Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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SECTIO QUARTA.
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quidem impedimenta nunc majora nunc minora nunquam omnem aquæ ve-
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locitatem permittant, quam vi theoriæ, qua horum impedimentorum ra-
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tio nulla habetur, acqui
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ere deberet.</
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<
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xml:space
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xml:space
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">6. </
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<
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xml:space
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">Ex præmiſſis nunc ſatis patere puto perfectum conſenſum fore
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inter quantitatem aquæ effluentis ejuſque velocitatem, ſi modo foramini, quod
<
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/>
eſt in vaſe, ſubſtituatur aliud foramen eo uſque diminutum, donec ſectionem
<
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venæ maxime contractæ non ſuperet: </
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<
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xml:space
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preserve
">atque perinde erit, in quonam venæ
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loco, aut in quânam profunditate à ſuperficie aquæ foramen hoc eſſe conſti-
<
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tuatur, ſive in a c ſive in d e, quandoquidem velocitates ſemper proxime re-
<
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ſpondebunt toti altitudini aquæ ſupra eum locum, quo foramen fingitur: </
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>
<
s
xml:id
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xml:space
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">am-
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plitudinem hujus foraminis mente concipiendi vocabo deinceps Sectionem ve-
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næ aqueæ contractæ.</
s
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<
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</
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<
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<
s
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xml:space
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">§. </
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<
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xml:space
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">7. </
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<
s
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xml:space
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">Quod ſi jam Sectio iſta, de quâ modo diximus, conſtantem
<
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haberet rationem ad orificium, in eadem ratione diminuendum cogitatione
<
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foret foramen effluxus, poſtmodumque calculus de quantitate aquæ dato tem-
<
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pore effluentis inſtituendus. </
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<
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xml:space
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">Ita nempe poſita iſta ratione = {1/α} nominatâque
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amplitudine orificii n, cenſenda eſſet Sectio venæ ſolidæ = {n/α}.</
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>
<
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xml:space
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</
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<
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<
s
xml:id
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xml:space
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">At variabilis cum ſit ſub diverſis circumſtantiis, regulas in hanc'
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rem à
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priori dare non licet: </
s
>
<
s
xml:id
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echoid-s1759
"
xml:space
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preserve
">mutatur autem maxime à craſſitie laminæ, in quâ
<
unsure
/>
fora-
<
lb
/>
men eſt, aucta vel diminuta: </
s
>
<
s
xml:id
="
echoid-s1760
"
xml:space
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preserve
">aliquid etiam, quamvis id parum, conferre po-
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teſt magnitudo foraminis, amplitudines vaſis, hæque tam abſolutæ, quam rela-
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tivæ, ut & </
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<
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xml:space
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">fortaſſe altitudo aquæ ſupra foramen. </
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<
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xml:space
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">Interim aſſumtis lamina te-
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nui, vaſe ampliſſimo, foramine ad 4. </
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<
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xml:space
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">vel 6. </
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xml:space
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">lineas in diametro aſſurgente; </
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<
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ratio inter foramen & </
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<
s
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xml:space
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">Sectionem venæ contractæ non multum recedere ab illâ,
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quam Newtonus ſtatuit, nempe ut √ 2 ad 1. </
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<
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xml:space
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">Sæpe autem ab aliis major ob-
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ſervata fuit, atque ab aliis etiam minor.</
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<
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<
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">8. </
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<
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xml:space
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">Quæcunque vero ſit, in quolibet caſu illam indicabimus, ut an-
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te, per {α/1.</
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<
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xml:space
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">} Huicque poſitioni nunc calculum pro temporibus ſuperinſtruemus;
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</
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<
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xml:space
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">brevitatis autem gratia conſiderabimus tantum vaſa cylindrica, atque in his
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duo potiſſimum examinabimus temporum genera; </
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<
s
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xml:space
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">primum quod punctum
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maximæ velocitatis definit, alterum, quod depletioni reſpondet. </
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<
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xml:space
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">In utroque
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vero caſu motum à quiete incipere ponemus.</
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