This is a deceptively simple problem in fluid mechanics that I can't quite figure out because it produces a paradox.
Suppose that there is a straw and a small column of water inside the straw, such that the height of the column is significantly smaller than the height of the straw, and that the top of the column is initially at the same height as the top of the straw. Suppose also that the cross sectional area of the straw at the top is $A_1$, and at the bottom it is $A_2$, such that $A_1>A_2$, and that this change in the cross sectional area of the straw occurs somewhere around its midpoint.
Now suppose that the water column accelerates from rest due to the gravitational force until the bottom of the column is at the same height as the bottom of the straw. As the column falls through the midpoint of the straw its cross section changes from $A_1$ to $A_2$. Therefore, its velocity must increase due to the decrease in cross sectional area, as follows from the continuity equation. This means that there is a force acting on the bottom portion of the column as it accelerates through the midpoint, and that this force cannot be the gravitational force because that accelerates the entire column uniformly.
So the question is this: what is the additional force?
Typically this force comes from a pressure differential, but in this case both the top and bottom of the water column are at atmospheric pressure, so there is no pressure differential.
The paradox is that if this force doesn't exist then the continuity equation is violated. If the continuity equation is not violated then a force exists without a pressure differential.