Empty a gel from one tank to another tank (closed system)

[katchum]

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.

 

[Nate810]

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.

 

[nlightner]

I would like to clarify some assumptions and variables before providing a response to this content.

Firstly, I am assuming that the gel solution is incompressible and that the tanks are completely sealed, making it a closed system. I am also assuming that the tanks are cylindrical in shape, with a uniform cross-sectional area and height.

Given these assumptions, the equilibrium height of the solution inside the tank can be calculated using the following steps:

1. Determine the volume of gel solution in the first tank using the formula V = A * pi * R^2, where A is the cross-sectional area and R is the radius of the tank.

2. Calculate the mass of gel solution using the density formula, rho = m/V.

3. Use the ideal gas law, PV = nRT, to calculate the pressure of the air inside the first tank, assuming that the volume remains constant.

4. Since the air in the second tank is also at equilibrium, the pressure inside the second tank must be equal to the pressure inside the first tank. Use this pressure value to calculate the height of the solution in the second tank using the formula P = rho * g * h, where g is the acceleration due to gravity and h is the height of the solution.

5. The equilibrium height of the solution inside the tank will be the same as the height calculated in step 4.

The excel file provided can be used to perform these calculations and verify the results. However, it is important to note that the accuracy of the results will depend on the accuracy of the assumptions and variables used. Any deviations from these assumptions, such as changes in temperature or pressure, may affect the equilibrium height of the solution.