Tea Leaves: CR4 Challenge (08/12/08)

Simple. The center has the lowest velocity of fluid and the leaves precipitate out there versus the outer section where the higher fluid velocity keeps the leaves in suspension longer.

Kind of like a whirlpool you make in your pool to get all the junk in the middle to vacuum it out quicker. After it settles they attract to each other trying to find their soul mates.

Another good (sweeter) example is when you add sugar to your cup of Tea, you stir, and it all draws to the centre.

after a while of adding, you get a nice pile in the centre that doesn't dissolve into the no really sweet cup of tea ;o)

Hi Slideruler,

I agree with your analysis except perhaps for the role of friction with the cup wall. Even if the cup was frictionless it would exert a force on the water particles in contact with it (towards the centre of the cup) of sufficient magnitude to result in circular movement around the cup which would result in a dimple shape on the surface. This force would be greater near the edge of the circular motion as this is where the particles are changing velocity fastest so there would be a decrease in pressure as you moved towards the centre resulting in the spiral motion that you described. The role of the friction of the cup is to slow and eventualy stop this circular motion so that the tealeaves can settle instead of continuing to spiral indefinitely.

Has anyone got a potters wheel or an old record deck? I'd like to see the results of an experiment where the tea is as evenly distributed as possible with the liquid spinning at the same speed as the mug. The whole thing should then be slowed down very very gradually.

In the initial steady state with the cup spinning at the same speed as the liquid (ignoring surface tension) the surface should form a parabola rather than a dimple. Even in this initial steady state it should be possible to resolve the difference of opinion between Slideruler and BobD.

Not a parabola I think, but an inverted cone. My reasoning is that the angular velocity is uniform, so the outwards centrifugal force must be proportional to the distance from the centre. That is a constant radial gradient, so it should be balanced by a constant radial slope of the surface. So far as I can see, that would allow a true dynamic equilibrium throughout the depth of the cup (in any event, I'm more with SlideRuler than BobD on this occasion)

[Naturally, you would also need to keep a lid on it (no pun intended) so that air drag doesn't spoil the uniformity]

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Whoops!.
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Yes a paraboloid.
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Pressure gradient provides force to counteract centrifugal force.
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So gradient of surface is proportional to radius.
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I suffered at the hands of the Scottish Education system where they used heavy lumps of metal to thump knowledge into our thick skulls. This was back in the sixties.

My memory however was not totally trashed in the following years but I do recall being told there is no such thing as centrifugal force but that it's centripetal force.

However as an aside, my wife offered to read my tea leaves and after the usual swirling about ritual keeping me in suspense she announced with undue ceremony 'Your teabag's split'.

Ray - Oxford, just outside England.

Slideruller

You are correct as far as I can see. The only thing I wish to add is The temprature of the water on the outsice of the cup is constantly cooling. The center of the cup is warmer due to the insulating quality of the mass amount of water. This in turn will cause the water colum to rise creating a current that starts at the outside of the cup, moves to the inside, rises to the top as warm liquids try to float ( are less dense), finially with no way to keep rising it spills to the edges of the cup to start the ride again. This current carries the tea leaves to the center where their density will not allow them to surface, unless the water swirl is of sufficient velocity. And finally the swirl of the water in a clockwise or counter clockwise flow will assist in stacking the tea leaves in a conical formation..

I tried it with cold water; even with cold water in a pre-heated mug. Didn't make any difference.

One problem with this answer is that you are assuming that stirring the cup just means one would swirl the liquid around the cup. The proper way to stir a cup is to swish the spoon straight back and forth across the cup in random directions to create the greatest turbulence. This provides better mixing and as a result a better cup of tea. Swirling does not work well at all.

I hate to be critical but should we really be so hasty to copy and paste an answer out of wikipedia for the challenge questions? Doesn't that take the fun out of thinking through the answer?

I think if anything we should vote Jim's answer above as the good answer. It's basically the same answer but he thought the challenge through and even did a crude experiment.

