The Inverted Whirlpool Paradox
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- Опубліковано 17 лип 2022
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The tea leaf paradox explained. A spinning vortex and cause liquids to seemingly defy gravity
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One of those rare occasions where fluid dynamics makes sense!
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Thanks for the incredible content!
I wonder how much of this applies to how a solar system or galaxies form... I would assume much of it, not velocity tho since we know much of what orbits on the outside of a galaxy is the same speed as the inner... as if on a wave
That response from your kids at the end is the best endorsement of any product by anyone ever
Yay, new video of yours always intrigues me
The reason the magnetic spinner works i think is because relative to the magnet OS the container (and the fluid) spinning around it
It would be interesting to see what would happen if you had three different liquids with different densities. The bottom layer would surely bulge up, but what would the boundary between the middle and top layer look like?
bulge up as well, not as much, its not about density, its about drag
This can be argued several ways. The only way to know is to try it.
@xraf32 its the liquid at the bottom that have a lot of drag because its touching the bottom of the glass, the drag force decrease as it go up
I think air is already making this a 3 fluids system
@@jayantabanik2751 absolutely
"The fluid on the bottom is water. I've dyed it brown, fittingly, with tea leaves."
I hate to break it to you Steve, but you've just made tea.
Who dyes water with tea anyway 😆
And if he knocks it over, he’s “spilled the tea”
If you ask for glass of water at Steve’s house, who knows what you might get.
Used to do curbside leaf pickup for a city. Puddles would be dark brown and readily stain pants. After a while, I realized I was stepping through cold-brewed maple and walnut tea.
😂
That genuine excitement from your kids is possibly the most compelling marketing I've ever seen.
If I'm not mistaken, this effect doesn't have anything to do with density at all. It's just pressure and drag, so it also occurs if you only have water in the container, but you can't see it happening. That made the tea leave paradox look even more like magic to me. I'm glad I now know how it works
Density is an active element here. Higher density implies more energy required for the same velocity, so as energy is bled out of the system via friction, the heavier particles slow disproportionately. Cyclonic vacuum cleaners use this principle to drop higher density particles out of air.
I think the tea leaves situation describes the fact it occurs even in homogenous water perfectly. When the tea leaves are suspended in the water, they are not a fluid that moves independently, they generally follow the flow of the water. So when they move towards the centre, they demonstrate the secondary flow of the water at the bottom, despite that water not being a different density.
@@BenWeigta density discrepancy may be a factor towards its magnitude, but it isn’t required. The disproportionate effect of friction is already caused by the fact that viscous effects fall off from distance from the surface. There is more of a slowdown from viscous forces near the bottom than higher up.
I already commented on it myself just now but, I agree, I like to think about it like an hour glass shaped vortex, fluids are flowing from the outer lower edges and converging in the middle before moving back outward, it's a steady current and it could probably be shown with two liquids of somewhat closer density with differing colors.
When we were kids our grandma's house had a circular pool, and when we were done playing late in the afternoon, me and all of my cousins would run in circles on the edge of the pool to Form a whirlpool, and all the dirt would bunch up in the middle making it easier to clean.
As a kid I always thought it unintuitive so this explanation was pretty interesting.
Wow, that just brought back a very similar memory for me! Very cool 😊
This is why humans are the dominant species on the planet (forget about ants for a moment). We just brain power our way out of bad situations.
@@redryder3721 my dad bought a pool and then a mud motor (those boat motors with a long stick to the propeller)
I assure you that all of his brainpower was used to give me and my sister serious back pains (told us to jump in way too early)
@@angrydragonslayer i don't understand what your dad was trying to accomplish, but it sounds dangerous?
I still do this now as an 'adult' 😁👌
Used to do this as kids to make cleaning above-ground pools easier. Send the kids into the pool and do 20-30 laps, all the leaves and debris gathers in the middle.
:D yep did the same thing
child labor was never this fun!
I haven't seen anyone mention this, but this video is probably the most comprehensive explanation of how Hilsch vortex tubes work from a fluid dynamics perspective. It's a shame that they are widely accepted as black magic, but a simple demonstration like the one you did with the liquids helps immensely in understanding the actual mechanics behind what's happening. Although there are a few differences, and you also have to account for pressure, the working principle is the same.
Amazing video! Thank you, Steve, for making the internet better!
The two fluids interacting with each other is so mesmerizing to watch.
Experiment: Try a vessel with a very smooth bottom surface vs one with a very rough bottom surface. Like, sandblast the bottom of the flask or glue down some sandpaper. Rougher surface should mean more drag so a bigger effect
it would be pretty hard to see what's going on through frosted glass, but you may be able to just be able to tell with enough light.
@@RockSleeper easy, just sand the bottom not the sides
Yeh a smooth bottom of the glass, or a fluid which isn’t a sticky as water on the bottom
@@teddybott3258 or try it with mercury
Using a flask with a hydrophobic spray applied to the bottom would also be an interesting experiment.
I'm constantly amazed at the explanations you choose to give that I must have witnessed 1000x in my daily life but never questioned. Then, on top of that, you make it SO INTERESTING and easy to understand! Keep up the amazing work Steve.
I second this idea
Through most of the video, I kept thinking of how the fluids would perform using a magnetic stirrer. You cannot understand how unreasonably excited I got when you said you actually did this!!!
