Sl.No.

Topics

Hours

1.

Introduction

1

2.

Vectors and tensors.

3

3.

Tensor calculus.

2

4.

Kinematics.

2

5.

The deformation tensor and its components.

3

6.

Leibniz rule. Mass conservation equation.

1

7.

Momentum conservation equation. Stress tensor.

2

8.

Angular momentum conservation. Symmetry of stress tensor.

1

9.

Energy conservation equation. Viscous dissipation.

1

10.

Constitutive relations for the stress tensor. Navier-Stokes equations.

3

11.

Viscous flows. Multipole expansions.

3

12.

Viscous flows. Lubrication theory

2

13.

Potential flow. Bernoulli equation.

2

14.

Two-dimensional potential flow. Complex variables.

3

15.

Boundary layer theory.

4

16.

Vorticity dynamics.

2

17.

Turbulence cascade. Spectral analysis. Turbulent flow in a channel.

4

18.

Summary

1

Total

40