What is fluid mechanics 

Fluid mechanics is the branch of physics which deals with the mechanics of fluids. Fluid are in the form of  liquids, gases, and plasmas. Fluid mechanics study their properties and force on it. Fluid mechanics  has applications in disciplines, including civil, mechanical, astrophysics chemical engineering , biomedical engineering, oceanography, geophysics, meteorology and biology.use computer.

Fluid mechanics classified into two type. one is fluid statics which study of fluids at rest condition. Anonther is fluid dynamics,which study of the effect of forces on fluid motion. Fluid mechanics is a branch of continuum mechanics. Continuum mechanics is  a subject which models matter without using the information that it is made out of atoms; that is, it models matter analyze  from a macroscopic point rather than from microscopic. In fluid mechanics,  fluid dynamics is an active field to research, typically mathematically method. Many problems are partly or wholly unsolved. To solve this type of problem are numerical methods is used by using computers. This modern discipline  called as computational fluid dynamics (CFD), is devoted to this approach. 

Content 
1) Main branches of fluid mechanics 
2) History of fluid mechanics 
3) Assumptions
4) Navier stroke equations
5) Inviscid and viscous fluids 

6) Newtonian and non-Newtonian fluids

Main branches of fluid mechanics 

Fluid statics 

Fluid statics or hydrostatics is the branch of fluid mechanics which studies fluids at rest conditions. The study of fluid at rest conditions is in stable equilibrium and is contrasted with fluid dynamics means the study of fluids in motion is called as fluid dynamics. By using Hydrostatics principle,  many phenomena of everyday life is explained by physically , e.g why atmospheric pressure changes with altitude, why wood and oil float on water, and why the surface of water is always level whatever the shape of its container. Hydrostatics is fundamental to hydraulics, e.g the engineering of equipment for storing, transporting and using fluids. Fluid statics is also used in geophysics and astrophysics. e.g, in understanding plate tectonics and anomalies in the Earth's gravitational field. It is also used in meteorology medicine (e.g in the context of blood pressure) and many other fields.

Fluid dynamics

Fluid dynamics is a branch of fluid mechanics that deals with fluid motion, to study science of liquids and gases in motion condition. Fluid dynamics gave a systematic structure to the fluid, which underlies these practical disciplines.  Empirical and semi-empirical laws are used to flow measurement during motions and this laws used to solve practical problems.  fluid dynamics used to calculating various properties of the fluid, such as velocity, pressure, density, and temperature, as functions of space and time. It has several branches itself, which is aerodynamics,the study of air and other gases in motion and hydrodynamics, the study of liquids in motion. Fluid dynamics has lots of applications, and they are calculating forces and movements on aircraft, determining the mass flow rate of petroleum through pipelines, predicting evolving weather patterns, understanding nebulae in interstellar space and modeling explosions. Some fluid-dynamical principles are used in traffic engineering and crowd dynamics.

Histroy of fluid mechanics 

In earlier day of Greece, During the study of fluid mechanics , when Archimedes study on  fluid statics and buoyancy. He formulated his famous law known now as the Archimedes' principle, which was published in his work On Floating Bodies. Generally this law considered as first major work on fluid mechanics. After this, Rapid advancement in fluid mechanics began with Leonardo da Vinci, he is a observations and experiments. Evangelista Torricelli invented the barometer, Isaac Newton study viscosity of fluid and Blaise Pascal is researched on hydrostatics, and formulated Pascal's law, and this study was continued by Daniel Bernoulli with the introduction of mathematical fluid dynamics in Hydrodynamica (1739).

Inviscid flow was further research by various mathematicians e.g Jean le Rond d'Alembert, Joseph Louis Lagrange, Pierre-Simon Laplace, Siméon Denis Poisson and viscous flow was study by a multitude of engineers including Jean Léonard Marie Poiseuille and Gotthilf Hagen. Further mathematical justification was provided by Claude-Louis Navier and George Gabriel Stokes in the Navier–Stokes equations. Boundary layers were investigated by Ludwig Prandtl, Theodore von Kármán, while various scientists such as Osborne Reynolds, Andrey Kolmogorov, and Geoffrey Ingram Taylor advanced the understanding of fluid viscosity.

