Calculation of buoyancy in a stratified water tank

Question

I'm trying to calculate the buoyancy force in a stratified water tank. The model of my tank looks like this:

Now I'm expecting cell 5 with Temperature $T_5 = 50^\circ C$ to have an upward buoyancy force. But as my cells do not "displace" water and have changing densities above (in this case even 4 different cell-temperatures) and below them I don't know which densities to use for my calculation.

Currently I'm calculating the buoyancy force $B$ by only comparing each cell with the cell above, like shown in this equation: $$ B_{Cell5} = g V_5 \left(\rho_{Cell4} - \rho_{Cell5}\right) $$ Is that correct or do I have to consider the densities of cells 1 - 4 and cell 6? Thanks in advance!

Answer 1

Your question is similar to No buoyancy inside liquid.

This shows that the buoyancy force on Cell5 provided by Cell4 depends on the extent to which the fluid in Cell4 surrounds that in Cell5. In your scenario none of the fluid in Cell4 surrounds Cell5, so there is no buoyancy force. There is only the weight of Cell4 pressing down on Cell5.

The following post explains how buoyancy works : What is the basic reason behind buoyancy?.