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Gas dynamics

Also listed as: דינמיקת הגזים

Compressible and high-speed flow, where fluid mechanics and thermodynamics finally meet. If you want anything to do with propulsion or aerospace, this is not optional in practice.

Semester
Semester A
Weekly hours
4h
Counts as
Core: fluids
Interest areas
Aeronautics and space · Flow and thermal design

Comes after

  • Fluid mechanics 1
  • Thermodynamics 1

Opens up

What it covers

One-dimensional compressible flow

  • Speed of sound, Mach number, the flow regimes and what changes between them
  • Isentropic flow, stagnation properties, the area-velocity relation
  • Converging-diverging nozzles, choking, the full set of operating regimes
  • Flow with friction (Fanno) and with heat addition (Rayleigh)

Shocks and expansions

  • Normal shocks, Rankine–Hugoniot relations, moving shocks
  • Oblique shocks, the θ–β–M relation, weak and strong solutions
  • Prandtl–Meyer expansion, shock reflection and interaction, the shock polar
  • Quasi-one-dimensional flow, diffusers, supersonic inlets, wind tunnels

Unsteady and high-temperature effects

  • Unsteady one-dimensional wave motion and the shock tube
  • Method of characteristics for nozzle contour design
  • Transonic and hypersonic flow, high-temperature gas effects

Results worth carrying out

  • Speed of sound and stagnation temperature

    a=γRT,T0T=1+γ−12M2a = \sqrt{\gamma R T}, \qquad \frac{T_0}{T} = 1 + \frac{\gamma-1}{2}M^2

  • Area–Mach relation

    AA∗=1M[2γ+1(1+γ−12M2)]γ+12(γ−1)\frac{A}{A^*} = \frac{1}{M}\left[\frac{2}{\gamma+1}\left(1 + \frac{\gamma-1}{2}M^2\right)\right]^{\frac{\gamma+1}{2(\gamma-1)}}

  • θ–β–M relation, oblique shocks

    tan⁡θ=2cot⁡β M12sin⁡2β−1M12(γ+cos⁡2β)+2\tan\theta = 2\cot\beta\,\frac{M_1^2\sin^2\beta - 1}{M_1^2(\gamma + \cos 2\beta) + 2}

  • Prandtl–Meyer function

    ν(M)=γ+1γ−1arctan⁡γ−1γ+1(M2−1)−arctan⁡M2−1\nu(M) = \sqrt{\tfrac{\gamma+1}{\gamma-1}}\arctan\sqrt{\tfrac{\gamma-1}{\gamma+1}(M^2-1)} - \arctan\sqrt{M^2-1}

Figures worth knowing

  • T–s diagram with Fanno and Rayleigh lines
  • Nozzle pressure ratio against position for over- and under-expansion
  • θ–β–M chart
  • Shock polar
  • Schlieren images of oblique shocks and expansion fans
  • Shock-tube x–t diagram

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The topic outlines are not official syllabi. The university publishes a catalogue blurb per course, not lecture-by-lecture material, so each outline describes what a course of that name, at those hours, with those prerequisites teaches at engineering schools generally, cross-checked against the standard textbook for the subject. Treat it as an informed map, not as a transcript of the lectures.