2. Faster Ways to Develop Balancing Skills for Omni Present & Non Countable Systems …… P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Pedagogy of Advanced Fluid Mechanics

3. Now I think hydrodynamics is to be the root of all physical science, and is at present second to none in the beauty of its mathematics. William Thomson (Lord Kelvin) 1824 --1907) You are not educated until you know the Second Law of Thermodynamics.

4. The Greatest Dispute of Understanding a Concept !!!! The incomparable Newton's Principia Mathematica was published in 1687. Around a century and half after this, first principles of Real life Fluid Mechanics started emerging: Major contributors: French engineer: C. L. M. H. Navier in 1823, Cauchy in 1828, Poisson in 1829, Saint Venant in 1843, and Irish scientist George G. Stoke: in 1845. There is always an easy solution to every human problem neat, plausible and wrong. (Henry Louis Mencken, 1880±1956)

5. The Law of Learning one fourth from the teacher, one fourth from own intelligence, one fourth from classmates, and one fourth only with time. Mahabharath

6. The Greatest Agreement With very few exceptions, the Navier-Stokes equations provide an excellent model for both laminar and turbulent flows. The anticipated paradigm shift in fluid mechanics centers around the ability today as well as tomorrow of computers to numerically integrate those equations. We therefore need to recall (Realize) the equations of fluid motion in their entirety.

7. Advanced Fluid Mechanics for Post Graduate Students Correctly balancing the physics and mathematics is the important educational aim. By pushing it to extremes one may end up in a course of descriptive presentation, rules of thumb and table or graph readings fit for conventional routine jobs only. It is then far from what one might expect from a graduate engineering course. On the other hand, little application and a very big mathematical apparatus may feature a kind of theoretical physics which should not be the goal when training Thermal Scientists/Engineers.

8. The Role of Mathematics in Learning Fluid Flows by Mechanical Engineers Fluid Flows - over and above its "physics" side offers an excellent opportunity to use mathematics. Fluid Flow is a best means even to clear the students' only formal understanding of the higher mathematical apparatus. The mathematical side of Advanced Fluid Mechanics is highly valuable due to; the frequent use of mathematics, the construction of mathematical models, is also an engineer's task. The fast increase of the subject matter in Fluid Flows on one hand, and the limited, in some cases even decreasing time available for teaching it, calls for the more mathematics.

9. Educational Aim of Learning Advanced Fluid Mechanics To demonstrate when and how deep an engineer is bound to dive into the problem, where he should use exact mathematical methods and where approximations. To use the proper numerical apparatus, a pocket or desk calculator if a calculator is justified, or a thoroughly checked computer program if the problem requires it. To offer ample opportunities and utilise them consciously.

10. Syllabus Introduction. Field theory, tensor algebra and calculus. Reynolds transport theorem. Constitutive relations and the Navier Stokes equation for Newtonian fluids. Inviscid flows. Analytical solutions of the transient and steady Navier Stokes equations for incompressible viscous flows. Boundary layer theory. Stability and transition to turbulence Derivation of RANS equations; turbulent shear flows. Compressible Flows. Special topics.

11. Books Fluid Mechanics for Engineers, A Graduate Textbook, Meinhard T. Schobeiri, 2010. http://www.petronet.ir/documents/10180/2324299/Fluid_Mechanics _for_Engineers Advanced Fluid Mechanics, W. P. Graebel, 2007. www.engmatl.com/...engineering-mechanics/204-advanced-fluid- mechanics White, F.M. 1991 Viscous Fluid Flow (second edition), McGraw Hill. Boundary Layer Theory, H. Schlichting. Sherman, F.S. 1990 Viscous Flow. McGraw Hill. McCormack, P.S. & Crane, L.J. 1973 Physical Fluid Dynamics, Academic Press.

12. 21 st Century Made Fluid Mechanics as Universal Engineering Tool.

13. Fluid Flows in Transportation Sector

14. Environmental Fluid Flows

15. Weather & Fluid Flows

16. Biological Fluid Flows

17. Knowledge of Viscous Fluid Flow for Design of Artificial Heart Valves

18. Fluid Flows for Sports