94 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE. 
would carry more air were the same opportunity offered at the intake for its entrain- 
ment. 
Concerning the various factors of the new formula: From the discussion it appears 
to be granted that this formula fits the basic observations better than any other for- 
mula. It should, of course, do this as it is an averaging formula based on all known 
observations. Two questions now arise : Should an average formula be used and should 
factors in new formulas be allowed to digress from time-honored factors in accepted 
formulas? If we do not accept an average formula we must do one of two things. The 
first is to accept a formula that will give the most conservative results. Such a for- 
mula for wood-stave pipe would be probably 25 per cent more conservative than the 
new formula or 40 per cent more than the Moritz formula, if all observations on wood- 
stave pipe are to be included. If we exclude any tests as abnormal we find it hard 
to draw the line — hard to find any tenable intermediate ground between the aver- 
age and the extreme. The other method that may be pursued is to follow Schoder 1 
and Moore, 2 and give the bounding limits for any particular factor, stating these 
limits as a variable feature of the formula. 
Unfortunately the practice of the average engineer is so general that he does not 
become qualified, nor has he the time, to properly choose the correct figure between 
the varying limits. He would rather that the one most familiar with the variables 
give him one formula without varying coefficients or exponents and with a statement 
as to its approximate accuracy. This was recognized by Moritz. 3 In the opinion 
of the author the averaging formula appeared best when used in connection with the 
suggested factors of safety. (See p. 66.) 
Mr. Moritz 's suggestion that the exponent of d or D in the new formula violates 
accepted exponents in parallel formulas does not appear to the author to be well 
taken when studied in connection with figure 7, which shows the same plotted points 
for wood pipe experiments as figure 4, and which in addition shows by small round 
dots the values of m for all the experiments given on Plate XI, Trans. Amer. Soc. 
Civ. Engin., vol. 51, "The Flow of Water in Pipes," by Saph and Schoder. These 
additional experiments are on various kinds of pipe, including brass, galvanized- 
iron, wrought, sheet, and cast-iron, brick, glass, lead, and riveted pipes. In figure 7, 
line A, is Saph and Schoder 's limiting line for " very straight and very smooth pipes" 
9Qfi 
with the equation n^-^^. Line B is their limiting line for tuberculated pipes, with 
687 
the equation m= t^i.25 ' These writers then state that most pipes in commercial use 
0.469 
will plot between lines A and C, the equation of the latter being m= ^ )1 25 - As the 
values of the exponent of V vary from 1.74 to 2.00 the general equation showing the 
. . , , ,. , „, -rr 0-296 to 0.469 ■ _, + 
variation between the lines A and C becomes H= j^s V 1 -' 4 t0 2 - 00 - 
38 V 1 - 87 
Note that equation H= t^i.25 — mentioned near the beginning of Mr. William's 
discussion on page 81 takes the average of these variants, m=line D, figure 7, while 
Dr. Schoder 4 in 1904 suggested exactly the same formula except that the exponent 
of V was given as 1.86 instead of 1.87. (See column 6, Table 10.) 
Again referring to figure 7, line E shows the author's curve, m/ = - ni , 17 or ~^-[ 7 ' 
Note how closely this line on a slope of —1.17 conforms to the plotted points for all 
1 Trans. Amer. Soc. Civ. Engin., 51 (1903), p. 308. 
2 Id., 74 (1911), p. 471. 
3 Id., p. 478. 
* Eng. Rec, Sept. 3, 1904, p. 281. 
