The famous French philosopher, mathematician and physicist of the XVII century Blaise Pascal made an important contribution to the development of modern science. One of his main achievements was the formulation of the so-called Pascal law, which is associated with the property of fluid substances and the pressure created by them. Let us consider this law in more detail.
Short biography of the scientist
Blaise Pascal was born on June 19, 1623 in the French city of Clermont-Ferrand. His father was a vice president of tax collection and a mathematician, and his mother belonged to the bourgeois class. From a young age, Pascal began to show interest in mathematics, physics, literature, languages and religious teaching. He invented a mechanical calculator that could perform addition and subtraction operations. He spent a lot of time studying the physical properties of fluid bodies, as well as developing concepts of pressure and vacuum. One of the important discoveries of the scientist was the principle that bears his name - the law of Pascal. Blaise Pascal died in 1662 in Paris due to leg paralysis - the disease that has accompanied him since 1646.
Pressure concept
Before considering the law of Pascal, we will deal with such a physical quantity as pressure. It is a scalar physical quantity denoting the force that acts on a given surface. When a force F begins to act on a surface of area A perpendicular to it, then the pressure P is calculated by the following formula: P = F / A. The pressure is measured in the International System of Units of SI in pascals (1 Pa = 1 N / m 2 ), that is, in honor of Blaise Pascal, who devoted many of his works to the issue of pressure.
If the force F acts on a given surface A not perpendicularly, but at a certain angle α to it, then the expression for pressure will take the form: P = F * sin (α) / A, in this case F * sin (α) is the perpendicular component forces F to surface A.
Pascal's Law
In physics, this law can be formulated as follows:
The pressure applied to a practically incompressible fluid substance, which is in equilibrium in a vessel having non-deformable walls, is transmitted in all directions with the same intensity.
You can verify the correctness of this law as follows: you need to take a hollow sphere, make holes in it in various places, equip this sphere with a piston and fill it with water. Now, creating a pressure on the water using a piston, you can see how it pours out of all the holes at the same speed, which means that the water pressure in the area of each hole is the same.
Liquids and gases
Pascal's Law is formulated for fluid substances. This concept includes liquids and gases. However, unlike gases, the molecules that form the liquid are located close to each other, which causes the presence of such a property as incompressibility in liquids.
Due to the property of incompressibility of a liquid, when a final pressure is created in a certain volume of it, it is transmitted in all directions without loss of intensity. This is precisely what is being discussed in the Pascal principle, which is formulated not only for fluid, but also for incompressible substances.
Considering in this light the question "gas pressure and Pascal’s law," it should be said that gases, unlike liquids, are easily compressed, without preserving the volume. This leads to the fact that when an external pressure is applied to a certain volume of gas, it is also transmitted in all directions and directions, but at the same time it loses intensity, and its loss will be the greater, the lower the gas density.
Thus, the Pascal principle is valid only for liquid media.
Pascal principle and hydraulic machine
Pascal's principle is applied in various hydraulic devices. In order to use Pascal's law in these devices, the formula is valid as follows: P = P 0 + ρ * g * h, here P is the pressure that acts in the liquid at a depth h, ρ is the density of the liquid, P 0 is the pressure applied to the surface of the liquid, g (9.81 m / s 2 ) is the acceleration of gravity near the surface of our planet.
The principle of operation of the hydraulic machine is as follows: two cylinders, which have a different diameter, are interconnected. This complex vessel is filled with some kind of liquid, for example, oil or water. Each cylinder is equipped with a piston so that there is no air left between the cylinder and the surface of the liquid in the vessel.
Suppose that a force F 1 acts on a piston in a cylinder with a smaller cross section, then it creates a pressure P 1 = F 1 / A 1 . According to Pascal’s law, the pressure P 1 will be instantly transferred to all points of space inside the liquid in accordance with the above formula. As a result, the piston with a large cross section will also be affected by the pressure P 1 with the force F 2 = P 1 * A 2 = F 1 * A 2 / A 1 . The force F 2 will be directed opposite to the force F 1 , that is, it will tend to push the piston up, while it will be greater than the force F 1 exactly as many times as the cross-sectional area of the cylinders of the machine differs.
Thus, Pascal's law allows you to lift large loads with the help of small balancing forces, which is a kind of lever of Archimedes.
Other applications of the Pascal principle
The law under consideration is used not only in hydraulic machines, but finds wider application. Below are examples of systems and devices whose operation would not be possible if Pascal's law were not fair:
- In the brake systems of cars and in the well-known anti-blocking system ABS, which prevents the wheels of the car from locking during braking, which avoids skidding and slipping of the vehicle. In addition, the ABS system allows the driver to maintain control in the management of the vehicle when the latter performs emergency braking.
- In any type of refrigerator and cooling system, where the working substance is a liquid substance (freon).