[Physics] Why is pressure on object in fluid dependent on height of water column above it whereas the *force* on object is not

buoyancyfluid-staticsforcespressure

According to Archimedes principle, the buoyant force is equal to weight of the fluid displaced.

Buoyant force = Weight of water displaced 

             =  (Mass of water displaced) x g

             =  (Density of water x volume of water displaced) x g

             =   volume x density x g

We can express this relation in the equation:$$F_B = v *\rho*
g$$ where $F_B$ = Force of buoyancy
, $v$= volume of water displaced,
$\rho$ is density of water and g is acceleration due to gravity

So, buoyant force is independent (not dependent) of the height of water above it according to the formula.
$$\text {Pressure} = \text {force} / \text {area}$$ Pressure by formula is equal to,$$ p = h* \rho*g$$ where h is the height of the water column above. So, pressure is dependent on height of water column. Area doesn't change in both cases.

Summary: Buoyant force is independent of height of fluid column above the object , whereas the pressure on the same object which is simply (force/area) is dependent on height, But Area in both cases is same ,How is this possible?

[NOTE: I've interchangeably used water sometimes to mean fluid]

Best Answer

Short and direct answer:

Buoyant force is not equal to simply pressure×area. It is, in a simplistic manner, (difference in pressure on upper and lower surface)×area.

Since pressure varies linearly with depth, difference in pressure would be the same for two surfaces at separation of 5 m anywhere in the liquid, be it just below the surface or at a depth of 100m.

Since the difference in pressure doesn't change with depth, the buoyant force, too, wouldn't change.

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