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 Bowing 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/ 



F= 1^486^ 0>87g 05 (2Q) 



in which n has approximately the same values as in the Kutter 

 formula; the Bazin (1897) formula, 



V=~-R™s™ (21) 



1+3= 



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 



{)art are laid on an even gradient, where the hydraulic grade line 

 ies 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 1SK9 (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 v 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 R. B, Buckley, London, 1911, p. 10; Engin. News, June 17, 1915, p. 1171; Engin. 

 Roc, vol. 75, Mar. 10, 1917, p.395; Engin. News-Rec., vol. 79, Aug. 9, 1917, p. 277; id., vol. 82, Mar. 13, 1919, 

 p. 536; id., Apr. 3, 1919, p. 686. Prof. If. 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.) 



66 



