Equilibrium gel height when transferring between two closed tanks

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katchum
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Homework Statement


We have a tank with some gel and it will be emptied into another empty tank. The air in the first tank wil stay in the first tank. The air in the second tank will stay in the second tank.
What is the equilibrium height of the solution inside the tank.

also, see Excel file.


Homework Equations



PV=cte
Downwards pressure of gel solution equals pressure difference between two tanks.
rho = m/V
V=A*pi*R^2


The Attempt at a Solution



I've made this excel file with all the relevant equations inside each cell. I'm just wondering if it's correct.
 

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The idea is that the pressure of the gel solution will be equal to the pressure difference between the two tanks when it reaches equilibrium. So we can use PV=cte and rearrange for P, which we can then equate with the pressure difference between the two tanks. We can then find the density of the gel solution and rearrange for V, which we can then plug into the equation for the volume of a cylinder. Once we have the volume, we can then find the height of the solution inside the tank. So, is my excel file correct? Thanks in advance.