THE FLOW OF WATEE IIST WOOD-STAVE PIPE. 49 



t<^ have been used to any great extent, probably for the reason that it 

 was based on tests covering only a few pipes, namely, a 4-inch pipe 

 tested by Noble and Harris, Adams's 14-inch and 18-inch pipes, 

 Noble's 44 and 54-inch pipes, and the Ogden tests of 1899 on the 

 72-inch pipe (Nos. 20, 23, 41, 44, and 48, Tables 2 and 3, and PL VII). 



In 1911 E. A. Moritz proposed the fourth set of formulas ^ (see 

 p. 6) with the following qualification: "This formula is not recom- 

 mended for adoption until more data are available and some of the 

 uncertain points have been cleared up." 



A fifth set of formulas is now offered by the writer, who has fully 

 appreciated the inadvisabihty of extending the number of formulas 

 already existing except as must be required by continued investigation. 

 xJis own experiments, especially those on large pipes, when studied in 

 contrection with all previous data, would seem to supply convincing 

 proof that a new formula is needed. 



With the exception of formula 15 aU of the formulas referred to 

 are of the exponential type; that is, they are based on the fact that 

 for any particular series of observations, if losses of head are plotted 

 logarithmically as one set of ordinates and velocities as the other, 

 the resulting points will lie more or less along a straight line. Such 

 a straight line on logarithmic paper represents an equation of the 

 form 



H = mV^ (17) 



which, expressed for logarithmic study, may be stated 



log H = log m + z log V (18) 



where m is the intercept on the axis of H, for V = 1 foot per second 

 and z measures the inchnation of the line, being the tangent of the 

 angle which it makes with the axis of V. 



For a series of pipes of the same general characteristics but of 

 varying diameters the values of m follow the general equation 



m = Kd^ (19) 



Substituting in formula (17) 



H = Kd^V^ (20) 



This expressed logarithmically becomes 



log H = log K + xlog d + zlogV (21) 



Smith's tests (No. 1) were made on a pipe too smaU for any irri- 

 gation usage and the graphic representation of the results, while 



1 Trans. Amer. Soc. Civ. Engin., 74 (1911), p. 442. 

 42463°— Bull. 376—16 4 