Assumptions

The assumptions inherent to a fluid mechanical is physical system can be explained in terms of mathematical equations. Fundamentally, every fluid of fluid mechanics mechanical system is assumed to obey the follownig assumptions such as

Conservation of mass

Conservation of energy

Conservation of momentum

The continuum assumption

For example, the assumption that mass is conserved means that for any fixed control volume e.g a spherical volume, enclosed by a control surface. The rate of change of the mass contained in that volume is equal to the rate at which mass is passing through the surface from outside to inside subtract the rate at which mass is passing from inside to outside. This can be expressed as an equation in integral form over the control volume.

The continuum assumption is an idealization assumptions in continuum mechanics. Under the condions which fluids can be treated as continuous, even though on a microscopic scale, they are composed of molecules.

 Under the certain continuum assumption, macroscopic properties are density, pressure, temperature, and bulk velocity are taken to be well-defined at infinitesimal volume elements, small in comparison to length scale of the system, but large in comparison to molecular length scale. Fluid properties can change continuously from one volume to another volume and  average values of the molecular properties. Continuum hypothesis can gives inaccurate results in applications such as supersonic speed flows, molecular flows on nano scale. These problems can not be solved by continuum hypothesis. But can be  solved using statistical mechanics.

To determine the continuum hypothesis applied or not, the Knudsen number defined as the ratio of the molecular mean free path to the characteristic length scale, is evaluated.  Knudsen numbers below 0.1 can be evaluated by using the continuum hypothesis, but statistical mechanics can be applied knudsen numbers  all ranges of fluids

Navier and Stokes equations

The Navier and Stokes equations named after Claude, Louis Navier and George Gabriel Stokes. These equations are differential equations that indicate the force balance at a given point in a fluid. For an incompressible fluid with vector velocity field , the Navier–Stokes equations are

Newton's equations of motion for particles and the Navier and Stokes equations denote changes in momentum or force in response to pressure and viscosity. Occasionally, body forces, like a gravitational force or Lorentz force are added to the equations.

Solutions of  Navier and Stokes equations for a given problem must be solved by using the help of calculus. By this equations, simplest cases can be solved exactly. These cases generally inform non-turbulent, steady flow in which the Reynolds number is small. More complex cases, specially those involving turbulence, e.g  global weather systems, aerodynamics, hydrodynamics and many others, solutions of the Navier and Stokes equations can currently only be found by the help of computers. This method is called as computational fluid dynamics

Inviscid and viscous fluids

fluids has no viscosity, these fluid called as inviscid fluid . An inviscid flow is an idealization, which has facilitates mathematical treatment. In fact, purely inviscid flows are only found to be realized in the case of superfluidity which has no viscosity. Otherwise, fluids are generally viscous, a property of the fluid that is often most important within a boundary layer near to a solid surface, where the flow must have no-slip condition at the solid. In some cases of fluid, the mathematics of a fluid mechanical system can be research by assuming that the fluid outside of boundary layers is inviscid, and then matching that solution into the thin laminar boundary layer.

For fluid flow over a porous boundary, velocity of the fluid can be change because of the free fluid and the fluid in the porous media, this conditon is related to the Beavers and Joseph condition. Further, this method is useful at low subsonic speeds to assume that gas is incompressible, that is, the density of the gas does not change even though the speed and static pressure change.

Newtonian and non-Newtonian fluids

A Newtonian fluid named after Isaac Newton.  Defined of Newtonian fluid is to be a fluid whose shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear. This definition means stress is directly proportional to the velocity gradient. E.g water is a Newtonian fluid. Important fluids, like water as well as most gases as a Newtonian fluid under normal conditions on Earth.

By contrast, stirring a non-Newtonian fluid can leave a hole behind. This will gradually fill up over time, this behavior is seen in materials such as pudding, oobleck, or sand although sand isn't strictly a fluid. Stirring a non-Newtonian fluid can cause the viscosity to decrease, so the fluid appears thinner e.g this is seen in non-drip paints. Many other types of non-Newtonian fluids, as they are defined to be something that fails to obey a particular property, e.g most fluids with long molecular chains can react in a non-Newtonian manner.

Another type of fluid is ideal and non-ideal fluids. An ideal fluid is non-viscous and  no resistance to a shearing force. An ideal fluid really does not exist,means that they are not present on Earth. But in some calculations, these fluids assumpted to solve a problem. E.g this is the flow far from solid surfaces. In many ohter cases, the viscous effects are concentrated near the solid boundaries such as in boundary layers while in regions of the flow field far away from the boundaries the viscous effects of solid can be neglected and the fluid there is treated as it were ideal flow. If the viscosity is neglected, these fluid called as viscous stress tensor.