Why does bathwater in a plughole spin AT ALL

[AdrianMay]

I don't care whether it goes clockwise or anticlockwise so this is not the usual Coriolis conversation.
Why doesn't it just go down straight?

 

[Grinkle]

I think it can just go down straight given the right initial conditions, but there is a much larger count of initial conditions that end up with a swirl. The water has non-zero angular momentum (I think) before the drain is opened, and the swirl manifests because of that. CW / CCW is also dependent on the initial conditions.

 

[anorlunda]

I think @Grinkle nailed it. It is much more difficult to get zero swirling than nonzero.

Here's one that appears to be specifically designed to suppress swirling.

 

[AdrianMay]

Ah, but if it was just a kind of focusing of preexisting currents, then the speed of the rotation down the plughole would depend on the speed of the initial currents.

It doesn't look that way to me. I think the equilibrium speed of rotation down the hole depends on the geometry around it, and the initial currents only kick it into clockwise or anticlockwise.

 

[anorlunda]

It doesn't look that way to me. I think the equilibrium speed of rotation down the hole depends on the geometry around it, and the initial currents only kick it into clockwise or anticlockwise.

You marked this thread as level B, but your remark sounds like only a mathematical answer using fluid dynamics will suffice. Fluid dynamics is pretty difficult. Is that the kind of answer you're looking for?

 

[AdrianMay]

No mathematical smoke and mirrors required. I have a theory of my own in mind, and it's within reach of a five year old, but I've had such fun torturing my family and colleagues with the question that I thought I'd pester you lot with it too. I won't spill the beans just yet.

 

[Noisy Rhysling]

I asked this question at the Vortex Lab at Purdue one time. I had to offer beers to get them to stop explaining.

 

[Grinkle]

It doesn't look that way to me. I think the equilibrium speed of rotation down the hole depends on the geometry around it, and the initial currents only kick it into clockwise or anticlockwise.

Maybe the geometry of the situation is dominant in determining the velocity of the swirling. So what? What do you mean when you say it doesn't look that way to you? I'm not seeing any contradiction to previous posts so I'm not sure where you are wanting to take the discussion.

 

[AdrianMay]

> What do you mean when you say it doesn't look that way to you?

I'm referring to my own previous paragraph.

 

[Nidum]

I would have to look up references to be sure but I think that under the right conditions this type of vortex can be self sustaining .

The vortex then only has to be first started by random perturbations in the initially relatively smooth linear flow . Once started it will become stable .

Flow rate would probably have to be within a certain range (for any particular plug hole geometry) for this to happen .

 

[AdrianMay]

I agree with everything @Nidum said, but it still doesn't explain why the water spirals.

 

[berkeman]

No mathematical smoke and mirrors required.

Kind of a strange comment. Mathematics is not usually used to cloak anything -- it's used as a tool for characterizing the real world.

I have a theory of my own in mind

As you know, we don't discuss personal theories at the PF. If you can post a link to a reputable source that discusses a similar idea, that would probably be a good way to proceed.

 

[AdrianMay]

Well I did try to Google for an answer, but I just get stuff about whether it goes clockwise or anticlockwise. So I apologise for resorting to personal theories. Feel free to illuminate us with the official answer.

 

[berkeman]

I don't care whether it goes clockwise or anticlockwise so this is not the usual Coriolis conversation.
Why doesn't it just go down straight?

That makes no sense. I just flushed my toilet and confirmed the Coriolis force explanation. Why do you have a problem with that?

In the mean time, you might enjoy Helmholtz's 1858 paper on integrals of hydrodynamic equations that correspond to vortex motions.

Sure, sounds fun. Can you provide a link please? My local library doesn't have that on their shelves...

 

[RobertF]

I was emptying a jug of water and it was taking forever going glug, glug, glug, so I gave it a swirl and the water shot out, and the air didn't have to fight its way in. So I would say that's the answer, also why an inversion layer is ripe for a tornado to form, and why hurricanes develop in the fall when the ocean is warmer than the air above the sea. Is this in line with your thoughts, Adrian?

