An Old Fashioned Glass Milk Bottle with a narrow neck is delivered to your doorstep in the morning and because it is no homogenized, the Cream has risen up into the narrow(er) region.
The fluid pressure exerted on the bottom of the bottle is (rho) g h.
Where (rho) is the average density of the column of milk/cream that extends from the top surface to the bottom.
Now we will thoroughly MIX the bottle of milk and we note that the average density of this same column of milk is GREATER than (rho). Let’s call this new density (RHO).
How can the pressure have increased while the area of the bottom has stayed constant?
How can we accept a greater amount of downward fluid force caused by ‘just’ mixing the milk?
(This is reprised from back in the last century.)
Probably presented better back then.
;-)