Based on your turntable demonstration, this effect seems to have something to do with the velocity distribution in vortex flow versus uniform solid-like rotation. Another interesting experiment would be to have a higher level of the lower fluid, to get away from the boundary layer at the bottom, and also possibly a taller container for the same reason.
Its just surface tension...
I think the difference between the example with and without the turntable is simply whether there is relative motion between the fluid and surface, causing viscous forces. Maybe that’s what you said and I just didn’t get it, if so, sorry. A further interesting extension to the experiment would be to find the boundary where the layer between the two fluids is not a vortex nor an inverted vortex, it’s completely flat.
I require both a 2D version of this and a whistle version.
lol
And something being smashed to achieve it!
@@WhiteWave3 and then a challenge video on another channel telling he's wrong
While the majority of what you describe here makes good sense, it also overlooks a fundamental reason this exists.
I learned about this when I was in school studying atmospheric physics in the Navy.
First of all, the pressure gradient you are describing and showing is accurate, water column depth is directly proportional to the "weight" of the column when measured at the bottom, but likely will not be the primary driver behind this phenomenon. If it were, then you should be able to set up a flat wave tank with the same different densities of liquid and see inverted wave patterns in the more dense liquid than in the lighter top liquid. I suspect you won't.
Secondly, you can observe in your videos portions where the vortex depth of the lighter liquid is nearly nil, yet the bulge height of the more dense liquid in the bottom doesn't diminish proportionally.
These observations alone should give anyone pause when considering the pressure gradient as the primary cause of this phenomenon.
Now lets consider what happens to a contained fluid in motion.
When you stir your cup of water, as you note, inertia wants the water/fluid to travel in a straight line, but because there is a physical barrier the fluid must turn. Starting at the glass, pressures build up to a peak from the SIDE of the glass, not from the height of the fluid. The real culprit of pressure related causes here is not the height of the fluid but instead the "traffic jam" of molecules being forced to follow the path of the curved glass, so that pressures near the glass are much higher than the pressure at the center of the glass because of this.(although, while there is a 'funnel' in the center of the vortex, there technically is a difference in 'column weight', but the resulting pressure gradient would not be enough to overcome or balance with the fluid inertia).
Even in an open body of water, such as an ocean we can see this horizontal pressure gradient have substantial impacts to fluid. In the Ocean, as you probably know, there exist eddy currents where for whatever reason (orographic disturbances, speed gradients, etc) closed circulations of water form. The same fundamental thing occurs where the area of max speed around the circulation is generally the highest pressures, despite the actual height difference of the water within the circulation compared to say, the center, is practically nil. And whatever difference that may exist there is certainly "washed out" by wind and swell wave features that move across the circulation. Now, in open ocean eddy currents, you get into other things that effect water density, such as temperature and salinity, where you can end up with a warm core eddy or a cold core eddy as those circulations become 'cut off' from the surrounding waters, but I digress.
Love the video, and I don't intend to be a muck raker, I just hope that you could better explain where the source of the pressure gradient that causes this comes from. Again, it is not the height difference of the less dense liquid, but instead the pressure gradient caused by the lateral motion of the water.
Cheers!
-A
Indeed, the drawing in Einstein's explanation has the surface of the tea cup perfectly flat, not curved at all. It's all about the vorticity of the velocity field created by the boundary layer. In fluid flow, pressure isn't just proportional to depth, but also depends on velocity, and that's the main factor here. Einstein draws an analogy between the tea cup flow and a bend in a river.
I was wondering the same thing, glad there was someone to explain it well!
Isn't the height difference actually caused by the pressure difference due to the 'traffic jam'?
Glad I'm not alone in thinking this. To me it seems intuitive that it behaves this way because as you are stirring and imparting energy the top liquid is being force out from the centre, but then hits the edge of the container so as there isn't any further it can travel horizontally it's forced to travel vertically, both to the top of the container and to the bottom of the container. At some point this downward force generated at the edge of the container will be larger then the downward force in the middle of the container thus causing the heavier liquid to rise in the middle.
+
Love your videos !! The way you explain things is very clear and easy to follow whilst providing a brilliant visual way of seeing the forces and physics behind things.
Excellent lighting and filming! The Fresnel effect on the liquid to liquid boundary looks so pretty!
It's amazing how I was stumped over this solution until you said 'when the container itself isn't spinning' and I got a bolt if lightning and suddenly had no idea how I didn't get it before. Your presentation skills are absolutely phenomenal
@Repent and believe in Jesus Christ is this in any way relevant?
Another nice video! I agree that "inverted whirlpool paradox" sounds much cooler than "tea leaf paradox".
7:20 The critical mechanism for this phenomenon is the drag from the bottom of the container.
I would explain it this way:
Only the heaviest liquid is in contact with the entire surface at the bottom of the container, which provides an exceptional amount of drag, lowering the moment of inertia for the heavier liquid as a whole. Since the lighter liquid does not experience as much drag, it has a higher rotational inertia, and it displaces some of the heavier liquid near the edges of the container.
