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

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            <s xml:id="echoid-s8349" xml:space="preserve">
              <pb o="282" file="0296" n="296" rhead="HYDRODYNAMICÆ"/>
            p = (α√2v + {mdv/√2v}): </s>
            <s xml:id="echoid-s8350" xml:space="preserve">{a/√2v}, ſive
              <lb/>
            p = 2v + {mdv/a}.</s>
            <s xml:id="echoid-s8351" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8352" xml:space="preserve">(α) Apparet inde ultimam definitionem quæſtionis pendere à ratione
              <lb/>
            quæ intercedit inter d v & </s>
            <s xml:id="echoid-s8353" xml:space="preserve">α; </s>
            <s xml:id="echoid-s8354" xml:space="preserve">hanc vero in Sectione tertia generaliter defini-
              <lb/>
            vimus, nulla tamen impedimentorum, quæ debentur caſui, facta attentione.
              <lb/>
            </s>
            <s xml:id="echoid-s8355" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s8356" xml:space="preserve">figura fiſtulæ hic aliquid confert.</s>
            <s xml:id="echoid-s8357" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8358" xml:space="preserve">(β) Sequitur porro, ſi fluxus uniformis factus ponatur, eſſe p con-
              <lb/>
            ſtanter = 2v, quia tunc dv = o: </s>
            <s xml:id="echoid-s8359" xml:space="preserve">Id vero conforme eſt cum eo, quod
              <lb/>
            demonſtravimus §. </s>
            <s xml:id="echoid-s8360" xml:space="preserve">5. </s>
            <s xml:id="echoid-s8361" xml:space="preserve">Donec vero fluxus incrementa accipit (quod qui-
              <lb/>
            dem facit notabiliter, idque diu ſatis, ſi canalis E I longior fuerit) vas aliam
              <lb/>
            atque aliam patitur vim repellentem.</s>
            <s xml:id="echoid-s8362" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8363" xml:space="preserve">(γ) Habet dv ad α ſemper rationem realem: </s>
            <s xml:id="echoid-s8364" xml:space="preserve">ergo vis repellens nun-
              <lb/>
            quam eſt nulla, ſic ut à primo fluxus tempore vas repellatur, etiamſi tunc
              <lb/>
            aquæ fere nullæ effluant ob exiguam earundem velocitatem. </s>
            <s xml:id="echoid-s8365" xml:space="preserve">Verum, ut
              <lb/>
            uſus regulæ noſtræ generalis unicuique pateat, eam nunc ad caſum ſpecia-
              <lb/>
            l
              <unsure/>
            em applicabimus, tribuendo fiſtulæ EHID figuram cylindricam amplitu-
              <lb/>
            dinis 1.</s>
            <s xml:id="echoid-s8366" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8367" xml:space="preserve">§. </s>
            <s xml:id="echoid-s8368" xml:space="preserve">9. </s>
            <s xml:id="echoid-s8369" xml:space="preserve">Si igitur fiſtula ponatur cylindrica tota aperta in H I retentis
              <lb/>
            cæteris poſitionibus & </s>
            <s xml:id="echoid-s8370" xml:space="preserve">denominationibus, erit vis viva aquæ in fiſtula con-
              <lb/>
            tentæ = mv; </s>
            <s xml:id="echoid-s8371" xml:space="preserve">hujus incrementum = mdv, cui addenda vis viva columel-
              <lb/>
            læ H L M I ſeu a v, eorumque ſumma æqualis facienda facto ex altitudine,
              <lb/>
            quam habet ſuperficies aquæ A B ſupra orificium H I, quamque vocabimus
              <lb/>
            a, & </s>
            <s xml:id="echoid-s8372" xml:space="preserve">ex maſſula α. </s>
            <s xml:id="echoid-s8373" xml:space="preserve">Eſt igitur mdv + αv = αa, unde hic fit {dv/α} = {a - v/m}.
              <lb/>
            </s>
            <s xml:id="echoid-s8374" xml:space="preserve">lſto autem valore ſubſtituto in æquatione ſuperioris paragrahi fit
              <lb/>
            p = a + v. </s>
            <s xml:id="echoid-s8375" xml:space="preserve">
              <lb/>
            unde talia deduco conſectaria.</s>
            <s xml:id="echoid-s8376" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8377" xml:space="preserve">(α) Longitudo fiſtulæ nihil ad vim repellentem, quam vas ſuſtinet,
              <lb/>
            tribuit, ſi velocitas eadem ponatur, quia littera m è calculo evanuit, facit
              <lb/>
            autem hæc longitudo (ſicuti in ſuperioribus ſatis ſuperque demonſtravimus)
              <lb/>
            ut velocitates citiora aut lentiora incrementa capiant; </s>
            <s xml:id="echoid-s8378" xml:space="preserve">quo longior enim </s>
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