1. Fluid dynamical equations (Navier-Stokes equations)

2. Fluid dynamical equations (Navier-Stokes equations) Dimensional reduction: from QM to Boltzmann eq. to the fluid equations Continuum hypothesis: d T

3. Mass conservation (continuity equation)

4. Mass conservation (continuity equation)

5. Incompressible fluid

6. Conservation of linear momentum (Navier-Stokes equations)

7. stress tensor for surface forces commons.wikimedia.org/ wiki/File:Stress_tensor.png The stress tensor is symmetric!

9. constitutive equation (relationship between stress and strain) for a Newtonian fluid (with the Stokes assumption)

10. Conservation of linear momentum (Navier-Stokes equations)

11. Thermodynamic equation: first principle of Thermodynamics

12. Till now:

13. Equations of state: Perfect gas (e.g., dry air)

15. Fluid dynamical eqns. for a perfect gas

16. The static solution

17. Adiabatic processes

18. Static stability of a perfect gas (adiabatic processes)

19. Neutral stability of a perfect gas (adiabatic processes)

20. For a general, non adiabatic process Relationship between potential temperature and entropy

21. Fluid dynamical eqns. for a perfect gas

23. The Boussinesq approximation (adiabatic process, ideal fluid)

24. The Boussinesq approximation (adiabatic process, ideal fluid)

25. The Boussinesq approximation

26. (adiabatic process, ideal fluid)

27. The Boussinesq approximation (real fluid)

28. The Boussinesq approximation (real fluid)

29. The Boussinesq approximation (real fluid)

30. The Boussinesq approximation (real fluid)