Who copied and pasted from Wikipedia? SlideRuler? He references Wikipedia but if you read the Wikipedia article you will see that there was no copy and paste.

The following link is to Einstein's discussion of the teacup paradox. Can not say I really understand it.

http://www.ucalgary.ca:80/~kmuldrew/river.html

See post #34 " short sweet & complete. No baffelem with bs.!

TMF

But why does the vortex get created. It has to have something to do with the friction against the side wall and or the bottom but what is the mechanism that causes the vortex. In my experiments there is what appears to be a vortex in the bottom that is pulling leaves toward the middle but there is also a vortex at the center middle of the top that is pulling the surface down. Why one at the top and one at the bottom. I like simple solutions. I like compete ones better.

Hi Jim35848

"But why does the vortex get created"

According to my understanding, a vortex is simply fluid moving around a circle. There are two kinds of vortices: Free and Forced.

Free cylindrical vortices have stream lines which are horizontal concentric circles. This configuration is unstable (due to the secondary flow which is set up) and they degenerate into a Free spiral vortices.

Free spiral vortices have streamlines which are a combination of Free vortex + radial flow. This is the flow we see of water emptying out of the bath, and piling tea-leaves in the middle of the cup.

Forced vortices are circular streams of liquid caused by power from an external force. They are present in a centrifugal pump, or in the tea cup whilst the tea is being stirred.

Stirring the tea initially generates a forced vortex. When the spoon is removed the tea moves in a free vortex. The free vortex then degenerates into a spiral vortex due to secondary flow.

SR

I'll give it a try:
The one at the top is because the stationary air above the surface means the surface is rotating slower than the bulk.

Loosely, that means that (overall) the liquid near the surface experiences less centrifugal force than the bulk below it, which sets up a (non-thermal) convection current from the outside top to the inside centre. As liquid is driven from the outside towards the centre, conservation of momentum means that its speed tends to increase (the old ballet-dancer trick). So the surface liquid near the centre experiences far greater centrifugal force than the liquid at the edges - the classic situation for a visible vortex.

Other than being upside-down, and the cause of the slower-moving liquid being the drag of the vessel, the basic process at the bottom is identical. Of course, you need an indicator (such as tea-leaves) to see what is happening.

I hope that didn't just cause confusion.

Regards

Fyz

Such modesty! Or perhaps you accidentally deleted a few characters when editing. Presumably it originally read "short sweet and completely inadequate"

I was out of town for a few days, and amazingly I return to this puter and find that we are up to about 80 comments about absolutely nothing. I suppose some folks simply have nothing to do. However: for those who are doing nothing, I wish to thank you for your doing nothing here on the net. Unfortunately, I have just returned from an 1100 mile round trip and I found that there literally thousands of people on the highways, seemingly with nothing to do, and nowhere to go and they all are doing their thing on the highway between Sebring Fl. and Florence S.C.

I'm out of here folks, I have a minor hurricane to prepare for. By the way, They go round and round and stuff often falls in the middle, sort of like TEA LEAVES IN A CUP.

Tmf

Thank you. Einstein's explanation of the tea-cup effect seems simpler to me than SlideRuler's (maybe it's just the way I was taught). So, at least as regards the tea-cup, I give AE a "very GA".

I read AE's as saying that viscous drag makes the speed of rotation less at the bottom than in the centre, so the outward centrifugal force is less, and consequently the pressure gradient is smaller. That means that the pressure at the centre of rotation increases more rapidly with depth than would be expected from hydrostatic forces, and the pressure at the edge increases less rapidly**. Consequently, the water at the lower edge is driven downwards and the the water in the lower centre is driven upwards.
What about the position at the top of the cup? If the liquid moved as a body (i.e. no external drag), the surface would be conical, with centrifugal effects balancing the slope of the surface. However, the air slows the top surface in the same way that the bottom of the bucket slows the bottom. So the top surface also moves towards the centre. [That correlates with politics - both scum and dross gravitate to the centre].

