HYDRODYNAMICS. 



495 



By applying the general laws of motion to the lateral 

 fluid filaments of the stream which issues through AB, 

 / it a found that they tend to describe a curve which 

 B commences within the reservoir, for example at A, and 

 _ _. continues towartls CSE. In order to determine the na- 

 ture of this curve, it is necessary to know and to com- 

 bine together, by calculation, the mutual couvergen- 

 cy of the fluid filaments in AB, the law of the la. 

 teral communication of motion between the filaments 

 themselves, and their divergent progression from C to 

 E. These combinations and calculations are consider- 

 ed by Venturi as beyond the efforts of analysis. When 

 the tube ABFE has a figure different from this na- 

 tural curve, the experimental results will always differ 

 taore or less from those deduced from theory. 



PHOP. IV. 



The quantity of fluid discharged through cylindrical 

 tubes is leat than through conical tubes which diverge 

 from the commencement of the contracted vein, and 

 have the same external diameter. 



The general theory is the same for tubes both of a 

 cylindrical and a conical form, but the loss of living 

 force is greater in the cylinder, and the effect of the 

 communication of motion in these tubes cannot approach 

 its maximum as in the cone. Let the compound tube 

 ACXM, Plate CCCX VII I. Fig. 1 1 . have the part ACFD 

 form of the Ttma contracts, and let the cylindri- 

 cal part GINM have its rlisaistrr MN greater than 

 1)1. 1 lence it follows, from the rsasnning in the pre. 

 ceding proposition, that the lateral communication of 

 motion tends to produce a vacuum in the solid zone 

 SXQTZ. It the communication of motion in the 

 tube were completely made, it would follow that the 

 pressure of the atmosphere would increase the velocity 

 of the contracted vein in the ratio of DF' to M.S'. 

 The form, however, of the cylindrical tube, always 

 destroys a considerable part of the effect ; for the fluid 

 filaments AD, in describing the curve DR, strike the 

 side* of the tube CM at R with considerable force, and 

 thus lose a part of their motion. Eddies or circular 

 whirls are produced in the space DGR, as in a bason 

 which receives water by a channel. These eddies are to 

 a certain extent a failure in the eftct, and retard the 

 efflux of the water. A much less increase of the ex- 

 penditure takes place in the cylindrical tube than cor- 

 responds to the ratio of DF' to M 



the reader will be able to form a general notion of 

 the effects of these internal shocks and eddies upon the 



'* 



clHux of a cylindrical tube, by , 



riinents in Table XII. p :>(>",, of this article. 



Venturi next considers, whether, in the internal 

 part of the simple cylindric tube KI.V, Fig. 12. there 

 is the same augmentation of velocity, and the same 

 contraction of the strain, a* in the compound tube of 

 Fig. 11. By reasoning according to the principles 

 which be has established, he concludes, 1. That in the 

 section Kl. t 1 ! 12. there is the same increase of 

 velocity as takes place in the section AC of Fig 1 1. 

 (See Prop. II.) The fluid particle* which pass through 

 these sections have in both cases the same direction ; 

 lor this direction can depend only ou the impulse re- 

 ceived within the reservoir, which is the same in both 

 In Fig 12. the fluid particles, after having 



passed through the section KL, immediately begin to Lateral 

 experience the effect of the lateral communication of Communi- 

 motion, and therefore they must deviate laterally """" f 

 through the curve L x :, before they arrive at the place 

 of contraction, which they assume at DF, Fig. II. and _ 

 which they likewise assume when the orifice is made PLATE 

 in a thin plate. If we suppose a tube of glass y K, cccxvui. 

 Fig. 12. to have one of its extremities applied at K, Fig- I! - 

 and the other opening into the reservoir, it will be seen 

 that the pressure of the atmosphere which is exerted 

 upon the coloured fluid T, (see p. 503. Table XI 1. exp. 7.) 

 must act likewise upon the surface of the reservoir, 

 and aid the pressure of the fluid in the reservoir in for- 

 cing the water into the tube y K, as it presses the co- 

 loured liquor into TS. In like manner, the pressure 

 of the atmosphere must increase the impulse of all the 

 fluid particles which arrive at KL, and consequently 

 must increase the expenditure. As a part of the active 

 force of the fluid most always be destroyed by the ed- 

 dies in an additional cylindric tube, it follows that the 

 effluent column can never have the velocity which is 

 due to the real head, and which is observed nearly en- 

 tire in orifices in a thin plate ; and the diminution of 

 velocity corresponds with the increase of the time be- 

 yond that indicated by the theory. 



SCHOLIUM. 



The theory of the lateral communication of motion 

 in fluids must apply in a similar manner to asrencHny 

 and dteat ruling tubes, whenever the form admit* of 

 this lateral communication. In descending tubes, the 

 increase of expenditure occasioned by this cause, must 

 be added to that which is produced by the acceleration 

 of gravity, and which has been estimated in Prop. II. 

 But in ascending tubes, we must subtract this effect 

 from that which is produced by gr.. 



Pnor. V. 



By means of proper adjutages applied to a given cy- 

 lindrical tube, it is possible to increase the expenditure 

 of water through that tube in the proportion of 2* to 

 10, the head or the altitude of water in the reservoir 

 remaining the i 



Fig. lo. 



The truth resiUinnl in this proposition is deduced 

 from the experiments which we have given in Table 

 XII. p. MS and 5O4 of this article, and the form of 

 the adjutages is explained in p. SO*, and represented 

 in Plate CCCXV 1 1 1. Fig. 16. 



SCHOLIUM. 



" At Rome,* says Venturi, " the inhabitants pur. 

 the right of conveying water from the public 

 into their houses." The law prohibits them 

 from making the pipe of conveyance larger than the 

 aperture granted them at the reservoir, as far as the 

 distance of 50 feet. The legislature was therefore 

 aware, that an additional pipe of greater diameter than 

 the orifice would increase the expenditure ; but it was 

 not perceived that the law might be equally evaded by 

 applying the conical i'mstum CD beyond the 5O feet. 

 From the structure of this compound pipe, we learn, 

 that it is not proper to make the flues of chiranies too 



M. Cteoxnt, in torn* wry txnt rifwriMMa on tW ducbarg* of wsur through cylindrical sad eoekal tube*. IMS 

 Tinj tbc xpcndituri ot water m ir.ueb gruicr raUe by changing th form of I be compound tube uicd by .Vcoluri. 

 ' 'port on M. tlKlxiu'i >Um/, Part 111. 



