Bernoulli, Daniel
,
Hydrodynamica, sive De viribus et motibus fluidorum commentarii
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SECTIO SEXTA.
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(Fig. </
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<
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<
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">inæqualis amplitudinis; </
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<
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">in ramo ampliore moveri ponatur flui-
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dum B G F C verſus P velocitate quæ reſpondeat altitudini v. </
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<
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cuum eſt nullam motus mutationem adfore, priusquam ſuperficies G F
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pervenerit in M N; </
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<
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">ab hoc autem temporis puncto motum continue variari
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donec fluidum omne ſubingreſſum fuerit tubum ſtrictiorem. </
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<
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xml:space
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que cum fluidum fitum tenet b g f c, quænam futura ſit velocitas ſuperficiei
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f g; </
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<
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">altitudinem autem hujus velocitatis deſignabimus per V.</
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<
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<
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<
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<
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</
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<
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">b M = b, erit O g = {nn/mm} X (a - b); </
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<
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<
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aſcenſus potent. </
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<
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xml:space
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a - n
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b + m
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b/n
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a} X V; </
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<
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V = {n
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a/n
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a - n
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b + m
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b} v.</
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<
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">Ex his intelligitur velocitatem primæ guttulæ in tubum ſtrictiorem ir-
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rumpentis reſpondere altitudini {n
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/m
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} v, hanc vero velocitatem citiſſime decre-
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ſcere, ita ut poſtquam parvula fluidi pars transfluxit, jam poſſit cenſeri V = {a/a - b} v,
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& </
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<
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">cum omne fluidum transfluxerit, priſtinam aſſumat velocitatem. </
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v. </
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<
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">diameter tubi amplioris decupla@ alterius, & </
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tubo ampliore in ſtrictiorem velocitate debita altitudini 10000 v: </
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<
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cimam fluidi partem jam transfluxiſſe ponas, invenies altitudinem, quæ con-
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veniat velocitati fluidi in tubo ſtrictiori progredientis, proxime æqualem {10/9} v.</
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<
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">Sitempus quæras, quo fiat transfluxus fluidi O f, invenies illud æquale
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{2(n
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a - n
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b + m
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b){3/2} - 2m
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a√a/3mm(n
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- m
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)√av}. </
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<
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{2n
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a√a = 2m
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a√a/3mm(n
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- m
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)√av} = {2(n
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+ mmnn + m
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)a/3mm(nn + mm)√v}, ubi per {a/√v} intelligitur tem-
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pus, quo fluidum in tubo ampliori libere motum abſolvit ſpatium a. </
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<
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vero, ut dixi, ſe ita habebunt ſi nulla ſint motus impedimenta, ſimulque
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in toto tractu canalis compoſiti velocitates amplitudinibus reciproce propor-
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tionales ponantur. </
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<
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