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Alright, so I'm trying to understand in detail what occurs the moment the water covers the outlet tube in a bell siphon. Most sources hand wave and just say "SIPHON HAS OCCURED" or "VACOOOOOOM", but what specifically causes the formation of the vacuum or siphon effect.

If the air in the bell is at 1 ATM the second the water cuts it off, how is a vacuum formed? The volume doesn't change, so this leads me to think it is the added water pressure of the formed water seal plus the ATM in the bell that causes the water to beat the air in the tube thus causing the water to fall. Once this motion is in place the siphon is created due to adhesion pulling the water along plus the pressure of the water column.

Please let me know if I got this wrong.

practical engineering claims it is only a vacuum

enter image description here

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3 Answers 3

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The vacuum is not important in the first instants where the siphon is operating. Indeed, there will not be a vacuum at first. It will be atmospheric pressure inside the bell, as you point out.

The vacuum becomes important as the siphon picks up speed and starts emptying the tank. As the water drains out of the drain tube, something has to occur to take the space of that volume of water. Either air needs to flow into that space, or water does. While the water level in the tank is above the level of the top of the drain, its pretty easy to see that what replaces it is water, because the water level outside of the bell is higher than inside.

Once the water level in the tank is below that of the drain, the vacuum becomes important. The volume of air in the bell can grow, as you show in your pseudo-answer. However, when it does so, the pressure in that air volume decreases, which pulls more water into the bell. Once there is enough water in the bell, gravity will smooth out the surface of the water to cover the siphon hole, and that will feed more water into the siphon.

If you cannot develop a sufficient vacuum, meaning you did not get the bell sufficiently full (because you didn't put enough water in the tank), then the slug of water that falls into the drain tube can further down the drain tube before the vacuum is strong enough to pull enough water up into the bell. When this happens, the slug of water in the drain tube is eventually pulled to one side by the difference in pressure between the outside air below the drain and the low-pressure area in the bell, and a bubble of air gets to travel backwards into the bell. This further reduces the pressure difference, so it can't pull the water up into the bell, and we quickly find the siphon fails to start.

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  • $\begingroup$ How did you learn this by the way? Do you have a good source to learn this concept from or did you test it IRL? I'm finding google search is rampant with pop science making it hard to find nuanced answered to questions like these. $\endgroup$ Commented Sep 29, 2020 at 2:29
  • $\begingroup$ @Ductile_Iron I've made a reasonably large number of siphons for aquariums, from my own designs. Being from my own designs, I had an awful lot of failures. So in this case, I approached the problem in a sort of "scratch out all designs that fail, and the one that works must have the right physics." For example, I've had more than my share where the bell was too narrow, and the vacuum could not pull the liquid up fast enough due to all the fluid friction against the sides. In this failure mode, you end up with not enough water in the drain tube to maintain a seal. $\endgroup$
    – Cort Ammon
    Commented Sep 29, 2020 at 3:17
  • $\begingroup$ That particular failure mode shows lots of things that have to go right for a bell siphon to work, so I used it as a sort of framework to figure out what the right physics had to be to avoid it! But I'll be the first to say that it wasn't my first way of thinking about the problem. Or the third. I've got lots of wasted PVC tubing in my past! =D $\endgroup$
    – Cort Ammon
    Commented Sep 29, 2020 at 3:18
  • $\begingroup$ I appreciate the answer! I am coming closer to being a patron saint of scientism and I need to understand how things actually work. $\endgroup$ Commented Sep 29, 2020 at 4:35
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Perhaps this, but water needs to fall in order to create the increased air geometry, so was my first part correct?

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As the water level rises inside the bell it crests the riser and joins together forming a high pressure area above the water and a low pressure area in the riser tube. This pressure difference forces the water to travel down the riser tube. This primes the riser and the siphoning begins.

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