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

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          <p>
            <s xml:id="echoid-s3219" xml:space="preserve">
              <pb o="113" file="0127" n="127" rhead="SECTIO SEXTA."/>
            (Fig. </s>
            <s xml:id="echoid-s3220" xml:space="preserve">32.) </s>
            <s xml:id="echoid-s3221" xml:space="preserve">inæqualis amplitudinis; </s>
            <s xml:id="echoid-s3222" xml:space="preserve">in ramo ampliore moveri ponatur flui-
              <lb/>
              <note position="right" xlink:label="note-0127-01" xlink:href="note-0127-01a" xml:space="preserve">Fig. 32.</note>
            dum B G F C verſus P velocitate quæ reſpondeat altitudini v. </s>
            <s xml:id="echoid-s3223" xml:space="preserve">Ita perſpi-
              <lb/>
            cuum eſt nullam motus mutationem adfore, priusquam ſuperficies G F
              <lb/>
            pervenerit in M N; </s>
            <s xml:id="echoid-s3224" xml:space="preserve">ab hoc autem temporis puncto motum continue variari
              <lb/>
            donec fluidum omne ſubingreſſum fuerit tubum ſtrictiorem. </s>
            <s xml:id="echoid-s3225" xml:space="preserve">Quæritur ita-
              <lb/>
            que cum fluidum fitum tenet b g f c, quænam futura ſit velocitas ſuperficiei
              <lb/>
            f g; </s>
            <s xml:id="echoid-s3226" xml:space="preserve">altitudinem autem hujus velocitatis deſignabimus per V.</s>
            <s xml:id="echoid-s3227" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3228" xml:space="preserve">Sint diametri G F & </s>
            <s xml:id="echoid-s3229" xml:space="preserve">g f ut n & </s>
            <s xml:id="echoid-s3230" xml:space="preserve">m: </s>
            <s xml:id="echoid-s3231" xml:space="preserve">longitudo B G vocetur = a;
              <lb/>
            </s>
            <s xml:id="echoid-s3232" xml:space="preserve">b M = b, erit O g = {nn/mm} X (a - b); </s>
            <s xml:id="echoid-s3233" xml:space="preserve">aſcenſus potent. </s>
            <s xml:id="echoid-s3234" xml:space="preserve">aquæ B G F C = v; </s>
            <s xml:id="echoid-s3235" xml:space="preserve">
              <lb/>
            aſcenſus potent. </s>
            <s xml:id="echoid-s3236" xml:space="preserve">aquæ b g f c = {n
              <emph style="super">4</emph>
            a - n
              <emph style="super">4</emph>
            b + m
              <emph style="super">4</emph>
            b/n
              <emph style="super">4</emph>
            a} X V; </s>
            <s xml:id="echoid-s3237" xml:space="preserve">ergo
              <lb/>
            V = {n
              <emph style="super">4</emph>
            a/n
              <emph style="super">4</emph>
            a - n
              <emph style="super">4</emph>
            b + m
              <emph style="super">4</emph>
            b} v.</s>
            <s xml:id="echoid-s3238" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3239" xml:space="preserve">Ex his intelligitur velocitatem primæ guttulæ in tubum ſtrictiorem ir-
              <lb/>
            rumpentis reſpondere altitudini {n
              <emph style="super">4</emph>
            /m
              <emph style="super">4</emph>
            } v, hanc vero velocitatem citiſſime decre-
              <lb/>
            ſcere, ita ut poſtquam parvula fluidi pars transfluxit, jam poſſit cenſeri V = {a/a - b} v,
              <lb/>
            & </s>
            <s xml:id="echoid-s3240" xml:space="preserve">cum omne fluidum transfluxerit, priſtinam aſſumat velocitatem. </s>
            <s xml:id="echoid-s3241" xml:space="preserve">Fuerit
              <lb/>
            v. </s>
            <s xml:id="echoid-s3242" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s3243" xml:space="preserve">diameter tubi amplioris decupla@ alterius, & </s>
            <s xml:id="echoid-s3244" xml:space="preserve">effluet prima guttula ex
              <lb/>
            tubo ampliore in ſtrictiorem velocitate debita altitudini 10000 v: </s>
            <s xml:id="echoid-s3245" xml:space="preserve">ſi vero de-
              <lb/>
            cimam fluidi partem jam transfluxiſſe ponas, invenies altitudinem, quæ con-
              <lb/>
            veniat velocitati fluidi in tubo ſtrictiori progredientis, proxime æqualem {10/9} v.</s>
            <s xml:id="echoid-s3246" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3247" xml:space="preserve">Sitempus quæras, quo fiat transfluxus fluidi O f, invenies illud æquale
              <lb/>
            {2(n
              <emph style="super">4</emph>
            a - n
              <emph style="super">4</emph>
            b + m
              <emph style="super">4</emph>
            b){3/2} - 2m
              <emph style="super">6</emph>
            a√a/3mm(n
              <emph style="super">4</emph>
            - m
              <emph style="super">4</emph>
            )√av}. </s>
            <s xml:id="echoid-s3248" xml:space="preserve">Igitur omne fluidum transfluit tempore
              <lb/>
            {2n
              <emph style="super">6</emph>
            a√a = 2m
              <emph style="super">6</emph>
            a√a/3mm(n
              <emph style="super">4</emph>
            - m
              <emph style="super">4</emph>
            )√av} = {2(n
              <emph style="super">4</emph>
            + mmnn + m
              <emph style="super">4</emph>
            )a/3mm(nn + mm)√v}, ubi per {a/√v} intelligitur tem-
              <lb/>
            pus, quo fluidum in tubo ampliori libere motum abſolvit ſpatium a. </s>
            <s xml:id="echoid-s3249" xml:space="preserve">Hæc
              <lb/>
            vero, ut dixi, ſe ita habebunt ſi nulla ſint motus impedimenta, ſimulque
              <lb/>
            in toto tractu canalis compoſiti velocitates amplitudinibus reciproce propor-
              <lb/>
            tionales ponantur. </s>
            <s xml:id="echoid-s3250" xml:space="preserve">Interim jam alibi monui non poſſe aquas lateri M N </s>
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