THE FLOW OF WATER IN CONCRETE PIPE. . 47 



then the center is an open circle, and if its points are given as solid 

 dots, then the center is a solid dot. The centers of gravity of the 

 upper and lower zones for a given series are shown by two concentric 

 circles. The straight line representing the curve for that series 

 passes through these three points, and the equation for this line is 

 the equation for that particular pipe, so far as the observations 

 developed it. 



On Plate VI are shown three lines indicating slopes for three 

 values of z. The slope of 1.80 conforms to that of the Moritz formula 

 and to the slope found by both Moritz and the writer for the flow in 

 wood-stave pipes. The slope of 1.85 conforms to that of the 

 Williams-Hazen formula, while the slope of 2 conforms to the slope 

 in the original Chezy formula and has been adhered to by later 

 authorities. The border lines of the plate are also drawn at the 

 slope of 2 for ready comparison. The slope of 2 agrees with the 

 belief, so long honored that it became an axiom but was later proved 

 not necessarily true, that the loss of head must vary as the square of 

 the velocity. 



With the desire not to increase the number of already numerous 

 formulas, Plate VI was studied, on a tracing made over 10-inch 

 logarithmic paper, in connection with sets of parallel lines based on 

 the above-mentioned definite slopes. On this basis it was obvious 

 that a slope of 2 most nearly applied, not only for the average slope 

 of the various curves, but also in following the zone for a given size 

 pipe from one series through a range of velocities to another series at 

 higher or lower velocities. 



Accepting this value for z of 2 and recognizing that there are 

 several typical concrete surfaces, it is now necessary to determine x, 

 the exponent of d and a set of coefficients, K. Allen Hazen has 

 stated, 1 in discussing the Saph and Schoder experiments : 



It has seemed to the writer [Hazen] that the most accurate value for x could be 

 secured by comparing the results obtained for very small and very large pipes. Of 

 course it is impossible to secure very large pipes with precisely the same kind of 

 interior surface as obtained in very small pipes, but it seems safer to compare the 

 results obtained from very large and very small pipes, even though their interior 

 surfaces do differ somewhat in character, than to take the indications of experiments 

 more closely comparable, but covering a shorter range. 



It is to be borne in mind that Hazen was speaking of brass pipes 

 less than 2 inches in diameter when he referred to "very small pipes." 

 However, the reasoning was sound, and this suggestion has been 

 followed by the writer. Concrete pipes were divided into four 

 general classes, as discussed on page 7: (1) Old Calif ornia pipes ; (2) 

 modern " dry-mix" cement pipe and wood-form monolithic pipe; (3) 

 wet-mix cement pipe and average steel-form monolithic pipe; (4) 



1 Trans. Amer. Soc. Civil Engin., 51 (1903), p. 320. 



