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My question is when these two liquids above mix and don't mix, does the pressure at the bottom change ? When they don't mix the pressure is 2hdg + 3hdg = 5hdg (d:density) But what happens when they mix ? The volume of the liquids is needed or not ? I saw someone says the pressure is equal either they mix or not. I'm confused, thanks in advance :)

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Knowing a specific density is rather handy, because it allows us to relate the volume and the mass of a substance.

But to calculate the pressure, the density isn't necessary. What is needed is the mass.

If the fluids mix, the volume (and therefore the density) may change, but the mass does not. The total mass remains constant. If prior to mixing, the two fluids have mass $m$, then the pressure at the bottom of the vessel due to the fluid, assuming a straight-sided vessel with area $A$: $$ P = \frac{mg}A$$

Note that neither the volume nor the density appear here. As long as the mass and the shape of the container are constant, so is the pressure.

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  • $\begingroup$ So the question was: "the pressure at the bottom", and not at any arbitrary depth ? $\endgroup$ Oct 29, 2015 at 16:19
  • $\begingroup$ @FabriceNEYRET Yes yes, at the bottom $\endgroup$
    – ysn_akst
    Oct 30, 2015 at 20:35
  • $\begingroup$ it would have been better to specify this in the question... (and it might be that the different opinions you heard was about pressure elsewhere, then). $\endgroup$ Oct 30, 2015 at 20:37
  • $\begingroup$ @FabriceNEYRET I didn't see any necessities for that. Also I got my answer $\endgroup$
    – ysn_akst
    Nov 1, 2015 at 13:40
  • $\begingroup$ It's like asking "what is the velocity of water in oceans accounting for currents" when you just want it on the ocean bottom. :-) And you have your answer, but your question reminds here forever for next students looking for answers, possibly misleading them. $\endgroup$ Nov 1, 2015 at 13:45
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The pressure at a given depth below the surface is the one of the atmosphere above + increments of $\rho(z)~ dz$. So the pressure at a given depth, which corresponds to the weight of the pile above, depends of the $\rho$ values encoutered above: all at 1 then all at 3, or all at 3 then all at 1 (not very steady ;-) ), or mix of average 2, does not give the same curve $P(z)$.

Besides, mixing sometime have strange effects, even if no chemical reaction occurs. E.g. alcool and water mixed occupy less volume than when separated. Which change the liquid level and the curve $P(z)$.

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