# Hydrostatic

The branch of mechanics that is responsible for studying the state of rest that fluids have is known as hydrostatics . Hydrostatics is responsible for analyzing the pressures exerted by a fluid in a state of rest , and when we speak of a fluid we refer to any fluid, not specifically to water. The definition of a fluid deserves special consideration and although time is not a determining factor in the field of hydrostatics, it enters the hydrostatic equilibrium approach . Generally, we say that a fluid is a substance that cannot withstand a shear stress, so the pressures are normal in confined surfaces .

## What is hydrostatics?

Hydrostatic is one of the important branches of mechanics of fluids whose function is to study the fluids are in a state of rest without their having forces that alter either in motion or at its position .

• What does hydrostatics study
• History
• Fluid characteristics
• Principles of hydrostatics
• Pascal’s principle
• Archimedes’ principle
• Fundamental equation of hydrostatics
• Applications
• Examples

## What does hydrostatics study

Hydrostatics is a branch that belongs to the area of fluid mechanics or hydraulics that is responsible for studying the different types of fluids that are in a state of equilibrium ; in other words, without any forces that alter its movement or position . There are two important and main theorems that support the study of hydrostatics and these are Pascal’s principle and Archimedes’ principle .

It is important to mention that a hydrostatic study can also include capillarity , ideal gas laws , speed of sound and hygrometry. Hydrostatics is a very concrete science that avoids esoteric concepts and advanced mathematics . It is also much easier to prove than Newtonian mechanics .

## History

The history of hydrostatics is based on Archimedes who was called by King Heron of Syracuse to help him solve an important problem he had. King Heron had given a silversmith a certain amount of gold to make a crown. When the crown was finished, people began to think that the silversmith had substituted silver for a part of the gold, and that for this reason he had deceived the king.

The king asked Archimedes to find out if he had been cheated and to determine whether the jeweler had stolen some of the gold or not, but he couldn’t break the crown to find out. Archimedes thought about how to solve the problem, without finding a solution, until one day when he was bathing in a tub, he put a lot of water and when he submerged , the water began to spill . It was at that moment that he understood what had happened to the king’s crown.

## Fluid characteristics

The main characteristics of fluids are the following:

• Fluids do not have a fixed shape but they do have volume .
• They have variability in shape and have very specific properties.
• Liquids take the shape of the container that contains them.
• They have the ability to flow or drain very easily if they are not contained in a container.
• They can expand and contract like solids.
• It has cohesion that allows the molecules that exist in the same substance to be held together.
• They have surface tension due to the attraction that exists between the molecules on the surface of a liquid.
• They enjoy adhesion , an attractive force that is manifested between the molecules of two different substances in contact.
• It has capillarity which occurs when there is contact between a liquid and a solid wall, due to the phenomenon of adherence.

## Principles of hydrostatics

Hydrostatics has two main principles by which it is governed, and these are as follows:

## Pascal’s principle

It consists of a law that was enunciated by the French physicist and mathematician Blaise Pascal and that tells us that “the increase in pressure applied to a surface of an incompressible fluid contained in a non-deformable container is transmitted with the same value to each of the parts of it ” . In other words, we can say that when a certain pressure is applied to a liquid in a closed container, it will be transmitted with the same intensity in all directions and senses.

## Archimedes’ principle

The Archimedes principle is that tells us that any solid body that is submerged in a full or partial within a fluid will be pushed in direction upward by a force equal to the weight of the volume of the liquid displaced by the solid body . This object does not have to be completely submerged in the fluid, since if the thrust it receives is greater than the apparent weight of the object, it will float and be only partially submerged .

## Fundamental equation of hydrostatics

The fundamental equation is the following:

2 – p 1 = ρg (h 2 – h 1 )

It indicates that for a given liquid and for a constant external pressure , the pressure inside will depend only on the height and for this reason, all points of the liquid that are at the same level support the same pressure.

## Applications

Some of the applications in which we can observe the use of hydrostatics are the following:

Hydrostatics is used for example in the system of a hydraulic jack in which there are two pistons. Force is applied to the small plunger to create pressure in the fluid, and that same pressure is the same for the other plunger that has a larger area. So, to achieve equal pressures , the force must be greater, to be able to generate a large force with a small one and this is what allows lifting a car with only the strength of our arm.

In hydraulic brakes , movement of the brake pedal forces a piston to move in the cylinder which puts pressure on a fluid in front of the piston, forcing it to pass through the brake lines and into the wheel cylinders.

## Examples

Some examples of hydrostatics are:

• The hydraulic press.
• The flotation of a boat.
• The pressure exerted by the water in a tank on the taps.
•  The pressure supported by a person submerged in the sea.