Why does water spin in funnel?

In summary, the conversation discussed the phenomenon of water spinning as it is pulled into a hole by gravity. It was mentioned that conservation of angular momentum causes the water to spin at different speeds, with the speed increasing as the radius decreases due to water going out. There was also mention of conservation of energy and the role of torque from the tub in the spinning process. The conversation also touched on the fact that the entire volume of water may not participate in the spinning, with only a smaller volume surrounding the drain being involved. The question posed was about the significant increase in the speed of the spinning a minute after the process begins, with possible explanations being the decrease in mass of water and the transformation of potential energy into kinetic energy.
  • #1
jdg812
84
0
As water is pulled into an opening by gravity, it begins to spin. Why does it spin?
 
Physics news on Phys.org
  • #2
Because angular momentum from the initial state of the water is preserved. It's the same thing that a skater uses to start in an open, slow spin and pull their arms into go into a closed tight spin.
 
  • #3
DaveC426913 said:
Because angular momentum from the initial state of the water is preserved. It's the same thing that a skater uses to start in an open, slow spin and pull their arms into go into a closed tight spin.

Thanks DaveC426913,

Actually, there are two regimes of spinning with two different speeds of spinning: immediately after opening a hole in the bath and about a minute later.

Immediately after opening the hole, conservation of angular momentum already works and one may see very slow spinning far from hole and faster spinning close to hole.

A minute later, the spinning becomes many times faster than in the very beginning. So, what is the reason of the fast spinning? Or what is the reason of increasing of the speed of spinning a minute later?
 
  • #4
Angular momentum for a spinning object is mass times velocity times radius. As momentum is preserved and as the radius decreases (because of the water going out), the velocity must increase.
 
  • #5
mr. vodka said:
Angular momentum for a spinning object is mass times velocity times radius. As momentum is preserved and as the radius decreases (because of the water going out), the velocity must increase.
That's corect, but that was an answer to a different question.

Consider the numerical exapmle.
R = 30 cm, r = 3 cm.

Immediately after opening the hole in the bath, we have:
v(R) = 1 cm/sec, v(r) = 10 cm/sec

A minute later, BOTH of the speeds, the speed far from the funnel and the speed close to funnel becomes much larger,
for example
v(R) = 12 cm/sec, v(r) = 120 cm/sec

The question is:
Why a minute later the speed at the distance 30 cm from funnel increased from 1 cm/sec to 12 cm/sec? Why a minute later the speed at the distance 3 cm from funnel increased from 10 cm/sec to 120 cm/sec?
 
  • #6
jdg812 said:
That's corect, but that was an answer to a different question.

Consider the numerical exapmle.
R = 30 cm, r = 3 cm.

Immediately after opening the hole in the bath, we have:
v(R) = 1 cm/sec, v(r) = 10 cm/sec

A minute later, BOTH of the speeds, the speed far from the funnel and the speed close to funnel becomes much larger,
for example
v(R) = 12 cm/sec, v(r) = 120 cm/sec

The question is:
Why a minute later the speed at the distance 30 cm from funnel increased from 1 cm/sec to 12 cm/sec? Why a minute later the speed at the distance 3 cm from funnel increased from 10 cm/sec to 120 cm/sec?
i probably think that in this case what is decreased is the fluid mass, so it start to spinn faster... L=mvr. that's it.
 
  • #7
[nitpick]In the case of water down a drain angular momentum is not precisely conserved. The tub (and maybe gravity?) does exert torque on the water.[/nitpick]Accounting for that amount of torque the rest of what has been said about angular momentum is correct.

In addition to the conservation of angular momentum there is also conservation of energy. As the water moves down into the drain there is some loss of PE. By conservation of energy you can also get an overall increase in KE in the tub depending on the KE of the water going down the drain. [nitpick]Of course, accounting for energy lost to viscous heating etc.[/nitpick]
 
Last edited:
  • #8
Marco_84 said:
i probably think that in this case what is decreased is the fluid mass, so it start to spinn faster... L=mvr. that's it.
There is a large bath, about 100 gallons of water and a small hole, about 1 inch diameter. A minute later there is still about 95 galons of water. Decrease of the mass of water is only 5%, but increase of rotation speed of the whole funnel is about 1200%.
 
