THE FLOW OF WATER IX DEAIIT TILE. 
COMPARISON OF VARIOUS FORMULA. 
47 
Since from a practical standpoint we are interested only in the 
tile flowing full, velocities as computed by formula 34 are compared 
with velocities as taken from figures 1 to 12, Plate IX, for the tile 
flowing full. These results are shown in Tables 8 and 9. The differ- 
ence is sho^^TL, rather than the ratio, between each two determina- 
tions of velocity, in order that the variations in the low velocities shall 
be given only equal weight with equal variations in the high veloci- 
ties. To get the average differences given in Tables 8 and 9, the arith- 
metical sum of the differences is divided by the number of item's. 
S/ope tr) Feet per /OO Feet 
4^67 .8 ,9 1.0 
Fig. 5. — Comparison of velocities computed by various formulae. 
Both the Poncelet and the Beardmore formulas gave greater dif- 
ferences when appli'ed to the experimental data than does the ten- 
tative formula, No. 13. The velocities from the curves in Plate IX 
were substituted in the WiHiams-Hazen formula, and the average 
value of Cy,, was found to be approximately 120. Using this value 
in the Williams-Hazen formula, recomputing the velocities, and 
comparing them \dth the velocities from the curves in Plate IX, it 
was found that the average differences were practically the same as 
the average differences stated at the bottom of Tables 8 and 9. 
A comparison of the velocities computed by the various formulae 
for one size of tile may be obtained from text-figure 5. This figure 
shows the velocities for 8-inch tile as computed by the Poncelet, the 
Winiams-Hazen, the Chezy-Kutter (^^ith the coefficient of roughness 
n, taken equal to 0.013), the EHiott, and formula 13 herein derived 
from the experimental data. The observed experimental velocities 
are also shown. 
