THE FLOW OF WATER IN WOOD-STAVE PIPE. 
8& 
elimination of the same is impossible, and this fact should be taken into full account 
when the proposition of offering a new formula is considered. 
With the above ideas in mind, the writer has examined figure 4, from which the 
exponent of d and the coefficient of m have been developed. He assumes the point 
in the center of the diagram with the two concentric rings represents the center of 
gravity of all the points, taking into account the assumed weights, and that the points 
on either side of the center with one concentric ring represent the center of gravity of 
all the points on the respective sides. He has drawn a line (A, fig. 4) through the 
central point on a slope of 1.25, which gives an intercept of 0.43. If this be accepted, 
H=0.43 v 1 - 8 , . _ . • . . , ,,.--, 
the formula becomes 37^5 which gives velocities and consequently discharges 
H=0.38v 1 - 8 . 
that are about 7.6 per cent smaller than those given by the writer's formula tt^3 
If the figures in column 20 of Table 3 are now corrected by the addition of 7.6, the 
"grand average per cent' ' of deviation of the observed velocities from those calculated 
from the above formula becomes 0.04. On its face this would seem to indicate that 
this formula is more accurate than the Scobey formula, which is not necessarily true, 
and this leads the writer to remark that the deductions at the foot of this table are 
misleading. 1 The same remark applies to Table 2. However this may be viewed, 
he thinks a better comparison of the formulas could be presented by grouping the ob- 
servations or pipes by percentage deviation from each formula, somewhat as follows: 
Table 10. — Comparison of observed velocities to velocities computed by various formulas. 
Number of observations differing by given per cent. 
Author of formula. 
Less 
than 
+ 5. 
+5 to 
+ 10. 
+ 10 to 
+ 15. 
+ 15 to 
+20. 
+20 to 
+25. 
More 
than 
+25. 
Less 
than 
+ 10. 
Less 
than 
+ 15. 
Scobey 
30 
44 
43 
42 
37 
24 
30 
12 
39 
20 
19 
24 
5 
36 
6 
20 
16 
6 
20 
4 
8 
14 
1 
4 
5 
5 
8 

11 
1 
54 
74 
55 
81 
57 
73 
Williams-Hazen 
98 
Moritz 
60 
Tutton 
117 
Weisbach 
63 
Author of formula. 
Less 
than 
-5. 
—5 to 
-10. 
-10 to 
-15. 
-15 to 
-20. 
-20 to 
-25. 
More 
than 
-25. 
Less 
than 
-10. 
Less 
than 
-15. 
Scobey 
46 
49 
29 
46 
29 
48 
40 
18 
40 
36 
39 
16 
42 
13 
30 
12 
9 
49 
11 
39 
1 
1 
41 
1 
14 
2 
2 
8 
5 
11 
92 
89 
47 
86 
65 
131 
Williams-Hazen 
105 
89 
Tutton 
99 
Weisbach 
95 
The writer is convinced that his formula should be modified to the extent of increas- 
ing the coefficient m from 0.38 to 0.43, which will reduce the calculated carrying 
capacities by 7.6 per cent. He is not convinced that the exponent of d should be 
1 A uthor's note. — The line A (fig. 5) or any other line drawn through the center of gravity will give a formula 
in which the "grand average per cent" will be very close to zero as the moments of the various individual 
points neutralize each other, the percentages for all pipes on one side of the center of gravity being too low 
and for those on the other side too high. The heavy line in figure 5, representing the author's formula, is 
the only line that satisfies not only the "grand average per cent" but also satisfies similar comparisons for 
only those pipes above the center of gravity or those below the center of gravity. This is true because this 
line is the only one that can and does pass through the center of gravity of all points and likewise through 
thecenters of gravity of the points in the two zones into which the main center of gravity divides all points. 
Viewed in this light the deductions at the foot of the columns mentioned are not misleading. 
