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  • I have here a pipe of sorts by blowing air here on their current comes out through the spout just so that you are convinced the air is coming out.

  • What?

  • The Aires coming out.

  • Okay, No, I'm going to put this very light bull just above the spout.

  • Okay, On the blow on it.

  • The upward streaming is supporting the weight of the ball so that its invitation is floating in in the middle of the air.

  • So fast of it.

  • But now I can support it completely off the vertical.

  • Let's see if I couldn't do it in the other direction too.

  • Did you see that while it's off the vertical, the bull is spinning.

  • This phenomenon has to do with a ll sort of question a whole range of questions that are often discussing popular literature on the technical literature on has to do with, for example, how a plane flies Now The usual explanation is that it's Bernoulli's serum.

  • That's the technical term that people always invoke on.

  • It's supposed to say that if you have a flow off fluid water, what have you the some off density times Velocity squared over two.

  • So speed squared Plus, the pressure is supposedly constant.

  • So if there's a large speed, this small pressure on, if there's a large pressure this small speed on, they'll say they'll have you believe that where there is fast air flow on this side on days slow, airflow undecided.

  • So the fast side has it.

  • Low pressure on the slow side has a high pressure, so the high pressure region is pushing a little pressure region.

  • And so it's going to be lifted in this direction.

  • Fighting the gravitational fall on day will say that that's the same thing.

  • Why the airplanes flying now?

  • This is not quite the right because Barry Sveum, if you read the actual proof and the statement and so on, says that for each streamline that is the floor line of fluid particle.

  • That's true.

  • But you cannot apply to automatically to different streamlines, and in this case there is a streamlined coming above the ball on.

  • Then streamline.

  • Be laudable, but Jesus different streamlines.

  • You can't apply their night boats at the same time.

  • You can't say, well, this streamline this streamlined.

  • They have the same kind of constant.

  • No, it's it's not implied in the serum There is another version.

  • Bill knew it, which has got the time dependent veterinary for potential flow, which means that if there's no vortex in the system you can apply, don't do it to the entire flew the region.

  • But in this case, there's a lot of vortex.

  • You saw the whole thing spinning so you can apply to either either s.

  • So it's actually a nonce application you can't use, been read, explain.

  • It's so what is happening is the question.

  • What is really happening has to do with something that is settled, but in some sense even more primitive than Billy.

  • You see, when we do this, the air is streaming above the ball on is being deflected along the ball like this.

  • Why does it deflect?

  • Because there has to stick the ball on.

  • You know, fluid is a continuum he doesn't want to.

  • So the snap snap out and create a vacuum.

  • So if there's a solid boundary, for example, somebody like this, he wants to go along the boundary of this thing, and that's what gets deflected on underneath.

  • It kind of goes like that also, So the long and short of it is that the whole airflow comes in like this but goes out like this, so it curved.

  • But whenever the tragic three off a moving object curves, for example, fluid curves, there must be a force that's carving it.

  • Yeah, on that force is being supplied by the ball because ball is leading the fluid around this because the fluid wants to call here.

  • That's the technical term on the ones that go around a ball.

  • Well, action and reaction.

  • If nature has produced in one effect, he has to pay for it by having the counter effect on.

  • The reaction is from the fluid surrounding fluid heir to the ball.

  • And if the ball has supplied this kind of force in order to deflect the airflow, the air has to supply the counter force in order to lift the ball.

  • So whenever there is a curvature off the floor line that creates what we call the pressure Grady in If it's curving like this, the inner part has high pressure on out.

  • Apart has low pressure.

  • On mathematically speaking, it's really related with centrifugal force.

  • So center of 444 speed V is like V squared over R R is the sort of radius of this curvature on that's actually the pressure radiant that you're creating.

  • So the again long and short with you because you have a high pressure original pressure region, it's going to be lifted upward.

  • The ball is providing this, deflecting a curving trajectory so the ambient fluid has to apply a force which compensates for that which is in this direction on this is really an effect of curving trajectory of any kind.

  • So if you have a curving trajectory, for example, the radius of the sculptures are and it's going at speed V on its going around.

  • It turns out that there's a centrifugal force which is like this, and that's a row is the density.

