On the cantraSJed Stream and Velocity of fpouting Fluids. i^ 



It is evident that the contra6lion of the vein, as found by experiment, is incomparably 

 greater than can be produced by the acceleration of gravity, even in defcending flreams. But 

 what can we fay of horizontal and afcending jets, in which, afluredly, the acceleration of gra- 

 vity does not take place, but in which, neverthelefs, the contraftion is obferved nearly in the 

 fame manner as in defcending currents ? The contraftion of the ftream is, therefore, very 

 different from the Newtonian hyperboloid. 



Defirous of proving that the vein does notpoffefs the whole velocity arifing from ths height 

 of the fluid above the centre of the orifice, Lorgna relates the experiments of Kraft*, which are 

 not applicable to the queflion, becaufe they were made with cylindrical pipes ; and we have 

 feen, that fuch pipes always deftroy part of the velocity of the fluid ; confequently, we cannot 

 eftablifh any rule from them which fhall apply to orifices through thin plates f. He wifhes not 

 to determine the velocity of afcending jets by the height to which they rife, becaufe he is appre- 

 henfive that the preceding part of the flream or jet is urged, and fupported by the fucceeding 

 part nearly to the height of the charge. Neverthelefs, if we interrupt the jet all at once, the 

 laft portions of water fly to the fame height as thofe which preceded them, without having any 

 continued columnx)f the fluid below to follow and fupport them : thefe laft portions muft con- 

 fequently have received, at their pafTage through the orifice, all the velocity which was neceffarjr 

 to raife them nearly to the furface of the fluid in the refervoir. 



Let us confine ourfelves, if it be thought proper, to horizontal jets ; the experiment, which 

 I have related as a term of comparifon, appears to me to be decifive. Under the charge of 32,5 

 inches the vertical line PM, fig. i, PI. VllI, vol. II, being 54 inches, the horizontal line 

 M N was always 81,5 inches, which was only 2 inches lefs than it would have been if the jet 

 had prefervcd in the diredion of the horizon, all the velocity which a heavy body acquires in 

 falling from the height of 32,5 inches. The di.imeter of the contracted vein was 14,3 lines 

 very nearly. Since the quantity of 81,5 inches in MN fuppofes in the contradled vsin a ve- 

 locity of 149,5 inches per fecond i this number multiplied by the area of the contrafted 

 vein itfslf, gives the expenditure of 4 cubic feet in 41 feconds of time, which is alfo the refult 

 of experiment. We have, therefore, three meafures determined \>y experiment, which agree 

 and mutually confirm each other ; namely, the quantity M N, the contraction of the flream, 

 and the time of expenditure. And fince the quantities obferved by BofTut, Michelotti, and 

 Poleni, give nearly the fame refults, it can no longer be doubted ; i. That the contraction of the 

 ftream is nearly 0,64 of the orifice ; 2, That the velocity of the contracted view is nearly the 

 fame as that of a heavy body which may have fallen through the height of the charge. 



Thefe two experimental principles are true in all cafes where the orifice is confiderably fmall 

 in proportion to the feCtion of the refervoir, where that orifice is made through a thin plate, and 

 the internal afflux of the fluid filaments is made in an uniform manner round the orifice itfelf. 

 But what would be the confequence if this internal afflux fhould be modified in a manner 

 different from what ufually happens ? The following experiments were made with the in- 



• Afta Petrop. vol. 8. 



+ Torricelli took notice of this difference at page i68, of his works, " Quoticfcumque autem aqua pet tiibum 

 " latentem dtcurtenj per anguftias tranfwe debuerit, falfa omnia reperifi." • • 



D 2 tention 



