Lecture Timeline · PC316
Fluid Mechanics in teaching order — the course follows the ten chapters of the lecture notes across semester 2.
| Chapter | Topics | Wiki pages |
|---|---|---|
| 1 · Introduction | Continuum hypothesis, what is a fluid | What is a fluid? |
| 2 · Fluid statics | Pressure, hydrostatics, buoyancy, submerged surfaces, surface tension | Pressure · Hydrostatic equilibrium · Buoyancy · Forces on surfaces |
| 3 · Fluid kinematics | Rigid-body motion, Eulerian/Lagrangian, material derivative, RTT, Bernoulli | Rigid-body motion · Eulerian vs Lagrangian · Material derivative · Reynolds transport theorem · Bernoulli |
| 4 · Inviscid flow | Continuity, Euler's equation, potential flow, conformal maps | Continuity (eq.) · Euler (eq.) · Potential flow · Conformal mapping — 🔬 Potential-flow builder |
| 5 · Viscous flow | Viscosity, Navier–Stokes, exact solutions | Viscosity · Navier–Stokes (eq.) · Couette · Poiseuille |
| 6 · Dimensional analysis | Scaling, Buckingham Pi, Reynolds number, Planck units | Dimensional analysis · Buckingham Pi · Reynolds number |
| 7 · Jumps & shocks | Characteristics, hydraulic jump, Rankine–Hugoniot, entropy jump, Sedov–Taylor | Shock waves · Rankine–Hugoniot (eq.) · Blast waves |
| 8 · Vortex dynamics | Vorticity, circulation & Kelvin, Helmholtz theorems, vorticity equation, Rankine vortex, point vortices, wingtip vortices | Vorticity · Circulation & Kelvin · Helmholtz theorems · Vorticity equation · Rankine vortex · Point vortices · Wingtip vortices — 🔬 Point vortex sandbox |
| 9 · Hydrodynamic instabilities | Stability analysis, Kelvin–Helmholtz, Rayleigh–Taylor | Hydrodynamic stability · Kelvin–Helmholtz · Rayleigh–Taylor — 🔬 KH billow tank |
| 10 · Turbulence | Energy cascade, Kolmogorov, RANS, TKE budget | Turbulence · Energy cascade · Reynolds averaging · TKE budget (eq.) — 🔬 Energy cascade sandbox |
🔬 = an interactive widget covers this chapter. See all four in Simulations.
Where the vorticity thread leads
Chapter 8 is the hinge of the course. Kelvin's theorem is the fluid twin of the frozen-in theorem in plasma physics; vortex stretching is the engine that makes Chapter 10's cascade run; and the vortex sheet of Chapter 9's Kelvin–Helmholtz instability is just a concentrated sheet of the vorticity defined here.