CATALOGUE. THEOUY OF HYDRAULICS, RiVEUS. 





Zendrini de motu aquarum. 



Bossut. 



Genette Tableau des rivieres. 



Buat. 



Measurement of the depth of a river. Roz. 



III. 64. 

 Lespiiiasse and Frisi on the velocity of rivers. 



Roz. IX. 145, 398. XI. 58. 

 Lorgna Memorie intorno all' acque correnti. 



Veron. 1777. 

 Lorgna Ricerche intorno alia distributione 



delle velocita nella sectione de fiumi. 4. 



R. S. 

 Rennel on the Gansres. Ph. tr. 



o 



Brilnings iiber die geschwindigkeit des flies- 



senden wassers, von Kronke. Frankf. 

 Woltmann's beitr'age zurhydr. arch. III. 

 Aubry on the force of torrents. Roz. XIV. 



101. 

 Bernhard Hydraulique. 

 Stratico on rivers. Ac. Pad. III. 3S3. IV. 



114. 

 Trembley on the course of rivers. A. Berl. 



1794. 3. 1798.62. 1799- 8. 

 Hennert on the velocity of water in rivers. 



Hind. Arch. I. 1. 

 Smeaton's reports. 

 Fabre sur Ics torrens et les rivieres. Par. 1797. 



R.I. 

 Robison Enc. Br. Art. River. 

 Silbenchlag Theorie des fleuves. 



Ace. Montucl. and Lalande. III. 712. 

 Venturi on the motions of fluids. 

 On friction in watercourses. Nich. III. 252. 

 Edelbrooke on the Ganges. As. Res. VII. 1. 

 Cavallo Nat. Phil. 11. 173. 

 . .Chiefly from Venturi. 



The friction of rivers is not quite proportional to the 

 square of the velocity, the velocity increasing somewhat 

 more rapidly than the square root of the fall. The excess 

 VOL. II. 



of the siiperficial velocity v above the vc-locity at the bottom, 

 is 2v/k — li V being expressed in French inches. The 

 mean \'elocity is z) — ^v-\-l. Buat. 



Gerstner finds Buat's formula not perfectly accurate at 

 any temperature, for small pipes. But in fact the formula 

 can by no means have been intended to be applied to such 



47Si 



pipes. Buat's theorems are i=- 



l being the length 



~478A — v'' 



of the pipe wrhich employs the pressure of an inch of the 

 head of water in overcoming its friction, I the length of the 

 pipe, h the whole height of the head, and v the velocity, 

 all in French inches; but for the number 478 Langsdorf 



substitutes 4S2; then un^ 



•1) 



— .l),e being the hydraulic mean depth, or one fourth of the 

 diameter d ; and for the determination of v, I- may be taken 



_H-45£ 

 ~ k 



/+45rf 



In English measures, we may use the same valutj 



•fori,andt)~Cv'e — .l).i . ,V 



^ Vv^i— h.l.v/(/'+i.e) / 



Instead of h.l.^/ (1+1.6), we may substitute .851"' which 

 is nearly the same, for moderate velocities. The ex- 

 pression f^aorCv'e — iJ.(J_+i:L_.ooi)wiIlalso 



be found to agree extremely well with Buat's formula, and 

 will perhaps be in many respects more useful ; and we may 

 employ, with very little inaccuracy, i-*" instead of i-", 



1.6 ^ . i.ei' ^. , 

 the term -r—— becoming — ; — , which may be determin- 

 l'-° 



ed without logarithms, and the whole formula may be 



thus e^tpressed: vz:i53(y/d — .'i).[-/l )+1.6 



\ \l-\-4id I 



(-— — -j" — .001.1. These formulas may also be <in- 

 ployed for rivers-— being the sine of thei nclination. 



CI 



When the pipe is bent in one or more places, the efTect 

 of the flexure may be found by adding into one sum j tlie 



squares of the sines, then ?■— . or more 



k—( + ) 



\ 482 3000/ 



/ 4 82rfA \ 



Simply ^=^{ a+j_i+,{ ^)- Langsdorf, fK,m Buat, 



A floating log descends faster than a chip, its ovv'n weight 

 tending to accelerate it. Robison. 

 Gg 



