remark 31.89 The Mach number and the regimes it separates

open in the book · parts/03-classical-mechanics/14-fluid-dynamics.tex:3079 · p. 1077

remark -- no derivation owed by its kind

Rests on

depends_on definition 31.51 The other similarity groups ¶
- depends_on phenomenon 31.49 Dynamical similarity ¶
  - depends_on theorem 31.37 The Navier–Stokes equations ¶
    - depends_on theorem 31.36 The Newtonian constitutive relation ¶
      - depends_on definition 31.32 Newtonian fluid; dynamic and kinematic viscosity ¶
      - depends_on proposition 31.9 Cauchy–Stokes decomposition ¶
      - proves proof ch:14-fluid-dynamics@proof-17 ¶
    - depends_on theorem 31.22 Euler's equations of motion ¶
      - depends_on definition 31.21 Ideal fluid ¶
      - depends_on lemma 31.11 Transport theorem for a material volume ¶
      - depends_on theorem 30.21 Cauchy's equation of motion ¶
      - proves proof ch:14-fluid-dynamics@proof-11 ¶
    - proves proof ch:14-fluid-dynamics@proof-18 ¶
  - proves proof ch:14-fluid-dynamics@proof-24 ¶
- depends_on theorem D.2 Buckingham's $\Pi$ theorem ¶
  - depends_on equation D.3 eq:E-kernel-condition ¶
  - proves proof app:E-dimensionless@proof-1 ¶
depends_on phenomenon 31.88 Sound travels at the adiabatic speed ¶
- depends_on theorem 31.12 Conservation of mass ¶
  - depends_on lemma 31.11 Transport theorem for a material volume ¶ ↺
  - proves proof ch:14-fluid-dynamics@proof-5 ¶
- depends_on theorem 31.22 Euler's equations of motion ¶ ↺
- proves proof ch:14-fluid-dynamics@proof-44 ¶

Supports

depends_on phenomenon 31.93 The Mach cone ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	The other similarity groups	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:3093
`depends_on`	→	Sound travels at the adiabatic speed	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:3093
`depends_on`	←	The Mach cone	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:3185