Introductory Fluid Mechanics - Topical (PHY-402.5)

Venue: Online
Class timings: 9 - 10:30 am on Mondays and Wednesdays
First meeting: 12th January 2021

Course description: Following is a course summary but is subject to change depending on students' interests:

1. Continuum formulation of fluid mechanics, limitations
2. Lagrangian and Eulerian perspectives 
3. Conservation of mass (the continuity equation) 
4. Similarity transforms 
5. Stream functions, Angular momentum, Velocity gradient tensor – Symmetric and Antisymmetric parts etc. 
6. Conservation of Momentum – Euler and Navier-Stokes Equations 
7. Dynamic similarity – Buckingham Pi theorem 
8. Kelvin’s Circulation theorem 
9. Couette and Poiseuille Flow 
10. Introduction to Turbulence – Scaling laws, and energy budget equation 
11. Fully developed turbulence – K41 hypothesis 
12. Singular Perturbation Theory 
13. Bernoulli’s function and principle 
14. Boundary layer theory 
15. Flow past a plate, Blasius equation 
16. Vortex Dynamics 
17. Use of complex techniques for inviscid, incompressible vortex and mass source induced velocity fields.
18. Method of images 
19. Potential flow past a cylinder 
20. Blasius theorem – Force and torque on a solid body in a fluid (inviscid, incompressible) 
21. Conformal Mapping 
22. Flow instabilities – Study of Linearized equations for stability 
23. Rayleigh Plateau instability 
24. Orr-Sommerfeld equation 
25. Benard Problem 
26. Taylor problem on centrifugal instability 
27. Reynolds-averaged Navier-Stokes Equations

Evaluation: Homeworks, one midterm, and one final exam.