My difficulty with the river explanation is that AE assumes you know all about the detail of Coriolis effects before you start reading it.

**You may if you wish read this as a phenomenological explanation of how Bernoulli's effect is maintained under these conditions - but I see AE's version as far more direct.

That makes sense. On the basis that momentum becomes more dominant over viscosity as the speed increases, the vortex that stops the tea-leaves reaching the middle will collapse as the speed reduces. (Blame Mr Reynolds if you like).

But I'm still not certain that the reason my largest (~6-mm) stones stayed at the outside was the speed of swirl or that the bucket had a very slight dome towards the centre (I just checked with a straight-edge); I'll try to find a flat-bottomed receptacle to repeat the experiment.

Having spent a little time surfing, I've come up with a few references that describe what the mechanisms involve in the challenge question. There are two frictional, viscous layers involved in this problem. One is across the bottom and is called the Ekman layer after Vagn Walfrid Ekman, a Swedish oceanographer. The one on the vertical walls of the cylinder is called the Stewartson layer after Keith Stewartson, an English mathematician. The majority of the literature about Ekman and Stewartson layers deals the flows on a much larger scale such as ocean current and atmospheric phenomena. (I guess we might be dealing with a tempest in a teacup).

The best visual description I have found is at a Colorado State University Department of Atmospheric Science web site http://einstein.atmos.colostate.edu/~mcnoldy/spintank/. (Notice that Einstein is in the website name). There are pictures and movies of fluids with dye in a spinning cylinder with the camera mounted to the spinning cylinder. The material presented is about experiments with slight changes in the rate of rotation and generally for slightly increasing velocities which is the opposite of the teacup problem. However, the website provides a lot of insight into the mechanisms involved. Below is a picture taken from their website that shows the flow paths. The flow directions are reversed from the teacup because the picture is for an increasing cylinder rotational velocity.

This provides more insight into the steady state behavior of the teacup system as the flow drops to zero but I still think there is a lot of interesting transient dynamic responses left to explain.

A tempest in a teacup indeed! But I have to wonder how close an approximation we actually have to atmospheric/oceanic conditions, given the walls of the container? Surely this introduces effects that would not be present out in the wild blue yonder!

Oceans and atmospheres are large systems with a great deal of temperature variation and they are usually cold at the bottom and hot at the top, whereas if we assume any temperature gradient in our teacup it would be colder at the top (assumed) due to greater losses of energy by convection to the air above, maybe the flow(secondary circulation) in the teacup would revolve in the opposite direction. It is a fascinating question that tests our imaginations and our application of physics principles. Jim Tarver

This is an excellent description of secondary circulation which is indeed the primary driving force that concentrates the tea leaves. Interestingly if you stirred the water and spun the cup at the same rate so that there was no fluid drag the leaves will concentrate at the rim of the bottom because of the combined effects of centripetal acceleration and gravitational acceleration acting on the mass of the leaves.

Centripetal acceleration is the primary cause of the dimple in the top surface and viscous fluid drag combined with centripetal acceleration and gravitation are the driving mechanism of the secondary flow at the bottom. Centripetal acceleration cause a low pressure area in the center of the bottom the same as at the top the velocity of the moving fluid in all regions of the main flow creates a fluid dynamic balance between the pressure drop caused by the circular motion of the fluid and the pressure increase due to centripetal acceleration. In the outer layers of the main flow viscous drag causes the fluid velocity to fall while that layer still experiences pressure due to the centripetal acceleration acting on the corpus of the fluid in the main flow.

The creeping, secondary flow across the bottom of the cup is driven by gravity acting on the slower speed higher density flow layers falling down the outside of the cup and across the bottom to the center which limits the degree of this pressure imbalance. If the tea is stirred vigorously especially if in a tall glass and you look carefully at the outer edge of the curve of the top surface you may see that this surface is actually lower than the 4/5 R surface. (In slow flows or short cups this effect is completely hidden by the surface tension interaction of the fluid with the cup which causes the meniscus curve at the cup or glass edge.)

