Intuitive explanation of Archimedes' principle? https://en.wikipedia.org/wiki/Archimedes%27_principle
The wikipedia entry for Archimedes' principle (buoyant force = weight of fluid displaced) has interesting formulas explaining why it's true, but is there an intuitive explanation?
 A: The intuitive explanation to is:
Consider an ideal fluid in equilibrium, now all small sections of this fluid are at rest at all times, this implies the all the forces on any small section balance each other out.
Now let's say you take out a part of the fluid from the top which is of any random shape this segment was at rest earlier , this means the upward force on it by the liquid beneath is equal to the weight of part we took out of the fluid!
Eureka!
When you place an object on the surface on or even inside a fluid and it goes into a place  where earlier there was fluid now the fluid below remains unchanged and applies the same force on the object placed
and that force my friend is as explained previously equal to the weight of the liquid we displaced!
A: The value of buoyant force is given by
$$F = \rho V g$$
(the weight of the displaced fluid). We also know that pressure
$$P = \frac{F}{A}$$
where $P$ is the pressure on the submerged (part of) object and $A$ the area of the same. Now the reason I bring up pressure, is because understanding how pressure affects a submerged object can help you understand buoyancy.
Now the reason behind buoyancy lies in the fact that pressure changes as a function of depth according to the equation
$$P = \rho g h$$
As you can see pressure increases as depth $h$ increases. The area of the object which is at a greater depth, and therefore subject to a greater hydrostatic pressure, will be pushed upwards, towards a lower depth and therefore lower hydrostatic pressure. Think of the fluid as several layers sitting on top of each other with pressure increasing the further down you go.
The same principle applies to say a helium balloon. The pressure of the air beneath the balloon is slightly greater than the pressure above the balloon which results in it floating.
