Let's do a simple experiment: take a weakly inflated rubber ball and “immerse” it in the water. If the immersion depth is even 1-2 meters, then it is easy to see that its volume will decrease, i.e. from all sides the ball squeezed a certain force. Usually they say that hydrostatic pressure is “guilty” here - a physical analogue of the force acting in stationary liquids on an immersed body. Hydrostatic forces act on the body from all sides, and their resultant force, known as the Archimedean force, is also called buoyant, which corresponds to its direction of action on the body immersed in the liquid.
Archimedes discovered his law purely experimentally, and its theoretical justification waited almost 2000 years before Pascal discovered the law of hydrostatics for a stationary fluid. According to this law, pressure is transmitted through the fluid in all directions, regardless of the area on which it acts, on all planes that bound the fluid, and its value P is proportional to the surface S and directed along the normal to it. Pascal discovered and tested this law by experiment in 1653. According to it, hydrostatic pressure acts on the surface of a body immersed in a liquid from all sides.
Let us assume that a body in the form of a cube with an edge L to a depth H is immersed in a vessel with water — the distance from the surface of the water to the upper face. In this case, the lower face is at a depth of H + L. The force vector F1 acting on the upper face is directed downward and F1 = r * g * H * S, where r is the density of the liquid, g is the acceleration of gravity.
The force vector F2 acting on the lower plane is directed upward, and its value is determined by the expression F2 = r * g * (H + L) * S.
The vectors of forces acting on the lateral surfaces are mutually balanced, therefore, are excluded from consideration in the future. The Archimedean force is F2> F1 and is directed from the bottom up, and is applied to the lower face of the cube. Define its value F:
F = F2 - F1 = r * g * (H + L) * S - r * g * H * S = r * g * L * S
Note that L * S is the volume of the cube V, and since r * g = p is the weight of a unit of liquid, the Archimedean force formula determines the weight of the volume of liquid equal to the volume of the cube, i.e. this is precisely the weight of the fluid displaced by the body. Interestingly, talking about the Archimedes law is possible only for an environment where gravity is present - in zero gravity the law does not work. Finally, the formula of the law of Archimedes has the following form:
F = p * V, where p is the specific gravity of the liquid.
Archimedean force can serve as the basis for the analysis of the buoyancy of bodies. The condition for analysis is the ratio of the weight of the immersed body Pm and the weight of the liquid Pj with a volume equal to the volume of the body part immersed in the liquid. If Pm = Pg, then the body floats in a liquid, and if Pm> Pg, then the body sinks. Otherwise, the body pops up until the buoyancy force is equal to the weight of the ejected recessed part of the body of water.
The law of Archimedes and its use have a long history in technology, starting with the classic example of application in all known craft and to balloons and airships. Here, the fact that the gas belongs to such a state of matter that completely models the liquid played a role. Moreover, in the air, any object acts Archimedean force, akin to the same as in a liquid. The first attempts to carry out an air flight in a balloon were made by the Montgolfier brothers - they filled the balloon with warm smoke, so that the weight of the air enclosed in the balloon was less than the weight of the same volume of cold air. This was the reason for the appearance of lifting force, and its value was determined as the difference in weight of these two volumes. A further refinement of the balloons was the burner, which continuously heated the air inside the balloon. It is clear that the flight range depended on the duration of the burner. Later, on airships, gas with a specific gravity less than that of air was used for filling.