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.
Well, in this reading, we’ll explore what fluid mechanic is, its applications, types, and branches
Let’s get started!
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 or 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 good examples of fluids. A fluid will offer no internal resistance to change in shape and they must take on the shape of their containers.
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 aircraft 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.
Historical Background of Fluid Mechanics
Fluid mechanics have played a very vital role in human life and will continue to have 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 16th century, the development of governing equations of fluid flow started.
In the 18th and 19th centuries, the conservation laws for mass, momentum, and energy were known in their most general form. In the 20th 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.
Related: What is a Pump? its Diagram and How it Works
Applications of Fluid Mechanics
With the vast majority of observations 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.
Despite the fact that a nonlinear field theory describes it and that fluid phenomena are simple to observe, it draws from almost all fields of expertise.
So, the applications of fluid mechanics include this expertise, including mathematicians, physicists, biologists, geologists, oceanographers, atmospheric scientists, and almost all kinds of engineers.
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.
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. Hydrostatic 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 hydrostatics include geophysics and astrophysics (for example, understanding plate tectonics and anomalies in the earth’s gravitational field).
Areas such as 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.
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.
Different Types of Fluid Flow
Below are the various types of fluid flow:
Steady and Unsteady Flow
A flow is said to be steady when its fluid characteristics such as density, velocity, and pressure at a point do not change with time. It can be mathematically expressed as:
Where V is the velocity of the fluid
P is the pressure of the fluid, and
J is the density of the fluid.
A flow can also be known to be unsteady when the fluid characteristics like velocity, pressure, and density at a point change with respect to time. It is mathematically expressed as:
Uniform and Non-uniform Flow
The uniform flow is a type of fluid flow in which the velocity of the flow at a given time does not change with respect to space (along the length direction of the flow). It can also mathematically express as:
On the other hand, non-uniform flow is a type of fluid flow in which its flow velocity at a given time changes with respect to space. Mathematically, a non-uniform flow can be expressed as:
Laminar and Turbulent Flow
Laminar types of fluid flow are flow in which their fluid particles move along a well-defined streamline or paths. This happens in a way all the streamlines are straight and parallel to each other. In this type of flow, fluid particles are said to move in laminas.
The layers in laminar flow glide smoothly over the adjacent layer. The flow is said to be laminar when the Reynolds number is more than 4000.
Nevertheless, turbulent flow is a type of flow in which the fluid particles move in a zig-zag manner. This zig-zag movement forms high turbulence and eddies, leading to high energy loss. The flow is turbulent when the Reynolds number is also greater than 4000.
Well, a fluid flow in a pipe that has a Reynolds number between 2000 and 4000 is said to be in a transition state. Now you can see laminar and turbulent flow in pipe flow is characterized base on Reynold number.
Compressible and Incompressible Flows
In a compressible flow, its fluid density changes from one point to another point. That is, density is not constant. For instance, J not constant.
On the other hand, incompressible flow is a type of flow in which the density of the fluid is constant from a point to another. i.e., liquids are generally incompressible and gases are compressible. J=constant. Where J is the density of the fluid.
Rotational and Irrotational Flows
A rotational flow is a type of flow in which the fluid particles rotate about their own axis while flowing along the streamlines. Irrotational flow occurs if the fluid particles do not rotate while flowing along the streamline about their own axis. Finally,
One-, Two-, and Three-Dimensional Flows
One dimensional fluid flow is a type of fluid flow in which its flow parameter like velocity is expressed as a function of time and one space coordinates. It can be express as,
u = f (x, y), v=0; w=0;
The velocity along y and z directions i.e., v and w are considered negligible.
Secondly, two-dimensional flow is a flow in which the velocity is a function of time and two rectangular space coordinates. It is considered to be negligible when the velocity flow along the third direction. That is,
u = f (x, y); v = g (x, y); w = 0;
Finally, three-dimensional flow is a kind of fluid flow in which the velocity is a function of time and three mutually perpendicular rectangular space coordinates (x, y, and z). that is,
u = f (x, y, z); v = g (x, y, z); w = h (x, y, z)
Types of Fluids
Below are the various types of fluid:
- Ideal fluid – these types of fluid cannot be compressed and its viscosity does not fall in the category of an ideal fluid. It is said to be imaginary, that is, the fluid doesn’t exist in reality.
- Real fluid – these fluids are real because they possess viscosity.
- Newtonian fluid – this is when a fluid obeys Newton’s law of viscosity.
- Non-Newtonian fluid – when fluid does not obey Newton’s law of viscosity.
- Ideal plastic fluid – these types of fluid are known when the shear stress is proportional to the velocity gradient and the shear stress is more than the yield value.
- Incompressible fluid – this is when the density of the fluid does not change with the application of external force.
- Compressible fluid – is when the density of the fluid changes with the application of external force.
The table below shows the density and viscosity of different types of fluids
| Types of fluid | Density | Viscosity |
| Ideal fluid | Constant | Zero |
| Real fluid | Variable | Non-zero |
| Newtonian fluid | Constant/ Variable | T=u(dudy) |
| Non-Newtonian fluid | Constant/ Variable | T≠u(dudy) |
| Incompressible fluid | Constant | Non-zero/ zero |
| Compressible fluid | Variable | Non-zero/ zero |
Related: What is Turbine? its Diagram and How it Works
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.
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.
