491 



HYDRODYNAMICS. 



Lateral Exp. II. The fluid next used was water, and the 

 mun '- pipe was coated within with wax. The water flowed 

 Motion in as '^ tnrou g' 1 a small orifice, without filling the tube. 

 Fluids. But whenever the water was made to moisten the wax, 

 the pipe was instantly filled, owing to the wax being 

 replaced by the first coat of water which covers it. 

 Hence the reason why a disc of glass at last adheres to 

 water with the same force whether it is covered or not 

 with a coating of wax ; for as soon as the wax is wetted, 

 it is merely the action of water on water which deter- 

 mines the phenomena, as M. Laplace has explained in 

 his Theory of Capillary Action. 



Another important fact determined by M. Hachettc 

 is, that in a vacuum, or in air rarefied to a certain de- 

 gree, the phenomena of pipes ceases to take place. 

 Thus, if water is made to run in a full stream through 

 a tube under the receiver of an air pump, then, upon 

 rarifying the air in the receiver, the fluid vein was ob- 

 served to detach itself from the sides of the pipe, when 

 the internal pressure was reduced from 0.76 of a metre 

 to 23 centimetres of mercury. By thus diminishing 

 the internal pressure, the effect of the external pressure 

 is increased, which is transmitted to the pipe by means 

 of the fluid contained in the vessel, and to which is 

 added the pressure of the fluid. But there is a point 

 at which these two pressures are sufficiently powerful 

 to detach the fluid vein from the sides of the pipe, in 

 the same manner as a disc of glass or metal may be de- 

 tached from the surface of a fluid to which it adheres 

 by the application of a sufficient force. The phenome- 

 na, therefore, exhibited in a vacuum, or in rarified air, 

 agrees perfectly with the explanation of M. Hachette, 

 and does not prove, as might be supposed, that the 

 phenomena of pipes are produced by the pressure of 

 the air in which the fluid is discharged ; an opinion 

 which is inconsistent with the two preceding experi- 

 ments, for in these experiments the action of the air 

 was the same, and yet the phenomena were different, 

 according to the nature of the fluid, and the matter of 

 which the pipe was composed. 



When the fluid vein has been detached by rarefying 

 the air, M. Hachette observed, that the water does not 

 again begin to flow in a full stream when the air is re- 

 admitted. This contraction of the vein, which took 

 place in the rarefied air, continues to subsist though the 

 pressure of the atmosphere is restored. Hence he con- 

 cludes, that the adhesion of the water to the sides of 

 the pipe takes place only at the commencement of the 

 motion, before the fluid has acquired a sensible velocity 

 in a direction which separates it from the sides. In or- 

 der to verify this conjecture, M. Hachette made the fol- 

 lowing experiment : The water flowed in a full stream 

 through a pipe without the receiver of an air-pump. A 

 small hole was made in this pipe very near the orifice. 

 The external air then'entered into the pipe, as ought to 

 have happened according to the theory of D. Bernoulli. 

 It interposed itself between the water and the sides of 

 the pipe. The contraction of the vein takes place in 

 the inside of the tube, and the water ceases to flow in a 

 full stream. This being the case, the small hole was 

 exactly shut. The adhesion of the water to the pipe 

 was not again produced, and the flowing of the water 

 continued as if the pipe had not existed, so that it might 

 have been removed or replaced without any change in 

 the flow of the water. This experiment succeeded 

 equally well whatever was the direction of the jet ; but 

 care must be taken not to agitate the apparatus, for a 

 very small lateral motion of the fluid causes it to ad- 

 here again to the moist sides of the pipe. It was pro- 



bably from having neglected this precaution, that M. 

 Venturi obtained a result apparently different from the Communi. 

 preceding. See Thomson's Annals of Philosophy, July cation f 

 1 817, vol. x. p. 34. 



PROP. III. 



If water is discharged from a short tube of a coni- 

 cal form, the pressure of the atmosphere will increase 

 the expenditure in the ratio of the exterior section of 

 the tube to the section of the contracted vein, what- 

 ever be the position of the tube, provided that its in- 

 ternal figure be adapted throughout to the lateral com- 

 munication of motion. 



Having already shewn that the atmospherical pres- 

 sure increases the expenditure through additional tubes 

 whatever be their position, Venturi next proceeds to 

 examine the mode of action by which the atmosphere 

 produces this augmentation, and he begins with the 

 case best adapted to favour the action of the atmosphere, 

 which is that of conical diverging tubes. 



Let AB, Plate CCCXVIII. Fig. 14, the extremity PLATE 

 of the tube ABEPF, be applied to an orifice in a thin cccxvnr 

 plate, and let the part ABCD have the form nearly of the Fig. H. 

 contracted vein, which is found by experiment to make 

 no perceptible alteration upon the expenditure by the 

 simple orifice AB. The water which issues through 

 CD is disposed to continue its course in a cylindrical 

 formCGHD; but if the lateral parts CFGDFH con- 

 tinue, the cylindrical stream CGHD will communicate 

 its motion to the lateral parts successively from part to 

 part, as shewn in Prop. I. Hence, if the divergence of 

 the sides CE, DF be such as is best adapted to the 

 speedy and complete lateral communication of motion, 

 all the water contained in the truncated conical tube 

 CDEF will at last acquire the same velocity as that of 

 the stream which continues to issue through CD. Upon 

 this supposition, while the fluid stratum CDQR, pre- 

 serving its velocity and thickness, would pass into 

 RQTS, a vacuum would be formed in the solid zone 

 R m r SQ n o T. Or if it should be supposed that the 

 stratum CDQR, preserving its progressive velocity, 

 should enlarge in RQTS ; this cannot happen without 

 its becoming thinner and detaching itself from the 

 stratum which succeeds it, and by that means leaving 

 a vacuum equal to the zone R mr SQ n o T. A similar 

 effect would obviously take place throughout the whole 

 of the tube CE, and if the quantity C m is supposed in- 

 variable, the sum of all these empty spaces will be 

 equal to the solid zone VE x G z YFH. 



From this reasoning it follows, that the lateral com- 

 munication of motion produces the same effect in a co- 

 nical tube, whether horizontal or vertical, as is produ- 

 ced by the action of gravity in a descending cylindrical 

 tube, as described in Prop. II. In this case, also, a 

 part of the pressure of the atmosphere is active on the 

 reservoir, and at the outer extremity EF. If the ac- 

 tion of the atmosphere upon the surface of water in 

 the reservoir increases the velocity at the section CD, 

 this velocity will likewise communicate itself to the 

 whole fluid CDFE, and the tendency to a vacuum will 

 take place as before; but since the atmospherical action 

 is as powerful at EF, it will take away at EF all the 

 velocity which it added at CD ; so that being deduct- 

 ed from the same mass, and in the same time at EF, the 

 fluid will not cease to be continuous in the pipe. It is 

 found by computation, that this will happen when the 

 velocity of CD is increased in the ratio of CD to EF 2 . 





