THE FLOW OP WATER IN WOOD-STAVE PIPE. 



89 



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^-* 

 the formula becomes -rjTas which gives velocities and consequently discharges 



H=0.38v^-^. 

 that are about 7.6 per cent smaller than those given by the writer's formula ^rijs "' 



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 acciirate 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.' 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- 

 Bervations 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 



Williamfs-TTayfin. . ., 



105 



Moritz 



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 



^Author'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 onlylhie 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. 



