The surface of the liquid at rest, contained in a communicating vessel, remains on the same horizontal
According to Stevin’s law, the pressure difference between two points inside a static liquid is equal to the product of the liquid’s density and the gravity module and the height of the liquid column.
We can then say that the pressure difference between two points of a liquid column is directly proportional to the difference in level, that is, the height between these points. But for different points situated at the same height, that is, on the same horizontal surface, the height is equal to zero h = 0 and the pressure change is also zero.
Therefore, we can conclude that for points situated at the same height the pressure is equal. This pressure is usually the local atmospheric pressure itself. Thus, as the atmospheric pressure in a region can be considered constant, points on the same surface are subjected to the same pressure.