So at 9:15 when the experiment was to use a magnetic stirrer at the bottom of the container I was certain that the inverted whirlpool paradox would not be present. Since the stirring action is coming from the bottom of the container, the rotational velocity of the heavier liquid would NOT be lower than that of the lighter liquid, and thus the whirlpool would be regular and not inverted.
Would a magnetic-contained 2-fluids system not make those whirlpools? (I.e: without a container to be dragged, isn't the system just beeing heavier on the sides than on the middle, due to centrifugal forces, thus easing the way in the center?)
I'd like to see this done with a sealed container, 2 fluids (no air), and using the turntable method to impart the rotation. Rotate until both fluids are at the same speed as the glass. 1:1 ratio of the fluids to start with, then tweak the ratios to see if that has any impact.
This is extremely interesting as it also happens to describe the mechanics of the whirlpool process in brewing. Instead of dealing with liquids of different densities, the pressures exerted by the whirlpool force solids such as proteins and hops to accumulate at the bottom of the kettle after boiling the wort, greatly reducing the amount of suspended solids. Absolutely love your videos, thanks again for all the amazing content!!
I've observed this for almost sixty years, as a mechanic, I never realized the questionable behavior, perhaps because I've never seen it behave any other way. This makes sense, it falls exactly in line with the rest of my physics experience. Thanks for making this video, very interesting, informative.
I really like that for the sponsor segment for kiwico you demonstrated how much your kids like the product, without showing them.
Parents these days, especially influencers, show their kids far too much, robbing them of their privacy.
Definitely speaks for you! :)
I think Ice cream for breakfast is a great idea
9:24 It may have more do do with which liquid is primarily being stirred, not the horizontal stirring location.
I wonder if you had three liquids would you see the effect once, or twice. Or if you could get two liquids with different densities, but the same viscosity, what would happen?
I also predicted this would be more due to viscosity and the lower viscosity fluid simply went faster than the higher viscosity fluid. So in the example of air vs oil what if he stirred the air really fast but never touched the liquid?
@@mysterymusician4748 would love to see that. Altho you can easily see that when a tornado happens. It picks up water (and houses and cars) making the water technically bulge out in the middle of the stir (stationary air at the edges of the storm would be like the glass in this case, providing the analog of the stickiness based resistance of the glass)
Sort of my comment as well except that it's the drag between the 2 liquids when the top liquid is stirred the bottom bulge is inward because it's traveling slower it's not experiencing the same amount of force applied the top liquid, only what transfered from it, It's not really the density that matters only accept that the denser liquid is on bottom And only happens when you stir the top
@@Czeckie the tea leaves are part of the secondary liquid. This secondary liquid consists of packets with different density compared to just water (new liquid density per packet = water density * (packet volume - tea leaf volume) + (tea leaf volume)*(tea leaf density))
The new, composite liquid is a higher density one. Mathematically speaking it's still two liquids.
Of course I can be misunderstanding something too
Depends on the center of rotation for the fluids. If you start at the bottom, all will vortex downward towards the bottom fluid. Once you stop the magnetic stirring, it would move to the "easier to move" location, resulting in the bottom two fluids showing the "paradox"
I would love to see another experiment of this but with fog and the magnetic stirring plate to see if the fog is rotating for longer after the top fluid has stopped
Hey man, I've been watching your videos for many years. I'm an HVAC tech. I've never had formal training, but you and other channels like you taught me to analyze things on a fundamental energy transfer level. It seems like it should be obvious, but now I'm spending the slower months traveling across Texas teaching a 2 day class for my distributor to help other techs. This kind of stuff makes a real difference, even if we don't notice it all the time. Thank you!
Dude, your channel is incredible. I appreciate you.
Hi Steve, can you try the same experiment but without air in the glass with just two liquids ...
I thought exactly the same thing. There shouldn't be a difference in pressure so there would be no bulge forming I guess. Would be really interesting to see... or maybe as the liquid at the bottom is more dense it would be flung out like water in air...
Having a vacuum would cause the liquids to boil. Having just enough air to avoid boiling would still have interesting results. It just requires careful consideration when analyzing the results.
@@johnbennett1465 I think he meant just filled to the cap. It's an interesting idea.
@@DustyKillswitch there's still the pressure of the water, so I wouldn't expect the result to be any different. That said, I'm not sure how stable white spirits are in a vacuum, so some different fluids may be necessary.
I would also be interested to see what happens with 3+ liquids, I would expect the middle would bulge up like here, but that would also increase the relative pressure on the lower liquid since the denser liquid would be thicker in the middle, but I don't know if that would be enough to equalize and result in a flat bottom layer or if the bulge would be smaller, or if we would get a small non-inverted whirlpool, or if it would depend on the liquid densities used.
I was thinking the exact same thing. that if the there weren't any bulge at the top then there would be no pressure difference and therefore not bulge at the bottom. you could make a closed container with only the two liquids in and use the magnetic stirrer on the top instead of the bottom to do this.
I would love to see this experiment again with three liquids on top of each other. How would the middle one behave?
Pressure difference at the bottom would need to factor in density difference as well, for not having the same depth of collum made of the same substance in all points.
The top layer can only cave in, the bottom layer can only rise.
So my guess is that the center would be more misaligned to the walls than now.
And the heigher bulge should form in whatever boundary density difference is larger?
Well it WAS done with 3 fluids...
