HYDRODYNAMICS. 



CHAP. II. 



ON Tin LATIBAL COMMUNICATION or MOTION IN 

 FLUIDS. 



THIS branch of hydrodynamics has been cultivated 

 almos.1 solely by M. Venturi, professor of natural philo- 

 sophy at Modena, who published an account of his in- 

 genious investigations in 1798- Sir Isaac Newton was 

 acquainted with the fart that such a lateral communi- 

 cation took place, and has deduced from it the propa- 

 gation of rotatory motion from the interior to the ex- 

 terior strata of a whirlpool ; but M. Venturi has the 

 sole merit of explaining the different phenomena which 

 it produces, and of applying it to the explanation of 

 many curious phenomena. The following propositions 

 contain a brief and general view of the subject. 



PROP. I. 



The motion of a fluid is communicated to the lateral 

 parts which are at rest. 



In order to establish this proposition by direct expe- 

 riment Venturi introduced the horizontal cylindrical 

 pipe Ac (Plate CCCXVIII. Fig. 5. No 3.) into a ves- 

 selDEFB, filled with water as high as DB. Opposite 

 the aperture C, and at a little distance from it, u pla- 

 ced a small rectangular canal of tinned iron SMI'.l:, 

 open at the top SIC, and having its inclined bottom 

 resting on the edge B of the vessel The breadth 

 of this canal is 2V lines, the diameter of the tube 



lines, and the extremity A is inserted in a reser- 

 of which the water U kept at a constant height. 

 When the water of the reservoir is permitted to flow 

 through AC, the current rises alon^ the canal MB, and 

 of course rushes out of the vessel in the current BV. 

 In this way a current U created in the fluid in the 

 TM .v, This fluid is carried into the canal SR, 



and issues at B along with the water in the reservoir. 

 In a few seconds, therefore, the water DD falls to 

 Mil. A similar effect will be obtained if we bring 

 any light bodies near a stream of water issuing from a 

 reaervoir. These bodies will be carried along by the 

 air which descends with the stream. 



in these experiment*, it follows that the lateral 

 parts of a fluid are carried along with any stream that 

 flows through the fluid, and consequently that the mo- 

 tion of the fluid U communicated to the lateral parts 

 which are at rest. 



SCHOLIUM. 



Vcntiiri has applied the principle in the proposition 

 explain the theory of the water blowing machine. 

 e baa also shewn that the eddies of the water in ri- 



c 



Mo(ion ^ 



te 



rers are produced by motion communicated from the 

 more npiil parts of the stream to the lateral parts 

 which are more at rest ; and has pointed out a method, 

 which he baa actually tried with success, of draining, 

 by means of a fall of water without the help of ma- 

 chines, a piece of ground, even though the pi-omul 

 should lie on a lower level than the et. rrrnt 



below the fall. See Prop. VI. and p. 564, iJ;., of this 

 article. 



PROP. II. 

 In descending cylindrical tubes, the upper extra. 



493 



mities of which have the form of the contracted vein, 

 the velocity of the effluent water is that which corre- 

 sponds with the height of the fluid above the inferior 

 extremity of the tube. t imUi. 



M. Venturi has established this proposition upon the PLATE 

 principle of virtual ascension, combined with the pres- cccxvur. 

 sure of the atmosphere, in the following manner. Let F * 6 - 

 BLKO, Plate CCCXVIII. Fig. 6, be a conical tube, 

 having the form of the vena contracta, and let the cy- 

 lindrical tube LCQK have the same diameter as the 

 contracted part LK. Now, the fluid stratum LK con- 

 tinuing to descend through the height LC, will tend 

 to have its motion accelerated in the same manner as 

 all other bodies falling by the force of gravity. Hence, 

 when it passes from LK to LM, it tends to detach it- 

 M If from the stratum which lies immediately above it ; 

 or, which is the same thing, it tends to produce a va- 

 cuum between LK and MX, and the same effect is 

 produced through the whole length LC of the tube. 

 The pressure of the atmosphere becomes active, as far 

 as is necessary, to prevent the vacuum, and its action 

 is the same, both at A, the surface of the fluid, and at 

 C, the inferior extremity of the tube. The atmosphe- 

 rical pressure at A increases the velocity of the fluid 

 which issues at CQ, while the atmospherical pressure 

 at C destroys the sum of the accelerations which would 

 be produced along LC, so that the fluid remains con* 

 tinuous in the tube. 



Let T be taken to represent the time in which the con 

 tinuou* column of fluid LCQK passes through the tube 

 . whatever be the velocity at L, *nd the successive 

 acceleration from L to C. Then, if we suppose this 

 column to return upwards from D to E, it will pass 

 through the space DE, which is equal to LC in the 

 same time T, and during this time it will lose all the ac- 

 celeration which it acquired in its descent from Lto C . 

 The pressure of the column ED, continued during tin 

 time T, is therefore the force necessary to destroy the 

 luccessive acceleration from L toC, and to prevent the 

 fluid from losing its continuity in the tube LC. Hence 

 it follows that the part of the pressure of the atmo- 

 sphere which is exerted at CQ to destroy the sum of 

 the auastratiuni along LC U equal to the pressure of a 

 ) of a fluid of the same nature as that of the 

 reaervoir from which the water flows. And since the 

 same pressure moat also be exerted upon the surface 

 A of the reaervoir, if we take FA = LC, the fluid at 

 LK will issue with a velocity due to the height F L- 

 abatracting the retardation produced by the external 

 inequalities of the tube U.-QK. 



ScuoLiim. 



The theory of Venturi has been recently controvert- 

 ed by M. Hachettc, who supposes, that the principal 

 cause of the increased expenditure by tuUi is the ad- 

 hesion of the fluid to the sides of the tubes arising from 

 capillary attraction. The following account of Hu- 

 chettt's experiments, taken from M. Poison-, Kiport, 

 will enable the reader to determine which of the two 

 theories U the most plausible We conceive, that 

 experiment* are necessary t'> decule the question. 



I. The fluid in motion was mercury, am' 

 jipe was made of iron. \Vh.n thi- mercury was per- 

 ;'eitly pure, it had no affinity for the iron, and flowed 

 out as it would have done from a small orifice equal to 

 the diameter of the pipe. But when the mercury was 

 coven d with a pellicle, formed of an a.loy of tin and. 

 other metals, this alloy 'ovre 1 the inside of the pipe, 

 and the mercury then flowed with a full stream. 



pi 



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