communicating vessels formula

Question

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

Answer 1

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