@@onradioactivewaves was looking for this reply
Can you find three liquids that don't mix?
@@cxpKSip The bottom would be a heavier-than-water oil like those typically used in experiments that look similar to this but use water as the lighter of two fluids. (Not counting air here.) It might be tricky, however, to find an oil light enough to be stirred properly - without flinging the mineral spirits out - but dense enough not to emulsify into the water and make a visual mess.
these careful explanations make it so easy to understand the thought process. I wonder now, what would happen with 3, 4, .... fluid boundaries.
yessssss. thank you for considering the magnetic stir bar. That was in my head the WHOLE video
Steve you're honestly such a treasure. I don't know where else I could have learned how this complex intermingling fluid-dynamic quirk of physics works, other than your channel. Breaking this down and iteration it in such an easy to understand way is such a gift. I truely feel like I understand our world a little more. Thank you Steve.
If I recall correctly, similar concept is used in the process of separating spent grain from the wort in breweries. The liquid part is recirculated to the side of the wort grain mix at an angle causing circular flow with the tank. The centrifugal force causes the liquid part to swirl on the wall of the cylindrical tank and the grain to pile up in the middle. The outlet of the tank is on the bottom edge of the tank and lets only the wort out after sufficient circulation.
As usual, another fantastic and interesting video Steve! Thank you!
I am surprised that you did not try the stirring magnetic rod with a container that is sealed and FULL of the two liquids .
That would be interesting to see .
A vortex occurs at the boundary of two fluids in a cylinder because one fluid is spinning faster - or more accurately has a higher angular velocity times density - and is flung toward the outside of the cylinder. The difference in how fast each fluid is spinning can be caused by the source of the stirring motion and/or drag.
I like your explanation. Not only it's short, it can also be used for more complex cases, like what if we have three layers instead of two.
That's pretty much what I was thinking while watching. Steve's usually great with his explanations but he seems to have overthought this one a bit.
I’ve always loved science and phenomenons like this but your videos make them even better. I’ve heard about this paradox but never understood it until now so thank you!! 🙏🏽
Great vid indeed! White spirits have very similar specs to crude oil as far as aliphatics and aromatics percentages (despite appearing cleaner). We use them and similar controlled solvents (exxol D80 is one) to mimick crude in corrosion testing all the time. Very useful hydrocarbon mixtures indeed. They are essentially like crude oil for salts and chemical solubility but do not have the side effect of interfering severely with sensitive electrochemical measurements that are required to effectively simulate systems that we are trying to replicate succinctly.
0:40 this mug is awesome!
I just have to stop watching this video for a sec to say: Great content again!🔥🔥
That's an interesting explanation of why whirlpools happen in the first place. There are probably a lot of ways you could look at them, but considering the centripetal force as being supplied by pressure differentials due to depth is not something I'd considered before. Quite a cool thought!
As to the inverted whirlpool, before you provided your explanation based on pressure differentials I'd come up with my own explanation which does also appear to be valid. My initial thought was that when you stirred the fluid, you were only stirring the lighter fluid on top and the heavier fluid was only orbiting as a result of friction with the lighter fluid on top and was likely orbiting as a lower speed. As a result, there would be a greater tendency for the lighter fluid to be flung out and therefore would displace the heavier fluid into the middle. Friction with the bottom of the flask would also be slowing down the bottom fluid. I'm still trying to resolve in my head whether this is an additional factor that might drive the formation of these vortices or whether it's just the same pressure differential phenomenon looked at from a different perspective.
You are describing the forces that push the fluid towards the pressure-velocity equilibrium, Steve is describing the resulting equilibrium. Same phenomenon, different perspective.
@@jrvanwhy Yeah. There was another comment that I found after posting that from a navy guy that made that more obvious. The pressure differentials are the effect, not the cause. Still, the pressure differentials are something I hadn't thought about in the context of whirlpools before and it was an interesting realization all the same.
Oh this was more complex than expected.
Nice explaining.
I'm glad you mentioned the magnetic stirrer, because i had a slightly different idea.
What if you had the stirrer at the TOP, same mechanism, with a "lid" that completely seals-off the top, with no air pocket, and the stirrer capsule is in the inside with it's electronic mechanism above the sealed line at the top ?
Think of those "executive toys" with the oil and water completely sealed in a transparent container, no air gaps, and you flip the whole thing to see the coloured oil trickle down in various patterns.
So the stirrer stirs the top liquid, but there's no air to cause the displacement that would allow the top vortex, and hence the pressure delta. So would there still be the bottom inverted vortex ?
I like your idea, but the coloured droplets falling down inside those toys were actually water and the transparent fluid would be oil. ;)
@@mucia55 the point was the separation of the fluids, not the irrelevance of which one is coloured :)
Yes but less? There's no difference in pressure from height...but the water will still be slower on the bottom with it's friction. I was gonna wonder how high you could get the magnet off the bottom and still work, with a pizza box spacer, eg.
With the magnetic stirrer, you also have a not unsubstantial portion of the bottom surface (where the drag for the vortex is generated) now providing the propulsion for the liquid and overcoming the drag. You have the reverse situation to before, where the liquid at the base of the container is moving faster than the liquid at the top.
the fitness gram pacer test is a multi-stage aerobic capacity test that progressively gets more difficult as it continues
I was hoping to see a test where you put a lid on the container and fill it all the way to the top so no whirlpool can form. What happens if you swirl it then?