 

[berkeman]

I like your sarcasm, but I hope nobody misinterprets it as trolling. That would be incongruous in a mentor.

Not meant as trolling, just honestly confused by your confusion about basic physics.

I flush my toilet 10 times in a row (we no longer are in a drought in Northern California thank goodness), and it swirls per the right hand rule every time. Which hemisphere of the Earth do you live in? When you flush your toilet, which way does it swirl? Where is the rocket science here (or 5th grade science as you put it)? I'm just honestly not getting it. It's not early April...

 

[Drakkith]

I don't care whether it goes clockwise or anticlockwise so this is not the usual Coriolis conversation.
Why doesn't it just go down straight?

See this website: http://www.flowillustrator.com/fluid-dynamics/case-studies/bathtub-vortex.php

The basic explanation is that the water has non-zero angular momentum that accelerates the rotational speed of the water molecules as they are pulled inwards towards the narrow drain. This magnified rotational speed creates the vortex that you see.

 

[Dale]

Ah, but if it was just a kind of focusing of preexisting currents, then the speed of the rotation down the plughole would depend on the speed of the initial currents.

Hmm, this seems like an unjustified conclusion, at least to the precision obtainable by merely looking at the water. Do you have any justification for this?

 

[Dale]

Several posts discussing the forum rules were moved to the feedback section.

 

[Asymptotic]

In "Chemical Process Engineering: Design and Economics" pages 273 to 275 mention vortex formation and the 'vortex breakers' used to prevent them. http://www.pumpfundamentals.com/help11.html doesn't go much into their cause, but doe have a series of descriptive sketches.

Why doesn't it just go down straight?

As pictured in post #3, shooting straight down is one possibility, but typically a vortex does form. Although the vortex may spin in either CW or CCW direction, it appears that if there isn't a countervailing force strong enough to overpower the Coriolis effect , that's the direction it'll end up going.

 

[Tom.G]

The basic explanation is that the water has non-zero angular momentum that accelerates the rotational speed of the water molecules as they are pulled inwards towards the narrow drain. This magnified rotational speed creates the vortex that you see.

Emperical experiment conducted in the kitchen sink, Latitude about 34N. Sink approx 14 x 16 x 6 deep inches with center drain 3.25 inches diameter. Drain choked due to feeding a garbage disposal. About 2/3 to 3/4 fill.

• insert outstretched hands several sec. to eliminate any swirl
  • 1 test, no swirl to drain, completely radial
  • 1 test, very slight clockwise swirl
• induce counter-clockwise swirl of about 5 sec. per revolution
  • 4 tests, counter-clockwise swirl to drain
• induce counter-clockwise swirl of longer 5 sec. per revolution
  • 1 test, counter-clockwise swirl to drain then it reversed to clockwise swirl to drain (not reproducible)
• induce clockwise swirl of about 5 sec. per revolution
  • 3 tests, clockwise swirl to drain

Conclusions: I can't draw any. Come to your own conclusion!

 

[AdrianMay]

Wow! Lots of responses. Let me work through them:

@RobertF
I agree with you if there's a closed vessel involved like a jug or a wine bottle, but the drainpipe from my bath just opens into the garden somewhere near another drain in the ground. The air can return via the bathroom window. Both ends of the pipe will stay at atmospheric pressure and there'll be no pressure difference along the pipe to drive any backflow of air, in fact, there's probably a strong downward flow of air because of it being dragged along by the water. So I don't think this theory covers every case. Another comment is that even for the wine bottle, the water could leave a gap by just going down one side of the neck without spinning, and that would involve less drag on the backflowing air.

@berkeman
All over the web you can see the Coriolis thing debunked - the numbers are just too small. I think the pipes in a toilet are designed to set up a wild vortex to scrub away those klingons.

