94 BULLETIN 376^ U. S. DEPARTMENT OF AGKICULTTJEE. 



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 Une — 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* 

 and Moore, ^ 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.^ 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, 

 Une A, is Saph and Schoder 's limiting line for "very straight and very smooth pipes" 



with the equation tsi=-j^^. Line B is their limiting line for tuberculated pipes, with 



the equation m= jji^- These writers then state that most pipes in commercial use 



0.469 

 will plot between Unes A and C, the equation of the latter being m= pi. 25 ' As the 



values of the exponent of V vary from 1.74 to 2.00 the general equation showing the 

 variation between the lines A and C becomes H=-^ — J)^-'^^ — ^^'^^ *" ^■''°* 



0.38 V'-*^ 

 Note that equation H= " t-vi.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* 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^= " ^^^ or -^7:1-7* 



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. 



sid., 74(1911), p. 471. 



« Id., p. 478. 



* Eng. Rec., Sept. 3, 1904, p. 281. 



