106 HYDRAULIC I V VESTIff ATIONS. 



«4 through degrees of pressure; and I found, that the friction could 

 ferentT res - not ^ e re P resente( * by an y single power of the velocity, al- 

 surts compar- though it frequently approached to the proportion of that 

 power, of which the exponent is 1*8*, but that it appeared 

 to consist of two parts, the one varying simply as the velo- 

 city, the other as its square. The proportion of these parts 

 to each other must however be considered as different in 

 pipes of different diameters, the first part being less percep- 

 tible in very large pipes, or in rivers, but becoming greater 

 than the second in very minute tubes; while the second also 

 becomes greater for each given portion of the internal sur- 

 face of the pipe, as the diameter is diminished. 



Formula. If we express, in the first place, all the measures in 



French inches, calling the height employed in overcoming 



the friction f, the velocity in a second v, the diameter of the 



/ / 



pipe dj and its length /,we may make f-zza~v % -\- 2 c-jv; 



for it is obvious, that the friction roust be directly as the 

 length of the pipe; and since the pressure is proportional 

 to the area of the section, and the surface producing the 

 friction to its circumference or diameter, the relative mag- 

 nitude of the friction must also be inversely as the diameter, 

 or nearly so, as Dubuat has justly observed. We shall then 



f 75 1440 180 \ 



find that cmustbe -0000001 ( 430 4--——.—-- — -— — ), 



v a d + 12 a-f-j/ 



and c = -0000001 ^ rf7TT ^ 4- ;7dt 10S0 + 7 + a)> 

 Hence the ve- Hence it is easy to calculate the velocity for any given pipe 

 locity may or r i v er, and with any given head of water. For the height 

 ilto/fbrtty" required for producing the velocity, independently of fric- 



pipe or river v % 



with any head. t ion, is, according to Dubuat, — , or rather, as it appears 

 from almost all the experiments which I have compared, 

 — ; and the whole height h is therefore equal to /-f ~ • 

 /al 1 V 2c/ 1 



%\ =1 Vd t ssi) I * T v > and ^ aki "S 5 =^4^oTi^ 



and 



