FLUID MECHANICS -1- INTRODUCTION

FLUID MECHANICS-1- INTRODUCTION

  1. Definition of a fluid

Fluid is a common name for a liquid, vapor and a gas.

 (a) Liquids

Liquids have definite volume but not definite shape. These do not fill the container fully. These are in-compressible and are heavy as compared to a gas.

 (b) Vapor

When liquid on heating changes phase at its boiling point, it is a vapor. It remains a vapor as long as degree of super  heat is ≤ to 500. No gas laws are applicable. Equations for vapors are highly complex. Therefore, tables and charts have been prepared for vapors in order to save time.

(c) Gases

However, gases do not have definite volume as well as definite shape because these fill the vessel completely in which these enter. These are compressible and light. Therefore study of liquid flow and gas flow differ distinctly.

2. Properties of a fluid

Properties Playing Prominent Role in the Study of Fluid Mechanics are
Weight plays a predominant role in the fluid statics.
Density and viscosity play predominant roles in fluid dynamics.
Vapor pressure play predominant role when dealing with Vacuum.
Surface tension plays an important role for both fluid at rest and in motion

in SMALL PASSAGES like Capillary tubes.
Principles of thermodynamics play predominant roles while dealing with the

compressible fluids (gases and vapors).

3. Fluid mechanics

There are two main branches of fluid mechanics.

  1. Fluid Statics: Which deals with fluids at rest. The resultant force is zero.

The resultant moment is zero.

  1. Fluid Dynamics: Which deals with fluids in motion.The resultant force

= mass x Acceleration= (Newton’s second law for accelerating bodies)

FURTHER BRANCHES OF Fluid Dynamics 

(a)    Fluid Kinematics: Which deals with geometry of motion without the forces

acting on the fluid. Geometry of motion means  velocity, acceleration and displacement of a fluid.

(b)   Fluid Kinetics: Which deals with velocity, acceleration and displacement of a fluid along

with forces acting on the fluid.

4. Practical applications of fluid mechanics

Practical applications of fluid mechanics are found in Mechanical engineering, chemical engineering, civil engineering, weather forecasting, renewable energy systems, computer engineering  and pharmaceutical industry.

5. Study approaches in fluid mechanics

Fluid mechanics is studied under two approaches, namely, differential vs integral and Lagrangian vs Eulerian.

6. Fluid flow

It is mass transfer process  which helps to calculate the size of a pump and  a pipeline for transferring fluids. Fluid flow  effects  rates of heat transfer, mass transfer and  reaction rates .

7. Laws of conservation

Fundamental laws governing the fluid flow are Conservation of Mass, Conservation of Energy and   Conservation of Linear Momentum, Newton’s Laws of motion , First and Second Laws of Thermodynamics.

8. Equations in fluid mechanics

The three conservation laws will form the basis for developing Continuity Equation, Bernoulli’s Equation, and the Momentum Equation. Firstly these will be derived for  the Ideal fluids and then it will be extended  to the Real Fluids. As we know that a solid body under shear stress gets distorted but comes to original shape on release of the stress. However a fluid will continue to deform as long as the shearing stress is acting and will not come back to the original position on the release of shear stress.

STUDY APPROACHES

There are two approaches for studying fluid mechanics.

1. Langrangian Method
It considers the movement of a single FLUID PARTICLE. It studies the path taken

by the fluid particle, changes in velocity, acceleration, density, pressure etc. of the

fluid particle. The resulting equations are tedious, complex and cumbersome.

These are difficult to solve. SO THIS METHOD IS NOT IN USE.

Eulerian Method
This considers the path, velocity, acceleration, density, pressure etc. at a SPACE POINT

in the FLUID FLOW. This method makes the study simple and resulting equations are

simple and easy to understand. IT IS THE COMMONLY USED METHOD OF

ANALYSIS IN FLUID DYNAMICS.

In this velocity components are taken as follows:

u = f(x, y, z, t)

v = f(x, y, z, t)

w = f(x, y, z, t)
The components of acceleration etc. can be found by use of partial derivatives.