Cavitation?
It depends on how you stir it. If you have a magnet stirring the top fluid thru the cap, you would get the inverted whirlpool on the bottom fluid.
One thing I observed when seeing this inverse whirlpool effect with tea leaves is that when you stir it, the leaves at the bottom move to the middle because of the drag you explained, but some of the leaves that float up higher in the cup will spread to the outside of the whirlpool, sinking again to the bottom after sometime and then move again to the middle, it's kind of a circular motion if you ignore the orbit motion
It’s a toroidal vortex. Like all things, including magnetic fields
My intuitive understanding during the intro was that the differential in angular velocities of the two liquids would result in the behavior we witness, but I hadn't considered that the effect itself is caused by a differential in /pressures/ resulting from the differential in velocities, not did I understand that the differential in velocities was caused by the differential in viscosities and their relationship to the counterforce from the unmoving container. Thank you for another excellent video!
Steve, if you are looking for your next fluid dynamics video idea, consider vortex tubes. They're used primarily for industrial cooling applications (commonly machining), and are able to separate a stream of compressed air into hot and cold using no moving parts.
What would this experiment look like with three liquids of different densities? Would all they all bulge up or would the middle fluid do something different?
They bottom two would bulge up.
this phenomenon is dependent on the formation of a boundary layer on the bottom surface, so the bulging effect would depend on how far up the boundary layer extends
Assuming that there is a significant drag coefficient between the bottom fluid & the middle fluid, as well as the top fluid being a liquid. then then my hypothesis is that the top fluid bulges down, the middle bulges up, and the bottom little to no bulge.
What makes this channel delightful is the non-trivial resolution of an apparently trivial problem. This combination, plus the intelligent delivery and Steve's amicable personality turn this channel into my favorite science-oriented one. Just to emphasize what I mean, there are (is, rather) a channel that often tackles issues in Quantum Mechanics where the person delivering the material is clearly pretending to understand what he is talking about, while his body language and speech subtly betray he is totally lost. This never happens with Steve, as far as I can tell.
Years ago i remember thinking about this problem in my teenage years. I wasn't able to figure it out. Probably because of my lack of knowledge of in fluid dynamics.
At the start of the video i paused the video and thought about it again and i was able to figure it out. Seems like i've made some progress in physics (after my bachelor in chemistry and physics and 10 years of teaching physics and adding to my repertoire). I'm pretty happy about that.
Thanks for the video! I enjoyed it very much :)
I would argue that the difference in pressure doesn't come from the difference in depth, but the other way around. The pressure differential comes from the centrifugal force and the surface of the water changes to minimize potential energy. If the liquid was encased in a sealed container without air, no whirlpool could form at the top, but I would still expect the bottom whirlpool to form.
It is also interesting that the bottom whirlpool forms because of friction, not because the liquid is more dense. It happens to the denser liquid only, because the denser fluid settles at the bottom.
I suspect, in a completely sealed container without air, the direction of the whirlpool depends on the level of the boundary between the two liquids. If it is close to the top the lighter liquid would form a regular whirlpool, but there would also now be friction with the top surface, so maybe not. If it is close to the bottom, the denser liquid would form an inverted whirlpool.
It would be cool to see some follow up experiments.
But it can't just be about friction not density because it's not actually the case that there is less liquid on the sides at the bottom and more in the center. Rather, it's that the heavier liquid moves in and the lighter liquid takes its place on the outside.
If density didn't matter you'd expect that once the heavier liquid bunched up and moved higher it would have less drag and the lighter liquid that's now lower then it would be pushed in to take it's place and you would expect circulation.
Yes, speed and friction, not pressure.
Filled sealed container, magnet stir thru top, you get the inverted whirlpool at the bottom. But stir thru bottom, the heavy fluid gets flung out by the stir.
I'm glad you did the stir stick as well, I was curious what effect that would have.
We used this phenomenon to quickly vacuum our pool when I was a kid. Never understood why it worked til now. It was a 4-foot above-ground circular swimming pool. We'd start running laps around the interior of the pool rubbing our feet along the bottom to kick up any algae we felt and once we felt we had a strong enough whirlpool, we'd get out, grab the vacuum, start at the center from the top down, then pick up any straggling pieces of debris.
Yes, we did this too. Fun!
Yummy
LETS DO A WHIRL POOL
Wow, I love it when you answer questions about fluid dynamics and forces that I didn’t even consider before :D So much cool stuff you can do with this!
You could make an awesome self sustaining kinetic sculpture by combining this concept (using water/air interface) with the fire tornado(offset glass for air intake/tea light) experiment (hopefully the air gets enough velocity to make a significant bulge in the water)!!
Also I wonder what happens when the fluid on top is less dense but more viscous (but doesn’t emulsify) and at what difference in viscosity the effect is overcome
I was actually hoping you'd try the magnetic stirring. However I was also hoping you'd put on a lid to force the surface to stay flat.
This is exactly what I was hoping for too.
I want that because I want the boundary friction to be the same for all surfaces. Open to the air the top surface has no boundary layer and is free to move.
