Undergrad How does gauge pressure affect the buoyant force on a submerged object?

[Any Help]

How can we relate gauge pressure (pg) to the buoyant force , in a completely submerged object?
is it as follow: Buoyant force= pg.Area +Density(water).volume.gravity ?

 

[gleem]

How can we relate gauge pressure (pg) to the buoyant force , in a completely submerged object? is it as follow: Buoyant force= pg.Area +Density(water).volume.gravity ?

The buoyant force on a submerged object is equal to the weight of the volume of the fluid displaced. This weight depends on the density of the fluid. In so far as the density increases with pressure the buoyant force will increase. But density increases only very slowly for liquids which is determined by its compressibility which is determined by its Bulk Modulus. For water for example the density increases only a few percent at a depth of 20,000 ft, so the buoyant force will only increase by this amount. Gauge pressure will have increase from zero to over 9,000 psi at this depth. So the buoyant force can be related to gauge pressure by the equation

BF = density _{@ zero GP} *Volume( 1 + GP/E_B)

Where E_B is the bulk modulus of the fluid: For water it is 3.1x10⁵ lbs/in²

So you see GP makes negligible difference in BF except at extreme depths.