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

Table of contents

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[201.] Scholium.
Page: 275 (261)
[202.] Corollarium 3.
Page: 276 (262)
[203.] Problema.
Page: 276 (262)
[204.] Solutio.
Page: 277 (263)
[205.] Corollarium.
Page: 278 (264)
[206.] Exemplum 1.
Page: 279 (265)
[207.] Exemplum 2.
Page: 279 (265)
[208.] Exemplum 3.
Page: 280 (266)
[209.] Exemplum 4.
Page: 281 (267)
[210.] EXPERIMENTA Hydraulico - ſtatica pro Sectione XII. Ad §. §. 3. & 4.
Page: 287 (273)
[211.] Experimentum 1.
Page: 288 (274)
[212.] Experimentum 2.
Page: 288 (274)
[213.] Experimentum 3.
Page: 289 (275)
[214.] Experimentum 4.
Page: 289 (275)
[215.] Experimentum 5.
Page: 289 (275)
[216.] Experimentum 6.
Page: 290 (276)
[217.] Experimentum 7.
Page: 291 (277)
[218.] Experimentum 8.
Page: 291 (277)
[219.] Experimentum 9.
Page: 291 (277)
[220.] Experimentum 10.
Page: 291 (277)
[221.] HYDRODYNAMICÆ SECTIO DECIMA TERTIA. De reactione fluidorum ex vaſis efflluentium eo-rundemque, poſtquam effluxerunt, impetu in plana quibus occurrunt. §. 1.
Page: 292 (278)
[222.] Problema.
Page: 308 (294)
[223.] Solutio.
Page: 308 (294)
[224.] Problema.
Page: 309 (295)
[225.] Solutio.
Page: 309 (295)
[226.] Corollarium.
Page: 309 (295)
[227.] Problema.
Page: 310 (296)
[228.] Solutio.
Page: 310 (296)
[229.] Scholium.
Page: 311 (297)
[230.] Problema.
Page: 311 (297)
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        <div xml:id="echoid-div260" type="section" level="1" n="196">
          <p>
            <s xml:id="echoid-s7581" xml:space="preserve">
              <pb o="258" file="0272" n="272" rhead="HYDRODYNAMICÆ"/>
            ficium H. </s>
            <s xml:id="echoid-s7582" xml:space="preserve">Eadem methodus inſervit ad preſſiones aquarum in reliquis vaſis,
              <lb/>
            quæ in Sectione octava tractavimus, determinandas. </s>
            <s xml:id="echoid-s7583" xml:space="preserve">Differunt autem omnes
              <lb/>
            hæ quæſtiones ab iis, quæ ad motum fluidorum per canales pertinent, quod
              <lb/>
            aquæ ob infinitam vaſorum à nobis poſitam amplitudinem veluti quieſcant in
              <lb/>
            cavitatibus & </s>
            <s xml:id="echoid-s7584" xml:space="preserve">nihilominus preſſionem longe aliam exerceant, quam aliter ſo-
              <lb/>
            lent. </s>
            <s xml:id="echoid-s7585" xml:space="preserve">In canalibus autem aquæ preſſionem ſuam eo magis mutant, quo majo-
              <lb/>
            ri velocitate præterfluunt, & </s>
            <s xml:id="echoid-s7586" xml:space="preserve">omnem fere conſuetam preſſionem exerunt, ſi
              <lb/>
            velocitas iſta ſit valde parva.</s>
            <s xml:id="echoid-s7587" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7588" xml:space="preserve">Hæc ita, cum velocitates fluidorum determinari poſſunt per methodos
              <lb/>
            jam ſuprà à nobis traditas. </s>
            <s xml:id="echoid-s7589" xml:space="preserve">Singulari autem methodo res pertractanda eſt, cum
              <lb/>
            aquæ per canales fluunt, hancque doctrinam potiſſimum titulo hydraulico-ſtati-
              <lb/>
            cæ intelligo: </s>
            <s xml:id="echoid-s7590" xml:space="preserve">Hic non tam preſſio ex velocitate quam reciproce velocitas, ſi
              <lb/>
            foraminulum in lateribus canalis fiat, ex preſſione definiri poteſt. </s>
            <s xml:id="echoid-s7591" xml:space="preserve">Et de iſta
              <lb/>
            hydraulico-statica, cujus uſus ampliſſimus eſt, in præſenti ſectione potiſſimum
              <lb/>
            agere conſtitui.</s>
            <s xml:id="echoid-s7592" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div261" type="section" level="1" n="197">
          <head xml:id="echoid-head254" xml:space="preserve">Problema.</head>
          <p>
            <s xml:id="echoid-s7593" xml:space="preserve">§. </s>
            <s xml:id="echoid-s7594" xml:space="preserve">5. </s>
            <s xml:id="echoid-s7595" xml:space="preserve">Fuerit vas ampliſſimum A C E B (Fig. </s>
            <s xml:id="echoid-s7596" xml:space="preserve">72.) </s>
            <s xml:id="echoid-s7597" xml:space="preserve">aqua conſtanter ple-
              <lb/>
              <note position="left" xlink:label="note-0272-01" xlink:href="note-0272-01a" xml:space="preserve">Fig. 72.</note>
            num conſervandum, tubo inſtructum cylindrico & </s>
            <s xml:id="echoid-s7598" xml:space="preserve">horizontali E D; </s>
            <s xml:id="echoid-s7599" xml:space="preserve">ſitque in
              <lb/>
            extremitate tubi foramen o aquas velocitate uniformi emittens; </s>
            <s xml:id="echoid-s7600" xml:space="preserve">quæritur preſſio
              <lb/>
            aquæ in latera tubi E D.</s>
            <s xml:id="echoid-s7601" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div263" type="section" level="1" n="198">
          <head xml:id="echoid-head255" xml:space="preserve">Solutio.</head>
          <p>
            <s xml:id="echoid-s7602" xml:space="preserve">Sit altitudo ſuperficiei aqueæ A B ſupra orificium o = a; </s>
            <s xml:id="echoid-s7603" xml:space="preserve">erit velocitas
              <unsure/>
              <lb/>
            aquæ in o effluentis, ſi prima fluxus momenta excipias, uniformis cenſenda
              <lb/>
            & </s>
            <s xml:id="echoid-s7604" xml:space="preserve">= √a, quia vas conſtanter plenum conſervari aſſumimus; </s>
            <s xml:id="echoid-s7605" xml:space="preserve">poſitaque ratio-
              <lb/>
            ne amplitudinum tubi ejusque foraminis = {n/1}, erit velocitas aquæ in tu-
              <lb/>
            bo = {√a/n}: </s>
            <s xml:id="echoid-s7606" xml:space="preserve">Si vero omne fundum F D abeſſet, foret velocitas ultima aquæ in
              <lb/>
            eodem tubo = √a, quæ major eſt quam a; </s>
            <s xml:id="echoid-s7607" xml:space="preserve">Igitur aqua in tubo tendit ad ma-
              <lb/>
            jorem motum, niſus autem ejus ab appoſito fundo F D impeditur: </s>
            <s xml:id="echoid-s7608" xml:space="preserve">Ab hoc
              <lb/>
            niſu & </s>
            <s xml:id="echoid-s7609" xml:space="preserve">reniſu comprimitur aqua, quæ ipſa compreſſio coërcetur à lateribus
              <lb/>
            tubi, hæcque proinde ſimilem preſſionem ſuſtinent. </s>
            <s xml:id="echoid-s7610" xml:space="preserve">Apparet ſic </s>
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