@@billshiff2060 I want this, because it is the one test missing from the started hypothesis that the effect described is caused by the difference in depth across the surface and thus pressure.
I had thought that the tea leaf paradox was due to a fast moving fluid being less dense than a slower moving fluid. Tea leaves attracted to the faster moving fluid in the middle like a plane wing in flight is attracted to the faster moving air over the top of the wing. The tea leaves at the middle always appear to be moving much faster than those further out (friction with side walls?), though a slow motion camera and some math might prove me wrong. More revolutions per minute doesn't always mean greater linear speed.
I thought about it like it's harder to move the middle section because it's less dense, so it would be moving slower and NOT be flung out to the sides.
As a kid, we used to use this to clean our round swimming pool. When you've got leaves and dirt and junk on the bottom of the round pool, you get in and walk around the outside edge of the pool making the water spin with you. Eventually, all the crud on the bottom settles in the middle (where kinetic energy is lowest) after you've whipped it up, and the stuff starts to settle. Then you get the vacuum hose and just have to suck up a small pile instead of millions of tiny piles all over the bottom of the pool.
Thank you for making our boring day better and imparting knowledge in the process
This explanation suggests that the effect only occurs if the top of the liquid can be displaced - but what would happen if the container was sealed and a stir bar is placed at the top of the container?
A magnetic stir on the bottom would fling the bottom fluid out just like demonstrated. Disagreeing with Steve on vertical pressure.
A stir on the top would create the inverted whirlpool.
@@jsbrads1 agreed with the bottom stir, but not so sure about the top stir - since the container is sealed there is no displacement of water. By that logic surely there's no whirlpool effect either?
@@qqii with the top stir, the top fluid is moving faster than the bottom fluid and it will “take the wall” all the way to the bottom, creating the inverted whirlpool. Friction at the bottom helps prevent the bottom liquid from speeding up eventually.
no, the top need not displace for the effect to occur. As long as there exists a pressure gradient toward the center from general rotation, and a drag from the container at the bottom, you will have the effect, lid or no lid.
Brilliantly explained!! Thank you
Lovely work! There is one effect which I don't think you mentioned but which did strike my eye. The height of the oil column on the edges is higher bc of the primary vortex. This would mean more vertical pressure being delivered to the edges of the aqueous layer below. Would this not simply force the water inward as observed? Perhaps this and the drag effect operate in tandem?
I always thought it was because the liquid near the surface was spinning faster than the liquid near the bottom, so it had a tenfency to flow outwards on the top, near the surface, and inwards near the bottom, pushing the dense stuff to the center.
Yes, that's a proper explanation.
Time to test this in some lower gravity environments to see how the results compare
Very nice video with a beautiful, intuitive explanation. I loved it. Small remark on the explanation of the pressure difference staying equal at any depth (around 6:40): the pressure does not only depend on the depth but also the density of the liquid that is above it, the pressure will increase more in the center once you're in the denser liquid. So, the pressure difference is smaller in the denser liquid than higher up. I suppose this decrease in pressure difference is relatively small and therefore does not nullify your explanation on the inverted whirlpool paradox, yet is something to take into account when one would build this on a larger scale or with a larger density difference between the liquids.
If you would model this phenomenon, this decrease in pressure difference is definitely important and would result in a smaller bulge compared to when you assume pressure to be solely dependent on depth.
TL;DR: the explanation around 6:40 is not completely correct (pressure depends on the density of the liquid column above a certain point), but I think the main take-away of the video is still correct and very educational.
But as he said, it's the pressure difference inside each liquid, not the absolute pressure, so the pressure difference in a dense liquid is the same relatively to the pressure difference in a less dense liquid, since the pressure comes from the density of that liquid. It's not like a pressure difference between a point in a dense liquid Vs a less dense liquid. It's the pressure difference between a point in liquid A to another point in liquid A, then a point in liquid B to another point in liquid B.
Basically, it was fine.
If you listened to what he said, he SPECIFICALLY said "pressure difference not absolute pressure". He didn't assume it was due to depth at all. If you're going to make "corrections" at least listen to what it is you're attempting to correct.
He very clearly explained why he wasn't using absolute pressure, as depth affects pressure, and the relevant issue was the DIFFERENCE in pressures caused by the vortex.
@@NateTheScot I feel like you're missing my point as I am also talking about pressure differences, not absolute pressure. Maybe you should read my comment again or maybe I just explained my point poorly. Either way, I don't feel like starting an online discussion about this topic. It is of negligible importance for us both and this UA-cam video.
So I won't reply to comments in this thread anymore and would like to wish you a wonderful rest of your day (whenever you may read this). Keep enjoying interesting physics videos!
great explanation, stunning visuals!
Love the mug. I remember my father giving me that puzzler when I was a kid. Thx for the vid
I notice that in all the jars, you have more spirits than water. Does that matter? Would it work with equal parts of each? Or more water than spirits?
Guessing, when you use less brown water the inverted whirlpool is more startling.
The pressure difference drawing for the two spots at 4:54 seems wrong to me. Pascal's principle would say that those two spots would have the same pressure, at least for a body of stationary water in that shape. I definitely believe there's a pressure difference there, but I wonder if it has more to due with velocity differences or something, and not the column of water height.
