HYDRODYNAMICS. 



419 



rr. The attention of the Chevalier Bunt, Lieutenant Co- 

 "* lonel of the Royal Corps of Engineer*, was called to 

 * the subject of hydraulics by the publication of Bos- 

 |j alt sut's Hydrodifoamique in 1771. In studying the mo- 

 tion of canals and rivers, it occurred to him, that it' 

 water pussnsfrl perfect fluidity, and flowed in a chan- 

 nel infinitely smooth, its motion would be constantly 

 accelerated like that of heavy bodies descending upon 

 an inclined plane. Rut as the velocity of a river is not 

 accelerated ad infinilirm, but soon arrives at a state of 

 uniformity, ami is not afterwards increased without 

 some cmnse, it follows that there is some obstacle 

 which destroys its accelerating force, and prevents it 

 from impressing upon the water new degree* of veloci- 

 ty. This obstacle must therefore be the viscidity of 

 the water, which gives rise to two kind* of resistance, 

 one, namely, which proceeds from the intNtine mo> 

 tion of an imperfect fluid, and the other from the natu- 

 ral adhesion of its parts to the channel in which it flows. 

 Our author, therefore, found it to be a general princi- 

 ple, " that when water runs uniformly in any channel, 

 the accelerating force which obliges it to run, is equal 

 to the sum of all the resistance* which it experiences, 

 either from its own viscidity, or from the friction of its 

 channel." Encouraged by the discovery of this prin- 

 ciple, and by its application to the solution of many 

 important problems, it occurred to M. Buat, that the 

 notion of water in a conduit pipe had a groat analogy 

 to the uniform motion of a river, and upon this idea he 

 composes! formula founded on the experiments of 

 HoMut en conrioit pipes and artificial canals. The 

 rrnlt of this investigation was publinhed 

 the first edition of his I'rnmprt J Hydrautta**- M. 

 Huat, however, was speedily convinced that a theory s 

 which led to remits so different from the 



Benew 



bBe/i 



i theory, mjuhsjd the sanction of new experi- 

 Dore direct and varied than those which had 

 hitherto been made. Through the influence of M. de 

 Fourcroy, director of the itoyal Corps of Engineers, the 

 French Minister ordered an annual torn to be put 

 at the command of the Chevalier Hint, for the purpose 

 f performing a set of experiment* upon this important 

 subject; and during the yean 1780, 1781, 17*8, and 

 1785, he was constantly occupied with these experi- 

 ment*, with the assistance of Mew* Dobenheim and 

 t Honor*, two officer, of the Royal F.n- 

 The latter took a particular interest in these 

 , and Ana fcj> great mathematical knowledge, 

 _ - tttrticalar service to M. Bnat, not only by the 

 general aid m hich be gave him, but from the nmnber of 

 Li>ifU prabltmi and important rmeenhss which he 



the experiments of Burnt had been made only 

 on pipe* of moderate declivity, M. Huat supplied this 

 defect by uting declivities varying from 90* to the 

 40,000th part of a right angle, and channel, which va- 

 ried from a line and a half in diameter to arae* of seven 

 or eight square toise*. Experiment* were alto mad* 

 with ijphiBi and pipe* bent at various angle*, and on 

 the resistance both of i niapteariLls and incompreseible 

 fluid*. In thi* way our author ha* collected an im- 

 mense number of facts, which he classed according to 

 their resemblance in one particular point; and by i-tiidy- 

 ing the cause of the difference* which accompanied 

 their differences in other circumptancp*, he was led to 

 general rules, by which these difference, formed a re- 

 gular series. The experiment* were again rUmd 

 under another point of resemblance, and the same me- 

 thod followed ; and by pursuing thi* plan, lie obtained 



the following general formula, which represents, in a 

 most surprising manner, the great variety of facts which 

 he hat collected ; namely, 



History. 



v = 



V'T Log.Vj+1.6 



0.3(ST0.l) in which 



V is the mean velocity in inches per second. 



d the hydraulic mean depth, or the quotient which 

 arises from dividing the area of the section of the ca- 

 nal in square inches by the perimeter of the part in con- 

 tact with the water in linear inches. 



* the slope or declivity of the pipe, or of the surface 

 of the wnter. 



=1(>.087, the velocity in inches per second which 

 a heavy body acquires by falling in one second. 



n An abstract number which was found by experi- 

 ment to be = S+S.7. 



In 1783, when M. Buat's experiments were finished. 

 they were submitted to the Academy of Sciences through 

 the minister of war, and were afterwards published in 

 1786, under the title of Principes d"Hydralique reri~ 

 JUi par tut grand nombre d'txperiencei faitet par ordre 

 dm FDHvcrtitment. A third volume of this work was 

 lied in 1816, under the title of Principal a* Hy* 

 Jrnu/ufHe ft Pyrodynamiqtte. It relates chiefly to the 

 phenomena of heat and elastic fluids. 



In the year T78t, M. I.'Fspinasse, corresponding M. t 

 merober of the Academy of Thoulouse, published two nuw, 

 memoirs in the Transaction* of that society, which con- A - n - 

 tain very interesting observations on the motion of 

 water through large orifices, and on the junction and 

 separation of river*. The experiments which are con- 

 tained in these two memoirs were made in 'the Fres- 

 quel and Aude, two rivers in the department of the 

 r (iaronne, and on part of the Canal ilu Midi, 

 which i* below the lock of Fresquel, towards the point 

 where it meets with the bed of that river. 



Dun George Juan IXUIloa, an eminent mathematician, 

 and inspector of the naval academies of Spain, nropo. Jun 

 ed a new |>'i\ - "'-mathematical theory of colli-ion, in lom - 

 his Exam, m, a work which was published ?"J 



at Madrid in 1771, in '2. vols. 4to. This theory in- 

 cludes all the circumstances of motion, both during the 

 continuance of the shock and after the shock, and em- 

 brace* the laws of the collision of hard bodie*, of soft 

 bodies, and of bodies perfectly or imperfectly ! 

 whether they are moved in virtue of constant velocities 

 and accelerating farces, or by both of these causes com- 

 bined. Thi* theory i* however not applicable, as might 

 at firt sight have been expected, to the impulse of fluids; 

 but the same author has favoured us with a new theory 

 of the resistance of fluids, which has been adopted by 

 Prony and revera) other French writers. This theory 

 has, in Prony's opinion, been confirmed by very good 

 experiments, and also by its conformity with the pro- 

 grew and other motions of vessels. It has also, a* 

 Prony has remarked, the advantage of presenting the 

 discussion of the question with the different physical 

 circumstances which it involves, an advantage which is 

 not possessed by the ordinary theory. In order to con- 

 firm hi* theory, Don George Juan made the following 

 experiments : He exposed a plane surface of the form 

 of a parallelogram a foot wide, to the action of a current 

 of water which moved with the velocity of two feet 

 per second. When it was immersed jut one foot un- 

 der the water, it supported a weight of I5J pounds 

 ( English measure). When the same plane was sunk 

 two feet m a current of water moving with the velo- 





in 1- 

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