THE FLOW OF WATER IN WOOD-STAVE PIPE. 11 
Gardner S. Williams 1 says: 
One of the mcst interesting features of the investigation is the light it throws upon 
the inapplicaDility 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 literature 
until J. L. Campbell 2 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 3 asks, "Was 
the first appearance or the average time of appearance, accepted for 
computing the velocity of flow?" to which Campbell replies (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 Cornell 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- 
plied 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, 
i 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. Civ. Engin., 70, p. 186. 
