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

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          <pb o="174" file="0188" n="188" rhead="HYDRODYNAMICÆ"/>
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            <s xml:id="echoid-s5047" xml:space="preserve">(γ) Videbitur forta@@e rem non ſatis perluſtrantibus fore, ut omni-
              <lb/>
            bus in ſtatu permanente jam poſitis, nullisque præſentibus obſtaculis alienis,
              <lb/>
            aqua per foramen E velocitate exiliat, qua aſcendere poſſit ad altitudinem co-
              <lb/>
            lumnæ aqueæ in æquilibrio poſitam cum preſſione emboli: </s>
            <s xml:id="echoid-s5048" xml:space="preserve">atque ita ſane fo-
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            ret, ſi preſſio emboli ſine interr uptione adeſſet, nullusque in aqua aſcenſus po-
              <lb/>
            tentialis perderetur: </s>
            <s xml:id="echoid-s5049" xml:space="preserve">quia vero in utroque res aliter ſe habet, non poteſt non
              <lb/>
            alia oriri in jactu aqueo velocitatis æſtimatio: </s>
            <s xml:id="echoid-s5050" xml:space="preserve">Hinc quiſque non obſcure videt
              <lb/>
            animum advertendum eſſe ad temporum rationem, quibus embolus deprimi-
              <lb/>
            tur, retrahiturque, tum etiam ad rationem amplitudinum in canaliculo D & </s>
            <s xml:id="echoid-s5051" xml:space="preserve">
              <lb/>
            orificio E.</s>
            <s xml:id="echoid-s5052" xml:space="preserve"/>
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            <s xml:id="echoid-s5053" xml:space="preserve">(δ) Ponamus igitur tempus quo embolus deprimitur = θ tempus
              <lb/>
            unius integræ agitationis = t, amplitudinem orificii E = μ, & </s>
            <s xml:id="echoid-s5054" xml:space="preserve">diabetes D = m:
              <lb/>
            </s>
            <s xml:id="echoid-s5055" xml:space="preserve">deinde comparata potentia embolum detrudente cum ſuperincumbente colum-
              <lb/>
            na aquea, faciamus hujus columnæ altitudinem = a, altitudinem vero aquæ
              <lb/>
            exilientis velocitati debitam = x. </s>
            <s xml:id="echoid-s5056" xml:space="preserve">His ita ad calculum præparatis licebit duo-
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            bus indagare modis rationem quæ futura ſit inter velocitates aquarum in
              <lb/>
            orificio E & </s>
            <s xml:id="echoid-s5057" xml:space="preserve">diabete D, atque hinc valorem incognitæ x; </s>
            <s xml:id="echoid-s5058" xml:space="preserve">elicere. </s>
            <s xml:id="echoid-s5059" xml:space="preserve">Primò enim
              <lb/>
            patet tempore θ (quo ſcilicet embolus detruditur) tantum aquæ fluere per
              <lb/>
            diabeten D, quantum tempore t (quo embolus deprimitur retrahiturque) ef-
              <lb/>
            fluit per E. </s>
            <s xml:id="echoid-s5060" xml:space="preserve">Eſt igitur velocitas in D ad velocitatem in E ut {1/mθ} ad {1/μt}: </s>
            <s xml:id="echoid-s5061" xml:space="preserve">& </s>
            <s xml:id="echoid-s5062" xml:space="preserve">
              <lb/>
            quum poſterior hæc velocitas ſit = √ x, erit altera = {μt/mθ} √ x. </s>
            <s xml:id="echoid-s5063" xml:space="preserve">Secundò quia
              <lb/>
            velocitas aquæ effluentis debetur preſſioni aëris in catino, ſequitur hanc preſ-
              <lb/>
            ſionem æquivalere ponderi columnæ aqueæ altitudinis x; </s>
            <s xml:id="echoid-s5064" xml:space="preserve">ſed ſi à preſſione
              <lb/>
            emboli auferas preſſionem aëris, habebis preſſionem, quæ velocitatem aquæ
              <lb/>
            in D generet; </s>
            <s xml:id="echoid-s5065" xml:space="preserve">hinc quia differentia preſſionum exprimitur per a - x, repræ-
              <lb/>
            ſentabitur velocitas aquæ in D per √ (a - x); </s>
            <s xml:id="echoid-s5066" xml:space="preserve">Igitur nunc eſt velocitas aquæ
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            in D ad velocitatem aquæ in orificio E ut √ (a - x) ad √ x. </s>
            <s xml:id="echoid-s5067" xml:space="preserve">Combinatis ratio-
              <lb/>
            nibus utroque modo inventis, fit
              <lb/>
            √ (a - x):</s>
            <s xml:id="echoid-s5068" xml:space="preserve">√x = {1/mθ}: </s>
            <s xml:id="echoid-s5069" xml:space="preserve">{1/μt}, ſive
              <lb/>
            x = {mmθθ/mmθθ + μμtt} X a.</s>
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