it doesnt matter how you word it.
when its time to turn the cards its density that wins.
you can say its the great purple rinoceros if you like.
you can call it what ever you choose , but density by any other name
or deffinition is still density.
you can call it weight if you like.
but in my world what causes buoyancy or the reason a object floats
or sinks in a fluid is the density dfferential.
and I dont care how far under water an object is , even if the waters pressure is
at 50,000 psi.
the surrounding water will have basically the same density per unit volume
as it has at the surface.
even if the water is inside a container that has a large vacuum thrown on it
where the water pressure at the bottom of the container is at -100 kpa
in this situation the pressure gradient you speak of is negligible or
and the only two forces that apply in that type of situation are the force of gravity and the resultant force of buoyancy of an object due only to the density differential between the water and the object.
if I take a 10 ft tall pipe and attach a pressure guage and a vacuum guage at the bottom of the pipe and at the top of the pipe and seal it at the bottom and fill it with water and seal it at the top in 1 atm
then when I look at the vacuum guage at the bottom it reads zero
if I look at the pressure guage at the bottom it reads 4.33 psi.
if I add 1 lb of air pressure at the top
the vacuum guage at the bottom of the pipe still reads zero.
the pressure guage at the bottom of the pipe reads 5.33 psi
if I remove the 1 psi air pressure and throw a - 50 kPa vacuum on the air at the top
the vacuum guage at the bottom of the pipe reads -50 kPa
the pressure guage at the bottom of the pipe reads zero
but in each situation either in 1 atm , pressurized , or a vacuum
the only reason a object will have buoyancy is the differential between the
density of the water and the object.
and to try to continue our discussion if a HHO cell is at the bottom of the 10 ft pipe
more energy will be required to convert water into HHO at 4.33 psi guage pressure and even more
at 5.33 psi guage pressure
and less at -50 kPa guage pressure.