Bell siphon: output rate multiple times higher than the input rate?..

[Blokle]

TL;DR Summary

Bell siphon: is it possible to achieve the output flow rate multiple times higher than the input flow rate?

I must say that I don't have too much background in physics/engineering. I'm experimenting with hydroponics systems and wonder whether it is theoretically possible to achieve the output flow rate multiple times higher than the input flow rate in a bell siphon? I'm not sure, but my intuition says me that if one can create very high pressure for some time (for example by making a very high bell/standpipe) during the siphon effect then the output flow rate might become higher than the input flow rate that has initiated the siphon cycle.

Important to stress: I'm talking about flow rate, not amount of water. I.e., e.g. constant input flow rate of 1 cubic meter per hour (which means during 1 hour - 1 cubic meter will flow in) and output flow rate of 2 cubic meter per hour (which might mean that during the first 30 minutes of that same hour there will be no output flow at all, and during the second 30 minutes - 1 cubic meter of the water will flow out). In that example we got output flow rate twice as high as the input flow rate for half the siphon cycle (i.e. 30 minutes).

To be more specific - how should I design my bell siphon so that output flow is at least double as high as the input flow for at least N seconds during one siphon cycle (in a generic case, if possible, - at least Y times as high as the input flow rate). What should be the relations between the bell/standpipe height/radius (and maybe other geometric parameters as well)?

It feels like the above mentioned time N should depend on the overall tank's volume, while the Y factor should probably depend on the height of the bell/standpipe. But I don't know how to get exact formulas for all this.

In order to get the idea about the absolute dimensions - my input tube has 2mm inner radius and is powered by a small USB pump.

 

[Tom.G]

Should be rather straight forward. You do need to run some experiments though.

You need to find the flow rate thru the drain pipe for various cross-section areas and how deep the water is in the main container.

The pressure in the drain will depend on the water height in the tank. The higher the water level, the higher the pressure and the higher the flow rate.

The flow resistance will depend on the length of the drain pipe and how rough it is; for instance with the same inside diameter and length, a plastic tube wil have a higher flow rate than a cast iron pipe.

That said, you will need to run some experiments. Set up your tank and connect some tubing or pipe to the drain, fill the tank, and time how long it takes to drain 1 liter of water.

Given your 1 cubic meter in 1/2 hour, the fill time of 1 liter should be 1.8 seconds... Hmm, maybe you should use a bigger container for testing.

From that, you now can calculate how long it will take to drain a cubic meter.

If it's too slow, use a bigger drain pipe.
If it's too fast, use either a smaller drain or put a valve at the drain outlet of the tank (or where-ever is convenient in the drain); then adjust for desired flow rate.

Cheers,
Tom

 

[Blokle]

Thank you! When you say " If it's too slow, use a bigger drain pipe." - what do you mean? I can make the standpipe/drainpipe bigger by either increasing its diameter or its height. From what I observe - the diameter can't be too big, otherwise the input flow might be not enough to lock the air in the bell to initiate the siphon cycle. So I can increase only the height of the standpipe.

1. The question is - can I increase the output flow quasi-indefinitely by simply increasing the height of the standpipe/bell/tank leaving other parameters the same?

2. Another question - am I correct in my assumption that the diameter of the standpipe must be smaller than the diameter of my input tube, in order to achieve the air lock/initiation of the siphon cycle?

 

[Blokle]

I'll try to provide as much additional constrains as I can, so maybe it will help us to get to clear formulas (or at least estimations). [Input flow rate](https://www.vovyopump.com/usb-water-pump/) ~ 3 L/min, cylindrical geometry for the tank, bell and standpipe, material of the siphon that influence friction - plastic (e.g. PE). So how do I get 6 L/min output flow rate at least for 5 seconds?

 

[Tom.G]

" If it's too slow, use a bigger drain pipe." - what do you mean?

Increase diameter (more technically, the cross-section area). Just like comparing the flow from a garden hose and a fire hose.

Increasing the height of the drain pipe will have a very minor effect, and then only if it extends further below the tank water level.

If you want the output flow 2x the input flow, the output pipe will have to be at least 1.5 times larger diameter than the input tubing.

Considering that the input is fed with a pump, which increases the flow rate thru a given pipe size, the drain pipe may need to be even larger than the 1.5x noted above.

Try these links for more information/ideas:
How To Build a Bell Siphon - YouTube
How to Build a Bell Siphon - Instructables

By the way, the 3L/min pump rating is likely the rating without any hose connected to its input or output.

Paging @jrmichler for a more technical approach than I can give.

Oops! See CORRECTION in post #7 below.

Cheers,
Tom

 

[RicoGerogi]

Raise the standpipe and mess with the pipe sizes.

 

[Tom.G]

CORRECTION to post #5 above:

A larger diameter drain pipe likely will not work by itself.
This is because the drain must be filled with water to get the siphon to work. If the drain is larger than the inlet, the water will just spill over the edge of the drain to run out, without filling the drain pipe and emptying the tank.

A possible work-arouund could be a flapper valve with a counterbalance positioned in the drain pipe. This is starting to get complicated though.

Cheers,
Tom

 

[jrmichler]

Doing some quick research on bell siphons, I come to the following conclusions best guesses.

1a) A larger drain pipe will flow more water.
1b) Drain pipe too large will not work at all, so use the largest pipe that works reliably. Need to experiment.
2a) A longer drain pipe has a longer column of water, so larger gravity force.
2b) A longer drain pipe has more pipe friction. The total pipe friction is proportional to water velocity squared times the length of the pipe.
2c) There is a best length for the drain pipe. Need to experiment.
3) A smooth pipe flows more than a rough pipe. PVC pipe is about the smoothest low cost pipe you can get.
4) Water flows down the drain pipe at a velocity, and thus has a velocity pressure. A diverging section at the discharge end converts some of the velocity pressure back to static pressure, thus increasing the flow rate. Rough guess is discharge inside diameter about two times the pipe inside diameter is a good starting point.
See the diagram:

The angle is important, as is a smooth transition from straight to diverging.
5) A square inlet to the drain pipe has high entrance loss. Rounding the inside of the inlet will decrease the entrance loss, while increasing the effective inlet diameter of the drain pipe. A small edge radius can make a large change in flow, especially with short drain pipes. See the chart below from Cameron Hydraulic Data 16th Edition. Need to experiment.

 

[Blokle]

CORRECTION to post #5 above:

A larger diameter drain pipe likely will not work by itself.
This is because the drain must be filled with water to get the siphon to work. If the drain is larger than the inlet, the water will just spill over the edge of the drain to run out, without filling the drain pipe and emptying the tank.

A possible work-arouund could be a flapper valve with a counterbalance positioned in the drain pipe. This is starting to get complicated though.

Cheers,
Tom

That's was my experimental conclusion either. At first I also wanted to just make the standpipe with the diameter larger than the input tube diameter to get output flow higher than the input flow, but have realized that the siphon never starts. I was not sure whether it was my building failure or there is a fundamental theoretical problem with this approach. Now that you say that's not possible - I'm asking - is it possible to get doubled output flow with the standpipe having (a bit) smaller diameter (in order for the siphon to initiate at all) than the input tube, but making standpipe very high, thus increasing the pressure/gravity that presses/pulls the water out (thus increasing the water velocity)? @jrmichler - what are your thoughts on this? (that's probably what you've meant in 1b) above).