THE FLOW OF WATER IN WOOD-STAVE PIPE. 95 
kinds of pipe, and note also that Williams and Hazen found this slope for all hinds of 
pipe to be —1.167 (practically —1.17) as shown in formula 8a, page 6. Furthermore, 
by reference to pages 4 to 7 of their tables l 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 Williams 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 Williams- 
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 formulas, 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. 
