Bernoulli, Daniel - Hydrodynamica, sive De viribus et motibus fluidorum commentarii

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5743SECTIO TERTIA. (1 - {mm/nn})vdξ + ξdv = - xdξ
cujus integralis, quod patet multiplicatis terminis per ξ - {mm/nn} hæc eſt
v = ξ{mm/nn} - 1 ſ - xξ- {mm/nn} dξ.
Fuerit v. gr. canalis rectus & ita inclinatus verſus horizontem, ut ſinus anguli
intercepti inter utrumque ſit ad ſinum totum ut 1 ad g, erit ξ = gx; unde
v = {nna/2nn - mm} (({a/x}){nn - mm/nn} - {x/a})
quæ æquatio cum non differat ab æquatione §. 13. pro Cylindris verticalibus
data, ſequitur in utroque caſu velocitates aquæ easdem eſſe, poſtquam deſ-
cenſus verticales ſuperficiei aquæ iidem ſunt: Igitur accelerationes in locis
homologis utrobique ſimiles ſunt ratione altitudinum verticalium, & hoc tan-
tum diſcriminis intercedit, quod in canali inclinato lentius fiant, idque in
ratione ut 1 ad g: facile igitur ſenſibus percipi poterunt hæ accelerationes in
canalibus valde inclinatis, quæ in verticalibus ob nimiam mutationum celeri-
tatem non poſſunt. Cœterum patet per ſe ex eo, quod frictiones à longitu-
dine tubi augeantur, non poſſe non velocitates inde diminui, ad quod ani-
mum advertent ii, quibus experimenta hâc de re inſtituere animus erit.

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