Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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SECTIO QUINTA.
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communi menſura idemque ponemus = θ, & </
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<
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echoid-s2848
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">mutabitur pro vaſis ſeu ca-
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nalibus cylindricis æquatio (α) in hanc
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t = {nθ/2√(mm - nn)} X log. </
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<
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xml:space
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">{m√a + √(mmv - nnv)/m√a - √(mmv - nnv)}
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altera vera ſignata (β) talis fit
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t = {nθ/2m} X log. </
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<
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echoid-s2850
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xml:space
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">{√a + √v/√a - √v},
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ex quarum utraque apparet, non poſſe non breviſſimo tempore aquas om-
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nem fere velocitatem acquirere, idque eo citius quo amplior eſt tubus,
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quo brevior, & </
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">quo magis verticalis: </
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<
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">Neque accelerationes ullo modo eſſe
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perceptibiles, niſi prælongi ſtatuantur aquæ ductus & </
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<
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tempore omnes fere accelerationum gradus percurri, quod utrumque nunc
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exemplo illuſtrabo.</
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<
s
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">(I) Quæritur tempus quo fluidum ex cylindro conſtanter pleno verticali,
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ſedecim pedes anglicos longo & </
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<
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">cujus diameter quintupla ſit diametri fo-
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raminis, velocitatem acquirit quæ debeatur altitudini {99/100}a, idque in hypo-
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theſi, ad quam æquatio ſecunda pertinet; </
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<
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xml:space
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">ſic eſt {n/m} = {1/25}, v = {99/100}a,
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b = a, unde tempus quod corpus inſumit cadendo libere per ſpatium {bb/a},
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ſeu θ = uni minuto ſecundo; </
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<
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<
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">id eſt, proxime no-
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næ parti unius minuti ſecundi, quod tempusculum utique imperceptibile
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eſt; </
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<
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">Cum vero tempus notabile aſſumitur, fiunt mutationes altitudinum v,
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inſenſibiles. </
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<
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">Si tempus ſimile (quo nempe velocitas pariter nonaginta no-
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vem centeſimis partibus altitudinis, quanta poſt tempus infinitum fit, debi-
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ta generetur) in prima hypotheſi quæratur, nempe tempus quo obtinetur
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v = {99/100} X ({mma/mm - nn}) reperitur illud præcedente paullulum majus,
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ſed exceſſu inſenſibili: </
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<
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">unde patet in hujusmodi vaſis non poſſe fere aquas
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ſat celeriter affundi in vas ſuperius, ut hypotheſi ſatisfiat, nec adeoque ratio-
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ne ejusdem hypotheſeos experimenta alia ſumi poſſe, quam ut exploretur,
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num revera tanta ſit altitudo B P in figura trigeſima, quanta vi paragraphi
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quinti eſſe debet, ut punctum e aut f, durante fluxu ſitum ſervet, quem
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ante fluxum obturato orificio L M, nullaque exiſtente aqua in vaſe ſuperiore
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habuit.</
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