The continuum hypothesis. Definition of thermodynamic properties. Gas models.
Fluid kinematics. Eulerian and Lagrangian coordinates. Local and material derivative. The Reynolds transport theorem.
Continuity equation. Momentum equation and definition of the stress tensor. Energy equation. First thermodynamic principle. The Bernoulli¿s principle.
Fluid statics. Stevino¿s law. Hydrostatics. Forces on immersed bodies.
Non-dimensional version of the Navier-Stokes equations. The Buckingham PI theorem. Relevant non-dimensional numbers in fluid mechanics.
Boundary Layers
Irrotational motion. Velocity potential. Stream function. Plane potential flow. The complex potential. Superposition of elementary solutions. Flow over a cylinder.
The Mach number. Flow regimes. Total thermofluiddynamic properties.
Quasi-steady quasi-1D flow. Propagation speed of small pressure disturbs. Steady isentropic flow in ducts with slowly variable area.
Steady and unsteady normal shock waves. Oblique shock waves. Expansion waves: the Prandtl-Meyer relation.
Flow in converging nozzles and in converging-diverging nozzles.
Introduction to fluid dynamic stability. Kelvin-Helmholtz, Rayleigh-Taylor and Richtmyer-Meshkov instability.
