If a liquid is poured into a container with a base area $A$, then the entire weight of the liquid column acts on the bottom of the container. The resulting pressure is generally given by:
$$
p = \frac{F}{A} = \frac{mg}{A}
$$
The mass $m$ can be replaced by the product of the density $\varrho$ and the volume $V = Ah$, where $h$ is the height of the liquid column. After canceling the area $A$, we directly obtain the formula for calculating hydrostatic pressure (also known as gravitational pressure):
$$
\boxed{p = \varrho g h}
$$
This pressure depends — contrary to intuitive expectations — only on the density of the liquid and the depth below the surface. The shape of the container and thus the size of its bottom plays no role. This phenomenon is known as the hydrostatic paradox. It can be explained by the fact that particles in a liquid always rearrange themselves into an equilibrium state. As a result, forces from the container walls act on the liquid, ensuring that the pressure at a given layer within the liquid is always the same and depends only on the distance from the surface.
Moreover, the pressure at any point within the fluid has the same magnitude in all directions; in other words, it acts isotropically. This is often referred to as Pascal's Law in the field of hydrodynamics. For example, a diver lying horizontally at a depth of 10 m in a pool experiences a pressure of about 1 bar on both their back and stomach.
The physical concept of hydrostatic pressure is also used in medicine, for example in the treatment of edema — swelling of body tissue due to fluid retention. If a patient walks in water, the pressure is greatest in the area of the legs, resulting in a decongestive effect there.
From hydrostatic pressure, a pressure unit used today especially for measuring blood pressure is derived: millimeters of mercury column (mmHg or Torr). It denotes the hydrostatic pressure of a 1 mm high column of mercury, which is significantly higher than that of water due to mercury’s greater density. Although it is not an SI unit, it is still permitted for certain uses within the European Union.
The density of mercury under normal conditions is approximately $\varrho = 13.5951\,\mathrm{g}/\mathrm{cm}^3$. Combined with the acceleration due to gravity $g$, the conversion from mmHg to pascals is:
$$
\boxed{1\,\mathrm{mmHg} = 133.322\,\mathrm{Pa}}
$$
If one used water instead of mercury, the equivalent height could be calculated using the formula:
$$
\boxed{h_\mathrm{W} = \frac{\varrho_\mathrm{Hg}}{\varrho_\mathrm{W}}h_\mathrm{Hg}}
$$
Here, the gravitational acceleration cancels out on both sides of the equation.