Fluid mechanics is a broad study of fluid behavior (liquids, gases, blood, and plasmas) at rest and in motion. It has a wide range of applications today, this field includes mechanical and chemical engineering, biological systems, and astrophysics. Fluid mechanics study particularly the forces that fluid produces.

Today you’ll get to know the definition, applications, branches, properties, historical background of fluid mechanics. You’ll also be exposed to the following:

- Fluid mechanics with continuum mechanics.
- Inviscid and viscous fluids.
- Newtonian versus non-Newtonian fluids. The equation of Newtonian fluid will also be discussed.

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Contents

## What is fluid mechanics?

Fluid mechanics can be defined as the study of the behavior of liquids and gases, most especially the forces that they produce. Just as mentioned in the introduction, fluid mechanics is the study of fluids at rest (fluid statics) and in motion (fluid dynamics). It can also be defined as a substance that continually deforms (flows) under applied shear stress. It deforms regardless of the magnitude of the applied stress.

Liquids, gases, plasmas, and to some extent, plastic solids can be a good example of fluids. A fluid will offer no internal resistance to change in shape and they must take on the shape of their containers.

The above image shows the behavior of liquids, gases, and plasma in a container.

Most scientific disciplines have shown interest in fluid mechanics. For instance, physicists study the flow of extremely high-temperature gases through magnetic fields. This occurs in a search for an acceptable method of harnessing the energy of nuclear fusion reactions. Engineers showed interest in fluid mechanics because of the forces that are produced by fluid which is used for practical purposes. Some examples include aerofoil design, jet propulsion, wind turbines, and hydraulic brakes. This is further explained.

You should understand that fluid mechanics is the study of fluids at rest and in motion. A fluid can be defined as a material that continually deforms under a constant load. Kinematic, stress, conservation, regulating, and constitutive are the five important terms that are useful in fluid mechanics problems. Well, these problems can vary depending on the choice of the system of interest and the volume of interest, which govern the simplification of vector quantities.

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## Historical background of fluid mechanics

Fluid mechanics have played a very vital role in human life and will continue to take this effect. This is why it has attracted many curious people. In ancient Greek history, systematic theoretical works were carried out on this issue. In the 16^{th} century, the development of governing equations of fluid flow started. In the 18^{th} and 19^{th} centuries, the conservation laws for mass, momentum, and energy were known in their most general form. In the 20^{th} century, developments were in theoretical, experimental, and recently numerical form. Solutions of the governing equations for special cases were provided in the theoretical field. The experimental methods have been employed to measure flow velocities and fluid properties. Using computers, the numerical treatment of fluid mechanical problems opened new perspectives in research. The common belief in the 21st century is that the activities will be most intensive in the development of new experimental and numerical tools. Also, application of those for developing new technologies.

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## Applications of fluid mechanics

With the vast majority observation today, life would have been impossible without fluids. This is to say, the atmosphere and oceans covering the planet are fluids. Fluid mechanics serve unlimited scientific and practical purposes. It draws almost all fields of expertise even though it is described by a nonlinear field theory and also because fluid phenomena are readily observed. So, the applications of fluid mechanics include this expertise including mathematicians, physicists, biologists, geologists, oceanographers, atmospheric scientists, and almost all kinds of engineering. These days, artists have been drawn to study, harness, and exploit fluid mechanics. This is used to create and test formal and computational techniques to better understand the natural world. It also attempts to improve the human condition.

The application of fluid mechanics involves transportation, materials processing and manufacturing, power generation and conversion, civil infrastructure, and food production.

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## Main branches of fluid mechanics

Below are the two main branches of fluid mechanics:

### Fluid statics:

This branch of fluid mechanics is also known as hydrostatics. It is a study of fluids at rest and it embraces the study of the conditions under which fluids are at rest in stable equilibrium. Hydrostatics fluid mechanics shows physical explanations for many phenomena of everyday life. This includes the reason why atmospheric pressure changes with altitude, why wood and oil float on water, and why the surface of the water is always level regardless of the shape of its container.

Hydrostatics is the basis for hydraulics, transporting, using fluid, and the engineering of equipment for storing. Some relevant aspects of hydrostatic include geophysics and astrophysics (for example, understanding plate tectonics and anomalies in the earth’s gravitational field), meteorology, medicine in an aspect of blood pressure, and many other areas of expertise.