  • And this is the pressure radiant, which increases as you go from into out.

  • That's what.

  • The guy my size professor, that the bowl yes, turned the air around the corner like it made.

  • It made the lazy air change direction.

  • So the air gets its revenge in a way that if you're gonna do that, then I'm gonna push you in the opposite direction.

  • That's a very good language.

  • But for the air to get its revenge it has to touch the ball, just suggested it.

  • So where is the air punching the ball?

  • Is it from underneath or it's not pulling cannot, because I haven't got no.

  • Is there anything that can pull with?

  • Well, it can pool because you see the East you have inexorable on air leaves the ball well.

  • If you can just freely leave, the bullet's going to diva back backing behind.

  • But the fact the matter is the fluid next to a solid doesn't want to create a vacuum.

  • He doesn't want a candidate.

  • He wants to sort of cool here.

  • He wants to feel the whole space with some substance.

  • So when it's pulling away by that very effect, it's actually pulling the solid as well.

  • And on the molecular level, it's clear what's happening.

  • You know, molecules all attracting each other alot, the molecules a kind of fornicated by spring, too, the neighboring region on when you pull the spring that spring shrinks and then pulls the whole thing in and submitted.

  • If you push this spring, get compressed, and that's what the pressure is.

  • So Professor, as a mathematician and physicist, when you're sitting on a plane flying to Japan and you look out the window and you say the wing in your head, imagining the wing, being pulled up by the air or pushed up.

  • By the way, I think it's both.

  • You see, the wind is so designed that, roughly speaking, the air comes in like this only comes in like this and goes out like that.

  • So it's current easy, tragically deflected on.

  • That creates two effects, both of which conspiring, of course, that the underneath is pushing upward on the air above.

  • It's pulling.

  • That's a figurative way of speaking.

  • But essentially again.

  • What's going on is that pressure.

  • There's a pressure difference on dhe.

  • You have an effect from high pressure region low pressure region you're pushing against each other by the pressure is everyone knows its force divided by area.

  • If you multiply top and bottom numerator and denominator by length, you get force times.

  • Thanks.

  • Let's go the work That's a form of energy on area times length.

  • That's volume, so it's actually energy per volume.

  • Pressure is like potential energy.

  • Petroleum on were saying that if you have high pressure region, that's high potential energy region law, potential energy, region with the hope of low pressure region.

  • Then the stuff moves is pushed from high pressure, too low pressure, which is exactly same thing, as if you have a say, a slope like this hill on the valley.

  • Well, the balls wants the role from high potential region to the low potential region just rolls down on gain some Connecticut issued by doing this.

  • So the pressure.

  • He's acting like a potential energy.

  • Let's little the spoon, actually, so let's go.

  • Yeah, let's do the spoon because I like you and language of the taking revenge.

  • That's that's great.

  • That's wonderful.

  • So you can do another home expecting to see that whenever a fluid flow curves the trajectory of the fluid curves, it creates a pressure radiant difference in pressure, which sucks something in my side and pushes something out.

  • Don't get aside as soon as the spoon touches the water, the water gets defected.

  • You see from straight vertical down on to the side, and that's the effective pulling the schooling in.

  • You see that, and that's because if the water momentum is changed from this to this, that means that somebody must be providing the force from left to right on the counter force is applied to the spoon from right to left on.

  • That sucks in the spoon from this side.

  • And if I touch this school the water with a spoon from this side, it's the opposite effect.

  • That's especially like that levitating bowl, but the picture is seen sideways.

  • You see, the airflow was coming in like this on going up like this.

  • And if you turn it by 90 degrees, it's exactly the same picture.

  • Yeah, on this is the ball, which is sucked in the direction opposite direction, motivation of the fluid flow.

  • You see the cup here on the challenge is to just take the ball up and put it in the cup.

  • Now that's of course, very, very difficult to do so.

  • You shouldn't do this in public on because the chances of success are very small.

I have here a pipe of sorts by blowing air here on their current comes out through the spout just so that you are convinced the air is coming out.

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漂浮球和升降機 - Numberphile (Floating Balls and Lift - Numberphile)

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    林宜悉 發佈於 2021 年 01 月 14 日
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