theorem 31.71 Boundary-layer thickness

open in the book · parts/03-classical-mechanics/14-fluid-dynamics.tex:2249 · p. 1067

Rests on

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 theorem 30.18 Cauchy: the stress tensor exists ¶
    - depends_on definition 31.8 Rate of strain and vorticity ¶
      - depends_on definition 13.91 Symmetric and antisymmetric parts ¶
      - depends_on equation 7.126 eq:ana-nabla-curl ¶
  - 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 equation 7.124 eq:ana-nabla-gradient ¶
      - depends_on proposition 7.104 Chain rule in several variables ¶
      - proves proof ch:14-fluid-dynamics@proof-1 ¶
    - depends_on theorem 7.133 Gauss ¶
      - depends_on definition 7.127 Simple regions ¶
      - depends_on remark 7.128 What the derivations below take as given ¶
      - depends_on theorem 7.43 Fundamental theorem of calculus, II ¶
      - proves proof ch:05-real-analysis@proof-79 ¶
    - 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 ¶

Supports

depends_on proposition 31.73 Separation requires an adverse pressure gradient ¶
- depends_on remark 31.56 What of the drag curve is owed, and where it is paid ¶
depends_on remark 31.72 The Blasius solution and its numbers ¶

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)	→	Über Flüssigkeitsbewegung bei sehr kleiner Reibung	derived	parts/03-classical-mechanics/14-fluid-dynamics.tex:2261
`depends_on`	→	Steady ideal flow exerts no drag	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2262
`depends_on`	→	The Navier–Stokes equations	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2262
`depends_on`	←	Separation requires an adverse pressure gradient	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2328
`depends_on`	←	The Blasius solution and its numbers	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2314
`proves`	←	ch:14-fluid-dynamics@proof-33	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2265