IIT Kanpur Fluid Mechanics Notes

My sister is pursuing B.Tech Mechanical Engineering Course from IIT Kanpur. She wants important notes for Fluid Mechanics Topic. So will you please provide important notes for Fluid Mechanics Topic of B.Tech Mechanical Engineering Course of IIT Kanpur?

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As you want Important Notes for B.Tech Mechanical Engineering Course of IIT Kanpur, so here I am providing notes:

IIT Kanpur B.Tech Mechanical Engineering Course Fluid Mechanics Notes

Lecture 1 :
Definition of Stress
Consider a small area δA on the surface of a body (Fig. 1.1). The force acting on this area is δF
This force can be resolved into two perpendicular components

The component of force acting normal to the area called normal force and is denoted by δFn
The component of force acting along the plane of area is called tangential force and is denoted by δFt

When they are expressed as force per unit area they are called as normal stress and tangential stress respectively. The tangential stress is alsocalled shear stress

Definition of Fluid
A fluid is a substance that deforms continuously in the face of tangential or shear stress, irrespective of the magnitude of shear stress .This continuous deformation under the application of shear stress constitutes a flow.
In this connection fluid can also be defined as the state of matter that cannot sustain any shear stress.

If a shear stress τ is applied at any location in a fluid, the element 011' which is initially at rest, will move to 022', then to 033'. Further, it moves to 044' and continues to move in a similar fashion.

In other words, the tangential stress in a fluid body depends on velocity of deformation and vanishes as this velocity approaches zero. A good example is Newton's parallel plate experiment where dependence of shear force on the velocity of deformation was established

Distinction Between Solid and Fluid
Solid:
More Compact Structure
Attractive Forces between the molecules are larger therefore more closely packed
Solids can resist tangential stresses in static condition
Whenever a solid is subjected to shear stressIt undergoes a definite deformation α or breaks α is proportional to shear stress upto some limiting condition
Solid may regain partly or fully its original shape when the tangential stress is removed

Fluid:
Less Compact Structure
Attractive Forces between the molecules are smaller therefore more loosely packed
Fluids cannot resist tangential stresses in static condition.
Whenever a fluid is subjected to shear stress
No fixed deformation
Continious deformation takes placeuntil the shear stress is applied
A fluid can never regain its original shape, once it has been distorded by the shear stress

Concept of Continuum
The concept of continuum is a kind of idealization of the continuous description of matter where the properties of the matter are considered as continuous functions of space variables. Although any matter is composed of several molecules, the concept of continuum assumes a continuous distribution of mass within the matter or system with no empty space, instead of the actual conglomeration of separate molecules.

Describing a fluid flow quantitatively makes it necessary to assume that flow variables (pressure , velocity etc.) and fluid properties vary continuously from one point to another. Mathematical description of flow on this basis have proved to be reliable and treatment of fluid medium as a continuum has firmly become established. For example density at a point is normally defined as

Concept of Continuum - contd from previous slide
One of the factors considered important in determining the validity of continuum model is molecular density. It is the distance between the molecules which is characterised by mean free path ( λ ). It is calculated by finding statistical average distance the molecules travel between two successive collisions. If the mean free path is very small as compared with some characteristic length in the flow domain (i.e., the molecular density is very high) then the gas can be treated as a continuous medium. If the mean free path is large in comparison to some characteristic length, the gas cannot be considered continuous and it should be analysed by the molecular theory.

A dimensionless parameter known as Knudsen number, K n = λ / L, where λ is the mean free path and L is the characteristic length. It describes the degree of departure from continuum.
Usually when K n> 0.01, the concept of continuum does not hold good.

Beyond this critical range of Knudsen number, the flows are known as

slip flow (0.01 < K n < 0.1),

transition flow (0.1 < K n < 10) and

free-molecule flow (Kn > 10).

However, for the flow regimes considered in this course , K n is always less than 0.01 and it is usual to say that the fluid is a continuum.

Other factor which checks the validity of continuum is the elapsed time between collisions. The time should be small enough so that the random statistical description of molecular activity holds good.
In continuum approach, fluid properties such as density, viscosity, thermal conductivity, temperature, etc. can be expressed as continuous functions of space and time.