4:82 Transactions. 



In this work the resistance curve is regarded somewhat in the same 

 manner as a stress strain or magnetic force and magnetization curve is 

 regarded— that is to. say, it is a complicated function obtained by experi- 

 ment and expressed by means of a diagram which shows the relation 

 between two chosen functions. 



Professor Lees, on examination of Stanton's experimental results, finds 

 that within the limits of experimental error the law of resistance above the 

 critical value of a smooth pipe can be expressed very approximately in 

 the form 



^^=''(.^)'+^-'- (2) 



where a, b, and x ^^'^ experimental coefficients. When the equation is 

 expressed in absolute units he gives the following values to the coefficients, 

 viz. : — 



a = -0765 ; h = -0009 ; x = 0-35, 

 so that the equation becomes 



P / ,, \0-35 



Converting to foot pound units, and also transforming from resistance per 

 unit area and per unit of mass to energy per pound of fluid per foot of 

 length or " head " per foot of length, we have 



i -7^2 = -00801 ( -^ I + -000028 (4) 



where i is the hydraulic gradient or slope, or, in other words, the resistance 

 head per foot of pipe. This form is more convenient for practical purpose, 

 and conforms to engineering practice. The formula most commonly in use 

 is that known as Chezy's formula, or, rather, a modification of the same, 

 viz., — 



V — CVri (5) 



where C is an experimental coefficient, i the hj^draulic gradient, and r is 

 the hydraulic mean radius which for round pipe is equal to j. It will be 

 seen by comparing equation (4) and (5) that for smooth pipe 



— = .00801 f-5J +000028 (6) 



Returning to equation (4), this is plotted in fig. 1, curve a, with ij/v^ as 



ordinates and log vd/v as abscissae. The reason why it is necessary to adopt 

 logarithmic values is that the range is so great that a comprehensive 

 diagram could not otherwise be drawn within the limits of ordinary sheet. 

 The range covered by experiment and observation lies between the values 

 5'2 and 7*2 of the expression log vd/v, and it will be seen later that certain 

 observations on a wood stave pipe lie on an extension of the curve up to 

 a value of 7-7, which tends to confirm the law as expressed by Professor 

 Lees. 



Accepting curve a, fig. 1, as a sort of datum-line from which to gauge 

 experimental results, the sequel is an account of an examination of experi- 

 ments carried out by different observers on the resistance to the flow of 

 water in pipes with the object of determining whether it is possible in the 

 light of present' knowledge to systematize them and to deduce a law for 

 their behaviour. 



