THE FLOW OF WATER IN WOOD-STAVE PIPE. 85 
knowledge on this subject. They are digested and presented alongside of previous 
experiments in a manner which renders ready comparison possible on whatever basis 
is most suited to the mental habit as to use of formulas which the reader may have 
acquired. 
The Kutter formula is not adapted to wood-stave pipe, as has been clearly shown 
by the present as well as by previous authors on this subject. Nevertheless it is 
used by many engineers and its use is aided to so great an extent by existing tables 
and diagrams as to leave its intricacy a matter of relative indifference. 
The mind, having become used to dealing with it, and its value n, desires naturally 
to know how the new work now presented, if expressed in the above value, compares 
with previous conceptions. Moreover, if by means of tabulations it would be possible 
for any given diameter of pipe and velocity to select the required value of n, the 
results would conform to the best information available. 
The author has developed a new formula, the use of which is sufficiently easy, 
with the aid of diagrams furnished by him, for practical use. If this were the final 
word on the subject, it might be convenient and best to discard all other formulas in 
dealing with wood pipe. In the past, however, various experimenters have been 
inclined each in turn to work out a formula according to his interpretation of known 
data, and the future is likely to produce similar results. 
If any new formula could be made up which would correctly present the facts, the 
objection to a possible confusion would not be serious. To what extent the author 
has succeeded in this regard can be easily judged from his valuable presentation of 
the case in Plate VI T. 
This plate shows at a glance the deviation of the results of past experiments from 
that which would be obtained through the Scobey formula. Its exponential value 
and constant were determined with a view to minimizing the average of the deviations. 
Consequently the formula will give results which are as likely to be too large as too 
small. As will be noted from this plate, the extent of the overestimating of capacity, 
which its use may involve, frequently exceeds 10 per cent and sometimes reaches 15 
per cent (12-inch pipe, experiment 16). 
Thus the formula proposed does not give safe results. The extent of its possible 
error on the side of danger has been increased by the unexpectedly low friction found 
in the experiments on the White Salmon pipe in the State of Washington (13.5-foot 
pipe). Expressing the matter in the somewhat more readily understood value of 
Kutter's n, there appeared in previous experiments a decided tendency to higher 
values for n with increase of pipe diameter running for 4-foot velocity from 0.010 for 
4-inch pipe to 0.0113 for 14-inch, 0.0128 for 36-inch to 0.0133 for 72.5-inch pipe. This 
tendency is confirmed for lower velocities in experiments with 78-inch pipe. Yet 
for both the 144-inch and the 162-inch pipe values are now found below 0.012. 
It is evident that with further increase of our knowledge on this subject the average 
must change and that the new average can only be expressed in a new formula in 
which possibly the exponential value of H may remain close to 0.555, but in which 
that of D may change as well as the general constant. 
The possible error in the direction of overestimating is proposed by the author to 
be covered by some general factor of safety to be applied in accordance with the injury 
which may follow from a capacity overestimate. There is excellent merit in this 
proposition but it, as well as Plate VII, shows the lack of consistency which appears 
in the nature of the case to attach to the results of various experiments. 
Since, therefore, no definite capacity results can be predicted within 15 per cent 
degree of accuracy, it is somewhat doubtful whether any real advantage can be gained 
by the construction of a different formula with each addition to our available data. 
To the practicing engineer Table 9, showing values of n in Kutter's formula, inter- 
polated from found values for the nearest velocities, may be of use. 