@Drakkith, @Dale and http://www.flowillustrator.com/fluid-dynamics/case-studies/bathtub-vortex.php
I already touched on this above. Suppose we take two identical buckets with holes in the bottom. We start the water spinning clockwise in both, but a thousand times faster in one of them than the other. After a while, I reckon the water around both holes will be seen to spin at roughly the same speed. It is definitely not the case that that the vortex in the first bucket will persistently turn at a thousand times the speed of the other. So I reckon the preexisting currents (or even the coriolis effect if the water is very, very, very still) only serve to tip the system into clockwise or anticlockwise motion, but some other explanation is required for the turning itself, and the fact that it seems to have a favourite speed for a given geometry. In that light, the web page's discussion of angular momentum misses the mark.

Another way to debunk it would be to dangle the bucket on a string. I think you'd see it turn in the opposite direction to the vortex because of an angular recoil. If I'm right, the web page would be at a loss to explain the effect. You'd need an explanation like "something actively fires the water out with a *new* angular momentum and that something pushes against the bucket." The web page blames the effect on the attempt to conserve angular momentum, but when the bucket is on a string, it's easily conserved when the bucket turns. But then again, I didn't do that experiment so it might confound me.

@Asymptotic
I only got to read page 273, but it says that it's an active area of research.

-----------
A persistent comment above is that you don't always get a vortex. I'd elaborate on that by saying that you don't get much of a vortex when the bath is nearly full (at most a little dimple dancing around on the surface) but it goes like the clappers when the bath is nearly empty. If we characterise that by comparing the hole diameter with the depth, then the picture above shows the opposite extreme: it's like a bath with only a millimeter of water depth left.

So one necessary condition seems to be that the water is neither too deep nor too shallow. The answer must explain this. I don't think angular momentum can help.

 

[AdrianMay]

@Tom.G
I can draw a conclusion there. If I filter your results on numbers greater than 1, I see that the swirl goes the way you pushed it.
If I add the top two 1s to make 2, I get a result that's inconvenient for what I said above (I seem to have predicted that the water would reach a favourite turning speed in one direction or the other no matter what the initial conditions are) but you didn't say how long you waited. Did you let the water drain completely, and how long did it take? After about a minute or more, if the water depth is similar to the hole diameter, unless that blockage is extreme so the whole system was all full of water the whole time, I think you should see the favourite turning speed.

 

[Drakkith]

@Drakkith, @Dale and http://www.flowillustrator.com/fluid-dynamics/case-studies/bathtub-vortex.php
I already touched on this above. Suppose we take two identical buckets with holes in the bottom. We start the water spinning clockwise in both, but a thousand times faster in one of them than the other. After a while, I reckon the water around both holes will be seen to spin at roughly the same speed.

I'm not convinced this will happen except that the extra angular momentum you added will eventually be lost due to friction.

It is definitely not the case that that the vortex in the first bucket will persistently turn at a thousand times the speed of the other.

Ignoring frictional losses, why not?

Another way to debunk it would be to dangle the bucket on a string. I think you'd see it turn in the opposite direction to the vortex because of an angular recoil. If I'm right, the web page would be at a loss to explain the effect. You'd need an explanation like "something actively fires the water out with a *new* angular momentum and that something pushes against the bucket." The web page blames the effect on the attempt to conserve angular momentum, but when the bucket is on a string, it's easily conserved when the bucket turns. But then again, I didn't do that experiment so it might confound me.

That "something" is probably the intermolecular forces between the water and the bucket.

A persistent comment above is that you don't always get a vortex. I'd elaborate on that by saying that you don't get much of a vortex when the bath is nearly full (at most a little dimple dancing around on the surface) but it goes like the clappers when the bath is nearly empty. If we characterise that by comparing the hole diameter with the depth, then the picture above shows the opposite extreme: it's like a bath with only a millimeter of water depth left.

I'm betting that when the water level is high, most of the water near the top is circulating only slowly since the transfer of momentum from the bottom to the top drops off as the depth of the water increases. The water nearer to the bottom will likely be moving much more rapidly. Once the water level drops enough, the spin at the top becomes high enough that the centrifugal force on the water prevents it from moving straight into the center of the drain and you finally see a vortex with an air center.

