HYDRODYNAMICS. 



421 



Kstorr. of the disc, and 8 or 10 divisions, reckoned from the 

 " "~ ""' zero of the scale. The following are the principal re- 

 sults which Coulomb has obtained : 



1. That in extremely slow motions, the part of the 

 resistance proportional to the square of the velo- 

 city U insensible, and therefore the resistance is 

 proportional merely to the simple velocity. 

 That the resistance is not sensibly increased by 

 increasing the height of the fluid above the resisted 

 body. 



3. That the resistance arises solely from the mutual 

 cohesion of the fluid particles, and not from their 

 adhesion to the body upon which they act. This 

 result was obtained by covering the oscillating 

 disc with grease, and at other times with coarse 

 sand. In these cases the oscillations suffered no 

 particular change. 



4. That the resistance in clarified oil, at the temper- 

 ature of 69 of Fahrenheit, is to that in water as 



to 1 ; which expresses the ratio of the mutual 

 cohesion of the particles of oil to the mutual cohe- 

 sion of the particles of water. 



M. Coulomb concludes his experiments, by ascer- 

 taining the resistance experienced by cylinders that 

 move very slowly and perpendicular to their axes ; but 

 for an account of the results which he obtained, we 

 must refer the reader to the memoir itself, or to the 

 subsequent part of the present article. 



The first person who thought of applying the law of 

 the resistance of fluids, discovered by Coulomb, to the 

 determination of the velocity of water flowing in natu- 

 ral or artificial channels, was M. Girard, chief engi- 

 neer of roads and bridges, and director of the works on 

 the canal of Ourcq. In hia Ettci Mr It ntowrwtemt 

 tUt EOUJ L'tmranttt, and his Kapport lur It Canal dt 

 f Onrcf . h adopts as a measure of the resistance the 

 product of a constant quantity, by the sum of the first 



* 



and second powers of the velocity; and after determining 

 the value of the constant quantity, from twelve experi- 

 ments of Cbesy and Du Boat, he obtains a formula 

 much more simple than that of Du Buat, but represent- 

 ing the experiments with equal precision. Considering 

 that the water which moves over the wetted sides of the 

 channel, or over the film of water which adheres to these 



(paroi mftuillee). is at first retarded by the 

 ilit v , M li:ch tends to keep it upon this film, he coo- 

 dudes, that from this cause the water will experience 

 a retardation proportional to the simple velocity. From 

 the roughness of the channel be deduces a second re- 

 tardation, (analogous to friction in solid bodies, but 

 differing from it in so far as it does not vary with 

 the pressure,) which is proportional to the. second 

 power of the velocity, as it is in the compound ratio 

 of the force and number of impulsions which the aspc* 

 ritica receive during a given tune, fie then expresses 

 the resistance produced by cohesion by R x /' ' 

 being a quantity to be determined by experiments ; 

 p, the perimeter of the fluid section in contact with 

 the channel ; and V, the velocity ; and considering 

 the adhesion of the asperities to the wetted sides of 

 the channel as the same with, that of the fluid par- 

 ticks to each other, he makes the resistance due to 

 these asperities equal to R XpV*, whence he obtains 



the formula ^- = R (V+V). M. Prony is of opi- 

 nion, that the adhesion of the asperities to the paroi 

 mouillrc, or wetted sides of the channel, ought to be 

 supposed greater than that of the fluid particles ; for if 



the two adhesions were equal, the asperities would have HUtorjr. 

 no more tendency to unite to the wetted sides than to Nl """Y~"' 

 the mass of fluid in motion. 



! i was the state of hydrodynamics, when M. I-bo of 

 Prony published, in 180t, his Recherc/iex Physico-Ma- 

 llitmatiques tur la Thcorie dm Eaux Courantts. In or- 

 der to establish the theory of running waters on a pro- 

 per foundation, this eminont mathematician collected the 

 best experiments that had been published on the mo- 

 tion of water in conduit pipes, anil in natural and ar- 

 tificial channels. Out of this collection he st-k-ctdl 

 82 of the best, viz. 51 on conduit pipes, and Jl on 

 open canals ; and he endeavoured to combine t 

 data with the principles of physics and nu'chani 

 as to deduce from them general tbrmuL iiich 



the velocity might in every case be obtained by calcu- 

 lation. By these. means he has been able to express 

 the velocity of water, whether it flaws in pipes or open 

 canals, by a simple formula, tree of logarithms, and re- 

 quiring merely the extraction of a square root. The 

 formula, which is applicable both to pipes anil cau;il;, 

 *> ___ 



V 0,0*69734 + / 0,002*065 + ;.( > U , 1 7 X < ; , 

 which gives the velocity in metres ; or, when reiluct.il 

 to English feet, 



V = 0.15H131 + v' 0,023751 + 32806,6 x ' 

 When this foninila is applied to pipes, we must take 

 O = jDK, which is deduced from the equation 





When it is applied to canals, we must take Ci Itl, 



2 



which is deduced from the equation I = ' , R being 



Lf 



qua! to the mean radius of Buat, or the hydraulic 

 mean depth, as already explained. 



M. i'rony has drawn up extensive tables, in which 

 he has compared the observed velocities with those 

 which are calculated from the preceding formula-, and 

 from those of Du Buat and Girard ; and it is sur- 

 prising to observe their agreement with the obser- 

 ved results, and their decided superiority to those of 

 Du Buat and Girard. The progress of hydrodynamics 

 ha* likewise been greatly indebted to the NovvtUe Ar- 

 chitecture Hydmkmc of M. Prony, which appeared in 

 the year 17'W. This able work is divided into two 

 parts ; the first of which is a treatise on mechanics, in 

 which the author has explained the general principles 

 of equilibrium and motion, which are necessary for en- 

 gineers. The second part is divided into four sections : 

 The first section treats of statics, the second of dynamics, 

 the third of hydrodynamics, and the fourth of machines 

 and first movers, considered under the iliif. n nt p: 

 cal circumstances, which have an influence upon their 

 equilibrium and motion. In the chanter on hydrody- 

 namics, he resolves the general problem of the elllu.x 

 of water through an orifice in one of the sides of a 

 vessel, upon the sup|xniition that the fluid strata < 

 serve their parallelism, and that their particles descend 

 with the same velocity ; and from this he deduces, as a 

 corollary, all the ordinary theory of the motion of fluids. 

 He next gives an account of the experiments of Bossut 

 on the efflux of water, and deduces formula by which 

 the results msy be expressed with all the accuracy that 

 practice requires. In treating of the impulse and re- 

 sistance of fluids, he adopts and explains the thcoi 

 Don George Juan, and afterwards gives an account of 