  • #9
jdg812 said:
...

Immediately after opening the hole in the bath, we have:
v(R) = 1 cm/sec, v(r) = 10 cm/sec
I feel like I've been hustled. :rolleyes: Your OP belied the depth of your knowledge on the subject.
 
  • #10
jdg812 said:
There is a large bath, about 100 gallons of water and a small hole, about 1 inch diameter. A minute later there is still about 95 galons of water. Decrease of the mass of water is only 5%, but increase of rotation speed of the whole funnel is about 1200%.
But I don't think the whole volume participates at that point. Due to inertia and friction I imagine you can consider the dynamics of a smaller volume of only a few gallons surrounding the drain.
 
  • #11
DaleSpam said:
In the case of water down a drain angular momentum is not precisely conserved. The tub (and maybe gravity?) does exert torque on the water.
I am not sure about gravity, but the tub, actually bottom of it near the hole, exert friction. So it should reduce the angular momentum. But actually, the angular momentum increases a minute after beginning of the process.

DaleSpam said:
[nitpick]In addition to the conservation of angular momentum there is also conservation of energy. As the water moves down into the drain there is some loss of PE. By conservation of energy you can also get an overall increase in KE in the tub depending on the KE of the water going down the drain. [nitpick]Of course, accounting for energy lost to viscous heating etc.[/nitpick]
Yes. There are two mechanisms of the speed increase as the water approaching the hole. The first one is that water goes closer to vertical ax, momentum conservation and so on... The second one is that water goes to a lower level, PE => KE and so on... But the question was not about speed increase as the water approaching the hole, but about increase of the speed of the funnel as whole a minute after beginning the process.
 
Last edited:
  • #12
DaveC426913 said:
... the depth of your knowledge on the subject.
I am not satisfied with my knowledge of the subject... what I actually want is to find any effective measures against tornadoes and tropical storms that are too annoying in my lovely Florida. But in order to find something, I need deep understanding of rotation phenomena. :rolleyes:

So, I am not satisfied with the hurricanes in Florida and not satisfied with the present knowledge of the subject... :cry:
 
  • #13
jdg812 said:
But the question was not about speed increase as the water approaching the hole, but about increase of the speed of the funnel as whole a minute after beginning the process.
You cannot consider part of the water in isolation to the rest. Viscous forces "connect" the water approaching the hole to the rest of the water in the funnel. The viscous forces are small, but not negligible. That is why, as you observed, it takes a rather large amount of time.
 
Last edited:
  • #14
DaveC426913 said:
But I don't think the whole volume participates at that point. Due to inertia and friction I imagine you can consider the dynamics of a smaller volume of only a few gallons surrounding the drain.
Consider only FIVE gallons of water surrounding the drain.
At t = 0 (or t = 10 sec), the funnel spins slowly.

At t = 1 min, the first five gallons are gone. There are another five gallons of water surrounding the drain. The funnel spins quickly. Why behavior of the next five gallons, which forms quickly spinning funnel is different from behavior of the first five gallons, which formed slowly spinning funnel?
 
  • #15
DaleSpam said:
You cannot consider part of the water in isolation to the rest. Viscous forces "connect" the water approaching the hole to the rest of the water in the funnel. The viscous forces are small, but not negligible. That is why, as you observed, it takes a rather large amount of time.
That is exactly what I was thinking about, but I needed an independent opinion... thanks :smile:
 
  • #16
jdg812 said:
Consider only FIVE gallons of water surrounding the drain.
At t = 0 (or t = 10 sec), the funnel spins slowly.
The five gallons of water surrounding the drain is a very poor system to choose. It is not an isolated system and the boundaries and interactions are very difficult to define. You are much better off considering all of the water in the tub. That makes the boundaries much easier to define as well as the interactions with the surroundings.
jdg812 said:
Why behavior of the next five gallons, which forms quickly spinning funnel is different from behavior of the first five gallons, which formed slowly spinning funnel?
Different initial conditions.
 
