(upbeat music) - I made a video a while back about the greedy cup siphon or bell siphon in which I made a 2D version
to help with the explanation. And it occurred to me that
other hydrodynamic mechanisms would be easier to
explain with a 2D version. So in this video, we're
gonna do Heron's fountain. But before we get to
that, I wanna say a couple of things about the previous
video on the bell siphon. Well, two more examples, basically, of bell siphons in the real world. In the original video I said that toilets weren't really a good example of greedy cups siphons. I was talking about the
cistern, specifically cisterns in the UK, which it turns
out are completely different to the cisterns in every other
part of the world, it seems. But anyway, when people say that toilets are like greedy cup siphons, they're actually talking
about the bowl of the toilet which I didn't realize. And actually in the UK toilet bowls aren't greedy cup siphons either or at least not that I've seen. Though I have seen
toilets in other countries where you flush the toilet and the level of water in the bowl rises and rises and rises, which, frankly, is terrifying
the first time you see it for someone who's only
ever seen a UK-type bowl. And then it gets to a certain point anyway and it all drains out. That is a greedy cup siphon. For completeness, here's a collection of the most common toilet bowl
mechanisms around the world. This is the one you get in the UK. These two siphon ones are the types that you'll find mostly in North America. This one here, I actually
saw several of these when I visited the Hague years ago, and you get them all around
in Europe here and there. There's a little platform there and that's the thing that you poo on and then it gets flushed off the shelf. It's called a washed-out toilet or a (speaking in foreign language) but I call it the turd on the shelf. The main benefit is that
you don't get splash back 'cause it hasn't got as far to fall but the downside is just
the horrendous smell. The other example that
people have shared with me is laboratory glassware
called a Soxhlet extractor. It's really clever. You have this chamber that
repeatedly fills with solvent and then drains away and fills
with solvent and drains away. So you can put a solid in there that you're trying to
extract something from and it will be repeatedly
soaked with solvent through the greedy cup siphon mechanism. But anyway, this video is
about Heron's fountain. This is the traditional Heron's fountain. And when I say traditional, I
mean traditional in the sense that this is the one you would
make as a school project, not the one that Heron himself made in Alexandria in the first century. But anyway, the way to
get it started is simply to prime that first container. A Heron's fountain is really cool because at first glance
it looks like it could be a perpetual-motion mechanism. Of course, it isn't because
those things don't exist. But the fact that the level of water in the top container remains fixed while the fountain is
running is perplexing. It almost feels like a law of physics is being violated here. Like, balls always roll downhill, they never roll uphill
unless they're pushed. And it feels like something
like that is going on here. But actually we can convince ourselves that no laws like that are being violated by simply looking at this sped up version. Look, you'll see that all the liquid in the center container drains while the bottom container
fills up with liquid. In other words, the liquid is going from a position of high
gravitational potential energy to low gravitational potential energy, or, in our analogy, the ball
is rolling down the hill. But how does it work? It's actually really hard to tell by looking at this version
of Heron's fountain because all the tubes are
embedded within the containers and they're quite thin
and they're obscured. It would be better if we
could separate the tubes out and flatten the whole thing
into a two-dimensional version. It turns out that prototyping
two-dimensional versions of hydrodynamic mechanisms
is actually quite tricky. One of the hard parts is
finding the right thing to put between your two
sheets of glass or acrylic. I found that this wiring is pretty good. This is the sort of wiring that you find in the walls of a house. It's good because you can
bend it into the shape that you want and it will stay there, and it has this fixed width to it. (mellow music) I definitely had some failures. A lot of my issue was to do with making the whole thing watertight and, in this case, air tight. For the most part I was
using the wrong adhesive but I did get it working in the end. (liquid splashing) The 2D version doesn't last
very long, which makes sense. You can hold a lot more
liquid in three dimensions than you can in two, but it's much easier
to see what's going on. Side by side, here, you've
got the top container, the middle container and
the bottom container. And you can see various tubes
have been moved to the sides but in any case, the
mechanisms are equivalent. So the liquid in the
top container is falling into the bottom container
