What is Pascal's principle?
O principleinpaschal is a law of fluid mechanics that states that the pressure applied to a fluid in static equilibrium it is distributed evenly and without loss to all its parts, including the walls of the container in which it is contained. This principle was enunciated by the French scientist BlaisePascal.
The pressure difference between any two points of a fluid in static equilibrium must be equal.
Lookalso:Fundamentals of Hydrostatics
Pressure is defined by the ratio between the strength applied and the area of the application. This physical magnitude is measured in paschal (Pan). According to Pascal's principle, when applying a force on a hydraulic system, as in an assembly of pistons, the increase in pressure on the piston will be exerted uniformly at all points of the fluid.
Also, if the fluid is in contact with another area piston 10 times bigger, the force exerted on him will be 10 times bigger than the one exerted on the first piston. In this way, the pressure increase in each of the pistons will be equal.
In the figure below, there are two pistons connected by an incompressible fluid in static equilibrium. Watch:
According to Pascal's principle, the increase in pressure exerted on the first piston is uniformly communicated throughout the fluid.
When applying a force F1 about piston 1 of area A1, an increase in pressure is communicated throughout the fluid. Thus, as area A2 of piston 2 is greater than the area of piston 1, the force exerted on piston 2 should be proportionally greater in relation to their areas. Therefore, Pascal's principle can be written using the following equation:
Lookalso:How do hydraulic machines work?
Below, we have a figure that shows the effect of the Pascal principle: when compressing the piston of the syringe, the fluid contained within the punctured bladder is subject to increased pressure so homogeneous:
The pressure applied by the piston is transmitted equally to all parts of the fluid.
It is also important to know that the force exerted on the container is everperpendicular to its surface. For this reason, in the image above, the water is expelled at an angle of 90º in relation to the curvature of the bladder.
Lookalso: Communicating vessels
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Experiment on Pascal's Principle
It is possible to carry out several experiments to observe the effect of Pascal's principle on fluids. One of them consists of blowing continuously in a pipe inserted in a closed bottle, in which they contain open tubes and of the same diameter, connecting the fluid inside with the outside environment. The more air that is pumped into the bottle, the greater the pressure inside the bottle, therefore, the larger the column of liquid formed in the tubes.
Regardless of the direction or depth in which the lower end of these tubes is inserted, the liquid inside each of them should reach the same height, as they will all be subject to the same pressure.
Through this experiment, it is possible to visualize that the transmission of pressure in fluids occurs equally in all directions.
principle of stevin
O principleinstevin, also known as the principlefundamentalgivesHydrostatics, explains the dependence between the pressure exerted by fluids in static equilibrium and its depth: The greater the height of a liquid, the greater the pressure exerted against the walls of its container.
P – absolute pressure
P0 - atmospheric pressure
d – fluid density
g – local gravity
H – fluid depth
When we relate this law to the principleinPascal, we can conclude that the depth of a fluid determines the pressure it exerts, which is evenly distributed throughout its length. Also, the force exerted by this fluid must always be perpendicular to the walls of your container.
This relationship is easily observed if we pierce a plastic bottle filled with water at two points of different heights: in the lower holes, closer to the base of the bottle, the water will be expelled farther due to the increase in pressure hydrostatic.
Read too:Hydrostatics
Exercises on Pascal's Principle
1) Assume that, in the scheme shown below, the area of piston 1 is 10 cm², and that of piston 2 is 25 cm². If a force of 45 N is applied to piston 1, what force is expected to act on piston 2?
Resolution
To solve this type of exercise, it is necessary to apply Pascal's principle, which is presented in the formula below:
Pascal's principle states that pressure is transmitted homogeneously throughout the entire length of the fluid, therefore, the increase in pressure on piston 1 must be equal to the increase in pressure on the piston 2. Taking the data provided by the statement, we will have the following calculation to solve:
According to the calculation we made, it is possible to see that the ratio between the forces (112.5 N and 45 N) is equal to the ratio between the areas (25 cm² and 10 cm²) and is 2.5. Therefore, we can say that, according to Pascal's principle, the ratio between the areas of the pistons is equal to the ratio between the forces exerted on them.
Lookalso: Learn to do pressure calculations
By Me. Rafael Helerbrock
Would you like to reference this text in a school or academic work? Look:
HELERBROCK, Rafael. "Pascal's Principle"; Brazil School. Available in: https://brasilescola.uol.com.br/fisica/principio-de-pascal.htm. Accessed on June 28, 2021.
