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

Table of figures

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              <pb o="127" file="0141" n="141" rhead="SECTIO SEPTIMA."/>
            nam, quantum ſuper eandem elevata fuerat, provenit iſte defectus ab aſcenſu
              <lb/>
            pot. </s>
            <s xml:id="echoid-s3644" xml:space="preserve">aquæ durante deſcenſu ejectæ, cui debet eſſe proportionalis.</s>
            <s xml:id="echoid-s3645" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3646" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3647" xml:space="preserve">5. </s>
            <s xml:id="echoid-s3648" xml:space="preserve">Notabile eſt, quod cum eo profundius deſcendat aqua in cylin-
              <lb/>
            dro, quo magis ab initio deſcenſus fuerit elevata & </s>
            <s xml:id="echoid-s3649" xml:space="preserve">quo majori lumine perfo-
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            ratum eſtfundum, nunquam tamen omnis aqua ex cylindro effluere poſſit
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            quantumvis fuerit ante deſcenſum elevata & </s>
            <s xml:id="echoid-s3650" xml:space="preserve">pars cylindri ſubmerſa utlibet
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            parva, ipſumque ſimul foramen vel totum fundum exhaurire ponatur.</s>
            <s xml:id="echoid-s3651" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3652" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3653" xml:space="preserve">6. </s>
            <s xml:id="echoid-s3654" xml:space="preserve">Velocitas ſuperficiei aquæ internæ maxima eſt, cum ſumitur
              <lb/>
            x = ({a
              <emph style="super">nn - 1</emph>
            /nna - nnb - a + 2b})
              <emph style="super">1: (nn - 2)</emph>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s3655" xml:space="preserve">Si proinde n = 1, exiſtente ſcilicet orificio cylindri toto aperto, fit
              <lb/>
            x = b, & </s>
            <s xml:id="echoid-s3656" xml:space="preserve">maxima eſt velocitas, cum ambæ ſuperficies ſunt in eadem altitu-
              <lb/>
            dine poſitæ.</s>
            <s xml:id="echoid-s3657" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3658" xml:space="preserve">Quia vero multa ſunt, quæ ex hiſce æquationibus dignoſci nequeunt
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            in duobus caſibus, nempe nn = 1 & </s>
            <s xml:id="echoid-s3659" xml:space="preserve">nn = 2, hique multa habent particula-
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            ria, eoſdem ſeorſim jam attingam.</s>
            <s xml:id="echoid-s3660" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s3661" xml:space="preserve">§. </s>
            <s xml:id="echoid-s3662" xml:space="preserve">7. </s>
            <s xml:id="echoid-s3663" xml:space="preserve">Sit primo nn = 1, & </s>
            <s xml:id="echoid-s3664" xml:space="preserve">erit - xdv = (x - b) dx (per §. </s>
            <s xml:id="echoid-s3665" xml:space="preserve">3.) </s>
            <s xml:id="echoid-s3666" xml:space="preserve">vel
              <lb/>
            - dv = dx - {bdx/x}, quæ ſic integrata, ut ſit ſimul v = o & </s>
            <s xml:id="echoid-s3667" xml:space="preserve">x = a, dat - v =
              <lb/>
            x - a + b log. </s>
            <s xml:id="echoid-s3668" xml:space="preserve">{a/x}, ſeu v = a - x - b log. </s>
            <s xml:id="echoid-s3669" xml:space="preserve">{a/x}: </s>
            <s xml:id="echoid-s3670" xml:space="preserve">Exinde talia deduci poſſunt.</s>
            <s xml:id="echoid-s3671" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3672" xml:space="preserve">I
              <emph style="super">0</emph>
            . </s>
            <s xml:id="echoid-s3673" xml:space="preserve">Ut obtineatur maximus deſcenſus, faciendum eſt a - x - b log. </s>
            <s xml:id="echoid-s3674" xml:space="preserve">{a/x}
              <lb/>
            = o; </s>
            <s xml:id="echoid-s3675" xml:space="preserve">patet autem ex iſta æquatione, nunquam negativum valorem obtinere
              <lb/>
            litteram x, imo nequidem totam evaneſcere ſine contradictione, niſi pona-
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            tur {a/b} = ∞, quod indicat fieri non poſſe, ut omnis effluat aqua durante de-
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            ſcenſu in iſto caſu & </s>
            <s xml:id="echoid-s3676" xml:space="preserve">multo minus in reliquis, quod confirmat paragraphum
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            quintum.</s>
            <s xml:id="echoid-s3677" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3678" xml:space="preserve">II
              <emph style="super">0</emph>
            . </s>
            <s xml:id="echoid-s3679" xml:space="preserve">Velocitas maxima talis eſt, quæ debetur altitudini a - b - b log. </s>
            <s xml:id="echoid-s3680" xml:space="preserve">{a/b},
              <lb/>
            atque ſi differentia inter a & </s>
            <s xml:id="echoid-s3681" xml:space="preserve">b, quam ponam = c, ſit valde parva, exiſten-
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            tibus nimirum excurſionibus fluidi perexiguis ratione longitudinis, ad </s>
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