126112HYDRODYNAMICÆ
tiæ paragrapho ſecundo:
Igitur nihil ad ſolutionem quæſtionis amplius re-
ſiduum eſt: Neque tamen abs re erit unum alterumve ejus rei exemplum
attuliſſe.
ſiduum eſt: Neque tamen abs re erit unum alterumve ejus rei exemplum
attuliſſe.
Exemplum 1.
Si v.
gr.
canalis B g f C (Fig.
31.)
qui figuram habeat coni-truncati;
in
telligatur pars ejus B G F C fluido plena moto verſus g f; habeantque parti-
culæ fluidi in G F velocitatem debitam altitudini v; ac denique pervenerit
fluidum in ſitum b g f c: His poſitis quæritur velocitas fluidi in g f. Voca-
bo autem altitudinem velocitati aquæ in g f debitam = V; Sit vertex coni
in H; diameter in B C = n; diameter in G F = m: longitudo B G = a;
Gg = b, erit diameter g f = {m a - m b + n b/a}. Deinde quia ſolidum B G F C
eſt æquale ſolido b g f c erit B C2 X B H - G F2 X G H = b c2 X b H
- g f2 X g H: unde b c2 X b H = B C2 X B H - G F2 X G H
+ g f2 X g H: eſt vero b H = {BH/BC} X b c: igitur b c3 = B C3-.
{GF2 X GH X BC/BH} + {gf2 X gH X BC/BH} = B C3 - G F3 + g f3, ſeu
b c = √Cub. n3 - m3 + ({m a - m b + n b/a})3},
telligatur pars ejus B G F C fluido plena moto verſus g f; habeantque parti-
culæ fluidi in G F velocitatem debitam altitudini v; ac denique pervenerit
fluidum in ſitum b g f c: His poſitis quæritur velocitas fluidi in g f. Voca-
bo autem altitudinem velocitati aquæ in g f debitam = V; Sit vertex coni
in H; diameter in B C = n; diameter in G F = m: longitudo B G = a;
Gg = b, erit diameter g f = {m a - m b + n b/a}. Deinde quia ſolidum B G F C
eſt æquale ſolido b g f c erit B C2 X B H - G F2 X G H = b c2 X b H
- g f2 X g H: unde b c2 X b H = B C2 X B H - G F2 X G H
+ g f2 X g H: eſt vero b H = {BH/BC} X b c: igitur b c3 = B C3-.
{GF2 X GH X BC/BH} + {gf2 X gH X BC/BH} = B C3 - G F3 + g f3, ſeu
b c = √Cub. n3 - m3 + ({m a - m b + n b/a})3},
Eſt vero per §.
3.
ſect.
3.
aſcenſus potent.
aquæ in ſitu B G F C
= {3 m3 v/n(mm + mn + nn)}; pariterque aſcenſus potent. ejusdem aquæ in ſitu b g f c
reperitur = {3 α3 v; /β(αα + αβ + ββ)}, poſito brevitatis ergo α & β pro inventis valo-
ribus diametrorum g f & b c. Erit igitur
V = {m3 X (αα + αβ + ββ) X β X v/α3 X (mm + mn + nn) n}.
= {3 m3 v/n(mm + mn + nn)}; pariterque aſcenſus potent. ejusdem aquæ in ſitu b g f c
reperitur = {3 α3 v; /β(αα + αβ + ββ)}, poſito brevitatis ergo α & β pro inventis valo-
ribus diametrorum g f & b c. Erit igitur
V = {m3 X (αα + αβ + ββ) X β X v/α3 X (mm + mn + nn) n}.
Ex hâc formula facile colligitur, majori continue velocitate moveri
particulas anteriores, minori poſteriores, & ſic, ut ſi foraminulum g f cen-
ſeatur infinite parvum, fiat velocitas aquæ in g f infinita & in b c infinite parva.
particulas anteriores, minori poſteriores, & ſic, ut ſi foraminulum g f cen-
ſeatur infinite parvum, fiat velocitas aquæ in g f infinita & in b c infinite parva.
Exemplum 2.
Fuerit canalis compoſitus ex duobus tubis cylindricis B N &
O