How Physicists FINALLY Solved the Feynman Sprinkler Problem

as water is pushed through a garden sprinkler like this Newton's third law tells us that for every action there is an equal and opposite reaction so the force of the water exiting the sprinkler arms will cause the sprinkler head to spin in the opposite direction to the water's movement but what would happen if the same sprinkler was submerged in water and the pump Direction was reversed so that the arm sucked in water rather than pushed it out will the sprinkler spin forwards backwards or not at all pause here and think about it if the answer seems obvious to you let me know in the comments down below because for over 140 years some of the best physicists in the world including one of the greatest Minds in science ever Richard feeman haven't been able to decide or prove the answer winning this problem the name the Fineman sprinkler today I'm going to cover how scientists address this deceptively simple mystery which was ultimately incredibly difficult and impressive in terms of the Innovative techniques that they had to develop just to study this problem so I want to go through how they went about finding out the theory behind what was going on so that we get finally after 140 years to our answer but first let me tell you how this became known as the Fineman sprinkler because the story is a fun one in 1883 the first known description of the reverse sprinkler problem was published by physicist and philosopher Ernst Mark Mark found that a central spindle connected to c-shaped arms would spin away from the exit hole where the air was pumped through Mark found that on letting go of the hand pump he was using to drive air through the system the apparatus sucked air back in but interestingly it didn't cause the system to rotate in the opposite direction Mark chose words here that often are used before someone makes a mistake writing the reason is obvious as during suction air enters the tube from all directions into the inlet hole rather than a continuous stream of air that emerges while blowing air through the system this means that there's no overall momentum to the air intake meaning that no rotation of the apparatus should occur little more was thought of the concept until physics students at Princeton started debating it 60 years later they said hang on but air does become uniform in Direction it just does it inside of the tube and actually momentum can be imparted to the apparatus so in fact it should Spin and it should spin in Reverse of the direction that a normal sprinkler rotates working at Princeton at the time was one of the 20th Century's most famous physicists Richard feeman whose achievements include his major contributions to Quantum Mechanics the atom bomb project and being played by Jack Quaid in Oppenheimer fean was keenly aware of his own abilities and almost entirely unburdened with modesty so he thought that he could have a go at settling the debate where others had previously failed he submerged a sprinkler into water and applied a pump to pull water through the system and he saw a brief moment of movement but he decided the pump wasn't working hard enough to make that movement anything more than a momentary bump so he began to turn up the pressure seconds later Fineman found himself surrounded by water broken glass and Cloud chamber images that he had just ruined he had his theory of what should happen but actually proving it forever evaded him despite neither inventing the idea or solving it what happens when applying suction to a submerged sprinkler became known from that point on as the fan sprinkler problem earlier I said that normal sprinklers spin due to the momentum imparted by the exiting water let's start investigating the problem there this visualization is exactly that a sprinkler this time submerged in water so that we can see exactly what is happening with a pump as normal pushing water out of the sprinkler arms the green glow is a fluorescent dye mixed into the chamber that is now being pushed out of the arms we can watch as these Propel the sprinkler around like two rocket Jets and we need to understand exactly what's happening here so that we can understand the Fineman sprinkler going back a step though for those without large Lawns or for my viewers that are in rainy Britain like me who don't need sprinklers they come in a surprising variety of shapes sizes and mechanisms that drive them but the simplest just pump water out of a number of bent tubes to drive their movement but the question is where exactly does that momentum transfer this push happen to actually cause These Arms of the sprinkler to spin when water fires out of the end of a sprinkler arm it provides a tangential Force causing the top to spin we can imagine an ultra simple version of this system by considering two straight tubes with a 45° surface and a single high-speed water molecule moving through it as the molecule bounces off of the corner it imparts a radial and a tangential Force the radial force is absorbed by the structure the tangential force causes the head of the sprinkler to spin and redirects the water molecule this importantly is that momentum transfer event ultimately the system is a little bit more complicated and fluid mechanics in particular adds further complexity but using bent tubes and liquid still produces broadly the same result momentum is imparted to the water and as a result momentum is imparted to the sprinkler head the important part is that momentum transfer is happening at that sidew wall here and we'll come back to that point later so now we understand how a submerged sprinkler would work in the normal Direction has that changed how you think it would work when the sprinkler sucks water through the system rather than pushes it out most of fineman's students thought the answer was obvious but the only problem was they all disagreed which way it should spin some said suction through the tube would create a low pressure Zone and draw the sprinkler arm towards it causing the sprinkler to spin backwards others said yes this