example 31.15 The stream function of a plane flow

open in the book · parts/03-classical-mechanics/14-fluid-dynamics.tex:385 · p. 1045

example -- no derivation owed by its kind

Rests on

depends_on corollary 31.13 Incompressible flow ¶
- depends_on theorem 31.12 Conservation of mass ¶
  - 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 ¶
  - proves proof ch:14-fluid-dynamics@proof-5 ¶
- proves proof ch:14-fluid-dynamics@proof-6 ¶
depends_on proposition 7.136 Properties of conservative fields ¶
- depends_on definition 7.135 Conservative field ¶
  - depends_on equation 7.124 eq:ana-nabla-gradient ¶ ↺
- depends_on proposition 7.104 Chain rule in several variables ¶ ↺
- depends_on theorem 7.132 Stokes ¶
  - depends_on proposition 7.104 Chain rule in several variables ¶ ↺
  - depends_on proposition 7.105 Clairaut–Schwarz ¶
    - depends_on definition 7.20 Continuity at a point ¶
      - depends_on definition 7.16 Limit ¶
      - depends_on equation 7.7 eq:ana-limit-left ¶
      - depends_on equation 7.5 eq:ana-limit-right ¶
    - depends_on theorem 7.35 Mean value theorem ¶
      - depends_on proposition 7.29 Linearity ¶
      - depends_on theorem 7.34 Rolle ¶
      - proves proof ch:05-real-analysis@proof-19 ¶
    - proves proof ch:05-real-analysis@proof-64 ¶
  - depends_on theorem 7.131 Green ¶
    - 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-77 ¶
  - proves proof ch:05-real-analysis@proof-78 ¶
- proves proof ch:05-real-analysis@proof-80 ¶

Supports

depends_on definition A.715 Stokes stream function ¶
- depends_on lemma A.716 The creeping-flow equation for $\psi$ ¶
  - depends_on lemma A.717 The radial solution ¶
    - depends_on theorem A.718 Stokes' drag law with its coefficient ¶

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`	→	Incompressible flow	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:403
`depends_on`	→	Properties of conservative fields	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:403
`depends_on`	←	Stokes stream function	declared	appendices/A-long-proofs.tex:34611