lemma 31.67 Blasius' force formula

open in the book · parts/03-classical-mechanics/14-fluid-dynamics.tex:2105 · p. 1065

Rests on

depends_on theorem 8.6 Cauchy–Riemann equations ¶
- depends_on definition 7.98 Functions of class $C^{1}$ ¶
  - depends_on definition 7.20 Continuity at a point ¶
    - depends_on definition 7.16 Limit ¶
      - depends_on definition 7.2 Absolute value ¶
      - depends_on definition 7.9 Real function ¶
    - depends_on equation 7.7 eq:ana-limit-left ¶
    - depends_on equation 7.5 eq:ana-limit-right ¶
  - depends_on definition 7.97 Partial derivative; gradient ¶
    - depends_on definition 7.26 Derivative of a function at a point ¶
      - depends_on definition 7.16 Limit ¶ ↺
      - depends_on definition 7.9 Real function ¶ ↺
    - depends_on definition 5.15 Basis ¶
      - depends_on definition 5.12 Subspace generated by a set of vectors ¶
      - depends_on definition 5.14 Linear independence ¶
- depends_on equation 8.4 eq:cpx-derivative ¶
- proves proof ch:06-complex-analysis@proof-3 ¶
depends_on theorem 31.24 Bernoulli ¶
- depends_on equation 31.4 eq:fluid-lamb-identity ¶
- 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 theorem 30.18 Cauchy: the stress tensor exists ¶
  - 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-12 ¶
proves proof ch:14-fluid-dynamics@proof-31 ¶

Supports

depends_on theorem 31.68 Kutta–Joukowski ¶
- depends_on proposition 31.70 The lift-curve slope of a thin aerofoil ¶
- depends_on remark 31.69 The Kutta condition, and where the circulation comes from ¶
- depends_on theorem A.737 The lift-curve slope of the flat plate ¶

Neighborhood

Every logical edge within two steps of this node.

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partly declared
a check failed
not graded
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Edges

type	direction	node	provenance	where
`depends_on`	→	Cauchy–Riemann equations	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2114
`depends_on`	→	Bernoulli	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2114
`depends_on`	←	Kutta–Joukowski	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2158
`proves`	←	ch:14-fluid-dynamics@proof-31	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2117