newtonian mechanics - Confusion about the buoyant force applied by fluids

EDIT

I found that a similar question was asked by user Muno in this question in a follow up comment which is as follows (in short this is what I'm asking for)

to make my question more succinct: if buoyant force depends on a difference in pressure, and pressure at a particular depth depends upon the weight above it, why isn't a submerged object's weight factored into pressure?

---

I have heard of the reason that water applies buoyant force due to a gradient of pressure. But why does it arise?

Consider the following (the cause of my problem)

When analyzing the situation it's said that the object feels a force which is equal to the weight of water that it displaces. But I'm a bit (or say too much) confused on this too. It's as follows :

The water above the object (say at a depth $h_a$) is applying a force equal to its weight which is $\pi r^2 h \rho _{water}$. Now consider the lower portion, the object and the water column above are applying a force equal to

$$\pi r^2 h \rho _\text{water} g+W_\text{object}$$

but the water column below is applying a force equals to

$$-(\pi r^2 h \rho _\text{water} g +W_\text{object})$$ (via Newton's third law)

therefore the net force on the object is $-W_\text{object}$. So why is this not the case?

Answer

Buoyant force is a contact or "reaction" force. Microscopically it has the same origin as all contact forces

• the repulsion between molecules which are squashed together.

A solid cannot get out of the way because it does not flow and hence when a force is applied on it it gets compressed and a restoring force is generated, which increases in magnitude till it becomes equal to the force applied by the object. Whereas for the fluid they simply get out of the way rather than getting compressed (as their molecules are free to move) hence you cannot just say that the force applied by fluids equals the weight above it.

When you lower an object into a liquid, the reaction force increase because as the depth increases so does the speed with which the molecules bump into the object. But after the object is fully submerged molecules of water start pushing the object downward and in due process cancelling the effect of increasing upward force. So after that the buoyant force remains constant.

At each stage the reaction force from the fluid on the block ("upthrust") equals the force which the block exerts on the fluid. If the "upthrust" at the current depth or deformation does not equal the weight of the block, there is an unbalanced force on the block, which moves further down.