phenomenon 31.25 Pressure falls where the flow speeds up

open in the book · parts/03-classical-mechanics/14-fluid-dynamics.tex:695 · p. 1049

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

Rests on

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-13 ¶

Supports

depends_on example 31.26 The Venturi meter ¶
depends_on remark 31.27 What the 1738 source contains ¶

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`	→	Hydrodynamica, sive de viribus et motibus fluidorum commentarii	derived	parts/03-classical-mechanics/14-fluid-dynamics.tex:703
`cites`	→	Principes généraux du mouvement des fluides	derived	parts/03-classical-mechanics/14-fluid-dynamics.tex:703
`cites`	→	Description d'une machine pour mesurer la vitesse des eaux courantes et le sillage des vaisseaux	derived	parts/03-classical-mechanics/14-fluid-dynamics.tex:707
`cites`	→	Recherches expérimentales sur le principe de la communication latérale du mouvement dans les fluides appliqué à l'explication de différens phénomènes hydrauliques	derived	parts/03-classical-mechanics/14-fluid-dynamics.tex:710
`depends_on`	→	Bernoulli	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:711
`depends_on`	←	The Venturi meter	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:762
`depends_on`	←	What the 1738 source contains	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:778
`proves`	←	ch:14-fluid-dynamics@proof-13	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:714