THE FLOW OF WATEE IN CONCRETE PIPE. 63 
The values of the various coefficients are for favorable conditions, and 
factors of safety; as listed on page 54 should be used in design. 
For a comparison of velocities, as computed from various formulas, 
for various sizes of pipe and for varying friction heads, the reader is 
referred to table 10, page 62. 
Again taking up the various formulas mentioned on pages 5 
to 7; the Chezy formula (4, p. 6), will not be considered directly, 
but in its modified form, known as Kutter's formula (5, p. 6). 
THE KUTTER FORMULA. 
In discussing the Moritz experiments with reference to the value 
of n in Kutter' s formula, Hering states * that he "recognized as 
well as did Mr. Kutter 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 notwith- 
standing this the tables and diagrams 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. 
In the case of 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. The variations in the proper 
value of n to assume in the design of 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 original intended purpose, that of design of open channels, for 
which it is eminently fitted. 2 
However, for those who wish to use the Kutter formula, the follow- 
ing suggestions are made. Note that the value of n changes with 
diameter. If velocities are to exceed 8 feet per second, the next 
lower value of n may be safely used. The values of n given pre- 
suppose the use of some factor of safety about as given on page 54: 
Class 1. n=0.013 for pipes up to 10 inches in diameter. 
n=0.014 for pipes from 12 to 24 inches in diameter. 
n=0.015 for pipes from 26 to 42 inches in diameter. 
Class 2. n=0.013 for pipes up to 38 inches in diameter. 
Class 3. n =0.012 for pipes up to 24 inches in diameter. 
n =0.013 for pipes more than 24 inches in diameter. 
Class 4. n=0.011 for pipes from 12 to 24 inches in diameter. 
n =0.0115 for pipes from 26 to 48 inches in diameter. 
n =0.012 for pipes more than 50 inches in diameter 
In order to solve problems involving the Kutter formula, Plate XII 
is given. As being applicable to open channels rather than closed 
1 Trans. Amer. Soc. Civ. Engin., 74 (1911), p. 459. 
2 The Flow of Water in Irrigation Channels, by Fred. C Scobey, U. S. Dept. Agr. Bui. 194, p. 60. 
