HYDRODYNAMICS. 



423 



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Of instruments for measuring the velocity of current* 

 of water. 



During the year 1814, a very extensive series of ex- 

 periments was made by M. (iirard, on the motion of 

 fluids in capillary tubes. We have already seen, that 

 M. Coulomb had given a common co-efficient to the 

 two terms of his formula representing the resistance of 

 fluids, one of which was proportional to the simple ve- 

 locity, and the other to the square of the velocity. M. 

 A.D. 1614. Girard has, however, found, that this identity between 

 the co-efficients, which may suit particular fluids under 

 particular circumstances, is not generally admissible ; 

 and this idea is confirmed by the researches of M. Prony ; 

 from which it follows that the co efficients ought to be 

 different. M. Prony has deduced the value of these co- 

 efficients from a great number of experiments ; but as 

 his formula gives only the mean velocity, which is 

 much greater than the velocity of the fluid contiguous 

 to the pipe or canal, which ought alone to enter into 

 an expression of the retarding force, it follows that 

 the co-efficients deduced from all the experiments hi- 

 therto made, have a value greatly inferior to what they 

 outfit to have, for the motion of the fluid contiguous to 

 the side of the pipe. The object of M. Gi rani's expe- 

 riments was to determine this velocity. He observes, 

 that the velocity of the centra] filament in conduit pipes 

 differs less from the velocity of the sides of pipes as the 

 diameter of the tube is diminished ; and that the theory 

 of the linear motion of fluids, which was first given by 

 ; strictly applicable to the case where 

 the water flows in very small tubes. I fence the expe- 

 rimental result* obtained with tubes of a small diame- 

 ter, ought to accord best with the formula deduced from 

 theory. In order to nuke a correct series of experiments 

 of this kind, M. Girard constructed two sets of tubes 

 nude of copper, and of uniform calibre, and drawn 

 upon DMundrel* of steel. The first series was compo- 

 sed of tubes 2.96 millimetres in diameter, and 2 decime- 

 tres long. These tubes were made to screw on to one 

 another, and form as many tubes of different lengths, 

 from 90 to 822 centimetres. The second series was com- 

 posed of tubes 1.83 millimetres in diameter, and capable 

 of being screwed together These tubes were then fixed 

 horizontally on the sides of a reservoir, which was a cy- 

 linder of white iron 25 centimetre* in diameter, ami 5 de- 

 cimetres high. The reservoir was kept fiill by the usual 

 contrivances ; and the water discharged by the tube ob- 



jected to trial, was received into a copper vessel pland 

 and whose capacity had been accurately 



MMM* 



ascertained,' The filling of the vessel was indicated by 

 the instant when the water which it contained had wet- 

 ted equally plate of glais which covered almost tlie 

 whole of it* surface, and the time employed to fill this 

 vessel was measured with great accuracy. The tem- 

 perature of the water was also carefully noted. The 

 results thus obtained amounted to 1200, and were ar- 

 ranged by M. Girard into thirty-four table*, according 

 to the different circumstances of the experiment When 

 the capillary tube ha* such a length, that the term pro- 

 portional to the squsre of the velocity disappear* in the 

 general formula, the velocity with which the fluid is 

 i a very singular manner by a 



variation of temp, rat tire. If the velocity i* expressed 

 by 10, when the temperature i* of the centigrade 

 thermometer, the velocity will be so great as 42 ; or 

 increased more than 4 times when the temperature 



amounts to 85. When the length of the capillary tube History. 

 is below the al>ove mentioned limit, a variation of tern- S " P "Y""* 

 perature exercises but a slight influence upon the velo- 

 city of the issuing fluid. If the length of theadjutage,for 

 example, is 53 millimetres, and if the velocity is repre- 

 sented by 10 at 5 of the centigrade thermometer, it will 

 be represented only by 12 at a temperature of 87. In 

 conduit pipes of the ordinary diameter, a change of 

 temperature produces almost no perceptible change in 

 the velocity of efflux. M. (iirard also found, that the 

 quantity of water discharged by capillary tubes, varied 

 not only with the fluids which were used, but with the 

 nature of the solid substance of which the tubes were 

 composed. A full account of these valuable experi- 

 ments will be found in the Memoiret des Sfooam Eira- 

 gtri for 1815, which is not yet published. 



In the year 1815, the National Institute of France inmtiga- 

 propoaed as the subject of one of its annual prizes for tiom of M. 

 1816, the i/ifory of travel at the turf ace of a heavy 

 jt*id of an indefinite depth. The prize was gained by 

 M. Augustin Louis Cauchy, a young mathematician of 

 great promise. The differential equations which lie 

 has given apply rigorously only to the case, where the 

 depth of the fluid is infinite ; and he has treated only 

 of that species of waves which are propagated with ve- 

 locities uniformly accelerated. The same -ri>jrrt had 

 occupied the attention of M. Poisson, who, before he 

 had seen the Menioirof M. C'auchy, had laid before the 

 Institute formula.- similar to his for the case of infinite 

 depth. M. Poisson ha* himself *tud id the subject un- 

 der a more extended aspect, and has laid before the In- 

 stitute other memoirs, which we have no doubt, will 

 throw much light upon this difficult branch of hydrau- 

 lic*. He suppose* that the water has not received any 

 percussion at the commencement of its motion, and that 

 the waves have been produced in the following manner. 

 A piston of any form is supposed to be plunged in the 

 water to a small depth, and is left there till the equili- 

 brium of the fluid is restored. The piston is then sud- 

 denly vithdrawn, and waves are formed round the place 

 which it occupied In determining the propagations of 

 these waves, whether at the surface, or in the interior 

 of the fluid mas>, M. Poisson consider* only the case 

 where the agitations of the water are so small, that the 

 second and the higher power* of the velocities, and of the 

 displacements of the molecules, may be neglected ; for, 

 without such a restriction, the problem would be so com- 

 plicated, that no solution of it could be expected. Mr 

 supposes the depth of the water constant throughout 

 it* whole extent, so that the bottom is a fixed horizon- 

 tal planr, situated at a given distance below its nitur.il 

 level He then treat* successively in his memoir, tlir 

 CMC of a fluid contained in a vertical canal of an invari- 

 able width, ami of an indefinite length: and that of a 

 Hmd. whose surface is indefinitely extended in every di- 

 rection. This valuable memoir will, we trn-t. IK- pub- 

 lished in the Memoirs of the Institute for 1815. 



Having thus given a general view of the history and 

 progress of hydrodynamics, we shall conclude thin part of 

 the article, by a lit of the best works and most im|x>rt- 

 ant memoirs which have been written on the subject 



Archimedes De InttdeniUntt in /'/ iJ<> Id. J)r 

 ante i* liumiJo vrhuntur I Irr-nu \ri-ilnlni. Fdit. on hydro. 

 Commandini, 1575; Sexti Julii Frontini. I)c Aijur* dyoauiks. 

 (lucli'mt L'lt't Horace Commentann* (Polcni's edit.) ; 

 Stevini Hydrotlalica ; Schotti Mecliamca Hydraulico* 



trUfftd aceoiiol of M. KrltlwriiTi work, i* ukcn from an t anlkol abstract at It, drawn up bj Dr Thomas Young, and 

 *4 io ta Jouraab of UK ot*i institution. 



