phenomenon 31.53 Transition to turbulence in a pipe

open in the book · parts/03-classical-mechanics/14-fluid-dynamics.tex:1582 · p. 1059

phenomenon-tested: no experiment declares a \tests edge to it and it is not listed in untested.txt

Rests on

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 definition 31.1 Fluid ¶
      - depends_on definition 31.8 Rate of strain and vorticity ¶
    - depends_on proposition 31.9 Cauchy–Stokes decomposition ¶
      - depends_on definition 31.8 Rate of strain and vorticity ¶ ↺
      - proves proof ch:14-fluid-dynamics@proof-3 ¶
    - 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 definition 31.1 Fluid ¶ ↺
    - depends_on lemma 31.11 Transport theorem for a material volume ¶
      - depends_on definition 31.4 Material derivative ¶
      - depends_on theorem 7.133 Gauss ¶
      - proves proof ch:14-fluid-dynamics@proof-4 ¶
    - depends_on theorem 30.21 Cauchy's equation of motion ¶
      - depends_on theorem 7.133 Gauss ¶ ↺
      - depends_on theorem 30.18 Cauchy: the stress tensor exists ¶
      - proves proof ch:13-continuum-elasticity@proof-9 ¶
    - 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

depends_on remark 31.54 This one is not a gap in the writing ¶

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:1595
`cites` (evidence)	→	An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels	derived	parts/03-classical-mechanics/14-fluid-dynamics.tex:1591
`cites` (evidence)	→	An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels	derived	parts/03-classical-mechanics/14-fluid-dynamics.tex:1595
`depends_on`	→	The fourth-power law of pipe flow	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:1596
`depends_on`	→	Dynamical similarity	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:1596
`depends_on`	←	This one is not a gap in the writing	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:1695
`proves`	←	ch:14-fluid-dynamics@proof-25	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:1599