Your videos are awesome!
I used the effect to clean debris out of round pools. I think the surface on top has no boundary friction so the movement outwards there is easiest and the rest is forced to follow that pattern. Outward on the surface, inward at the bottom and downwards on the sides. I aimed the filter jet sideways to always generate a rotation and rigged up a surface net projecting in from the edge. It caught everything from the surface as it rotated and all the sunken debris gathered in the center of the bottom.
We use this concept in my circular outdoor pool. In order to get all the dead bugs into the center, all we do is walk around in the pool near the outer edge a few times to create a whirlpool, then all the bugs quickly group up at the bottom in the center where we can use the skimmer to quickly scoop them all up.
What is a more interesting question is what shape would a 3rd liquid layer under the water take? Would all layers below the first peak in the middle or would it alternate middle-sides-middle-sides?
Repent to Jesus Christ
“And when you pray, do not keep on babbling like pagans, for they think they will be heard because of their many words. Do not be like them, for your Father knows what you need before you ask him.”
Matthew 6:7-8 NIV
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I _think_ there’s an element to it, that you skipped. The denser liquid at the bottom is experiencing friction at the bottom of the beaker, so it’s slower, yes. But it’s also experiencing friction at the interface between the two liquids. That’s what makes it move in the first place. That’s also why the phenomenon does not occur when fully dipping the spoon/spatula into the beaker. Same for the magnetic stirrer. The crucial bit is the friction between the liquids.
There’s an interesting application of this to tornado formation. This effect occurs when the air feeding a rotating thunderstorm is not entering at the ground level. It explains why most rotating thunderstorms do not produce a tornado. There is a mode flip when the fastest inflow is no longer decoupled from the ground due to the combination of friction and slightly denser air settled near the ground due to evaporating precipitation nearby. When a tornado forms, the invisible ground-level bulge goes away, and this allows the vortex to contract to a much sharper point at the ground. Why it happens with some storms and not others is not easy to understand, but its definitely a type of dynamical tipping point, or mode flip.
I have an alternate explanation to what you gave.
1. When you stir the liquid you create a vortex in the top liquid.
2. There is greater force on a body with greater depth as you noted.
3. Therefore there is less force on the bottom liquid in the center than there is at the edges.
4. That pushes the bottom liquid toward the center again decreasing the depth of it and therefore the pressure on it in the center.
5. This continues until equilibrium is reached.
6. When the top liquid starts to slow down the vortex gets smaller.
7. This increases the pressure on the bottom liquid pushing some of it towards the side.
8. Again a positive feedback is set up where the more the top vortex shrinks the more level the bottom liquid becomes.
This also would explain the same effect seen yet has nothing to do with movement or orbits, rather it is just an effect of gravity.
people drink loose leaf tea without a strainer?! ...
strain it afterwards
@@azultarmizi huh.. most people here just use a strainer in the cup that you can simply lift out after its done infusing.
@@halsti99 Yea I'm aware but there are also people who do it in other ways.
in my country most people do
Dear Steve,
something behaving counterintuitively is not the same as being a paradox.
-kindly everyone
I really like the idea that instead of "here's why this surprising thing is true" the first part of this video is "here's why this true thing is surprising"
This is like seeing a stacked surface low pressure vortex (higher density fluid) under an upper level high pressure system.
I already intuitively knew this phenomenon (for once in your videos) I had guessed it would involve lower pressure in the center and drag at the bottom. Years of loose tea and sugar stirring finally paid off :D
With the magnetic stirrer, you're also stirring the denser lower liquid rather than the less dense upper liquid.Another difference you need to eliminate/control for/test.
I always looked at is as following the path of least resistance from outside to inside. Rotating around the outside has more friction over a longer distance, verse the center with a shorter distance and less friction. A round swimming pool with leaves and gravel is a great backyard example.
"Orbit" is one of those scientific terms that has a very specific technical definition in multiple fields. It's used in astronomy, atomic physics, and anatomy, for example, to mean very different things. Given a context in which the word isn't commonly used, so long as you use the word for something round, you can define it however you want.
I see this every day as an organic chemist. we utilize the inability of water and these organic solvents to selectively extract compounds between phases. I've never really thought about how weird it really was. nice video.
Holy smokes, what about a sep. funnel shape in place of a water glass? the pressure gradient would be different right?
This channel melts my brain down
I’m commenting this before watching the video. At the moment, the vortex on the bottom makes sense because in my head as it swirls out and the sides get taller, it creates more pressure on the bottom and a low pressure area in the middle.
I've been trying to find a video about this for so long and now finally this is on my feed.😂
In mind i simply thought about this as the less dense liquid starts moving before the denser liquid at the bottom, causing it to flung out to the sides. Due to this it creates a low pressure in the center and because the denser fluid is slow and yet to move, it is forced to bunch up in the middle. This also explians why it needs to be stirred halfway, if you just stir it at the bottom like the magnetic stirrer, the denser fluid is moving first causing it flung out and the inverted vortex not appearing!!
Very beautiful high quality closeup! Seeing ripples of the vortex is amazing 😍 thanks for the video!! 💪🍀🙏😇
@SteveMould
This is inertia and centrifugal force at its finest, as well as a perfect example of how forces on different subjects can vary results.
