518 



HYDRODYNAMICS. 



Motion of ag we did upon the real velocity, its value will be 



Water in i i / j ___ n \ 



Pipes and *L -J> a quantity which must always be 



Canals. 4/0 Log. v " 



S ^^" / subtracted from the velocity already determined. Hence 



the value of V will be V= ^"g^ -0 



i/s Log. Vs+ 1.6 



^(W-0.1) = oi / 



/ST LogVS V* 



V* Log. </ + 1.6 



= TJ, i. But since the term - , - 



\/S Log. yS/ y'S Log. \/S 



is composed of constant quantities, it may be expressed 

 in a single number. The value of it was determined 

 by many experiments to be 0.3 inches. By substitu- 

 ting, therefore, this value, we obtain 



v _ 



\/s Log. 



.6 



-0.3(v/4 0.1), or in numbers, 



s Log. </*+!. 6 

 07 



. nFrm 



1 __ () Q 



In these expressions the following are the values of 

 the letters employed. 

 V represents the mean velocity in inches per second 



of any current moving in a channel of indefinite 



length, of which the sections of the declivity are 



constant. 

 d is the mean radius or hydraulic mean depth, or a 



quantity which, when multiplied by the perimeter of 



the section of the channel, gives an area equal to 



the area of the section. In circular pipes d is 



equal to half the radius. 

 is an abstract and constant number, which is found 



by experiment to be equal to 243.7 

 g is the velocity in inches, acquired by a falling body 



at the end of a second of time, being always equal 



to 32.174. 

 s is the denominator of a fraction which expresses the 



slope of the channel, the numerator being supposed 



unity. 

 Log. denotes the hyperbolic logarithm of the quantity 



to which it is prefixed, and may be obtained by 



multiplying the common logarithm by 2.302581. 



In order to shew the agreement of the preceding 

 formula with experiment, M. Du Buat drew up the 

 following Table, which contains the observed velocities 

 as deduced from the experiments of Bossut, and from 

 many new experiments made by Du Buat himself, and 

 also the velocities calculated from the formula. 



In the first set of experiments on pipes, col. 1. con- 

 tains the number of the experh- ent: col. 2. the length 

 of the pipe; col. 3. the height of the reservoir; col. 

 4. the values of * as deduced from col. 2. and 3 ; 

 col. 5. the observed velocities ; and col. 6. the compu- 

 ted velocities. 



In the second set of experiments on canals and ri- 

 vers, col. 2. shows the area of the section of the chan- 

 nel ; col. 3. the perimeter of the channel in contact 

 with the water ; col. 4. the square roots of d, or the 

 mean radius or hydraulic mean depth ; col 5. the de- 

 nominator s of the slope ; col. 6. the mean velocities 

 cbserved ; and col. 7. the mean velocities calculated, 



Motion of 

 Water in 

 Pipes and 



TABLE X. Containing a Comparison of the Velocities Canals, 

 calculated by Du Bunt's Formula, with the Vtloci- -"~Y~ W 

 ties observed in the Experiments of Couplet, tfos- 

 sut, and Du Buat, on Pipes, Canals, and Kivers. 



SET I. EXPEJIIMENTS ON PIPES. 

 Experiments oy the Chevalier Du BUAT. 



Pipe $ofa Line in Diameter, placed Vertically, anil 

 ~~ 



