Pascal's Principle [easily explained]
The French physicist and mathematician Blaise Pascal (1623-1662), made various contributions to the theory of probability, mathematics and natural history. The best known is Pascal's principle, on the behavior of fluids.
Pascal's postulate it is quite simple, easy to understand and very useful. Through experiments, Pascal finds that the pressure in liquids, in a state of rest, is transmitted uniformly throughout the volume and in all directions.
Pascal's statement, Based on the study of fluids, it is used for the design of a wide variety of hydraulic equipment such as presses, elevators, car brakes, among others.
Basic Concepts to understand Pascal's Principle
Pressure
The pressure is the ratio of the applied force per unit area. It is measured in units such as Pascal, bar, atmosphere, kilograms per square centimeters, psi (pound per square inch), among others. [1]
The pressure is inversely proportional to the applied surface or area: the greater the area, the less pressure, the less the area, the greater the pressure. For example, in Figure 2 a force of 10 N is exerted on a nail whose tip has a very small area, while the same force of 10 N is applied on a chisel whose tip has a larger area than the tip of the nail. . Since the nail has a very small tip, all the force is applied to its tip, exerting great pressure on it, while in the chisel, the larger area allows the force to be distributed more, generating less pressure.
This effect can also be observed in sand or snow. If a woman wears a sports shoe or a very small heel shoe, with a very fine-toed heel shoe it tends to sink more since all its weight is concentrated in a very small area (the heel).
Hydrostatic pressure
It is the pressure exerted by a fluid at rest on each of the walls of the container that contains the fluid. This is because the liquid takes the shape of the container and it is at rest, as a consequence, it happens that a uniform force acts on each of the walls.
Fluids
Matter can be in a solid, liquid, gaseous or plasma state. Matter in solid state has a definite shape and volume. Liquids have a definite volume, but not a definite shape, adopting the shape of the container that contains them, while gases have neither a definite volume nor a definite shape.
Liquids and gases are considered "fluids", since, in these, the molecules are held together by weak cohesive forces, when they are subjected to tangential forces they tend to flow, moving in the container that contains them. Fluids are systems that are in constant motion.
Solids transmit the force that is exerted on it, while in liquids and gases pressure is transmitted.
PASCAL'S PRINCIPLE
The French physicist and mathematician Blaise Pascal made various contributions in probability theory, mathematics, and natural history. The best known is the principle that bears his name on the behavior of fluids. [2]
Statement of Pascal's Principle
The principle of Pascal states that the pressure exerted anywhere in an enclosed and incompressible fluid is transmitted equally in all directions throughout the fluid, that is, the pressure throughout the fluid is constant. [3].
An example of Pascal's principle can be seen in Figure 3. Holes were made in a container and corked, then filled with water (fluid) and a lid was placed. When a force is applied to the lid of the container, a pressure is presented in the water that is equal in all directions, making all the corks that were in the holes come out.
One of his best known experiments was that of Pascal's syringe. The syringe was filled with a liquid and connected to tubes, when pressure was exerted on the plunger of the syringe, the liquid rose to the same height in each of the tubes. Thus it was found that the increase in pressure of a liquid that is at rest is transmitted uniformly throughout the volume and in all directions. [4].
APPLICATIONS OF THE PASCAL PRINCIPLE
The applications of Pascal's principle They can be seen in everyday life in numerous hydraulic equipment such as hydraulic presses, hoists, brakes and jacks.
Prensa hidráulica
The hydraulic press it is a device that allows to amplify forces. The operating principle, based on Pascal's principle, is used in presses, elevators, brakes, and in a wide variety of hydraulic devices.
It consists of two cylinders, of different areas, filled with oil (or other liquid) and communicated with each other. Two plungers or pistons are also placed that fit into the cylinders, so that they are in contact with the fluid. [5].
An example of a hydraulic press is shown in figure 4. When a force F1 is applied to the piston of smaller area A1, a pressure is created in the liquid that is instantly transmitted inside the cylinders. In the piston with a larger area A2, a force F2 is experienced, much greater than that applied, which depends on the ratios of the areas A2 / A1.
Exercise 1. To lift a car, you want to build a hydraulic jack. What relationship must the diameters of the hydraulic ram pistons have so that by applying a force of 100 N it can lift a 2500 kg car on the larger piston? See figure 5.
Solution
In hydraulic jacks, Pascal's principle is fulfilled, where the oil pressure inside the hydraulic jack is the same, but the forces are “multiplied” when the pistons have different areas. To determine the area ratio of the hydraulic jack pistons:
- Given the mass of the car, 2.500 kg, that you want to lift, determine the car's weight using Newton's second law. [6]
We invite you to see the article Newton's laws "easy to understand"
- Pascal's principle is applied, equalizing the pressures in the pistons.
- The area relationship of the plungers is cleared and the values substituted. See figure 6.
The areas of the plungers should have a ratio of 24,52, for example, if you have a small plunger with a radius of 3cm (area A1= 28,27 cm2), the large plunger should have a radius of 14,8 cm (area A2= 693,18 cm2).
Hydraulic lift
A hydraulic lift is a mechanical device used to lift heavy objects. Hydraulic lifts are used in many auto shops to perform under-vehicle repairs.
The operation of hydraulic lifts is based on Pascal's principle. Elevators generally use oil for pressure transmission to the pistons. An electric motor activates a hydraulic pump that exerts pressure on the piston with the smallest area. In the piston with the largest area, the force is “multiplied”, being able to lift the vehicles to be repaired. See figure 7.
Exercise 2. Find the maximum load that can be lifted with a hydraulic lift whose area of the smallest piston is 28 cm2, and that of the largest piston is 1520 cm2, when the maximum force that can be applied is 500 N. See figure 8.
Solution:
Since Pascal's principle is fulfilled in hydraulic lifters, the pressures on the pistons will be equal, thus knowing the maximum force that can be applied on the smaller piston, the maximum force that will be exerted on the large piston is calculated ( F2), as shown in figure 9.
Knowing the maximum weight (F2) that can be lifted, the mass is determined using Newton's second law [6], thus vehicles weighing up to 2766,85 kg can be lifted. See figure 10. According to the table in figure 8, of the average vehicle masses, the elevator will only be able to lift compact cars, with an average mass of 2.500 kg.
Hydraulic brakes
Brakes are used on vehicles to slow them down or stop them completely. In general, hydraulic brakes have a mechanism like the one shown in the figure. Depressing the brake pedal applies a force that is transmitted to a small area piston. The applied force creates a pressure inside the brake fluid. [7].
In the liquid the pressure is transmitted in all directions, up to a second piston where the force is amplified. The piston acts on discs or drums to brake the vehicle's tires.
CONCLUSIONS
The principle of Pascal states that, for incompressible fluids at rest, the pressure is constant throughout the fluid. The pressure exerted anywhere in the enclosed fluid is transmitted equally in all directions and directions.
Among the applications of Pascal's principle There are numerous hydraulic equipment such as presses, elevators, brakes and jacks, devices that allow to amplify forces, according to a relationship of areas in the plungers of the device.
Do not stop reviewing on our website the Newton law, Thermodynamic principles, Bernoulli's principle among others very interesting.