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Fluids Mechanics

The study of fluids and the forces acting on them is termed as fluid mechanics. The fluid may be a gas, liquid or even plasma. The study of fluid mechanics is divided into

1. Fluid statistics- the study of fluids at rest.

2. Fluid kinematics-the study of fluids which are in motion, and

3. Fluid dynamics- It comprises the study of effect of forces on the fluid motion.

The fluid dynamics is the modeling of matter based on macroscopic viewpoint, rather than a microscopic viewpoint and the subject does the matter modeling without using the information that the matter is made up of atoms. The fluid mechanics discipline can be said to be an active field of research which has many unsolved and partly solved problems to its credit. The subject can also be very mathematically complex. Many a times, numerical methods are used by using a computer for solving the problems. For solving fluid mechanics problem of higher complexity, computational fluid dynamics is used, which is relatively very modern discipline of study. The particle image velocimetry takes the advantage of the highly visual nature of fluid flow and visualizes and analyzises fluid flow experimentally.

A brief history

The subject of fluid dynamics was born in the times of ancient Greece, when the famous scientist Archimedes investigated the fluid statistics concept and gave the law of buoyancy, which is also known as the Archimedes principle. Some other great names associated with fluid mechanics and dynamics are those of Isaac Newton (concept of viscosity), Leonardo da Vinci (experiment and observation), Blaise Pascal (hydro statistics) and Evangelista Torrilli (invention of barometer). Later, Daniel Bernoulli introduced mathematical fluid dynamics in his book Hydrodynamica in 1738. Some other prominent mathematicians like Leonhard Euler, Lagrange, Poisson and Laplace further analyzed the in viscid flow. The engineers which explored the viscous flow were Gotthilf Heinrich Ludwig Hagen and Poiseuilee. The navier strokes equations provided mathematical justification, which were given by George Gabriel strokes and Claude Louis Navier. The investigation of boundary layers was done by Theodore on Karman and Ludwig Prandt. Some other scientists which contributed to the understanding of fluid viscosity were Andrei Kolmogorov, Osborne Reynolds and Geoffrey Ingram Taylor.

Fluid mechanics and its relationship to continuum mechanics

Fluid mechanics can also be considered a sub discipline of continuum mechanics, which is the study of physics of the continuous materials. The other branch of continuum mechanics is solid mechanics, which is the study of physics of continuous materials which have a defined rest shape. These are further divided into elasticity, plasticity and theology along with the division of Newtonian and non Newtonian fluid.

The Assumptions in fluid mechanics

Like all other mathematical models dealing with real world, fluid mechanics also makes some basic assumptions regarding the materials which are studied. For these assumptions to be holed true, they are to be turned into satisfactory equations. We can consider an incompressible fluid in there dimension as an example. For the assumption to be true that mass is conserved, the mass passing form outside to inside of the surface must be the same as the rate of the mass which is passing in opposite direction in any closed and fixed surface. This also implies that the mass within the outside and inside boundaries of a system remains constant. The discipline of fluid mechanics believes that fluid obeys these following laws-

1. Conservation of mass

2. Conservation of momentum

3. Conservation of energy

4. The continuum hypothesis

The fluid is also assumed incompressible, which means that the density of fluid does not change.

The continuum hypotheses

Though the fluid is composed of molecules that are in constant collision with each other and with the sold objects, the continuum assumption believes the fluid to be continuous. Therefore, at infinitely small points, the properties of the fluid such as temperature, pressure, viscosity etc are considered to be well defending. It ignores the fact that the fluid is made of discrete molecules. It also assumes that the properties are moving continuously form one point to another and they also form the average values contained in the REV. The assumptions of the continuum hypothesis are the same as the approximations of the planets by the point particles in the subject of celestial mechanics, both of which give approximate solutions.

Newtonian and non Newtonian fluids

The fluid which has shear stress in linear proportionality of the velocity gradient which is in a direction which is perpendicular to the plane of shear is termed as a Newtonian fluid. Therefore, the fluid flows regardless of the direction of the flow. In contrast, the non Newtonian fluid leaves a hole behind.