phenomenon 31.18 Archimedes' principle

open in the book · parts/03-classical-mechanics/14-fluid-dynamics.tex:465 · p. 1046

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

Rests on

depends_on proposition 31.16 Hydrostatic balance ¶
- depends_on definition 31.1 Fluid ¶
  - depends_on theorem 30.18 Cauchy: the stress tensor exists ¶
    - depends_on definition 30.17 Traction ¶
      - depends_on definition 7.126 Line and surface integrals ¶
      - depends_on definition 30.2 Representative volume element; continuum field ¶
    - depends_on definition 13.5 Tensor under orthogonal transformations ¶
      - depends_on definition 13.4 Orthogonal coordinate transformation ¶
    - proves proof ch:13-continuum-elasticity@proof-7 ¶
- depends_on theorem 30.21 Cauchy's equation of motion ¶
  - depends_on theorem 7.133 Gauss ¶
    - depends_on definition 7.127 Simple regions ¶
      - depends_on definition 7.98 Functions of class $C^{1}$ ¶
      - depends_on definition 6.9 Compact set ¶
    - depends_on remark 7.128 What the derivations below take as given ¶
      - depends_on definition 7.125 Multiple integral ¶
      - depends_on theorem 7.40 Continuous functions are integrable ¶
      - depends_on theorem 7.25 Heine–Cantor: uniform continuity ¶
    - depends_on theorem 7.43 Fundamental theorem of calculus, II ¶
      - depends_on definition 7.41 Antiderivative ¶
      - depends_on theorem 7.42 Fundamental theorem of calculus, I ¶
      - proves proof ch:05-real-analysis@proof-25 ¶
    - proves proof ch:05-real-analysis@proof-79 ¶
  - 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-7 ¶
proves proof ch:14-fluid-dynamics@proof-9 ¶

Supports

depends_on example 31.46 Terminal velocity, and Millikan's droplets ¶

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`	→	The Works of Archimedes	derived	parts/03-classical-mechanics/14-fluid-dynamics.tex:476
`depends_on`	→	Hydrostatic balance	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:477
`depends_on`	←	Terminal velocity, and Millikan's droplets	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:1394
`proves`	←	ch:14-fluid-dynamics@proof-9	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:480