  • #17
DaleSpam said:
The five gallons of water surrounding the drain is a very poor system to choose. It is not an isolated system and the boundaries and interactions are very difficult to define. You are much better off considering all of the water in the tub. That makes the boundaries much easier to define as well as the interactions with the surroundings.
You are absolutely right!

DaleSpam said:
Different initial conditions.
And different boundary conditions!
 
  • #18
i might be wrong but i think as the rotation progresses, the viscous resistance decreases, so as letting the velocity increases. just might be

but one thing that kicks me is the fact, it rotates. why does it rotate at all?? i have a large tank, full of water, i punch a hole in it, water, a lil after, drops below forming a vortex. why does it happen?? i asked this question, all through my course, but didnt get any answer OR i am ultra stupid;))
 
  • #19
ank_gl said:
as the rotation progresses, the viscous resistance decreases
What exactly do you mean? The coefficient of viscosity decreases or the viscous resistance as a global phenomenon decreases at constant coefficient of viscosity?

ank_gl said:
but one thing that kicks me is the fact, it rotates. why does it rotate at all?? i have a large tank, full of water, i punch a hole in it, water, a lil after, drops below forming a vortex. why does it happen?? i asked this question, all through my course, but didnt get any answer OR i am ultra stupid;))
I believe that answer to the question why does it rotate at all?, is the same as the answer to the question "why it rotates faster and faster as the rotation progresses?".

So, there is a mechanism exists that accelerates spinning the funnel as whole. In such a situation an initial fluctuations of angular momentum are enough to develop global spinning until nonlinearity restricts it at some reasonable level.
 
Last edited:
  • #20
This question has got me thinking. The Wikipedia page (http://en.wikipedia.org/wiki/Vortex) mentions that for a free vortex "The tangential velocity v varies inversely as the distance r from the center of rotation, so the angular momentum, rv, is constant". I believe that this is constant as a function of r, not as a function of t.

As you indicate the whole thing can start spinning faster, so something must be exerting a net torque on the fluid in the same direction as the angular momentum. The viscous shear forces should exert a net torque in the opposite direction, the normal forces in a symmetric vessel should not exert a net torque, and I can't see how gravity would exert a torque about a vertical axis.

Where's the torque?

EDIT: I cannot reproduce the "points far away start spinning faster" thing in my sink even though anecdotally I think I have seen such occurences. The drain plug may be interfering. The situation you described above, was that just hypothetical, or have you done such an experiment?
 
Last edited:
  • #21
DaleSpam said:
The Wikipedia page (http://en.wikipedia.org/wiki/Vortex) mentions that for a free vortex "The tangential velocity v varies inversely as the distance r from the center of rotation, so the angular momentum, rv, is constant".
I don’t think that precise measurements are possible in hydrodynamics. Deviations about 1% from the law 1/r may 'save' the model. It takes about 1 minute to develop stationary fast spinning funnel. For that time liquid makes several hundreds turns around center of vortex. So, the process of acceleration of the whole thing is comparatively slow. The torque required for such slow acceleration may cause deviations of about 1% or less from exact 1/r law.

I think that wikpedia describes a stationary, developed vortex. But during the process of slow acceleration the law may be a little bit different from 1/r and again the model works.


DaleSpam said:
The viscous shear forces should exert a net torque in the opposite direction.
Yes.

DaleSpam said:
I can't see how gravity would exert a torque about a vertical axis.
Me too... :smile:

DaleSpam said:
Where's the torque?
I believe the torque is within 1% of experimentally measured 1/r law.
The question is why the torque accelerates the whole thing. Friction due to walls and bottom must decelerate the whole thing.
 
