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So this Youtube video has been around for a while now Veritasium Hydrodynamic levitation! .

Also these questions Fluid Mechanics explanation of an object levitated next to an air jet and Explain hydrodynamic Levitation may be related.

Description

To avoid rot links and people that do not want to see the video, I'll try to explain the phenomena.

You have a sphere and a water jet. The water jet is vertical (velocity goes against gravity), and touches the sphere almost tangentially. The ball not only rotates due to the water jet but also stays at constant height from the ground. The angular velocity can be defined in the direction of the cross product between the position of the contact point between the jet and the sphere (origin in the center of the sphere) and the direction of the jet. Some water drops fly away at the top of the sphere away from the jet. The whole system seems stationary, as long as the water flow is the same the height and frequency seem to stay constant.

Suggestions

Derek clearly states it is not about Bernoulli principle, as in this case the ball rotation is important.

There seems to be two explanations "water adhere to the sphere and is ejected conserving horizontal momentum" and "Magnus effect" (ME). The later is not so obvious to me as the system is at rest with respect to still air and there are two fluids, water and air, (does ME means air pushes the ball horizontally?).

Note that Coandă effect (another usual solution) is the typical hairdryer ping-pong ball levitation demo which is explained by Bernoulli's principle so I am not sure if it works as a satisfactory answer.

Doubts

Has any recent paper/videos discussed what happens if you do the same experiment with hydrophobic spheres? Can it be predicted with laminar flow theories or does it need turbulence? Would this phenomena occur without air for example?

Too many questions have been posed, but not so many responses on the internet yet.

I just wanted to know if any standard hydrodynamic formalism has been developed to model this phenomena or at least if there has been some experimental characterization of the phenomena (any study of the link between friction, density, frequency, height, radius, and so on).

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  • $\begingroup$ It's currently unclear what exactly this question is asking without clicking on the link you provided. To make questions more accessible and guard against link rot, please include all relevant information, such as the explanation of notation or specific terminology used, in your question. $\endgroup$
    – ACuriousMind
    Nov 22 '17 at 15:23
  • $\begingroup$ @ACuriousMind edited. $\endgroup$
    – Mauricio
    Nov 22 '17 at 15:41
  • $\begingroup$ Since you are revisiting this old question, consider this guidance. $\endgroup$
    – rob
    Jul 24 at 13:34
  • $\begingroup$ @rob thanks, would merging all edits into a coherent post with the same question be ok? $\endgroup$
    – Mauricio
    Jul 24 at 14:07
  • $\begingroup$ That's the idea: just make your post say what it ought to say. People who are curious about previous versions can click the "edited 5 hours ago" link. $\endgroup$
    – rob
    Jul 24 at 14:35
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This is because of Friction, Coanda effect followed by Magnus effect.

In the middle, he also showed how the water followed the curve of the ball. This is mainly because of 'Coanda effect'.

From Wikipedia,

The tendency of a jet of fluid emerging from an orifice to follow an adjacent flat or curved surface and to entrain fluid from the surroundings so that a region of lower pressure develops.

Here, the water is trying to entrain fluid from surroundings. When it comes near to a surface, it cannot pull air from surroundings which makes a low-pressure region between surface and jet. This is because, 'when something is emptied from its place, then something should fill the void to keep the balance.'

Firstly, the ball starts to rotate because of the friction between water and ball surface which is just like a Tesla turbine. As the ball is being hit by the water on one side (not centre), it will push the ball to the other side because it comes in the way of the water. Once the ball starts rotating, the fluid following the surface don't adhere to the surface much longer and drift apart tangentially.

This is where the 'Magnus effect' kicks in. The magnus effect creates a force perpendicular to the jet direction. This force pushes back the ball to remain in contact with the jet on one side. So, the weight of the rotating ball is born by the jet completely.

The magnus force is proportional to the speed of rotation of the ball which is proportional to the velocity of the jet of water.

So, the ball levitates in air as long as the jet discharge is kept constant.

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  • $\begingroup$ Well, in a boundary layer, due to no-slip condition, fluid adheres to the wall. and viscosity between the layers of fluid tend to slow down the further layers nearby due to viscous shearing thus a boundary layer forms. Here, by friction, I mean the no-slip condition at the surface. $\endgroup$ Nov 25 '17 at 6:47
  • $\begingroup$ Magnus force doesn't seem right. Do yo know an example of Magnus force between two fluids? My problem with Magnus effect is that the ball is at rest with respect to air. $\endgroup$
    – Mauricio
    Nov 26 '17 at 11:43
  • $\begingroup$ Magnus force is a phenomenon and Bernoulli's principle is merely a scheme to calculate the total amount of pressure; it is just a way to get the approximate amount of pressure, velocity trade-offs. Moreover, Bernoulli's theorem is only valid for incompressible, inviscid and irrorational flows across a streamline. In this case, the entire lateral force to keep it in contact with the liquid jet is provided by the liquid rotated across the ball as a result of Magnus effect. Forget about the air, think about a rotating ball or cylinder in a fluid, it experiences Magnus force. $\endgroup$ Nov 27 '17 at 13:30
  • $\begingroup$ Yeah, the problem is that it gets too descriptive and from principles you cannot get very predictive. Do you know any papers with similar experiments? $\endgroup$
    – Mauricio
    Nov 27 '17 at 13:33
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    $\begingroup$ I tried searching for some but couldn't find any. If you come across any of that kind, kindly post it in the comments. $\endgroup$ Nov 27 '17 at 13:43
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I am unconvinced by his (simplistic) use of Bernoulli's law to try to explain this effect. Clearly, the water adheres to the ball due to viscous effects and surface tension, where Bernoulli cannot be used because it assumes that viscous forces are negligible.

Instead this is an application of the Magnus effect which explains how a spinning ball curves away from its principal flight path as observed e.g. in ballsports such as baseball. Due to the rotation of the ball, it drags air faster around one side, creating a difference in pressure that moves it in the direction of the lower-pressure side.

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  • $\begingroup$ Actually tour link to NASA directly states that the lift is due to Bernoullis law. Last bullet point on that page.(what is a myth though.is the equaltime hypothesis) $\endgroup$
    – lalala
    Sep 9 '17 at 10:21
  • $\begingroup$ his? Actually nobody seems to be considering this experiment as a simple Bernoulli's law application. But using hydrodynamics equations (continuity-Euler eqs, Navier-Stokes) could you predict this phenomenon? Has anyone given a clear demonstration that it is adhesion based? $\endgroup$
    – Mauricio
    Sep 9 '17 at 10:52
  • $\begingroup$ @lalala - I was alluding to the longer path hypothesis, i realize now it is not so relevant so i have removed the statement. $\endgroup$
    – nluigi
    Sep 9 '17 at 11:16
  • $\begingroup$ @Mauricio - The presenter in the video (which is whom i mean by 'his') clearly mentions Bernoulli multiple times. The low-pressure region is caused by drag due to the spinning motion of the ball, this can be capture just fine using hydrodynamic equations in some rotational reference frame. I am not aware of any such demonstration for this particular case, but maybe this is of interest? $\endgroup$
    – nluigi
    Sep 9 '17 at 11:21
  • $\begingroup$ @nluigi Derek the presenter states clearly that is not a demonstration about the Bernoulli principle, also stated in the description of the video. He says thought the Coănda effect is explained using Bernoulli, but this experiment with water doesn't. $\endgroup$
    – Mauricio
    Sep 9 '17 at 12:49

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