pipes, I think at some point, atomic level attraction/adhesion between the liquid and the pipe will block it.
E

rahulpsharma

Joined Sep 5, 2010
55
hi,
Yes, But the TS, is including extremely small diameter pipes, I think at some point, atomic level attraction/adhesion between the liquid and the pipe will block it.
E
But the same blockage would also, atleast theoretically, be experienced in a normal size pipes too.. We may call it losses due to friction etc...

So wont the net result would be less flow towards the second empty tank and hence the difference in the level of two tanks, no matter howsoever small...!!

Regards

Marley

Joined Apr 4, 2016
489
Even glass, which is a super-cooled liquid, can flow (albeit extremely slowly) under gravity at room temperature.
`
I think this is not true, actually (Wikipedia).

With the two tanks, the liquid level in both tanks will eventually almost equalize.
I say "almost equalize" because as the levels approach being equal, the pressure driving the fluid through the pipe approaches zero. And therefore the flow approaches zero. Very similar to charging a capacitor.

Electrically, it's like having a single capacitor charged to a voltage. Then connect it to another similar capacitor via a high resistance. The voltage on the first capacitor will reduce as the voltage on the second capacitor increases. The voltages on the capacitors will eventually equalize at t = ∞. Time taken to get to a defined level (say 60%) will increase with resistance.

Alec_t

Joined Sep 17, 2013
13,229

crutschow

Joined Mar 14, 2008
31,122
I would guess that the two levels would equalize exponentially, as Marley alluded to for a capacitor.
So if you determined the time it takes for one time-constant of equalization (≈63%) then you can calculate how low it will take to reach any level of precision you want.
Of course, equalization down to one molecule could take a very long time.

MrSalts

Joined Apr 2, 2020
2,611
You must assume the pipes connect to the tank below the liquid levels at equilibrium and that the atmospheric pressure above each tank is equal and assume that "equal" means equal level at the surface and assume that micro-differences in gravity are not a concern (gravity changes based on the density and depth of the rock or soil or ground water at your location).

dl324

Joined Mar 30, 2015
15,452
Once we open the interconnecting valve, will the level of the liquid in two tanks become equal, eventually?
It depends on whether or not the tanks are at the same elevation.

They sell tubes that you attach to a garden hose to set things level over longish distances (when you don't have access to a laser level).

GetDeviceInfo

Joined Jun 7, 2009
2,125

Assume two tanks connected by a very very very long pipe...!!

Second tank is empty... Open to atmosphere...!!

Once we open the interconnecting valve, will the level of the liquid in two tanks become equal, eventually?

What if the liquid is more viscous OR pipeline diameter is small (thereby offering more friction)... Will the level in both tanks would still equalize eventually..??

Thanks & Regards,
Rahul
Yes
There is a myriad of forces that may draw the liquid towards or away from any point, but I don’t think that’s your intent.

rahulpsharma

Joined Sep 5, 2010
55
You must assume the pipes connect to the tank below the liquid levels at equilibrium and that the atmospheric pressure above each tank is equal and assume that "equal" means equal level at the surface and assume that micro-differences in gravity are not a concern (gravity changes based on the density and depth of the rock or soil or ground water at your location).
Yes, those things are assumed even if not stated in the original question... I mean we can assume the tanks to be close to each other and let the interconnecting pipes run around some long distance and come back...!!

The sticking point in the thot was, that after the initial rush of liquid to the empty tank, when the difference in height, between the two tanks, is reduced significantly, would the residual difference in height be able to exert enuf force, to overcome the frictional forces & viscous forces to 'exactly' equalize the level over a long period of time...!!

MrSalts

Joined Apr 2, 2020
2,611
The sticking point in the thot was, that after the initial rush of liquid to the empty tank, when the difference in height, between the two tanks, is reduced significantly, would the residual difference in height be able to exert enuf force, to overcome the frictional forces & viscous forces to 'exactly' equalize the level over a long period of time...!!
At some point,
- the viscosity is high enough
- the diameter is small enough
- difference in tank level is small enough
that flow will not be measurable.

But, nobody is going to connect tanks of cold honey with a 2mm level difference with a mile-long capillary. So what's the point?

dcbingaman

Joined Jun 30, 2021
798
It depends on whether or not the tanks are at the same elevation.

They sell tubes that you attach to a garden hose to set things level over longish distances (when you don't have access to a laser level).
True and it is just as accurate or probably even more accurate than a laser level! Reminds me when I went to a Walmart at one point and some older folks were checking out digital scales. They where astonished by the fact that their weight could vary by up to a pound or more depending on the scales. I told them digital scales are terribly inaccurate. I purchased a true 'balance scale'. The ones you move the weights on. IMHO these are extremely accurate and because it is a balance scale you are actually measuring your mass not your weight due to gravity. So you will weigh the same regardless of your altitude.

MrSalts

Joined Apr 2, 2020
2,611
It depends on whether or not the tanks are at the same elevation.
Only depends if the equilibrium level can be at the same level. The depth of the tanks (relative altitude difference of tank floor) doesn't matter. The OP only asked about the level of the liquid being equal, not the depth of the tank being equal.