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

Table of Notes

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            eſſe, quanta in aqua ſtagnante ad altitudinem a - b. </s>
            <s xml:id="echoid-s7734" xml:space="preserve">Ubi notari poteſt eſſe al-
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            titudinem b ad altitudinem o S, ſi nulla motus impedimenta aliena ſint, vena-
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            que effluens in o non contrahatur, in ratione quadrata foraminis o & </s>
            <s xml:id="echoid-s7735" xml:space="preserve">ſectionis
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            CE (aut c e).</s>
            <s xml:id="echoid-s7736" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div271" type="section" level="1" n="205">
          <head xml:id="echoid-head262" xml:space="preserve">Corollarium.</head>
          <p>
            <s xml:id="echoid-s7737" xml:space="preserve">§. </s>
            <s xml:id="echoid-s7738" xml:space="preserve">11. </s>
            <s xml:id="echoid-s7739" xml:space="preserve">Cùm b major eſt quam a, fit quantitas a - b negativa atque ſic
              <lb/>
            preſſio in ſuctionem mutatur, id eſt, latera canalis introrſum premuntur: </s>
            <s xml:id="echoid-s7740" xml:space="preserve">tunc
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            autem res ita conſideranda eſt, ac ſi loco columnæ aqueæ CT ſuperincumben-
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            tis & </s>
            <s xml:id="echoid-s7741" xml:space="preserve">in æquilibrio poſitæ cum aqua præterfluente, ſit columna aquea appen-
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            ſa e t, cujus niſus deſcendendi impediatur ab attractione aquæ præterfluentis:
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            </s>
            <s xml:id="echoid-s7742" xml:space="preserve">veluti ſi v. </s>
            <s xml:id="echoid-s7743" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s7744" xml:space="preserve">amplitudo canalis c e æqualis ſit orificio o, tunc erit b = o S, nul-
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            la habita ratione motus impedimentorum accidentalium: </s>
            <s xml:id="echoid-s7745" xml:space="preserve">hinc ſi tubulus ex ca-
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            nali deſcendat c r, hicque ſit aqua plenus à ſua origine c uſque in punctum t
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            cum orificio o ad libellam poſitum, manebit aqua c t ſuſpenſa ſine motu: </s>
            <s xml:id="echoid-s7746" xml:space="preserve">ſi verò
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            punctum t infra o poſitum ſit, deſcendet aqua per tubulum cr, & </s>
            <s xml:id="echoid-s7747" xml:space="preserve">effluet perpe-
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            tuo in r, neque tamen ut facile quis exiſtimare potuiſſet nondum hâc viſa theo-
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            ria, velocitas aquæ in r effluentis talis erit, quæ debeatur altitudini N P ſu-
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            pra r, etiamſi omnia impedimen@a auferantur, reſpondebit potius hæc velo-
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            citas, ſi modo tubulus admodum ſtrictus ſit ratione canalis, altitudini t r. </s>
            <s xml:id="echoid-s7748" xml:space="preserve">
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            Si punctum t altius poſitum ſit puncto o, aqua ſua ſponte aſcendet & </s>
            <s xml:id="echoid-s7749" xml:space="preserve">cum
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            omnis canalem ingreſſa erit, aër per tubulum attrahetur, moxque vena aquea
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            in o effluens ab admixto aëre turbabitur pelluciditate atque ſoliditate orbata. </s>
            <s xml:id="echoid-s7750" xml:space="preserve">Ap-
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            paret igitur, quando preſſio futura ſit affirmativa & </s>
            <s xml:id="echoid-s7751" xml:space="preserve">quando negativa: </s>
            <s xml:id="echoid-s7752" xml:space="preserve">nempe
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            eo major eſt in tubo preſſio, quo amplior eſt & </s>
            <s xml:id="echoid-s7753" xml:space="preserve">quo humilius poſitus: </s>
            <s xml:id="echoid-s7754" xml:space="preserve">Al-
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            titudo b eſt quidem in theoria = {1/nn} X oS, ſi {1/n} denotet rationem inter am-
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            plitudinem orificii & </s>
            <s xml:id="echoid-s7755" xml:space="preserve">ejus tubi ſectionis, pro qua preſſio eſt definienda. </s>
            <s xml:id="echoid-s7756" xml:space="preserve">Cum vero
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            obſtacula notabiliter diminuunt motum, conveniet potius in æſtimandis preſ-
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            ſionibus, ut'velocitas aquæ, qualis actu eſt, experimento cognoſcatur & </s>
            <s xml:id="echoid-s7757" xml:space="preserve">alti-
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            tudo illi velocitati debita pro b ſubſtituatur: </s>
            <s xml:id="echoid-s7758" xml:space="preserve">ſimiliter accuratius æſtimabitur
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            preſſio, ſi pro a non tam ponatur altitudo ſuperficiei aqueæ N P ſupra
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            effluxus locum, quam altitudo velocitatis, quacum aquæ actu effluant
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            ex canali eodem in loco abrupto: </s>
            <s xml:id="echoid-s7759" xml:space="preserve">Hæ tamen correctiones non ſemper locum
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            habent: </s>
            <s xml:id="echoid-s7760" xml:space="preserve">Iſtam vero theoriam generalem jam exemplis quibuſdam illuſtrabo.</s>
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