If you see my horrible reference picture, you will see that the U shaped tube is placed inside the field where gravitational force exist. And the bottom of the tube is opened, tube is filled with liquid. the density of liquid is ρ, acceleration of gravity is g, and each column's height is h
I used to conclude that the water won't flow down, because the pressure occurred from each side of water column would eventually cancel each other, thus no more pressure exist.
But if that should be the correct answer shouldn't there be a premise that " there exist attraction force between liquid molecules which is greater than the pressure exerted on the end of the liquid (=ρgh)"?