Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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SECTIO TERTIA.
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patet fore altitudinem, quæ velocitati aquæ effluentis reſpondet = {mm/nn} v,
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quæ proin, ſi vocetur z, erit nnNdz - mmzydx + {mmnnzdx/y} = mmyxdx.</
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<
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">Si foramen ſit valde parvum, ratione amplitudinum vaſis,
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fit n = o, totaque æquatio abit in hanc - mmzydx = - mmyxdx vel
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z = x; </
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<
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">tunc igitur aqua ea conſtanter effluit velocitate, qua ad altitudinem
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ſupremæ ſuperficiei usque aſcendere poſſit, quem ſolum caſum Geometræ
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hactenus fuerunt recte aſſecuti: </
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<
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">valetque hæc propoſitio pro omnibus vaſis
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utcunque formatis: </
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">at cum foramen non ut infinite parvum conſideratur,
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nequaquam negligenda eſt vaſis figura. </
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">Notari tamen poteſt, quod niſi fo-
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ramen ſit ampliſſimum, ſine notabili admodum errore idem ut infinitè par-
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vum conſiderari poſſit.</
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<
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">Cum fluidum non eſt ubique idem, ſimili modo inſtituen-
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dus eſt calculus, inquirendo nimirum tum in incrementum aſcenſus poten-
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tialis fluidi compoſiti, tum in Deſcenſum actualem, eaque inter ſe æquando.
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">Quod ſi autem foramen ſit valde parvum, per ſe patet, quod etiam calcu-
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lus oſtendit, fore ut fluidum velocitate exiliat altitudini debita tali, ut ſi vas
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ad eandem altitudinem liquore eodem, qui exilit, repletum ſit, eandem
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preſſionem latera foraminis ſuſtineant.</
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">Priusquam Corollaria ſpecialiora ex theoria noſtra dedu-
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camus circa motum fluidorum ex vaſis cylindricis, conveniet hic examina-
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re, quousque hypotheſes aſſumtæ cum rei natura conſpirent & </
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intervenire poſſint cauſæ, quarum in computo nullam rationem habuimus,
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motum fluidum diminuentes.</
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">Quod primo attinet ad Principium conſervationis virium vivarum ſeu
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perpetuæ æqualitatis inter aſcenſum potentialem deſcenſumque actualem nihil hîc vi-
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deo, quod ei notabili impedimento eſſe poſſit, ſi modo à frictionibus, te-
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nacitate, aëris reſiſtentia hujuscemodique aliis obſtaculis mentem </
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