# What is Pascal’s principle?

## Pascal’s Principle

The **principle of Pascal** ‘s law or a statement that was prepared by the physicist and mathematician of French origin **Blaise Pascal** and tells us that the increase in **pressure** applied to a **surface** having an **incompressible fluid** that is contained in a container non-deformable, it is **transmitted** with equal value to each of the parts of the container.

## What is Pascal’s principle?

This principle or law of the branch of **physics** tells us that when a certain **pressure** is applied to a **fluid** that is in a container, the same value will be distributed to each of the parts that make it up.

- What does Pascal’s principle consist of?
- History
- Statement
- Formula
- Applications of Pascal’s principle
- Hidraulic elevator
- Importance
- Demonstration
- Experiment
- Examples of Pascal’s principle
- Conclution

## What does Pascal’s principle consist of?

This principle consists in the explanation that is made of how the **pressure** exerted by a **fluid** that is in **equilibrium** and that cannot be compressed, housed in a container in which the walls are not deformed, is transmitted with the same **intensity** in all the points of said fluid regardless of direction.

## History

Blaise Pascal Blaise Pascal invented the first **mechanical calculator** in 1642 and succeeded in showing through an experiment in 1648 that the level of the mercury column of a **barometer** was determined by the **increase** or **decrease** exerted by **pressure** surrounding **atmospheric** . This discovery verified the hypothesis that the Italian physicist **Evangelista ****Torricelli** already had regarding the effect that atmospheric pressure had on the balance of liquids. A few years later, working with the French mathematician **Pierre de Fermat** , Pascal managed to formulate themathematical **theory** of **probability** , which has become of great importance in actuarial, **mathematical** and **social ****statistics** , as well as a fundamental element in the calculations of modern theoretical physics .

## Statement

The statement that defines Pascal’s principle is the following:

The **pressure** exerted on a **fluid that is** not very compressible and in equilibrium within a container with non-deformable walls is transmitted with equal **intensity** in all directions and at all points of the fluid.

## Formula

The formula for applying Pascal’s principle is as follows:

**p = p_0 + rho g h.**

Where:

- p is the
**total pressure**at depth - h is the
**measure**in Pascals - p_0 is the
**pressure**on the free surface of the fluid - rho is the
**density**of the fluid - g is the
**acceleration**of gravity.

## Applications of Pascal’s principle

Pascal’s principle can be used in jobs that require a great **effort** but that at the same time must be carried out by applying a **small force** , for example:

- Hydraulic
**brakes** **Tires**that cars have- Hydraulic
**lifters** - Hydraulic
**presses**

## Hidraulic elevator

Hydraulic lifts are **mechanical devices** that are used to **lift** objects that have a lot of weight. The elevators are used with all types of **vehicles** , from motorcycles to large automobiles, and can be used both in **professional** environments and in **domestic** activities .

The hydraulic lift works thanks to Pascal’s principle, which tells us that “the pressure exerted on a fluid that is not very compressible and in equilibrium within a container with non-deformable walls is transmitted with equal intensity in all directions and at all points of the fluid. ”.

They use the principle by combining two **cylinders** of different sizes, one small and the other large, to be able to exert an increase in **pressure** and in this way to be able to lift objects that are very heavy. Thanks to this, the energy needed to lift the load is transmitted by a **pump** with **an** electric drive motor that transmits a **hydraulic fluid** to a **cylinder** , which acts directly or indirectly to cause the ascent.

## Importance

The importance of this principle lies in the relationship between the **pressure** and the **depth** of a fluid, or in the height of the fluid column, from a reference value. It is important for its validity in the case of **compressible fluids** that vary with pressure.

Everything related to **atmospheric pressure** , use of barometers, pressure in pools, seas, lakes, calculation of submerged structures, such as dams, submarines, and even airplanes is based on Pascal’s principle. Pascal’s principle also allows an explanation to be given **to ****Archimedes’**** principle** .

The **hydrostatic** is based on this principle and is very important in calculations of structures and devices that are part of the activity of man.

## Demonstration

Pascal’s principle can be tested when we use, for example, a hollow **sphere** , which has been **drilled** in different places and provided with a **plunger** . When the sphere is filled with water and some kind of pressure is exerted on it by means of the plunger, it can be observed that the water comes out of all the holes with the same **speed** and therefore with the same **pressure** .

## Experiment

The following is an example that can be applied to explain Pascal’s principle.

#### Materials

A transparent container

- 1 large balloon
- 1 blunt tip scissors
- 1 glass dropper
- Water

#### Instructions

First we will take the scissors and cut the nozzle of the **balloon** . We fill the **container** with **water** , leaving it almost full. We introduce the empty **dropper** into the container and close the container with the balloon so that the surface of the balloon is **tight** . Then **we push** the surface of the **globe** toward **down** and noticed that the dropper is filled with water and sinks.

## Examples of Pascal’s principle

An example of Pascal’s principle is as follows:

Calculate the force and pressure exerted on a piston, if we know that the resultant force is 42N, the larger piston has a radius of 55 centimeters and the smaller piston has a radius of 22 centimeters.

**Largest**piston: (3.14) (0.55²) = (3.14) (0.3025) = 0.950 m²**Minor**piston: (3.14) (0.22²) = (3.14) (0.0484) = 0.152 m²

We calculate the pressure:

**F2 = p2S2**

Hence:

- p2 =
**F2 / S2** - p2 =
**42 / 0.95**= 44.21 Pa

We calculate the applied force:

- F1 =
**p1S1** - F1 = (44.21) (0.152) =
**72 N**

## Conclusion

By means of Pascal’s principle it has been possible to verify that when a **pressure** is applied to a liquid that is enclosed in a container and that is in a **static** way , it can be **distributed** in a uniform way to all the **particles** of the fluid and to the **walls** of the container that contains it. In this way he explains to us how an object that has been submerged in a fluid experiences a **thrust** of equal magnitude to the **weight of** the object.