 

[AdrianMay]

You hit the nail on the head about friction. Why ignore it? It's the clinching argument against the pre-existing currents theory. I can keep that vortex going forever by putting water in the top (being careful not to inject angular momentum of course) but I can see from the dramatic shear in the vortex that loads of energy must be lost to viscous friction. That energy must be replenished, and the source is clearly gravitational potential energy.

 

[Nidum]

(1)

I can see from the dramatic shear in the vortex that loads of energy must be lost to viscous friction

Not true I think . Some loss yes but not a large amount when compared to the total energy in the flow .

(2) The formation of the vortex is almost certainly not a single ended phenomena . There are likely to be both positive and negative contributions to it's formation from various influences anywhere in the complete flow path from bulk fluid in the bath to final free flow to waste .

(3) There is also almost certainly some feed back effect in action .

(4) The mechanics of formation of a plug hole vortex could be closely related to the mechanics of formation of systematic ripples in the free flow from a faucet .

 

[Nidum]

Anyway the only possible way to come to solid conclusions on all of this is to attempt to model the system .

 

[Dale]

We start the water spinning clockwise in both, but a thousand times faster in one of them than the other. After a while, I reckon the water around both holes will be seen to spin at roughly the same speed. It is definitely not the case that that the vortex in the first bucket will persistently turn at a thousand times the speed of the other.

Sorry if I was not clear, but what I am asking for is why you think that the claim along the lines of "the initial angular momentum results in a swirl" implies something like "the speed of the swirl is proportional to the magnitude of the initial angular momentum". You are taking the fact that the latter statement does not hold as a disproof of the former. I don't see the connection.

 

[AdrianMay]

@Dale My argument about friction in #25 supersedes that one.

Let's imagine we snugly fit a corkscrew into the drainpipe. At this point, nobody would be mystified at all. We'd say that the device converts gravitational potential energy into kinetic energy, that the latter goes round in circles because we constrained it to, and that the speed of the water down the corkscrew depends on its density and viscosity together with the geometry of the corkscrew. Nobody would expect the water to refuse to go down the pipe unless you stir the bucket, and we wouldn't be surprised to see it keep going forever as long as we keep pouring water in the top.

The only remaining question, then, is why we don't need the corkscrew, or even the pipe.

 

[jbriggs444]

Not meant as trolling, just honestly confused by your confusion about basic physics.

I flush my toilet 10 times in a row (we no longer are in a drought in Northern California thank goodness), and it swirls per the right hand rule every time.

One toilet? One hemisphere? Where are your controls?

 

[Grinkle]

The only remaining question, then, is why we don't need the corkscrew, or even the pipe.

Because ...

The fluid has non-zero angular momentum prior to the draining commencing - one needn't contrive mechanical inducements to put it there after starting the draining process.

 

[Nidum]

The only remaining question, then, is why we don't need the corkscrew, or even the pipe.

Basically for the same kinds of reason that end loaded beams can flip from a stable straight condition to a stable buckled condition .

 

[AdrianMay]

@Grinkle please see #25. That original angular momentum should decay by viscous friction. What keeps it going?

 

[AdrianMay]

@Nidum Or the way a pea can roll off the back of a spoon?

 

[ISamson]

Could it have to do with the rotation of the Earth?

 

[Grinkle]

That original angular momentum should decay by viscous friction.

It does not happen that way at least for water, or if it does, the decay does not go all the way to zero. If one experiments with fluids of varying viscosity, one might see the effects your intuition tells you should be present, it does seem to me that viscosity should play a big role in the swirling phenomena.

Edit:

Gravity keeps it going, there is no other force acting on the draining fluid to work against any friction that might be present.

You claim the equilibrium point for all forces acting on the fluid is zero angular momentum as though its obvious it cannot reasonably be any other number than zero. To me this is not at all obvious from inspection, and moreover it does not seem to happen that angular velocity decays to zero in practice.

