FLOW OF WATER IN CLEAN PIPES 251 



dence furnislied by all the different styles and conditions in order to cover 

 a sufficientl.y extensive range to evolve a law. 



In determining the constants for pipes the writer has gone through a 

 long and laborious process of plotting results graphically, drawing curves 

 of mean position, adjustments by trial and error and of arithmetical inter- 

 polations. Considering the miscellaneous nature of the pipes employed 

 the probable error of the final result is about as small as can be attained 

 with present information. It is believed that the forms of the rational 

 functions in (12) are essentially correct and that it is sufficiently flexible 

 through the variation of the parameters to fit the adjustment to any new 

 conditions that may arise in the future through an increased number of 

 more accurate experiments. 



Taking into consideration experiments on pipes of copper, brass, tin, 

 zinc, lead, glass, wood, tile, cast and wrought iron uncoated and coated 

 with tar or asphalt, the riveted iron pipes coated and uncoated, with 

 butt or taper joints, cement lined pipes, several hundred observations, 

 whose diameters vary from 0.1 of an inch to 10 feet, and whose velocities 

 vary from 0.1 of a foot to 50 feet per second, the writer has determined 

 the constants in m to be embodied in the following form 



0.0094+^:^ 

 Vr 



0.07 F 0.6 r 



1+ 7 ^i^T^^rr^ + 



(14) 



"l+(o.015 + M2HJ7 '" + 



0.1 



Strictly speaking Vr in (14) should be increased by a constant q as in(12) 

 but as q has a value nearly equal to p or 0.00003 it has been neglected 

 as not affecting the product Vr for any known values of V and r. This 

 is the value for long pipes, for short pipes it must be increased by r/2L. 

 The total static head H is 



8. The following table contains about four hundred experiments on 

 pipes arranged according to increasing diameters and velocities, in which 

 are tabulated in colunms under 1000s the hydraulic slope or loss of head 

 per 1000 feet of length, under V the observed velocity, under lOOilf o and 

 Co the experimental values of these constants. The relation between 

 7tt and c being nic^ = 2g, a table of corresponding values of m and c was 



