Introduction to Fluid Mechanics

Mechanics studies the motion and deformation of material bodies under applied loads like forces and moments.

It involves loads, energy, motion, deformation and material properties. 

When the material is either in the liquid or gas phase it is called fluid mechanics. With fluid referring to both liquids and gases. 

The most basic differences between solids, liquids and gases are presented below:

Mechanics deals with both stationary and moving bodies under the influence of loads. 

• Statics  deals with bodies at rest. 

• Dynamics deals with bodies in motion.

Fluid mechanics deals with how fluids at rest (fluid statics) and in motion (fluid dynamics) behave.

• Gas dynamics studies compressible flow of gases with high density changes. 

• Aerodynamics is similar to gas dynamics, but also covers low speed flows. It focuses on air flow.

• Hydrodynamics studies liquids (incompressible flow) in motion. 

The Concept of Continuum

At the microscopic level fluids consist of molecules. However, in engineering we deal with the fluid on a macroscopic level and ignore the behavior of each individual molecule i.e. we treat the fluid as a whole, a continuum.

In Continuum it is assumed that the fluid and flow properties like density, velocity, pressure, temperature, etc. vary continuously throughout the fluid. 
In continuum, the smallest element of a fluid is NOT a fluid molecule, but rather a fluid particle, which contains enough number of molecules to make meaningful statistical averages.
The Knudsen Number can determine whether the Continuum Assumption is valid for any case.

Continuum is valid when Kn < 0.01

Dimensions and Units

In the MLT system, the basic dimensions are: Mass [M], Length [L], Time [T]. All other quantities are expressed in terms of these three.
For some problems, Temperature [𝜃] also serves as a basic dimension.
Equations should be dimensionally homogeneous, i.e. dimensions of the left and right sides should be the same.

Fundamental Flow and Fluid Properties

It is common to use pressure (p) and temperature (T) to fix the thermodynamic state. Then other properties can be expressed as a function of these two:

                                       𝜌=𝜌(𝑝,𝑇),       ℎ=ℎ(𝑝,𝑇),       𝜇=𝜇(𝑝,𝑇)