remark 31.54 This one is not a gap in the writing

open in the book · parts/03-classical-mechanics/14-fluid-dynamics.tex:1673 · p. 1060

remark -- no derivation owed by its kind

Rests on

depends_on phenomenon 31.53 Transition to turbulence in a pipe ¶
- depends_on phenomenon 31.41 The fourth-power law of pipe flow ¶
  - 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-21 ¶
- depends_on phenomenon 31.49 Dynamical similarity ¶
  - depends_on theorem 31.37 The Navier–Stokes equations ¶ ↺
  - proves proof ch:14-fluid-dynamics@proof-24 ¶
- proves proof ch:14-fluid-dynamics@proof-25 ¶

Supports

Nothing declares a dependency on this node yet.

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
`cites` (evidence)	→	The Onset of Turbulence in Pipe Flow	derived	parts/03-classical-mechanics/14-fluid-dynamics.tex:1688
`depends_on`	→	Transition to turbulence in a pipe	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:1695