Last edited:
  • #22
DaleSpam said:
EDIT: I cannot reproduce the "points far away start spinning faster" thing in my sink even though anecdotally I think I have seen such occurences. The drain plug may be interfering. The situation you described above, was that just hypothetical, or have you done such an experiment?
First, you should remove drain plug at all and close the hole by your business card. Then wait 5 minutes until the water is in rest. After that remove business card using piece of wire (a long needle would be the best), moving it ALONG the bottom of the bath. After such non-disturbing opening of the hole, you should get the funnel WITHOUT spinning for a minute or more.
 
Last edited:
  • #23
Well, if there is no external torque in the right direction then the only way possible for the "far away" fluid to gain angular momentum is if the fluid going down the drain has less angular momentum per unit mass than the rest of the fluid. In the ideal irrotational vortex the angular momentum is uniform throughout the fluid, so you would get no such effect.

However, I don't know the derivation of the irrotational vortex equations, it could be that they are assuming no viscosity. If so then it would make sense that the innermost fluid would have the highest shear rates and therefore rotate slightly slower than the inviscid limit and therefore have less angular momentum than the bulk of the fluid.
 
Last edited:
  • #24
DaleSpam said:
Well, if there is no external torque in the right direction then the only way possible for the "far away" fluid to gain angular momentum is if the fluid going down the drain has less angular momentum per unit mass than the rest of the fluid. In the ideal irrotational vortex the angular momentum is uniform throughout the fluid, so you would get no such effect. However, I don't know the derivation of the irrotational vortex equations, it could be that they are assuming no viscosity. If so then it would make sense that the innermost fluid would have the highest shear rates and therefore rotate slightly slower than the inviscid limit and therefore have less angular momentum than the bulk of the fluid.
Yes, that is like Cheshire Cat smile... :smile:
 
  • #25
DaleSpam said:
... and I can't see how gravity would exert a torque about a vertical axis.

Where's the torque?

Try Focault's pendulum - coriolis effect.
The effect is due to the rotation of the Earth on its axis (of rotation...). We always subconciously assume Earth is staionary when it simply isn't.
And it's caused by moving in toward that axis (ever so slightly with Focault pendulum as it falls), and likewise opposite effect when it swings away away from the Earth's axis. It's like trying to keep a straight line as you walk inwards towards the centre of a roundabout or carousel. The fact you're already rotating throws you to one side of the line that you're trying keep.
You could also demonstrate the effect by dropping something verticlly from 100m at the equator. I think it should hit the ground about 1mm to one side.

So basically I think there wouldn't be any torque if you were on a planet that doesn't spin.

The reason the vortex speeds up is probably the positive feedback effect that somebody earlier mentioned. ie it's because all the particles in the water are connected by intermolecular forces :-) and obviously a larger effect from surface tension. -So what happens at the center has a knock on effect on the water further out. Especially true for the water on the surface where moleculr forces are stronger..

my 2cents
 
Last edited:
  • #26
Also the direction of the vortex rotation depends what hemisphere you're on, North or South. That's because the initial, very subtle, average rotation of the water has the same direction as the rotation of the earth.

So if you put the tank on a rotating carousel to begin with, and rotate the carousel very very slowly, you can cause the vortex to rotate accordingly.

If you match the rotation rate of the earth, then in theory no vortex would be formed.

In practise we have unstable dynamics here, so you'd need to control the carousel dynamically based on the feedback from your eyes looking at the water or something, and a human might not be responsive enough for such a highly non-linear system.
 
  • #28
YellowTaxi said:
Try Focault's pendulum - coriolis effect.
The effect is due to the rotation of the Earth on its axis (of rotation...). We always subconciously assume Earth is staionary when it simply isn't.
And it's caused by moving in toward that axis (ever so slightly with Focault pendulum as it falls), and likewise opposite effect when it swings away away from the Earth's axis. It's like trying to keep a straight line as you walk inwards towards the centre of a roundabout or carousel. The fact you're already rotating throws you to one side of the line that you're trying keep.
You could also demonstrate the effect by dropping something verticlly from 100m at the equator. I think it should hit the ground about 1mm to one side.

