proposition 31.73 Separation requires an adverse pressure gradient

open in the book · parts/03-classical-mechanics/14-fluid-dynamics.tex:2317 · p. 1068

Rests on

depends_on theorem 31.71 Boundary-layer thickness ¶
- depends_on phenomenon 31.30 Steady ideal flow exerts no drag ¶
  - proves proof ch:14-fluid-dynamics@proof-15 ¶
  - proves proof ch:14-fluid-dynamics@prooflink-1 ¶
- 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-33 ¶
proves proof ch:14-fluid-dynamics@proof-34 ¶

Supports

depends_on remark 31.56 What of the drag curve is owed, and where it is paid ¶

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`	→	Boundary-layer thickness	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2328
`depends_on`	←	What of the drag curve is owed, and where it is paid	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:1789
`proves`	←	ch:14-fluid-dynamics@proof-34	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2331