Sorry for being such a fuss budget about the technicalities of these fluid dynamics but CFD is a particular interest of mine.

Sincerely,

Mr. Gee

Its not simply centripetal acceleration - if there was no circulation there would be no vortex and no dimple. Vortices are produced as a result of the conservation of angular momentum; in the absence of viscous effects, the rotational velocity of fluid being accelerated moving towards the centre increases inversely with its radius. The centripetal acceleration is proportional to V²/R, so the outward force on the fluid would be proportional to 1/R³ - that is a much stronger effect than you would get at constant velocity (proportional 1/R), and the reverse of the effect you would see if the whole system was rotating at constant angular velocity (proportional R)

Guest is correct vortex flows are known to not conserve momentum according to centripetal acceleration rules alone, however, if you simply spin the cup and fluid at the same rate there is a dimple although there is no vortex.

Vortex flows do not perfectly conserve angular momentum like a solid does and there are some rather complex and interesting thermodynamic effects in vortex flows the participate in the energy balance. But these effects seem outside the scope of the tea leaves question.

http://en.wikipedia.org/wiki/Vortex_tube

Centripetal effects obey a=R(w^2) and in the rotational frame of reference of the fluid in the cup and can be approximated by F=ma when the rotational flow rate of the fluid is constant.

http://en.wikipedia.org/wiki/Centripetal_force

Centripetal acceleration gives rise to a centripetal force pressing the fluid outward the wall of the container provides a counter balancing centrifugal force keeping the fluid in, the only place the fluid has to go is up - which it does. The dimple in the middle forms as the result. The average level of the fluid does not changed.

The secondary counter flow forms strictly as a result of viscous drag slowing the rotational rate of the outer layer of fluid. The fluid in this layer sees high pressure being squeezed between the wall and the main rotational flow but the water column height for this layer is too great for its slower rotational rate and in this layer the water column is falling down the outside under the influence of gravity. At the bottom it flows toward the center due to the fluid pressure differential between the higher pressure outer layer and the lower pressure core.

To double check my thinking I spun a tea cup shaped container floating in a water bath and as predicted the tea leaves were indeed spun to the outside bottom of the container. Then I mounted a clear plastic cup filled with water on a drill motor and spun it. Even after the system had spun long enough the was very little acceleration other than centripetal acceleration due to uniform circular motion, there was still a dimple.

I am not sure I followed your line of reasoning about the v^2/R verses 1/R^3 compared to 1/R. From a purely mathematic point of view 1/R*R*R is NOT greater than 1/R. The centripetal acceleration is not proportional to (v*v)/R it is usually considered to be (v*v)/R. The centripetal force is then F=ma and the counter balancing centrifugal force is then required to be F=m*(-a).

Mr. Gee

According to common definitions of dimple and vortex, you can't have a dimple (= increasing slope on the surface as you approach the centre) in the top surface without a vortex (= spinning, turbulent flow). If you take the definition of "turbulence" as the condition where momentum conservation becomes more important than viscosity, you might even choose to define the observable onset of turbulence as the point where a dimple becomes visible??

If there is a lid, the top surface will be parabolic (most people would not call that a dimple).

"Vortex flow not conserve angular momentum like a solid does"???
OK if you mean fluids behave differently from solids, but why bring angular momentum into the statement? In short: angular momentum is always conserved - you just need to see where it resides (even in spite of its loose usage of terminology, the Wikipedia article doesn't even appear to contradict that)

I'll give you the dimple. I was taking a parabolic dip to be a dimple and you appear to be taking it to be a curved surface with two inflection points instead of one.

The point about conservation of momentum in vortex flow we appear to still have a disagreement. In the tea cup example the core flow of the vortex is weak or nearly non-existent. However, the draft of the core flow is what causes the circulation across the bottom of the cup.

