# Physics of a bell siphon

I'm trying to build a home aquaponics system, and a key component of the design I got off the internet is a bell siphon. So I'm trying to understand the physics of this siphon effect so I can optimize the weight and dimensions of the siphon to fit the size of my system.

From what I read on the internet, the siphon works as follows:
- When the water first gets sucked down the vertical standpipe, it sucks some air down the tube and thus leaves a bit of a vacuum in the top of the bell. This will encourage more water to flow into the bell and down the tube.
- When the water level in the tank gets low enough, outside air is sucked into the bell and breaks that low pressure zone.

Is that correct?
Also, are there some equations I can use to see what effect changing the geometry of the siphon components will have? Higher elevation from tank bottom, larger ID on the bell, larger ID on the standpipe, taller bell, etc. Or even using some kind of tapered design?

Thanks!

rcgldr
Homework Helper
The second diagram appears to be wrong. Due to reduced air pressure, the water level inside the bell will be higher than the water level outside the bell. The image should show the water level at or above the drain pipe opening, not being pulled up as a stream into the drain pipe.

Youtube video of a slightly different bell siphon:

sophiecentaur
Gold Member
2020 Award
There is a subtle difference between a syphon and a simple weir, over which excess water will flow. It is not totally straightforward to design a reliable automatic syphon because the initial stream of water into the down pipe has to be sufficient to block / reduce the pressure from the open end of the down pipe and make water flow up into the bell.
The second picture in the OP is clearly drawn wrong because you can't expect a jet of water to shoot over the top of the down pipe!! The syphon effect will only work when the level under the bell is higher than the lip of the down pipe.
Once significant water starts to flow, the level under the bell will go up and further reduce the air pressure inside - increasing the incoming flow accordingly.
I don't know a any specific equation to describe this and all the links I could find seem to use a practical approach. Virtually all the links are in the context of aquaponics (and a few on ancient systems used in British urinals).
This link discusses many of the issues. There are a few animations a You Tube videos, which you can easily find for yourself.

There is a subtle difference between a syphon and a simple weir, over which excess water will flow. It is not totally straightforward to design a reliable automatic syphon because the initial stream of water into the down pipe has to be sufficient to block / reduce the pressure from the open end of the down pipe and make water flow up into the bell.
Would increasing the flowrate into my tank and/or decreasing the ID of the standpipe help to reduce the pressure of the open end of the down pipe?
The second picture in the OP is clearly drawn wrong because you can't expect a jet of water to shoot over the top of the down pipe!! The syphon effect will only work when the level under the bell is higher than the lip of the down pipe.
My mistake on the drawing.
Once significant water starts to flow, the level under the bell will go up and further reduce the air pressure inside - increasing the incoming flow accordingly.
I don't know a any specific equation to describe this and all the links I could find seem to use a practical approach. Virtually all the links are in the context of aquaponics (and a few on ancient systems used in British urinals).
This link discusses many of the issues. There are a few animations a You Tube videos, which you can easily find for yourself.
Yes, I have read lots of aquaponics articles about this topic and also built bell siphons of my own. But my success only ever comes from tinkering and i don't really understand the physics behind the changes i make. I want to know the influence that changing the dimensions/geometry of the bell siphon components has, and also the influence of increasing/reducing my input volume from the pump.

I also just thought it could be interesting to learn the physics of this phenomenon that i've observed with the siphons i've built.

Thanks!

sophiecentaur
Gold Member
2020 Award
Thanks!
Funny. When you start YouTubing, you can get the impression that everyone is doing something. Is aquaponics really as popular as my search would suggest? I guess it can give a high yield if you get things right.

Funny. When you start YouTubing, you can get the impression that everyone is doing something. Is aquaponics really as popular as my search would suggest? I guess it can give a high yield if you get things right.

It's definitely growing in popularity! I think it's fun because you get to combine 3 hobbies: raising fish, growing plants, and building hydraulic systems (siphons, pumps, waterfalls, filtration, etc.)

Apparently the physics of a bell siphon are pretty complicated, but do you think you can help me derive a few equations to explain the impact of changing certain dimensions? Or even just an intuitive explanation if the equations are far too complex.

