To deal with the question “Liquid pressure”, we start with classic examples and gradually move on to consider more complex and confusing options. For a vessel of cylindrical shape, in which the walls are strictly vertical, and the bottom is horizontal, the hydrostatic pressure of the liquid poured to a height h will be unchanged for each bottom point. The formula for calculating this value will look like p = rgh, where r is the density of the liquid; g is the acceleration of gravity; h is the height of the liquid column. The value p for all points of the bottom is the same.
Introducing the vessel bottom area S into the formula, we can calculate the pressure force F. Considering that the liquid pressure at the bottom of the vessel is the same at each point, we infer the formula F = rghS.
It is easy to see that in this case the pressure force on the bottom is equal to the weight of the liquid poured into the cylindrical vessel of the correct form. It looks paradoxical, but it has a scientific and logical explanation that the formula F = rghS also works for vessels of various shapes. In other words, for the same values of S - the bottom area and h - the height of the liquid level, the liquid pressure at the bottom is the same for all vessels, regardless of how much volume each individual vessel holds. In this case, the weight of the liquid actually poured into vessels of arbitrary shape can be less and more than the pressure force on the bottom, but will always satisfy the above rule.
Following the basic principle of physics to verify theoretical conclusions in practice, Pascal suggested using a device named after him. The highlight of this device is a special stand that allows you to fix vessels of various shapes that do not have a bottom. The bottom of the vessels performs a tightly pressed bottom plate, which is located on one shoulder of the balance beam.
Set the weight on a cup of another rocker and begin to fill the vessel with water. When the fluid pressure creates a force in excess of the weight of the weight, the fluid will open the plate, and its excess will pour out. By measuring the height of the water column, you can calculate the numerical value of the force of its pressure on the bottom and compare with the weight of the weight.
Taking into account the possibility of achieving a greater pressure force with a small amount of water, only increasing the height of the water column, we can explain another interesting experiment, also described by Pascal.
A long tube was attached to the top cover of a new carefully caulked barrel, filled to the brim with water, along which water was poured. The tube had a small cross section, a pair of water mugs was enough to raise the water column to a considerable height. At a certain point, a new solid barrel could not stand it and burst at the seams. Regardless of the amount of liquid poured, it was the height of the water column that led to an increase in pressure on the bottom of the barrel. As a result, a critical value of the force was created, which led to the rupture of the capacitance.
The difference between the real weight of the liquid and the pressure force on the bottom of the vessel is compensated by the force that the pressure of the liquid causes on the walls of the vessel. It is the inclination of the walls of the vessel that leads to the fact that this pressure is either directed up or down, respectively, bringing the system into equilibrium.
A vessel that has a narrowing upwards experiences a fluid pressure directed upward. An interesting experience can be made by preparing a simple installation. It is necessary to put on a cylinder on a fixed piston, which goes into a tube mounted vertically. Filling water through the tube, we observe how filling the space above the piston leads to the raising of the cylinder up.
To summarize, the concept of “pressure” can be defined as the ratio of the force that acts perpendicular to the surface to its area. Unit pressure is a value equal to one Pascal (1 Pa) and corresponding to the action of a force of one Newton (1 N) per square meter (1 sq. M).
According to Pascal's Law, the pressure that a liquid (gas) experiences is transmitted unchanged to each point in the volume of the liquid (gas). The intrinsic pressure of a liquid (gas) is the same at a specific height. With depth, it increases.