is true but this would be balanced out because the water molecules when moving into the sprinkler arms would encounter that same corner Corner we saw before and would impart a forward momentum to the sprinkler head and that would cancel out the reverse suction causing the sprinkler not to move at all and still others said that suction is coming from all directions at the entry point of the pipe and this is a very small overall force and water would flow in to fill the Gap faster than the sprinkler head would start moving and actually the motion would be dominated by that forward momentum imparted at the corner of the sprinkler arm so the sprinkler head would start to rotate forwards so we have three options and we have three groups of intelligent individuals predicting each of them one topic that we need to cover before we start on the actual research is that sucking is not the opposite of blowing and I could take this conversation in a lot of directions from here but I'm going to stick purely with the physics I didn't think it was physically possible but this both sucks and blows this becomes pretty clear if you have a fan nearby put your hand in front of it and there is a pretty powerful Breeze but behind there is barely any air motion at all blowing involves a large number of air molecules that are given momentum in all roughly the same direction this can be by hitting them with a fan blade and here is an example the air leaving is all roughly aligned in its velocity and Direction putting your hand in front of this you feel a force of a large number of particles all pushing your hand in the same direction whereas when you see air entering the fan this is drawn in from all directions due to suction as a result there is less net force placed on an object in the path of this suction and also air flow entering the system from opposite sides of the pipe will cancel out their transverse momentum interestingly here due to our slightly imprecise use of language when we're describing sucking and blowing as air moves from being sucked in through the pipe's entrance it then becomes blown as its direction becomes uniform once it is actually within the pipe importantly though it isn't actually quite uniform we'll come back to that point later also this difference means that a small fan can blow objects from a few meters away whereas one that can suck objects in from a few meters away would need to be absolutely massive this gives some credibility to finean students that said suction wouldn't impart much force to the system and it was this difficulty in getting to a final definitive answer that like many physicist before them Drew in leaf risto and his scientific team risto is known for looking at some of the most pressing problems currently facing Humanity such as how to best blow a bubble or the aerodynamics of paper airlanes so this problem of the sprinklers was a Natural Choice he was joined by other researchers including lead author Kae Wang and this year's entry for nominative determinism Brenan sprinkle they began by exploring previous attempts to settle the debate finding largely inconsistent results that appeared to be due to subtleties in experimental design such as things like bearing friction preventing small forces like suction from taking effect or from vibrations and variations in the power from pump motors that obscured the experimental results in order to make make this research the definitive study into the Fineman sprinkler system Wang realized that he needed to avoid experimental details that would limit their results to this particular setup alone now my PhD was an experimental physics so I love a bit of meticulous experimental design let's take a look at exactly how they set up their experiment liquid pumps typically induce vibrations and fluctuations so connecting one directly to a sprinkler ran the risk that the results would be affected by the choice of pump used Wang's idea instead was to power the system by using the gravity of Earth his system would be powered by a siphon connected to the top of the sprinkler siphon operation is surprisingly subtle as a concept but the key part of it is that it can suck water uphill as long as the tube ends below the starting point to maintain a constant height difference between the two water containers he used a series of runoff pipes and a pump liquid leaves the main tank through the sprinkler at a rate of Q pulled through the siphon tube into a side tank the flow rate through the sprinkle is proportional to the height difference between the two tanks which is kept constant through an overflow tube that empties the side tank also at rate Q into a reservoir the reservoir is pumped continuously back into the main tank if the pump rate is faster than Q any additional water added to the main tank runs off through a separate overflow tube this keeps the vibrating pump out of the way of causing disturbances or changes in flow rate from causing error in the experimental setup the next challenge was to avoid any motion of sprinkler head being lost duee to friction while bearings are great at rolling under load but still introduce minor losses due to friction with the cage and viscous grease within in order to avoid this problem entirely Wang concluded the best way to reduce bearing friction would be not to use mechanical bearings at all instead he used water itself as the bearing system a meniscus is a slight rounding at the edge of a liquid surface you may have noticed these before particularly in narrow containers where it looks like water is climbing up the walls and it happen happens because the water molecules are more attracted to the glass walls than to each other a second type of meniscus occurs where a solid object rests on a liquid surface bending it downwards beneath the surface of the water this phenomena allows you even to float some metal coins on the surface of water and now an interesting and important property of these minisi is that they repel each other to produce that near frictionless bearing Wang combined the concave meniscus effect inside