Centrifugal force is best defined as when objects are being acted on by a rotational force and the velocity of the spinning object, combined with the friction of the container's surface against the contained fluid, which forces the fluid to, at first, spin against the walls (from rest), and then eventually be pulled alongside the walls (in motion); This pull (additive force) forms an origin, which may be defined as the center of the entire plane of motion, below which also acts as the shear point. As the pull increases, the shear point expands, with less and less mass at the origin. The more dense a fluid is, the more mass gets pulled from the origin. At their extremes, if you were to rotate the object at extreme velocities, you would cause a capitation reaction at the shear point, and upon the capitation collapsing on itself, the resulting shockwave would shatter/warp the container itself.
An example of this would be if you were to tape rope to an egg on two ends, and then spin it in one direction. Your result will be either an exploded egg, or a homogenous mixture of yolk and egg white when you crack it open.
*However,* If you were to stir the fluid inside a stationary container, the resulting reaction would be (a loss of force) being absorbed by the container (which is at rest). A shear point does not appear below the origin in this case -but rather, above or at it. This is due to the presence of gravity, and the fact that the fluid itself is doing the spinning, not the container which holds it. Atmospheric pressure also has very little to do with this reaction, as it would still persist if the container had a lid. At extreme velocities, this wouldn't cause capitation reactions due to the presence of a less dense fluid being sucked into the shear point, dampening the reaction itself.
Orbital terminology is better for describing multi-planar instances of movement. This instance is primarily Bi-planar.
Lovely explanation! Thank you.
"Guess what arived today while you where at school?"
For a few seconds i tought steve was talking to me, even tho its been more than a decade since i last went to school
This was an exam question in my fluid dynamics exam at university. It is a quite fun problem to unravel for the first time in an exam . 😅
Your kids' reaction to the Kiwi Co arrival was the best advertisement for that company that I've ever scene :D
Also an excellent video :D
I like to think about it like an hour glass shaped vortex, fluids are flowing from the outer lower edges and converging in the middle before moving back outward, it's a steady current and it could probably be shown with two liquids of somewhat closer density with differing colors.
2 things.
1. I brew my own beer, part of the process just after the boil is to do a whirlpool. This is done by recirculating the liquid & diverting it sideways to get it spinning. This then separates the solids into a central cone at the bottom, allowing the clear liquid to be pumped out from the outlet at the bottom edge of the boiler.
2. I used to transport patients home from hospital. Some patients had 'get well soon' helium balloons with them. As the ambulance accelerated the helium balloon would float towards the front of the vehicle, and would move towards the back when the vehicle braked. The total opposite of everything else in the vehicle affected by inertia.
This was caused by the air in the vehicle (which is affected by inertia) being pushed towards the back when accelerating & the front when braking. The balloon being lighter than air would travel towards the lower pressure. Quite fascinating to watch when in the back of the vehicle.
I'm more impressed with the gradient that is produced from the lower more dense liquid. It is as if the level is flat and is not affected until a certain point inward toward the center where it is then a linear progression of rise to the center. AND IT'S SMOOTH! That is not turbulent.
Another brilliant video... Thanks Steve...
Mathematic explanations of hermetic principles are amazing
This is an awesome video ! So much information, thanks !
The problem I see with the centrifuge comparison is the way the rotational force is exerted.
In stirring a liquid you are using an object, usually a spoon, to exert a rotational force in the container around the sides of the container, making the liquid move in a circular motion against the sides of the glass and the denser liquid wants to bunch at the bottom because the less dense liquid is moving at higher speed around the edges of the container.
In a centrifuge the force is exerted from the center of the centrifuge, not the containers. When the centrifuge begins spinning it will exert force on the liquids to push them against the side of the container that is furthest from the center of the centrifuge. Usually the containers are also slightly laying on their sides which is forcing them closer to the bottom of the container, not necessarily the sides, but it will work with either scenario. The denser liquid separates because the force is more powerful on it than the lighter liquid, and thus goes to the furthest side of the container away from the center of the centrifuge.
That is probably the reason the first example makes more sense to us in every day life, because it's the kind of fluid rotation we are used to. We do encounter it more often than a centrifuge.
As a note, even though air is a fluid in dynamics, I don't think using a stirring example can work with it as 2 liquids. While air is a fluid, it's far less dense than most liquid, if not all. It does not have the force to put pressure on a liquid in a container. Maybe try the example with 2 gases instead, maybe a thick fog that sinks down below air. That would better serve your example you want to try with gas-based fluidity.
I had a strong hunch early on that it was the poor coupling from the boundary of the two liquids - the spirits have a higher velocity not just because of the drag of the bottom of the vessel, but just the repulsive cohesion between the liquids isn't imparting as much momentum into the heavier liquid. The only way for the heavier liquid to gain angular momentum is from the lighter fluid having a higher velocity. By that logic the heavier liquid can never go faster than the lighter, and thus can never achieve a higher moment of inertia.
Nearly every brewery uses this penomen to separate the hot break material from the wort after boiling. There is a vessel, where the wort flows tangential into the vessel, so the wort starts to begin moving in circular motions. In the middle, the hot break material separates as a cone.
It's a nice fun fact for beer drinking people. Cheers from Germany🍺