420 



HYDRODYNAMICS. 



HKtouy. city of one foot four inches in a second, it supported a 

 s< ~"V' r weight of 2G pounds. The following Table shews 

 the theoretical and practical results. 



Velocity of Depth of Observed Calculated 



Water. Submersion. Resistance. Resistance. 



Exp. 1. 2 feet. 1 foot. 15^ pounds. 20^ pounds. 



Exp. 2. 14 2 20 391 



The ratio of the observed resistance is as 15 : 26|, 

 while that of the calculated results is as 15 to 28. Don 

 George Juan has printed two appendices at the end of 

 his first volume, in one of which he applies his theory 

 to the resistance of elastic fluids ; and in the other he 

 examines the experiments of our countryman Smeaton 

 on the maximum effect of water mills. He shews, 

 from this theory, that the velocity of the floatboards 

 ought to be a little less than one half the velocity 

 of the water, in order to produce a maximum effect ; 

 a result which is almost exactly the same which Smea- 

 ton found from experiment. It is a singular cir- 

 cumstance, that the experiments of Don George Juan 

 give resistances much greater than those of Bossut, 

 D'Alembert, and Condorcet, which were made under 

 great pressures; so that his theory will differ very wide- 

 ly from the best experiments which have been made on 

 the resistance of fluids. Dr Robison has remarked, 

 (see his System of Mechanical Philosophy, vol. ii. art. 

 Resistance of Fluids, which contains an examination of 

 this new theory), that Don George Juan's equation ex- 

 hibits no resistance in the case of a fluid without weight. 

 A new edition of the Examen Maritime, with copious 

 notes and additions, was published at Paris in 1783, by 

 M. L'Eveque, entitled, Examen Maritime, Theorique et 

 Pratique, ou Traits de Mecanique, applique a la Construc- 

 tion el a la Manceuvre des vaisseaux et autres batimens. 

 Researches In the year 1798, M. J. B. Venturi, Professor of Na- 

 of Venturi. tural Philosophy at Modena, published his experiments 

 A.D. 1798. an( j observations on fluids, in a work entitled Sur la 

 communication laterale du Mouvement dans les Fluides, 

 which was some time afterwards translated into Eng- 

 lish by Mr Nicholson. This work contains many new 

 and valuable results, of which the following are the most 

 important. He found, that in any fluid, the parts which 

 are in motion carry along with them the lateral parts 

 which are at rest. This proposition he established by 

 introducing a current of water, with a certain velocity, 

 into a vessel filled with stagnant water. The current, 

 after passing through a portion of the fluid, was recei- 

 ved in a curvilineal channel, the bottom of which gra- 

 dually rose till it passed over the rim of the vessel ; 

 and in a short time there remained in the vessel only that 

 portion of the fluid which was originally below the 

 aperture at which the current was introduced. By the 

 aid of this principle, which he calls the lateral commu- 

 nication of motion in fluids, and which he thinks is not 

 sufficiently accounted for by the cohesion of the fluid 

 particles, he explains many facts in hydraulics. In ex- 

 amining the effect of additional tubes, Venturi found, 

 that if the part of an additional tube, near the orifice, 

 lias the form of the vena conlracta, the quantity of wa- 

 ter discharged will be the same as if there was no 

 contraction ; that atmospherical pressure increases the 

 expenditure through a simple cylindrical tube, compa- 

 red with that which is seen through an orifice in a thin 

 plate ; that in descending cylindrical tubes, whose up- 

 per ends have the form of the vena contracta, the ex- 



penditure corresponds with the height of the fluid History. 

 above the lower end of the tube ; that, with additional N -"-Y""*' 

 conical tubes, the expenditure is increased by the pres. 

 sure of the atmosphere, in the ratio of the exterior sec- 

 tion of the tube to the section of the contracted vein ; 

 that cylindrical pipes discharge less water than conical 

 pipes which have the same exterior diameter, and di- 

 verge from the place of the contracted vein ; that, by 

 suitable adjutages applied to a horizontal cylindrical 

 tube, the expenditure may be increased in the ratio of 

 24 to 10, the head of water remaining invariable ; that 

 the expenditure by a straight tube, a quadrantal arc, 

 and a rectangular tube, each of which is placed hori- 

 zontally, is nearly as the numbers 70, 50, and 45 ; and 

 that the expenditure is diminished by the internal 

 roughness of a pipe, an effect which he conceives i* 

 not produced by the friction of the water against the 

 asperities themselves. 



Although, as M. Prony has remarked, " the results Expeti. 

 obtained by the Chevalier Du Buat, and his sagacious ments of 



mode of classifying the different kinds of resistances t!ou j Blb 

 , . , r* .!_ .. ,. a j t. L on the it- 



which appear in the motion of fluids, might have con- s^ta,,,.,, O f 



ducted him to express the sum of these resistances by fluids, A.D 

 a rational function of the velocity composed of two or 1800. 

 three terms only, yet the glory of this discovery was 

 reserved for M. Coulomb." This eminent philosopher, 

 who had applied the doctrine of torsion with such dis- 

 tinguished success in investigating the phenomena o? 

 electricity and magnetism, entertained the idea of exa- 

 mining in a similar manner the resistance of fluids ; 

 and in the year 1800 he laid before the National In- 

 stitute of France his memoir upon this subject, entitled 

 Des Experiences destinies a determiner la coherence des 

 Fluides, et les lois de leurs resistances, dans mouvemens tres 

 lenls, which was published in the third volume of the 

 Memoir es de I'Inslitul. In determining the resistance 

 of the air to the oscillations of a globe, Sir Isaac New- 

 ton employed a formula of three terms, one of which 

 varied as the square of the velocity ; the second, as 

 the 4 power of the velocity ; and the third, as the sim- 

 ple velocity : and in another part of the Principia he 

 reduces his formula to two terms, one of which is 

 constant, while the other is as the square of the velo- 

 city. Daniel Bernoulli * has employed a formula si- 

 milar to this of Newton's; and M. S'Gravesendet makes 

 the pressure of a fluid in motion against a body at rest, 

 partly proportional to the simple velocity, and partly 

 to the square of the velocity ; while, when the body 

 moves in a fluid, he makes the resistance in proportion 

 to a constant quantity, and to the second power of the 

 velocity. M. Coulomb, however, has proved, by many 

 fine experiments, that there is no constant quantity of 

 sufficient magnitude to be detected, and that the pres- 

 sure sustained by the moving body is represented by 

 two terms, one of which varies with the simple velo- 

 city, and the other with its square. The apparatus by 

 which these results were obtained, consisted of discs 

 of various sizes, which were fixed to the lower extre- 

 mity of a brass wire, and were made to oscillate under 

 a fluid by the force of torsion of the wire. By obser- 

 ving the successive diminution of the oscillations, the 

 law of the resistance was easily found. The oscillations 

 which Coulomb found to be best suited for this kind of 

 experiments, continued for twenty or thirty seconds ; 

 and the amplitude of the oscillations that gave the most 

 regular results, was between 480, the entire division 







Comment. Petropol. torn. iii. and v. 



Phyiices fkmenta Mathemalica, torn. i. 191 1. 



