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

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!

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  • $\begingroup$ Related: Buoyancy and natural convection in a stratified water tank $\endgroup$ – John Rennie Jun 21 '16 at 14:49
  • $\begingroup$ Yea that's my old post. But I felt it had to many different questions and unclear formulations in it. Besides that question one has been (most probably) resolved. So I thought it might be easier to just ask one of the questions. Sorry if that was not the good way to do it. $\endgroup$ – Scotty1- Jun 21 '16 at 14:54
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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?.

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  • $\begingroup$ Ok, thanks so far! I now approximated the buoyancy by using infinitesimal volume elements surrounding my Cell. $\endgroup$ – Scotty1- Jun 28 '16 at 9:07

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