# communicating vessels formula

i having trouble with this formula (asked first in math.Se, i Didn't know the existence of physics.se) $$Z1(t) = Ze+(\sqrt{Z1-Ze}-\frac{2S0}{S1}\sqrt{2g(1+\frac{S1}{S2})}.t)²$$

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

S0=2$\pi$0.3=1.884

S1=2$\pi$10=62.8

S2=2$\pi$10=62.8

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

thanks

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Checking the source of the formula, it seems that it's only valid until Z1(t) reaches the value Ze. Until that point the shape of the curve looks reasonable, though I haven't checked the derivation. – mmc Jun 4 '11 at 21:26

2
The sections $S$ are areas. One possible mistake could be that you have used the formula for the perimeter of a circle, where you should be using the formula for the area of a circle, cf. math.about.com/od/formulas/ss/areaperimeter_5.htm – Qmechanic♦ Jun 4 '11 at 21:36
@Qmechanic ,thanks a lot , this is exactly why the result was wrong – eephyne Jun 5 '11 at 10:49
Please add an answer identifying the mistake, and accept it, so that this question gets marked as answered in the system. – Christoph Jun 14 '11 at 20:29

## 1 Answer

like the comment aheadd said , i was doing it wrong , using perimeter instead of area ($2\pi R$ instead of $\pi R^2$).

if you wan to watch the result look here

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