i8 



On the contrafied Stream and Velocity »f fpoating Fluids, 



Mdit'ton rtfptUing the contra£ied Vein. 



Much has been written concerning the convergent directions affumed by the particles of 

 a fluid contained in a veflel, previous to their being emitted through an aperture in the fide 

 of the veflel itfelf, and concerning the form of the contradted vein which is thus produced. 

 The reflections and experiments, whiclv I fliall proceed to give, may afford fome farther ex- 

 planation in this refpeCt. 



I jhall begin by defending the fundamental doftrine of hydraulics againfl: the opinion of a 

 learned man, diftinguiflied by his labours and his zeal for the advancement of fcience: 

 Lorgna, the founder of the Italian fociety. He pretends * that the contradted vein is nothing 

 clfe but the continuation of the Newtonian catarad, and that the celerity of the fluid, ilTuing 

 from an orifice in a thin plate, is much lefs than that of a body which falls from the height 

 of the charge. 



Let-M D, fig. 22, PI. XXII, vol. II, reprefent the axis of the vein which ifliies. from B. 

 The radius of the circular orifice BC = B Dm ; M B=a. Lorgna pretends that 0,472 a = 

 H B, is the height which would produce, in an heavy body, the velocity of efflux in B C ; he 

 fupports this propofition by computations deduced from the mutual a£lion of the particles of 

 the fluid contained in the veflel. But after having feen the failure of the eflForts of the greateft 

 geometers on this fubjeft, we ought to miftrufl all thefe demonftrations founded on mechanical 

 principle, very true in themfelves, but of which the application to an infinity of bodies, which 

 move and are preflfed in every diretSlion, becomes extj-emely difficult, if not impoflible. 

 Let us fee whether the theory of Lorgna agrees with experiment. Suppofing the velocity of 

 the fluid at B, arifing from the elvation H 6=0,472 <?, the velocity of the fame fluid in D 

 will be increafed in the ratio of VHS" ■ a/hd; and the vein in D will be contraifted in the 



fame ratio: whence D E = V *( —2^111- ]• which is the formula of the hyperbolic conoid of 



\.i+o,47i«y -"^ 



Newton. If this be the fole caufe of the contraction, the dimenfions of D E ought, very nearly, 

 to agree with this figure when examined by experiment. But they, in reality, differ from it 

 Tcry much, as may be feen in the following table. 



Authors of the experiments. 



'Poleni (de Caftellis § 35.) 

 Michelotti (Sperim. Idraul. 



torn. I. exper. 46 ; torn. II. 



exper. 4) . • . 



Bofliit (Hydrodyn. art. 437 



exper. 5) 

 Myfelf, with 35 inches charge 



and an horizontal circular 



orifice of 18 lines in diameter 



Value of D E found by 



aCtual meafurement. 



0,79 



0,80 

 0,818 



by I 



Value of D E calculated by the 

 preceding formula. 

 c,97 



0,99 

 0,99 



*(') 



0,798 

 Mem. della focieta Italiaoa, vol. IV, 



0,984 



It 



