THE FLOW OF WATEE IN WOOD-STAVE PIPE. 11 



Gardner S. Williams ^ says : 



One of the most interesting features of the investigation is the light it throws upon 

 the inapplicaoility of the long-honored law that loss of head varies as the square of the 

 velocity. 



He offers the deductions, based on the study of more than 80 

 series of tests by 13 observers, that the exponent increases from 1.80 

 to 2 in pipes ordinarily used by engineers; that it increases as the 

 roughness increases; that it decreases as curvature increases, and 

 that it is different for different materials, being lowest for tin and 

 brass. 



After the Noble tests nothing was offered in engineering hterature 

 until J. L. Campbell ^ made tests on the El Paso & Southwestern 

 Railway pipe (Nos. 15 and 21). The values of n were so low that the 

 results were seized upon by some wood pipe manufacturers and given 

 out broadcast as the values of n to apply to wood pipe. These values 

 showed an enormously greater carrying capacity for wood than for 

 iron or steel pipe. The results are unquestionably too low for the 

 following reasons: In the discussion G. E. P. Smith ^ asks, "Was 

 the first appearance or the average time of appearance, accepted for 

 computing the velocity of fiow?" to which Campbell rephes (p. 188), 

 ''Referring to Mr. Smith's question about the velocity measurements 

 by bran, the first appearance of the bran and the colors was taken 

 because the intervals of time given thereby were in close accord 

 among themselves and with the weir measurements." (Italics are 

 the writer's.) 



In the opinion of the writer, who used color for many of his experi- 

 ments (see p. 23), the mean of the first and last appearance of color 

 comes quite close to the true mean. (See also the article by E. W. 

 Schoder in the ComeU Civil Engineer, December, 1911.) If the 

 first indication of color is taken, then the maximum thread of velocity 

 is used; or, if diffusion in addition to mechanical mixing occurs, 

 a velocity in excess of the true maximum is indicated. No one Would 

 suggest accepting as the average the velocity of a float down the 

 maximum current in an open channel without applying a coefficient 

 which varies from about 0.55 to 0.95. The fact mentioned by 

 Mr. Campbell, that the "intervals * * * were in close accord 

 among themselves," proves nothing but consistency. Regarding the 

 agreement with the weir it should be remembered that this device 

 gives discharge; color and bran tests give velocity. To permit 

 comparison with the results of weir tests the velocity must be multi- 

 pHed by the area of the bore. If the velocity as determined by the 

 colors were taken too high and the assumed area of the bore too low, 



1 Trans. Amer. Soc. Civ. Engin., 49 (1902), p. 155. 



2 Engin. News, 60 (1908), p. 225. Trans. Amer. Soc. Civ. Engin., 70 (1910), p. 178. 



3 Trans. Amer. Soc. Engin., 70, p. 186. 



