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The principle is 'dilution': with the first addition of clean water to dirty water, the dirty water becomes less dirty because it is diluted by the clean water. With the continued addition of clean water to dirty water, eventually the dirty water will be completely diluted and there will be no dirty water left; it will all be replaced by clean water.

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Q: Clean water is added to a tank full of dirty water. After some time the tank is full of clean water. Dirty water disappears. What is the principle and how does it work?
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