#PhysicsFactlet (335)
Yesterday, at a small playground where my son was playing, I saw this Kugel fountain, so here comes a short thread about Kugel fountains and how they work.
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(Alt Text: a Kugel fountain slowly rotating in a sunny day.)
Yesterday, at a small playground where my son was playing, I saw this Kugel fountain, so here comes a short thread about Kugel fountains and how they work.
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(Alt Text: a Kugel fountain slowly rotating in a sunny day.)
First of all, what is a Kugel fountain?
There are a few variations on the theme, but usually they are big stone spheres, sitting on a hemispherical hole, with water flowing from below. Despite their weight, they can spin with a small push, and keep spinning for a long time.
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There are a few variations on the theme, but usually they are big stone spheres, sitting on a hemispherical hole, with water flowing from below. Despite their weight, they can spin with a small push, and keep spinning for a long time.
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How does it work?
It can't be buoyancy, as the stone sphere is a a LOT more dense than the water (we all have direct experience of stones sinking when you put them in water, and this one is not any different).
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It can't be buoyancy, as the stone sphere is a a LOT more dense than the water (we all have direct experience of stones sinking when you put them in water, and this one is not any different).
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If you browse the internet you will find a ton of "answers" claiming that there is a film of water between the stone sphere and the hole, which reduce friction.
This is sort of correct, but doesn't explain how there can be a film of water at all
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This is sort of correct, but doesn't explain how there can be a film of water at all
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If you were to just fill the hemispherical hole with water and put the stone sphere in, all the water would be squeezed out, the two stone surfaces would touch, and you wouldn't be able to move the sphere at all!
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What those answers are missing is that this is a fountain, and thus you are actively pushing water in from below. If you do it with sufficient pressure, the only way the water has to escape is by lifting the ball a little bit, thus creating the water film we need.
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But how much pressure do we need?
Let's make a "order of magnitude" calculation, with a stone sphere with a radius of 1m and a mass of 10³kg, placed in a hemispherical "socket".
The sphere is pulled down by gravity with a force of ∼10⁴N.
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Let's make a "order of magnitude" calculation, with a stone sphere with a radius of 1m and a mass of 10³kg, placed in a hemispherical "socket".
The sphere is pulled down by gravity with a force of ∼10⁴N.
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Assuming we are pushing water up the fountain with a pressure P, this will exert a upward force on the sphere equal to
Fᵤₚ=∫ P cos θ dS=2π R²∼6 P N
so we need a pressure of approximately 10³Pa. We were a bit optimistic in our calculation, so let's say 10⁴Pa.
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Fᵤₚ=∫ P cos θ dS=2π R²∼6 P N
so we need a pressure of approximately 10³Pa. We were a bit optimistic in our calculation, so let's say 10⁴Pa.
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This is not all. The hemispherical hole must be a tiny little bit larger than the sphere for this to work, so there is a small rim where the water from below is pushed down by the atmospheric pressure (1atm∼10⁵Pa).
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So we need to push water into the fountain with a pressure of ∼1.1 atmospheres, which is not a lot, making a Kugel fountain actually quite easy to run!
If you want to go more in depth with this, the only good reference I found is aapt.scitation.org/doi/10.1119/1.…
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If you want to go more in depth with this, the only good reference I found is aapt.scitation.org/doi/10.1119/1.…
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