Bernoulli, Daniel, Hydrodynamica, sive De viribus et motibus fluidorum commentarii

Table of Notes

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            vorticum commendare hypotheſin, ſed quasdam tantum inde concluſiones
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            facere, ſine quibus ipſam hypotheſin ſubſiſtere non poſſe crediderim.</s>
            <s xml:id="echoid-s7419" xml:space="preserve"/>
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            <s xml:id="echoid-s7420" xml:space="preserve">Venio jam ad alteram ſectionis partem, qua breviter conſiderabimus
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            ſtatum fluidorum, quæ intra vaſa mota continentur: </s>
            <s xml:id="echoid-s7421" xml:space="preserve">Argumentum eſt fertiliſ-
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            ſimum infinitiſque modis variabile: </s>
            <s xml:id="echoid-s7422" xml:space="preserve">Sed pauca attingemus, ceu exempla, ad
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            quæ multa alia revocari poterunt.</s>
            <s xml:id="echoid-s7423" xml:space="preserve"/>
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            <s xml:id="echoid-s7424" xml:space="preserve">§. </s>
            <s xml:id="echoid-s7425" xml:space="preserve">18. </s>
            <s xml:id="echoid-s7426" xml:space="preserve">Si aqua in vaſe perforato contineatur ipſumque vas libere ca-
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            dat, ex ſe patet, nihil aquæ durante vaſis lapſu eſſe effluxurum, quia nem-
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            pe particulæ ſuperiores non gravitant in inferiores: </s>
            <s xml:id="echoid-s7427" xml:space="preserve">Si vas motu quidem acce-
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            lerato deſcendat ſed tardiore quam quo corpora naturaliter in vacuo accele-
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            rantur, effluet aqua, ſed minori velocitate ac ſi vas quiescat: </s>
            <s xml:id="echoid-s7428" xml:space="preserve">Contrarium erit,
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            ſi vas motu accelerato ſurſum trahatur: </s>
            <s xml:id="echoid-s7429" xml:space="preserve">Denique ſi vas horizontaliter accele-
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            rato motu feratur (jam enim ad reliquas non attendemus directiones) fieri po-
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            teſt, ut velocitas aquæ effluentis major ſit vel minor velocitate ordinaria pro
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            ratione ſitus foraminis: </s>
            <s xml:id="echoid-s7430" xml:space="preserve">Velocitates autem aquæ ſic determinabuntur.</s>
            <s xml:id="echoid-s7431" xml:space="preserve"/>
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            <s xml:id="echoid-s7432" xml:space="preserve">§. </s>
            <s xml:id="echoid-s7433" xml:space="preserve">19. </s>
            <s xml:id="echoid-s7434" xml:space="preserve">Sit v. </s>
            <s xml:id="echoid-s7435" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s7436" xml:space="preserve">cylindus A C D B (Fig. </s>
            <s xml:id="echoid-s7437" xml:space="preserve">67.) </s>
            <s xml:id="echoid-s7438" xml:space="preserve">aqua plenus usque in A B,
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              <note position="left" xlink:label="note-0266-01" xlink:href="note-0266-01a" xml:space="preserve">Fig. 67.</note>
            cujus fundum C D foramen habeat in E valde parvum per quod aquæ effluant,
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            dum interea totum vas ſurſum trahaturà pondere P deſcendente mediante funi-
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            culo ſuper duabus trochleis H & </s>
            <s xml:id="echoid-s7439" xml:space="preserve">G excurrente. </s>
            <s xml:id="echoid-s7440" xml:space="preserve">Denique conſtanter tantum
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            aquæ ſuperius affundi ponatur, quantum effluit per foramen E: </s>
            <s xml:id="echoid-s7441" xml:space="preserve">pondus vero
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            cylindri & </s>
            <s xml:id="echoid-s7442" xml:space="preserve">aquæ in eo contentæ indicetur per p. </s>
            <s xml:id="echoid-s7443" xml:space="preserve">lta apparet quamlibet gut-
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            tam aquæ in vaſe veluti ſtagnantis vi animari ad aſcenſum quæ ſe habeat ad vim
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            gravitatis naturalem ut {P - p/P + p} ad 1: </s>
            <s xml:id="echoid-s7444" xml:space="preserve">Quia vero reactio guttulæ in fundum æqua-
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            lis eſt vi, qua ad aſcenſum animatur quævis guttula, præter preſſionem natu-
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            ralem aliam exeret in fundum, quæ exprimenda erit per {P - p/P + p}. </s>
            <s xml:id="echoid-s7445" xml:space="preserve">Utraquè vero
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            preſſio ſimul ſumta erit ad preſſionem ſolam naturalem ut {2P/P + p} ad 1, adeo
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            ut fundum haud ſecus ab incumbente aqua prematur, quam ſi cylindrus quieſ-
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            ceret eſſetque altitudo aquæ = {2P/P + p} X A C, ex quo ipſo ſequitur altitudinem
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            velocitati aquæ uniformiter effluentis debitam eſſe = {2P/P + p} X A C.</s>
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