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i having trouble with this formula $$ Z1(t) = Ze+(\sqrt{Z1-Ze}-\frac{2S0}{S1}\sqrt{2g(1+\frac{S1}{S2})}.t)² $$

Z1 and Z2 are the heights of the vessels. S1 and S2 are the sections of the vessels. S0 is the section of the tube between them (for the exchange). Ze is the final height of the two vessels.

Z1(t) is the height at t

but i only get incorrect values and don't know if the formula is wrong of if its me.

for testing is use Z1 = 45

Z2 = 5




$Ze = \frac {S1.Z1 + S2.Z2} {S1+S2}=\frac {62.8.45 + 62.8.5} {62.8+62.8}=25$


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If you're wondering whether this is the right formula, I think the right place for this would be physics.SE. If you're wondering whether you're doing something wrong in substituting values, then you'll need to give us some of your results, since so far there's nothing for us to check in what you've written. – joriki Jun 4 '11 at 16:40
If by the period in the formula you mean multiplication, then this formula must be wrong, since it would make the height go off to infinity, whereas what one would expect would be some form of oscillation around the equilibrium value $Z_e$. – joriki Jun 4 '11 at 16:42
@joriki, didn't know physics.Se, i ll ask there . In fact i found this formula on a site and the notice isn't very clear : , it's in french – eephyne Jun 4 '11 at 21:02
First of all, there isn't any $Z_2$ in your formula for $Z_1(t)$, so what difference does the value of $Z_2$ make? Second, your computation of $Z_e$ seems to depend on a formula you haven't given us. Third, you haven't told us what $t$ is, so how can we figure out any values of $Z_1(t)$? And fourth, how do you know that you are getting incorrect values? Do you have some independent way of getting correct values? What is it? You have to do a lot of work on the presentation to turn this into a question anyone can help you with. – Gerry Myerson Jun 4 '11 at 23:59
up vote 1 down vote accepted

I'm thinking S0, S1, and S2 should be the cross sectional areas of the connecting tube and the two cylinders. The calculation above seems to be calculating the circumferences of the cylinders and connecting tube.

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Indeed, it's the $S$ of superficies. – Raskolnikov Jun 5 '11 at 9:13
Thanks ,here the result :…*980%281%2B1%29%5Dt%29%C2%B2+from+0+to+37 – eephyne Jun 5 '11 at 10:51

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