a cylinder with the convex type created by floating the sprinkler head apparatus underneath the water this is what his experimental setup looked like the outer Rings hold the sprinkler in place centralizing the inner sprinkler Hub through the concentric minisi the siphon tube and arms allow the liquid to flow through and a small amount of air at the top of the sprinkler Hub allows it to float the team was now ready to run the experiment they just needed a way to visualize the flow of water through the system earlier we saw the sprinkler in conventional operation with glowing green Florine but this eventually spreads throughout the water making everything green so wouldn't work for the reverse sprinkler instead Wang chose to use hollow glass micro particles to scatter light and a 1 watt green laser to illuminate them using a cylindrical lens Wang spread the laser out into a line This is called laser sheet Imaging and is used widely when researchers want to look at things happening in a slice of liquid or gas also reminds me of that one scene from Alien where they find the egg Hatchery and then naturally fall into it which is both bad laser safety and biological safety as far as I can tell this alone would have worked but the team also added a long exposure effect this means that for the videos that we're about to see the longer a particle Trail looks the faster that particle is moving to test this system let's see the sprinkler with these particles in conventional operation we can see the suspended particles directed out of the sprinkler as water flows through it producing a net momentum transfer to spin the sprinkler head but the question is in the moment we've been waiting for what happens when you move the system from pushing water out through the sprinkler to sucking water in through the system after the valve is opened the sprinkler begins to turn in the opposite direction to the normal sprinkler ever so slowly at first but clearly building speed as the system starts we can see that particles from all around are sucked in towards the sprinkler head and as the speed increases it becomes clear the Fineman sprinkler spins in the reverse Direction after 140 years is it looks like we have some experimental results that finally cast some light on what is happening in this system but at the moment it just tells us the what what about the why if we zoom into the system initially it looks like the ends of the arms are in fact pulling themselves forward like the tube of vacuum pulling itself forward if you put it too close to your hand it's an understandable Theory after watching this video but after running the numbers it turns out to be wrong it can't create enough Force to spin the spring sprinkler at the speeds that are observed here to understand what is actually happening the whole sprinkler system needs to be studied and for this Wang immobilized his sprinkler and centered the camera to see what was happening and he saw something strange the middle of this video is the center of the sprinkler seen from underneath as water enters the central cavity it creates this odd slightly asymmetrical full Vortex shape by modifying the tubes and increasing their internal area Wang was able to capture this slightly clearer result this revised visualization better highlights the asymmetry occurring within the system here we can clearly see four vortices with two of them being larger than the others these vortices are formed by the Collision of the two inward Jets by looking at the lengths of the lines drawn out by the particles in motion it appears that there are slightly faster particles entering the top right and bottom left vortices the researchers confirmed this suspicion using using a system called PIV particle image Velo Symmetry and in fact revealed that inward Jets have a variable velocity profile over their width flow within thin curved pipes has long been studied under the name of the dean flow problem it's known that centrifugal effects lead to higher velocity flows on the edges of tubes and this looks to be exactly what is happening here having the highest velocity flows off center means that the inward Jets each contribute Force at an offset from the central axis of of rotation this is a rotational torque on the system as these Jets enter from opposite sides of the sprinkler system they largely cancel out however not entirely some remaining rotational Force still exists even though it is low as in consequential as it might seem this small force is what spins the Fineman sprinkler in Reverse this ultimately causes the system to spin at about 40 times slower than a conventional sprinkler system so all those years ago Mark was actually right the arms don't suck themselves forwards but what he missed is that there could be forces on the other ends of those tubes Wang's paper continues in great depth with friendly fluid Dynamic equations such as this one down here for the angular momentum flux which I'm not going to go into the qualitative description I think is enough here this is a great Testament to the paper which really was A Cut Above most the authors combine visual logical intuitive and mathematical explanations for what is happening in this system which just tells you how complicated it was to most people that looked at it it also is a really good example of how a simple concept can be far more complex than initially seems and can found even some of the greatest minds of Science in case there was any remaining doubt the researchers leave us with a final video of the sprinkler leisurely rotating in the reverse Direction I had a ton of fun reading up on this topic shoot me a comment and a like down below if you enjoyed it too and if mesmerizing green fluorescent videos are your thing researchers just use florescent light to watch how plants talk to each other go check that video out here thanks for watching and as always I'll see you next week goodbye

Channel: Dr Ben Miles

Views: 482,593

Keywords: science, future, breakthrough

Id: EM-VWNb5Trk

Length: 17min 16sec (1036 seconds)

Published: Sun Mar 10 2024