through this tube. And so the bottom container
is filling up with liquid, and as it does, it's pushing
air out of the bottom container into the middle container
through this tube. And because the middle container
is filling up with air, that's pushing liquid out
of the middle container up through this tube, and that's how you get the fountain or in this case, the dribble. So overall, the liquid in
the middle container ends up in the bottom container. It's just, it goes via the fountain and that's the explanation. But for me, there's a
gap in the explanation because, like, that explanation
would you still apply if the entire thing was filled with liquid and there was no air and
it would go like this: liquid in the top container falls into the bottom container under gravity, and that forces liquid out
of the bottom container into the middle container, and that forces liquid out
of the middle container into the top container. But of course, that would never work. Intuitively, we know that when
the system is full of liquid it'll be in equilibrium. It's just like this
tube filled with liquid. The level of water at each end is fixed and equal and in equilibrium. So the fact that there's
air in the mechanism is clearly important. To figure out why, let's
simplify even further. Let's look at some important distances. You've got on the left here, the distance between the surface of the
water in the top container and the surface of the water
in the bottom container. You've also got the
distance between the surface of the water in the top container and the surface of the water
in the middle container. And you've got the distance
between the surface of the water in the middle container and the surface of the water
in the bottom container. And you'll see that two of those distances on the right add up to
the distance on the left. And you'll also notice that that distance on the left is a column of water, but on the right you've got
a column of water at the top. It's a circuitous column to be sure, but from a pressure point of view it's equivalent to a vertical
column of water this tall. And similarly at the bottom you
have this circuitous column. It's equivalent to a column of this height but it's a column of air. So let's really simplify that
into just a U-shaped tube with the same characteristics. I'm holding the two ends of the tube here to keep everything inside from moving. But you'll see I've recreated what's going on inside
the Heron's fountain. You've got a column of liquid on one side and you've got a column
of half liquid half air on the other side. Clearly the full column
of liquid is heavier than the half-liquid half-air column. So they're both pushing downwards but the heavier one is going to win. So when I release my fingers, the column of liquid on
the left will push down until equilibrium is reached. And there you do, that's what you see. And so really the reason
the Heron fountain works is because gas is less dense than air. So looking back at Heron's fountain, we have a situation of unequal pressure. So the pressure from this
column of liquid on the left is greater than the pressure of this half column of
liquid half column of water on the right. So the pressure here is
greater than the pressure here. Meaning the system is unstable. It will evolve until it
reaches a stable state. What does that look like? Well, it looks like a column
of liquid on the right which is as tall as the
column of liquid on the left. In other words, you need a
fountain of liquid on the right to reach equilibrium so that
the pressure from the water on both sides is the same. Clearly we don't have a
fountain that tall in this case which I assume is because of friction. So a Heron's fountain behaves essentially like this simple U-shaped tube
where there's an imbalance between the mass of liquids in each side. You even get the same
fountain effect here. The difference is that
the Heron's fountain creates a physical
barrier between the liquid and gas parts on the right-hand side. And it also creates a reservoir of liquid and gas to keep the system
going for a long time. There are a few gotchas when you're creating
2D versions of things. For example, I originally
had the various tubes going roughly through the
center of each container, but of course, in 2D, a tube in the middle actually partitions a container
into two separate sections. So I had to shift the
tubes around to the edges to make it work. I actually made the same mistake in the original greedy cup siphon video which is why you can see,
look, I'm having to try and evenly distribute the
liquid as I'm pouring it in here so it rises equally on both sides. If you have any other ideas
of hydrodynamic mechanisms that could benefit from the 2D treatment, let me know in the comments because I've got the whole
production process down pat now. (liquid gurgling) There are a handful of YouTube channels that I make sure I watch
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haven't put up anything new since I was last there, then I ended up wandering
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This guy just gained a new subscriber. Nice post OP super cool