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I am interested in learning the mathematical relationship between the siphon volume and the refugium volume.
Obviously, the volume/time of the pump is constant and the siphon volume/time varies with the height of the water.
How is that expressed mathematically?
 

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That is nearly impossible to answer.

The siphon (overflow) can be whatever you want it to be, it would however have to be going into a sump large enough to take the volume of water coming from it. The return pump would have to be able to handle the amount of water going back into the tank / or whatever it was pumping back into.

The maths involved in that is based on Bernoulli's principle, it is very complex maths though.
 
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