In a vortex flow occurring naturally in a free state the core flow is purely axial flow. There is essentially no component of it which is radial. This is in direct contradiction to your opinion that vortex flows conserve angular momentum. As that would have the core flow spinning radially at high rpm.

Even in the tea cup the central core flow is almost stagnant in terms of rotation. So, is the boundary layer at the outside. The strong turbulence in a tea cup comes from these effects. The core flow is mostly axial fed from the bottom, the middle flow is radial with good velocity and the outside is mildly axially downward and radially almost stagnate. These conditions cause a great deal shear in the fluid which is the observed turbulence.

The vortex must conserve total energy but can not conserve angular momentum so in the outer regions the is an abundance of thermal energy above the mean value and in the inner regions there is a attenuation of thermal energy below the mean.

This effect would be difficult to measure and observe in a tea cup, but in a hurricane it is universally observed that the core flow is gathered from the ocean surface passes up the middle and to the stationary observer the "weather" at the eye of the storm is quite nice, cool, dry, and quite still as in the core flow the air is moving straight up relative to a stationary observer on the ground in the eye of the storm. It is also very low pressure, an effect which corresponds to the dimple in the tea cup.

In a teacup, axial flow down the centre would imply that the flow is essentially laminar; that happens when viscosity dominates, so although there is rotation the angular velocity does not increase substantially in the region near the centre. Even here, the angular velocity never reduces as you approach the centre.

The region of purely axial flow will be a pure line down the centre. There will also be a pair of rotationally symmetrical surfaces (whose shapes depend on the shape of the cup and the levels of interaction with air and cup) where the flow is axial plus rotational. Plus the liquid contacting the cup will be stationary. Everywhere else the flow will have a radial component.

Angular momentum is still conserved - viscosity transfers it from fluid near the axis to that nearer the outside.

The reasons for the calm air in the eye of the hurricane (or other large-scale twister) are quite complex. But essentially the fluid here is drawn down from a region above the storm by the low pressure at the centre of the hurricane vortex. The reason this air is not rotating at any great speed is that the air being pulled down did not have net angular momentum in the first instance. This can also be true of air sucked into the centre of a liquid vortex, but not of the fluid rising from the bottom of the teacup.
_____________________________________

A little understanding goes much further than a little knowledge. But lots of knowledge plus deep understanding is better than either (anon)

Gosh we are close to a mutually agreeable understanding. However...(smile)

Hurricanes and tornadoes are very powerful heat engines which are initiated by appropriate seed conditions derived primarily from temperature, pressure, and humidity gradients like all atmospheric phenomena. One the vortex flow system is created it becomes self-sustaining and will continue until it has dissipated enough heat energy in the local area to reduce the gradients below that energy threshold that will sustain the flow.

My hypothesis is that the primary driving energy of both flow systems is heat energy and the primary heat carrier is water vapor.

Neglecting tornado's for the moment as they are more difficult to model a hurricane is observed to form over warm sea waters and track along the highest surface temperature path available to it given the constraint of typically east to west tracking due to the earths counter rotation beneath a dragging atmosphere. (Northern hemisphere only or I would be talking about cyclones.) The northern hemisphere southern hemisphere spin bias is derived from the greater lever arm the equatorial regions have on the atmosphere than the mid-latitudes.

Hurricane's cause massive amounts of rain fall. That rainfall is cooler than the water vapor that preceded the condensation. The passage of a hurricane will lower the surface sea water about 3 degrees over a very large area. The only way to reconcile these well known facts is to understand that the circulatory flow near the sea surface is being continuously tightened in its turning radius by the low pressure at the center. In a hurricane, exactly as in a tea cup, the bottom flow is strongly toward the eye.

The fact that this flow will try (but fail) and conserve angular momentum explains why the surface winds near the eye are so incredibly strong. They are increasing velocity to conserve momentum that was built at a much larger radius.

