Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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HYDRODYNAMICÆ.
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ticulæ aqueæ cdfe ſupra guttulam lonp = x, altitudo centri gravitatis aquæ
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efmi a fundo = b, erit altitudo centri gravitatis omnis aquæ in ſitu cdmi
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ſupra fundum = b - {ydx/M} X (x - b) & </
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<
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xml:space
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">in ſitu efmlonpi erit eadem
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altitudo = ({M + ydx/M}) X b; </
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<
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xml:space
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">unde differentia altitudinum ſeu deſcenſus actualis
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quæſitus = - {ydx/M} X x, quæ æquatio indicat, guttulam quæ effluxerit
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multiplicandam eſſe per altitudinem aquæ ſupra foramen, productumque
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dividendum per quantitatem aquæ, ut habeatur deſcenſus actualis, qui fit
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dum guttula effluit, Q. </
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<
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<
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xml:space
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">Determinare motum fluidi homogenei ex vaſe dato per fo-
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ramen datum effluentis.</
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<
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">Quoniam per hypotheſin noſtram aſcenſus potentialis ſingulis mo-
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mentis æqualis eſt Deſcenſui actuali, erit incrementum prioris dum guttula
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effluit æquale incremento poſterioris, quod ſimili tempuſculo oritur. </
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<
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tur ſi rurfus ſuperficies aquæ, poſtquam data ejus quantitas effluxit, pona-
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tur = y, amplitudo vaſis quocunque in loco ad libitum aſſumta = m, am-
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plitudo foraminis = n, altitudo aquæ ſupra foramen = x; </
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<
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quantitas N ea lege conſtruatur, quæ §. </
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<
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">indicata fuit, atque per v in-
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telligatur altitudo debita velocitati aquæ in loco aſſumto, ubi nempe am-
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plitudo vaſis eſt = m, erit per §. </
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<
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<
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">incrementum aſcenſus potentialis =
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(Ndv - {mmvydx/nn} + {mmvdx/y}): </
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<
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">M, minimusque deſcenſus actualis = {- yxdx/M}
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(per præced.</
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xml:space
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- yxdx: </
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<
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xml:space
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">MſeuNdv - {mmvydx/nn} + {mmvdx/y} = - yxdx, quæ æquatio ge-
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neraliter integrari poteſt, quandoquidem litteræ N & </
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<
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xml:space
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ipſius x & </
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<
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