Thanks!

View attachment 212164

sophiecentaur
Gold Member
2020 Award
All the designs I have seen have a long tube out of the bottom and many have a 45 degree bend. X should not be too great as you need the initial overflowing water to block air from coming up. You need to reduce the air pressure in the invert space.
People do it with standard plastic plumbing pipe so it ain't rocket Science.
How important is fast flow for you?

All the designs I have seen have a long tube out of the bottom and many have a 45 degree bend. X should not be too great as you need the initial overflowing water to block air from coming up. You need to reduce the air pressure in the invert space.
People do it with standard plastic plumbing pipe so it ain't rocket Science.
How important is fast flow for you?

In the past i've made these bell siphons following these instructions: http://www.affnanaquaponics.com/2010/02/affnans-valve-detailed-explanations-of_9459.html

I've had good success but that was just blindly following instructions and now I am just very interested in knowing the effects of changing w,x,y,z.

Fast flow is not important to me, the only thing i care about is consistent starting and stopping of the siphon. Some siphons i made in the past would randomly just continue sucking all the water out and never break the siphon-- and some also randomly would not start the siphon at all! So I wanted to use some science to match the flowrate of my pump (and thus the rate water rises in my growbed) to the geometry of the siphon.

Thanks!

sophiecentaur
Gold Member
2020 Award
As far as I can see, the basic requirements for operation are
1. The down pipe is narrow / long enough to block air from entering that way.
2. The inlet flow is less than the outlet flow when the reservoir level is at the bottom.

1 seems to be easy enough to achieve with a long down pipe. I also read about putting a small constriction near the top in it to hold back the initial falling water to form a slight plug or a small U section on the down pipe.

As the tank fills the water level will eventually reach the top of the inner tube and spill over the top. What happens next?
To begin with the water rate down the inner tube will match the fill rate of the tank. However if the water flowing down the inner tube succeeds in dragging a little air along with it then the water level inside the dome will rise as the air cap in the dome shrinks. A rise in the water level spills more water down the inner tube which carries more air until the inner tube is completely full of water and the siphon is flowing at its maximum rate.
However, if the water does not succeed in dragging any air down the inner tube then there is no siphon!
How do you fix this?
1. Increase the flow rate filling the tank.
2. Increase the water velocity running down the inner tube by;
• reducing the pipe size,
• keeping the pipe vertical (maximum gravitational axis for the water)
• lengthening the pipe (more time for water and air interaction)
• adding a flare on the top of the inner tube (does this give a bigger surge to the initial water flow rate down the pipe as the meniscus in the annulus breaks?)
Interactions between water and air in pipes have been extensively modelled as it is a reasonable analog for commingled gas and oil production in the oil industry. However in the case of downward flow in a siphon the situation is less studied. The one paper I found by Dukler suggests that the water will flow in an annular film down the inner wall of the inner tube (doing its best to ignore the air) until a superficial velocity of around 0.5 m/s is achieved. Using a ball park figure of 0.05 for the water void fraction that means annular flow will be happy up to a water wall velocity circa. 10 m/s.
The challenge therefore is to maximise the water velocity while at the same time trying to mix the water with the air without killing too much of the water velocity. I suspect that some nails through the inner tube and and angled downwards may do this.
Thank you for letting me clarify my thoughts by drafting this piece.

sophiecentaur
Gold Member
2020 Award
Welcome to PF.
You seem to have mentioned the relevant factors in the way it works.
The idea of falling water dragging air with it accounts for the 'over-centre' action. What always strikes me about the 'theory' is how it works in some very marginal cases. For instance, the most common use was always (in UK at least) for regular flushing of gents' urinals. The drop always seemed to be very moderate and the horizontal run with holes in it struck me as a quite high resistance system - in order to obtain uniform flow over a horizontal run of, say 3 metres.
The secret would have to be in the piping just below the tank output level because installation details would need to be fairly tolerant and require no 'tweaking' by the installers. I imagine the main adjustment would be to find the minimum feed rate that would make it work and then add a bit for reliability and limescale. The system is not water- efficient enough for moderate regulations but it's very impressive.