Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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SECTIO OCTAVA.
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<
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<
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foraminum mox dicendorum ubique amplitudinis & </
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<
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in duas diſtinctum cavitates inter ſe communicantes, mediante foramine G:
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</
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<
s
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xml:space
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">habeat præterea vas iſtud in infima ſui parte aliud foramen D: </
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<
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xml:space
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">deinde pona-
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tur vas aquâ plenum uſque in P Q, ſic ut cavitas inferior C E F R tota ſit hu-
<
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mido repleta, atque inſuper diaphragmati ſuperjaceat pars altera P Q F E. </
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<
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">His
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poſitis, fluidoque jam moveri incipiente, quæritur velocitas aquæ per foramen
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D in aërem effluentis velaltitudo genitri
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x hujus velocitatis.</
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<
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<
s
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">Fuerit altitudo ſuperficiei P Q ſupra foramen D = x, amplitudo fo-
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raminis D = n, alteriusque G = m. </
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<
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">Perſpicuum autem eſt aſcenſum potentia-
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lem cujuſvis guttæ per G transfluentis nihil promovere effluxum per D, totum-
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que impendi in motum aliquem excitandum inteſtinum, qui mox abſorbetur
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ſine alio effectu: </
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<
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">neceſſe igitur eſt ut ſingulis momentis motus generetur no-
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vus in particulis foramen G tranſeuntibus, non minus atque in particulis per
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D effiuentibus. </
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<
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">Sed ſi aſcenſus potentialis guttulæ per D effluentis dicatur v, id
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eſt, ſi aqua exilire ponatur per D velocitate, cujus altitudo genitrix ſit v, erit
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ſimilis altitudo ratione guttulæ mole ſua priori æqualis, per G eodem tempo-
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re transfluentis {nnv/mm}. </
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<
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">Multiplicatis iſtis aſcenſibus potentialibus per maſſam, quam
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æqualem habent, quamque vocabo M, erit aggregatum productorum =
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Mv + {Mnnv/mm}. </
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<
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">Et cum ob infinitam amplitudinem vaſis alius motus non
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generetur, erit præfatum aggregatum (per reg. </
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<
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maſſa omnis aquæ in ejusdem deſcenſum actualem. </
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">At vero ſi maſſa omnis aquæ
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dicatur μ, erit (per § 7. </
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fluit = {Mx/μ}, ita ut productum commune ſit = M x. </
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<
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Mv + {Mnnv/mm} = Mx, ſive v = {mmx/nn + mm}. </
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<
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<
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