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 a,nd 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) 
i Trans. Amer. Soc. Civil Engin., 51 (1903), p. 320. 
