THE FLOW OF WATER IN WOOD-STAVE PIPE. 57 
nized as well as did Mr. Kiitter himself, almost at the outset, that n 
was not to be considered a precise and unvarying constant, although 
it was more nearly so than any other constant before proposed.'' * 
The fact that n does vary has been understood by hydraulicians 
specializing in work involving the Kutter formula, but notwithstand- 
ing this the tables and charts which have been accepted as standard 
have assigned values of n to certain degrees of roughness without 
reference to other conditions. The usual understanding regarding 
variation occurring in the value for n has been that n is less in large 
channels than in small ones, although the writer has not been able to 
show from a study of all available data that this variation is as great 
as suggested by Johnston and Goodrich 2 . 
In the case of wood-stave pipes an opposite effect is noted; that is,' 
the value of n becomes greater as the value of R (which is directly 
proportional to the diameter) becomes greater. Referring to Plate 
VIII it will be noted that all of the straight lines are based on the new 
formula (13), page 7, while the n curves are determined in the fol- 
lowing manner: To determine the curve for n = 0.012, the inter- 
sections of the n curve with the diameter curves for various pipes are 
found and these give the locus for all pipes and velocities with 
n = 0.012. 
Each intersection is found by solving formulas 5 and 13 (pp. 6 and 
7) as simultaneous equations, eliminating V, substituting a known 
value for D (from which the known value of R is found, as R=-j- ) 
and solving for H, which is equal to 1000s in the Kutter formula. 
Note that the value of n increases for a given velocity as the size 
of pipe increases and that the value of n decreases for a given size 
of pipe as the velocity increases. These last two statements are 
borne out by a glance at the general trend of column 10, Table 2. 
Assume that Plate VIII, which is a graph of formula 13, page 7, 
correctly represents the flow of water in an average wood-stave pipe. 
This assumption is supported by the figures at the foot of columns 
19 and 18 in Tables 2 and 3 respectively. Assume also that the n 
curves represent the simultaneous values of n for any position on the 
graph. Then the variations in the proper value of n to assume 
in the design of wood-stave pipe become so complicated that the 
Kutter formula had better be abandoned in favor of the exponential 
type of formula. This would leave the Kutter formula for its 
originally intended purpose, that of design of open channels, for 
which it is eminently fitted. 3 
i E. Ganguillet and W. R. Kutter, translated by Rudolph Hering and John C. Trautwine, jr. A General 
Formula for the Uniform Flow of Water in Rivers and other Channels, New York, 1907, 2d ed. 
2 C T. Johnston and R. D. Goodrich. A Formula and Diagram for Determining the Velocity of Flow 
in Ditches and Canals. Eng. Rec, 64 (1911), No. 19, p. 542. 
s The Flow of Water in Irrigation Channels. Fred. C Scobey, U. S. Dept. Agr. Bui. 194, p. 60. 