### Fluid dynamics:

Fluid dynamics is a subdiscipline in fluid mechanics, dealing with fluid flow. That’s the science of liquids and gases in motion. It offers a systematic structure that reveals these practical disciplines, which embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The fluid dynamics problem has already been resolved. These involve calculating various properties of fluid, such as pressure, density, velocity, and temperature, as a function of space and time. This branch of fluid mechanics has several subdisciplines itself, such as aerodynamics, which is the study of air and other gases in motion. Hydrodynamics is another subdiscipline, which is the study of liquid in motion.

Just as earlier mention in the applications of fluid dynamics, it has a wide range of applications, including calculating force and movement on aircraft. It also determines the mass flow rate of petroleum through a pipeline, predicting evolving weather patterns, understanding nebulae in interstellar space, and modeling explosions. Finally, some fluid dynamics principles are used in traffic engineering and crowd dynamics.

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## Basic principles of fluids

Fluids are composed of discrete molecules; these molecules are so small and except in gases at very low pressures. The number of molecules per milliliter is so enormous that they need to be viewed as individual entities. In a liquid, known as liquid crystals, molecules are packed together in a way that makes the properties of the medium locally anisotropic. However, the majority of fluids including air and water are isotropic.

In fluid mechanics, the state of anisotropic fluids is described by defining their means mass per unit volume, or density (p), temperature (T), and their velocity (V) at every point in space. Also, the connection is between these macroscopic properties and the positions and velocities of individual molecules, having no direct use.

The difference between gases and liquids is very easy to perceive than to describe. But this still has to be examined. Molecules are sufficiently far apart to move almost independently of one another in gases. Gases tend to expand to fill any volume available to them. On the other hand, liquid molecules are more or less in contact and they cohere due to the short-range attractive forces between them. The molecules are moving too fast to settle down into the ordered arrays that are characteristic of solids. Even so, they can’t fly apart.

Although, liquid can exist as drops or as jets with free surfaces. They can even sit in beakers constrained only by gravity, in a way that samples of gas cannot. Such samples can evaporate with time as their molecules pick up with enough speed to escape across the free surface and are not replaced. The lifetime of liquid drops and jets is normally long enough for evaporation to be ignored.

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## Relationship of fluid mechanics to continuum mechanics

Fluid mechanics is a subdiscipline of continuum mechanics. Below is the list of subdisciplines concerning this field.

**Fluid mechanics** – this is the study of physics of continuous materials which deform when subjected to a force.

**Continuum mechanics** – the study of the physics of continuous materials.

**Solid mechanics** – the study of the physics of continuous materials with a defined rest shape.

**Rheology** – the study of materials with both solid and fluid characteristics.

**Elasticity** – describes materials that return to their rest shape after applied stresses are removed.

**Plasticity** – it describes that permanently deform after sufficient applied stress.

**Non-Newtonian fluids** – they do not undergo strain rates proportional to the applied shear stress.

**Newtonian fluids** – undergo strain rates proportional to the applied shear stress. This will be further explained.

Mechanically, fluid does not support shear stress, which is why at rest it has the shape of its containing vessel. A fluid at rest has no shear stress.

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## Inviscid and viscous fluids

An inviscid fluid has no viscosity, it is an idealization. That one facilitates mathematical treatment. A pure inviscid flow is realized in the case of superfluidity. Else, fluids are generally viscous. The mathematics of a fluid mechanical system can be treated by assuming the fluid outside the boundary layers is inviscid. The solution should be matched onto that for a thin laminar boundary layer.

## Newtonian and non-Newtonian fluids

The Newtonian fluid is named after Isaac Newton. It is defined as the fluid whose shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear. Meaning is that, regardless of acting force on a fluid, it continues to flow. Water is a good example of a Newtonian fluid because it continues to show fluid properties regardless of how much it is stirred or mixed.

A good example is the drag of a small object being moved slowly through the fluid is proportional to the force applied to the object. Important fluid like water and most gases behave to good approximation as a Newtonian fluid under normal conditions.

On our other hand, a non-Newtonian fluid can leave a hole when stirred. This will gradually fill up over time as it can occur in materials such as pudding, and oobleck. Stirring a non-Newtonian fluid can decrease the velocity of the fluid which makes it appear thinner. There are various types of non-Newtonian fluids out there. They can be defined as something that fails to obey a particular property. For example, almost all fluids with long molecular chains can react in a non-Newtonian way.

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## Conclusion

That is all for this post on fluid mechanics, where we give its definition, historical background, applications, branches, principles, and its relationship with continuum mechanics.

I hope you get a lot from this article, if so, kindly share it with other students. Thanks for reading. See you next time!