At the bottom of the eye the core flow is axial and basically straight up. Around the eye the flow is almost purely radial but near the core it has a low ascending helix further out it is purely radial, and beyond that the atmospheric flow is complicated by the fact that a enormous amount of water vapor containing heat energy has been condensed by cooling and is falling back to the sea. If the rain is not considered atmosphere then the net flow has a rising spiral and if the rain is viewed as atmosphere then the net flow has downward helix.

Near the top of the hurricane the low pressure does indeed create a downdraft, just like the dimple in the tea cup.

But, if you are attempting to model vortex flows like a hurricane and are neglecting the thermodynamics and the up drafted core you will have a very poor understanding of hurricanes. jim35848 in post #68 has an excellent schematic that depicts the same spinning tea cup experiments I did. If you reversed the flow vectors you would also have an excellent schematic of a hurricanes secondary flows, although there should be a clear axial core upflow, in a very large storm class three and up the downdraft may reach the surface as well, nested inside the updraft. One commentator mentioned that stirring in a bucket at high rates caused the solids in the center to form a ring which transformed into a mound as the flow slowed. This results from a nested downdraft reaching the bottom at high rotational rates and not reaching the bottom at low rates.

The best documentation I know of for the thermodynamic inequalities in vortex flow is the reference I gave to wikipedia previously.

The only addition the model that has not been so far discussed is the shear layer. Between the highly radial main flow and the highly axial core flow there is a shear layer that contains very small diameter mini or micro vortexes that have a very small diameter, large pressure drop high helix angle and tend to orbit about the core flow.

These are typically only easily observed in class 4 tornadoes and up where three sister twisters join and orbit a massive core flow. But, they exist in almost all high energy vortex flows and can even be observed in a tea cup, if you know what to look for.

Best regards,

Mr. Gee

Thank You Mr. Gee, for explaining in detail very accurately the statement I made way back in post #34 "I think". It was a long way back, and now the world around me is swirling east to west and dropping lots of leaves and other stuff along with the water. I truly believe that folks following this bolg, participants as well as viewers have made a "quantum Leap" regarding their knowledge about vortexes no matter whether they occur in your tea cup, or general neighborhood. Now I must prepare for the power to be that is going to stir the cup the other direction.

TMF {I'm smiling too!}

Are you saying that the whole of the base of the eye goes upwards? I had (mis?)understood that air at the edge of the eye base generally went upwards, but that air comes down to replace this at the centre. Unfortunately, I have not found any references to support or refute this.

In any event, eye velocities at ground level are relatively small, and the proportions of gas species in the air of the eye are generally similar to the air brought down, rather than to the air in the immediately surrounding vortex.

If a person were to start drinking their tea straight from the leaf

Are there any suggestions on what tea leaves are good. (I perfer something stout)

I know there are many "refined" contributers to this challenge and would like to get their ideas.

Respectfully,

An Instant Tea drinker from the mid-west of North America

Instant tea =

Good stout leaf? Best I've had was a black tea from Tibet/northern India. Can't find it? Try black Pekoe or orange Pekoe. Commercial teas MY tastes find palatable include Red Rose and Lauzianne.

You seems to have missed the world best tea CEYLON TEA!

Early Gray is excellent. Most of the Pekoe types too. Please try.

As the tea is stirred, the leaves swirl. The mixture in the center is moving slower than the outer edge. The leaves are more resistant to the flow of the liquid. The leaves in the outer area resist movement by moving to the center where they fall out of suspension and pile up in the middle.

that's where the fluid is moving the slowest. Same reason that people who pan for gold collect the sediments from the inside bend of the waterway or where it changes from fast and shallow to slow and deep.

The slower moving fluid brings it to the center, gravity brings it to the bottom.

