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Chuck, it seems to me that you are missing something important here.
If there is a buoyant force on something under water, it must come
from the fact that there is a surface that faces downward where the
pressure can exert its force upward. If the object is embedded in the
bottom in such a way that there is no connection underneath the
object with the water in which the rest of it is embedded, then the
water can exert no upward pressure on the object. No upward pressure,
no buoyant force. That's a complication that seems to me to require
consideration.
Now that seems to me to be a testable proposition. I would suggest
the following experiment. Take a plastic pole (plastic so it can be
very smooth with no small areas where water can exert upward forces
on it, and less dense than the water, so, under ordinary
circumstances it would float)), and embed it in a water bath in such
a way that the bottom of the pole is "dry" (i.e., has no contact with
the water). Then affix a strain gauge to the pole, oriented
vertically, so it can measure any vertical strain put on the pole by
the water (obviously, the strain gauge needs to be installed before
the pole is immersed in the water). I predict that the gauge will
read zero or very near to it. Perhaps the pole could be slightly
tapered upward to insure no possible surfaces where the water can
exert an upward force.
What do you think?
Hugh