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Imagine I have a clean toilet with some amount of water in the bowl. When I flush the toilet much of that water will be displaced by the tank's water. I want to work out (or model really) what amount of the original toilet bowl water will remain after the flush.

If there was B liters of water in the bowl and T liters was released from the tank I'd expect the proportion to be at most B/(B+T) of original water to tank water.. but this doesn't take into account how the water is released.

I assume this is studied in the design of toilets, so links to existing research would be interesting too! I also appreciate that it will vary for each toilet design, so feel free to answer the question for any common type or model; I'm most interested in a way of estimating or modelling it.

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I've been thinking how one can try to measure it. I suggest the following setting.

First one should find out the dependency of tap water resistivity on salt concentration. Likely it should be made by experiment rather than consulting tables because the results would depend on the tap water.

Having done the first part, one can conduct the experiment itself. Certain amount of salt is put into the bowl water and its conductivity is measured. Thus the salt concentration in the bowl is found.

Then one flushes with the pure water from the tank and measures the conductivity of the new bowl water again to find the new salt concentration. After that it is possible to calculate the percentage of the old water left in the bowl.

Note though, that's the main idea. To conduct the experiment properly you need to have some experience. Every detail should be elaborated. If you never done that you'll need some help.

I tend to think that would be a nice lab task. I remember we had a lab we students used to call "toilet" since we were flushing water to find out the effects of viscosity.

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Use a commercial blue dye in the tank, and flush until the blue color disappears. You can find the e-folding rate by eye. The amount of water removed per flush depends on the toilet, from memory, it's about .9 in a normal flush, so that 90% of the blue color is gone after one flush, so that you lose all noticible blue after about 4 flushes.

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There are some estimates when one googles. Somebody has applied Bernouli's Equation to the siphon.

It is not a simple physics task and better asked in an engineering forum.

From experience I know one can completely empty the siphon of a european toilet by pouring a bucket with 7 kilos of water from a height 30cm over the bowl. The difference to the flush comes from the delta(time), water falls faster and in more bulk and then the siphon effect takes over.

From this I suspect european toilets are designed so that the effect of the flush water clears everything and leaves clear water in the siphon.

A US toilet which for some reason has a water pond would be harder to trigger into a complete empty . You could try with ink to see how much remains.

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Since I've only just registered I can't comment, so I posted this as a question. Thanks Anna for an informative post. If I understand correctly you think that almost all the original bowl water in european models will be replaced with tank water? I googled the term water pond but couldn't find out exactly what it was, could you clarify for me? I guess a perfect experiment would be with food colouring. – user9828 Jun 13 '12 at 3:17
yes, the european ones empty completely if there is just water. A pond is a small pool of standing water. US bowls are full of water when at rest, european ones have water only in the siphon. – anna v Jun 13 '12 at 3:33
@yesimay, are you the same one who asked the question? If so I'll merge your accounts. – David Z Jun 13 '12 at 4:09

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