The tea leaves contain nicotine which is alkaloid with pyridine and pyrrolidine rings attached with C-C atoms of each. Perhaps the induction effect of a saturated carbon atoms in chain of the pyrrolidine and pi-conjugation effect of the pyridine rings exert almost equal hydrophilic + hydrophobic interacting forces. The N (nitrogen) atom of each ring equally contributes to hydrophilic interactions of the water of the tea. So these forces may apply cohesive forces and stabilize the molecules in the centre of the bottom of the tea in container. Further desnity of the nicotine is 1.01 g/cubic cm, and of the water is 0.99705 g/cubic cm. Thus the higher density of the nicotine too infer stronger cohesive force within the nicotine molecules and align to a centre of the bottom. Now a role of sugar which a 100% hydrophilic in nature is to be defined to control the dispersion of the tea leaves. Perhaps the sugar + water interactions are stronger than those of the nicotine which is in the tea leaves. The water+sugar forces may neutralies the surface forces of the container's inner wall. But from the tea leaves, an extraction of the nicotine occurs and weakly disperse in the solutions due to slightly higher hydrophobicity. So the extraction and disperson of nicotine in a above defined medium make tea leaves to be centred at the bottom of the cup. Further a hydrophobic methyl group of the pyrrolidine ring also weakens the disperson in the 100% hydrophilic medium of a tea solution.

I didn't get past the 5th word before I thought "huh???"

The effect happens with most solids in water, even coffee before it dissilves, sugar, marbels...

The 5th word is nicotine, it is a chemcial substance and alkaloid in nature. The alkaloids attack our nervous systems. so when we feel sleepy and drowzy on work, then we prefer to take tea because it contains nicotine that excites our nervous systems. And we feel fresh and litharziness goes away but too much use of such alkaloids is injurious for our body.

Very much appreciated!

Or perhaps the metal spoon that you stirred the tea with caused a build up of static electricity in the cup. That charge repelled the tea leaves away from the wall of the cup, leaving them in the center. Plastic spoons also contribute to the static charge.

Nicotine? Mainly in tobacco - I thought tea contained caffene (note my current avatar for molecular structure). And I think the gross physics of water motion would overcome the forces referred to from molecular attractions.

BTW, caffene IS a stimulant, but nicotine is a depressant for the CNS.

It's like good answers. The more specific weight they have the more they will cause fall out towards the centre. Never mind the initial stir. It just takes more energy to be out there. Don't shake!

Hi guys

I'll just have to have another go here. Imagine your self in a round pool with water swirling fast in one direction. (No, no, not both). If you were to try to get to the outside of the swirl, what would happen? You become a tea-leaf and will notice that for some reason you are not getting were you thought you would go. If you keep this going for a while and a bit longer you will end up at the bottom, right in the centre, were your struggle will end. Death by gravity, exhaustion, drowning. Some people can read out the results. So they say. Ky.

your upper body would be pushed to the outside as your feet are pushed to the centre?

Or you slip on the bottom, and get a mouth full of water as you try to grab a breath before you go under.

No, just the other way around. Most of your weight is in the head. This experiment will only work if you do not struggle. The amount of struggle needed, to stay out of the centre, is equivalent to the amount of resistance against the forces of centrifugal forces in relation to the density of the water. It will take energy to get out there. If you would be floating in a pool of liquid lead (Pb) you would be on the outer, and badly burnt. No last breath before you go under!

No, most of my weight isn't in my head, I have been told by many "There is nothing up there" apart from "1 too many kangaroos loose in the top paddock"

Same here mate. They are loose alright!

Consider a turn in a meandering river. On the outside edge of the turn the water is moving fastest and any object caught up in the water feels a large force which tends to keep it moving with the water. So you only find massive stones on the outer edge of the 'meander' where the water is moving fast. On the inside edge of the turn you find small particles of sand and silt because they are in slow moving water and feel less force, they can therefore fall down (sediment out) of the water. The centre of the tea cup is like the inner edge of the meander, there is least force pushing the tea leaves around and so when they drop out of the water, that is where they fall, in the centre. Jim Tarver

Close but not quite. Meanders in rivers are indeed caused by secondary flow. The big rocks at the outside of the bend are actually less dense than the sand at the inside. Just as the tea leaves are more dense than the tea. All the old prospectors knew that the placer deposits of gold were more likely to be found in the sand bars at the inside of the river bends, but I'll bet darn few of them knew why. Secondary flows mechanisms are the most likely reason.

