Full text: Bernoulli, Daniel: Hydrodynamica s. de viribus et motibus fluidorum commentarii

HYDRODYNAMICÆ v = {14x + b/14 + {nn/αα}}
atque ſi ratio foraminum D & G ſuerit ex gr. ut 3 ad 1, fiet
v = {14x + b/23}

§. 16. Patet quoque ratiocinium iſtud non excludere eos caſus, qui-
bus fluida ſuperiora ſunt inferioribus ſpecifice graviora, modo fluida infe-
riora non aſcendant per eadem foramina, per quæ ſuperiora deſcendunt: neque vero id futurum eſſe præſumo (nec tamen affirmo) cum loco ſimpli-
cis foraminis tubulus ſit quamvis exiguæ altitudinis, per quem liquor ſupe-
rior deſcendat in inferiorem cavitatem, velutiin fig. 40. ubi quidem duo tantum
liquores conſiderantur.

Hic autem altitudo C R variabilis eſt, & altitudo A C conſtans; in-
terim tamen uniformitatis litterarum gratia vocabimus alt@tudinem A C = x,
alteram C R = b; gravitatem ſpecificam fluidi per D erumpentis faciemus rur-
ſus = A, alteriusque fluidi per G transeuntis = B, & erit altitudo D O
ſeu
v = {Ax + Bb/A + {nn/αα}B}
Igitur ſi per foramina D & G reſpective fluant aqua & me [?] rcuri [?] us erit nunc
v = {x + 14b/1 + {14nn/αα}}

§. 17. Ut porro innoteſcat motus fluidi ſimplicis ex vaſe ſuperne
parvulo foramine aërem admittente, obſervandum eſt, nullam hic altitudi-
nem eſſe b; quia aër utrique orificio incumbere ad eandem altitudinem cen-
ſeri poteſt, erit proinde
v = {Ax/A + {nn/αα}B
atque ſi fuerit {A/B} = 850, quæ præterpropter ſolet eſſe proportio inter
gravitates ſpecificas aquæ & aëris, erit
v = {850x/850 + {nn/αα}};

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