PART 2. FLOW OF WATER IN GRADE LINE PIPES. 
PIPES PARTIALLY FILLED. 
All available data bearing upon the capacity of concrete pipes 
and other covered conduits flowing partially full are summarized in 
Table 11, page 68. 
The coefficient of retardation has been computed for five of the 
best known formulas in use in this country for the design of open 
channels. The formulas considered are the Chezy formula (No. 3, 
p. 6); the Kutter formula (No. 5, p. 6); the Williams-Hazen formula 
(No. 7, p. 6) ; the Manning formula, 1 
V=^^R °- Q7 s °- 5 (20) 
lb 
in which n has approximately the same values as in the Kutter 
formula; the Bazin (1897) formula, 
F= 15^6^0.5^0.5 (21 ) 
1+2!= 
For the smoothest cement channels a value of 0.109 for m is sug- 
gested in a table found in many textbooks, probably suggested 
by the first experiment on the Sudbury Conduit. See page 69. 
A glance at column 17, Table 11, shows that the value of m changes 
very rapidly with comparatively small changes of surface and of the 
various hydraulic elements. The writer believes that the formulas 
of Kutter, Manning, and Williams-Hazen can be applied with much 
more assuredness than that of Bazin, if a constant retardation factor 
is to be used for a given surface. 
As the pipes and conduits are not under pressure, but for the most 
part are laid on an even gradient, where the hydraulic grade line 
lies parallel to and just under the intrados, it is perfectly proper to 
regard the pipe as an open channel. 
In the opinion of the writer the Kutter formula appears to apply, 
and as this formula is undoubtedly the one most used in this country 
recommended values of n will be given. 
n=0.0115 for glazed pipes and conduits carrying filtered "water or water from which 
deposits or growths do not accrue. The pipes to be practically perfect in both surface 
and joints. 
n=0.012 for well-made pipes and conduits with first-class joints, smooth monolithic 
pipes or tunnels when new and clean. The surface to class as good, but not the equal 
of glazing. A surface such as is obtained by a " wash coat. " To be free from shoulders 
1 Robert Manning first offered his formula in 1889 (Trans. Civil Engineers of Ireland, 1890, Book No. 8, 
p. 175) in a slightly different form than as now accepted. It has been used extensively by some English 
and Canadian engineers, but has caused little comment in the United States until within the past two or 
three years. It is much simpler of solution than the Kutter formula, and there does not appear to be any 
sacrifice in accuracy if the engineer uses the same values of n to which he has become accustomed. Further 
comments upon the Manning formula are found under the following citations: The Design of Channels for 
Irrigation or Drainage, by iC B. Bucklev, London, 1911, p. 10; Engin. News, June 17, 1915, p. 1171: Enein. 
Rec, vol. 75, Mar. 10, 1917, p. 395; Engiri. News-Rec, vol. 79, Aug. 9, 1917, p. 277: id., vol. 82, Mar. 13, 1919, 
p. 536; id., Apr. 3, 1919, p. 685. Prof. H. W. King, of Michigan University, conducted computations that 
convinced him that the Manning formula is to be preferred to that of Kutter. (Handbook of Hydraulics, 
by H. W. King, New York, 1918, pp. 198, 403.) 
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