Sincerely,

Mr. Gee

At the boundary layer along the side of the cup, the fluid is not moving due to friction between the water and the cup. Since the level is higher there than at the center of the cup, there is a secondary circulation down the sides and up the center. This carries the tea leaves down and leaves them at the center.

One thing all has failed to mention is that a tea cup is not flat on the bottom. It is somewhat bowl shaped and as a result the heavier leaves tend to slide toward the center.

You folks are just trying to make things too complicated.

Why, when I stir in the sugar, does the note that the spoon and cup make change in pitch?

Different radio station?

Excellent!

That was actually asked awhile back on this site.

The answer was (and still is) due to the change of level of the liquid in the cup as the liquid is stirred.

Maybe the part of the cup that is free to vibrate is the part above the liquid. As you stir, the liquid at the edge rises changing the dimension and resonant frequency.

I Haven't read any other posts.

The centriphical force of the fluid spinning pulls the fluid to the sides or outward. this causes a lowering of pressure in the center of the fluid.

The gravity of the water/tea increases the further out from the center you go. The center being a lower pressure then the original gravity and the outer portion pulls the tea leaves to the center.

I glanced through most of the answers quickly and I think many of them are over complicated.

When the liquid containing the tea leaves is stirred a vortex is created in the center of said contained liquid, with a suction towards the middle being the greatest and strongest at the bottom. As the swirling action slows at the outside it is still slightly faster in the center and bottom. Even when the top of the liquid has effectively stopped there remains movement at the bottom center. This circular movement naturally draws the leaves toward the center, and as the vortex comes to a stop the leaves settle at the center, according to the law of gravity.

Tmf

Slideruler has the correct answer. It's the same principle (Bernoulli) that causes the shower curtain to move in toward the center of the shower and at the bottom. I read in a Scientific American magazine about a Physicist that used some extremely elaborate algorithms and a super computer to definitively come up with an answer to the shower curtain phenomenon but the only thing that he added to the already assumed answer of Bernoulli's principle and secondary flow was small tornado type vortices that form due to the water droplets from the shower head and how they contribute to the secondary flow towards the bottom center and the pressure differential between the center of the shower and the container walls. Einstein's interest in the phenomenon was on a planetary scale. Einstein was looking at how magma flows within the Earth cause gravitational waves to move in a manner similar to secondary flow in the tea cup. That's why gravity tends to always point toward the center of the Earth.

"That's why gravity tends to always point toward the center of the Earth."

I thought gravity was a property of mass, and since the center of mass of the Earth is the center of the sphere, that was why gravity "points to the center". Not so?

This is the basis of Hydrocyclone operation.When liquid contaiining solids is stirred,the solid will tend to be thrown to the wall of hydroclyclone and drawn to the bottom to be discharged from the bottom outlet.

In a cup, the diameter does not reduce like in a hydrocyclone.However ,a vortex does form when the liquid is stirred.Solids will be drawn to the bottm while the clear liquid will rise along the inner dia of the cup at the top.In fact tea leaves with air bubbles attached to them will rise to the top!Other wet leaves will stay at the bottom due to combination of two forces acting on them - centrifugal force due to rotation and gravitational pull.

Cowlagi

Just a little aside:

Rotating cylinders containing oil were used in engine testing as speedometers. My hydraulics text-book gives the example where a 3" parabaloid is generated in a vessel with a 3"dia - this translates into 32.12 rad/s. The speedo cylinder was geared up from the engine by 2:1 so the (steam) engine was running at 153rpm.

"Why do they end there rather than randomly dispersed in the cup?"

OK, a late entry, since the official answer is due tomorrow: to make it easier to read the fortune foretold by the tea leaves. If they were dispersed all about the cup bottom, it would take too long to gather the proper meaning of the pattern.

Just an extension on this.

What would be the effect in Zero G if this experiment was repeated?