So basically I think there wouldn't be any torque if you were on a planet that doesn't spin.

The reason the vortex speeds up is probably the positive feedback effect that somebody earlier mentioned. ie it's because all the particles in the water are connected by intermolecular forces :-) and obviously a larger effect from surface tension. -So what happens at the center has a knock on effect on the water further out. Especially true for the water on the surface where moleculr forces are stronger..

my 2cents
If coriolis effect is your claim. please provide some calculations to show the magnitude of this force?
 
  • #29
Integral said:
If coriolis effect is your claim. please provide some calculations to show the magnitude of this force?

Here's my little bit of help.

At the equator there is no rotational force. That's one way to tell where the equator is.

As for calculations, I think they are best done by using a non-inertial reference frame.
 
  • #30
Integral said:
If coriolis effect is your claim. please provide some calculations to show the magnitude of this force?

I don't need to.
If you'd watched the first video I linked to, at the end the guys at MIT demonstrate the coriolis effect on water falling down a funnel under idealised conditions. It rotated counter-clockwise and they attribute it to coriolis.

The OP. asked the question in this frame - ie as if in an ideal situation, so that is my answer - coriolis.

Obviously from our own experience we know that the water is just as likely to spiral either direction, so it's fair to assume that when water starts to fall into the vortex the situation is unstable. It's most probably like balancing one football on top of the other, it can fall either way due to the tiniest of displacements. But once started in that direction it will continue and at increasing speed.. It's a positive feedback effect. a.k.a. Unstable equilibrium. Presumably the vortex reaches a final speed dependant on viscosity.

I wonder if there's a maths explanation why the vortex can change direction. I'm pretty sure I saw it change direction last time I emptied the bath... Maybe something like vortex trails off the end of an aerofoil will spin one way and then the other. Each successive vortex that leaves the wing is turning in opposite sense to it's predecessor.

p.s. I can't do the maths, just as you probably guessed, but I trust the experts at MIT could, even way back in 1961.
;-)
 
  • #31
This is a good problem. I would be satisfied, if it was mathematically shown that the fluid could accelerate and get pushed into a small tube from a large tank, with smaller action by spinning than by going in symmetric manner. By "action" I mean the action of the Hamilton's principle. I have no idea if this indeed is the case, but I hope it is, and that it could be shown with some elegant proof.

If the initial condition is perfectly symmetric, then the water should start get into the tube without spinning, but I am probably not wrong to guess, that this is an unstable flow. That means, a small disturbance will make the flow find another stable extrema of action. So I don't think the Coriolis force claim is unreasonable.
 
  • #32
This is an interesting question / discussion. May I post the details of an experiment regarding this phenomenon and ask for advice on it?

Thanks,

-Arkham Angel-
 
  • #33
hey guys, i was just wondering if any of this angular rotation would occur if the Earth was not moving? because without a rotational 'nudge', the water would not begin to spin. this fact seems to be neglected here?
 
  • #34
meeeee5 said:
hey guys, i was just wondering if any of this angular rotation would occur if the Earth was not moving? because without a rotational 'nudge', the water would not begin to spin. this fact seems to be neglected here?

It has not been neglected. It has been ruled out. It is not a significant factor.
 
  • #35
The coriolis force seems to be unimportant, unless you're really careful to prevent any initial rotation. Ordinary bathtubs can rotate in the other direction as well, and also rotate on the equator.
It seems that apart from the direction, the speed of the vortex is independent of the amount of initial motion if you wait long enough.
Any torque driving the vortex can only come from the vessel that contains it. The only way that could happen, is if the direction of the flow near the bottom is in the opposite direction.
 

Similar threads

  • Mechanics
Replies
9
Views
1K
  • Mechanics
Replies
1
Views
675
Replies
3
Views
796
Replies
6
Views
1K
Replies
2
Views
680
Replies
66
Views
6K
Replies
4
Views
1K
Replies
27
Views
2K
  • Classical Physics
Replies
6
Views
1K
Replies
9
Views
3K
Back
Top