THE FLOW OF WATER IN WOOD-STAVE PIPE. 95 



kinds of pipe, and note also that Williams and Hazen found this slope for all kinds of 

 pipe to be —1.167 (practically —1.17) as shown in fonnula 8a, page 6. Furthermore, 

 by reference to pages 4 to 7 of their tables ^ and to the plotted points in figure 7, or 

 to Plate XI in volume 51 of the Transactions of the American Society of Civil Engi- 

 neers, it will be seen that WilUams and Hazen found this exponent of d and D to 

 be 1.167 from exactly the same experiments, except for a few additions, as those that 

 were included in a zone bounded by two lines (A and B, fig. 7) at a slope of, and indi- 

 cating an exponent of, 1.25 by Messrs. Saph and Schoder, while the author found 

 a value of 1.17 when experiments on circular wood pipe alone were considered. As 

 shown in the author's note on page 88, the exponent of 1.25 was determined from a 

 study of smooth brass pipes. 



Summing up, it does not appear from the above study that a value of 1.17 for this 

 exponent of the pipe diameter based on a line plotted through the centers of gravity 

 for all values of m'' in wood-stave pipe experiments is at variance with accepted 

 values of this exponent for flow in all kinds of pipe, as typified by the WilUams- 

 Hazen general formula. 



Dr. Schoder suggests that this paper be broadened to compare "the facts herein 

 established for wood pipes to the facts for pipes of all materials." 



In the author's opinion, however, the structural characteristics and the methods of 

 making joints in pipes of the various materials are so different that it will be extraor- 

 dinary indeed if any one formula can be found to even approximately fit all kinds 

 of pipes. The author believes that such a comparison and conclusions therefrom 

 would be premature at this time, especially in view of the meager information now 

 available concerning the flow in pipes of cement and concrete materials, which are 

 being used more and more for permanent pipe construction. 



In order that a final comparison may be made of various formulae, as suggested in 

 the discussion, the writer has prepared Table 11, which shows the computed veloci- 

 ties by various formulas for given sizes of pipe and given losses of head. The general 

 deduction may be made from a study of this table that it makes little difference 

 which of these formulas is used in the design of pipes up to 12 inches in diameter, 

 with velocities up to 4 feet per second. As larger pipes and higher velocities are 

 involved, the divergence' between velocities as computed by various formulas becomes 

 greater and greater. For instance, a loss of head of 1 foot per 1,000 feet of 12-foot 

 pipe will generate a velocity of 9.74 feet per second, according to the Moritz formula, 

 or 50 per cent more than the velocity computed by the Swickard formula, although 

 the latter was developed for the most part from a study of the Moritz data. 



1 Hydraulic Tables. Williams and Hazen. New York:, 1909. 