Edit 2:

Think of a marble swirling down a funnel. It swirls faster and faster as it goes down the funnel. There is viscous friction (wind resistance) acting against it, but the dissipative force is very obviously not sufficient to cause the marble to stop swirling and roll straight down the side of the funnel. This is an example of a system that does have dissipative forces but these forces are not sufficient to bring angular momentum to zero. It not sufficient to simply note that dissipative forces exist in a system to establish that the equilibrium point of the system is zero for whatever state one is talking about (angular momentum in this case).

One can blow a fan against the marble and cause it to stop swirling, but that would be a different system.

 

[AdrianMay]

@Grinkle.
1. It doesn't matter how viscous the stuff is. Yes it will eventually go all the way to zero. My point is that the vortex can keep going for a million years if you keep pouring water in the top despite not injecting angular momentum in the process. If we propose that the only reason why the vortex is turning is the amplification (like a ballerina pulling her arms in) of pre-existing currents, then we'd expect the currents to die away through friction, not intensify as they appear to. So something else must be driving the vortex.

2. I agree that gravity is that something else.

3. Actually, angular momentum is a conserved quantity, so *for an isolated system* it'll maintain whatever value it started with. A bucket on a string with *no* hole is isolated. Any currents in the water will decay to zero over time, but if the whole thing had a *net* angular momentum at the start, then the bucket will be turning on the string at the end. But if there *is* a hole and the water forms a vortex, then angular momentum is spewing out of the bottom and I think the bucket will recoil the other way.

But still we're nowhere near an explanation of why the leaking water arranges itself into a fast vortex after an infinitesimal initial current, let alone, why it goes like the clappers when the bucket is nearly empty.

 

[Grinkle]

then we'd expect the currents to die away through friction

I wouldn't necessarily expect that. See my Edit 2 in post 36.

we're nowhere near an explanation of why the leaking water arranges itself into a fast vortex

In my opinion, we are nowhere near any argument against the answer being the initial angular momentum in the fluid causing the vortex.

 

[AdrianMay]

@Grinkle
You're not distinguishing buckets with holes from buckets without. Your funnel has a hole. I said that buckets with holes can turn under recoil. In a bucket without a hole, I expect the currents to die away.

Edit: Your marble will come to rest before long. Edit 2: It's losing velocity, it's losing gravitational potential energy, and believe it or not its even losing angular momentum to the funnel or the air.

 

[berkeman]

I flush my toilet 10 times in a row (we no longer are in a drought in Northern California thank goodness), and it swirls per the right hand rule every time.

Turns out using the toilet for an experimental apparatus is fundamentally flawed (another Mentor pointed this out to me overnight via a PM). Toilets are designed to swirl the water as they flush. Duh!

Sorry for the misinformation. Filling the bathtub now...

 

[Grinkle]

It's losing velocity

You lost me here.

it's losing gravitational potential energy

Yes, so?

its even losing angular momentum to the funnel or the air

I expect its reasonable to conclude that in any real system dissipation of angular momentum is non-zero, but without modelling and quantifying this, I don't draw any conclusion the presence of some dissipative force in the system is a counter argument to intitial angular momentum causing swirling.

 

[AdrianMay]

@Grinkle
It's a counterargument because I can keep the vortex going forever by topping up the bucket.

When a fluid shears (parallel layers sliding against each other), it experiences friction that opposes the shear. That means the vortex must slow down. But it doesn't. Therefore, something must be continuing to drive the vortex.

If the only thing driving the vortex was initial currents, the energy of those currents would soon be exhausted by the friction and the vortex would stop turning.

The missing energy is harvested from the water's potential energy as it falls through the hole, but what's the mechanism that turns it sideways into a vortex when gravity just pushes downwards?

 

[Charles Link]

In the toilets in my house, it is clear that the water enters the bowl thrust in one direction, (somewhat clockwise or counterclockwise, I haven't looked that closely), and thereby Coriolis effects would be secondary.

 

[PeterDonis]

This thread is marked "B", but as was pointed out in an early post, to really answer the question requires an actual mathematical model, which is (a) beyond the "B" level (it's at least "I" and quite possibly "A"), and (b) not being tried, as far as I can tell, by anyone participating in the discussion.

Accordingly, this thread is closed.