THE FLOW OF WATER IN WOOD-STAVE PIPE. 81 
in all the waters tested, and the variation in specific gravity from that of distilled 
water was found to be very slight. As it was not practicable to make an ex amin ation 
of the interior of this pipe the nominal size was accepted as correct. It conveys water 
for several miles down the very rugged canyon spoken of in the discussion of pipe No. 
31. Both vertical and horizontal curves are numerous but not excessively sharp. 
These tests excited much comment at the time for the reason that they were the first 
to show that a value of about 0.010 for n in the Kutter formula would not apply to all 
sizes of pipe under all velocities. When compared with all other tests on large pipe, 
with the exception of Nos. 45 and 46, the capacity of this pipe is shown to be about 
equal to the discharge computed by formula. Compared to the new formula the 
capacity is from 5 to 8 per cent less than average. For further discussion of results on 
this pipe see page 9. 
DISCUSSION OF "FLOW OF WATER IN WOOD-STAVE PIPE." » 
By Gardner S. Williams, Consulting Engineer, Ann Arbor, Mc7z.; Theron A. Noble, 
Consulting Engineer, North Yakima, Wash.; D. C. Henny, Consulting Engineer, 
U. S. Reclamation Service, Portland, Oreg.; E. A. Moritz, Engineer, U. S. 
Reclamation Service, Denver, Colo.; E. W. Schoder, Professor in Charge of 
Hydraulic Laboratory, Cornell University; L. M. Hoskins, Professor in Charge of 
Department of Applied Mathematics, Leland Stanford Junior University. 
Mr. Williams: It may be interesting in connection with the Moritz formula as 
expressed by the author [formula 9, p. 6] 
0.38 V 1 - 8 
**-~ D 1 - 26 
to call attention to the fact that from the experiments of A. V. Saph and E. W. 
Schoder, published in the Transactions of the American Society of Civil Engineers, 
vol. 51, the writer derived from the form given at the bottom of page 308 a formula 
for general use with all kinds of pipe, 
0.38 V 1 - 87 
H= 
D 1.25 
which, it will be seen, is almost identical with the author's form of the Moritz for- 
mula and has been taught to the students of the University of Michigan since 1904. 
From the standpoint of exact experimentation slight errors may be expected in 
the author's results from the method of determining diameters of his pipe. The 
effect of swelling of the wood in the staves, where they are restrained by the hoops, 
may very probably change the diameter after they have become saturated from 
what it was when they were dry. 
There is also some question as to the uniformity of the diameters of the glass tubing 
and the author's practice of reading but one tube of his gauge (as indicated on p. 22) 
may very likely involve a small error in the head, as in the writer's experience upon 
careful examination he has never yet been able to find two pieces of tubing that were 
exactly of the same internal diameter. 
* Appreciating that the present knowledge of the flow of water in wood-staves pipe is due to careful ex 
perimentation and subsequent discussion, carried over a period of 20 years, the original manuscript of the 
preceding paper was submitted to the above-named men, each of whom has been closely in touch with the 
development of this knowledge. They were asked for criticism and comment. Acknowledgment is now 
made of the time and labor expended gratuitously by these authorities in preparing their comments which 
comprise the discussion given here. Many ot the changes suggested by them have been made and to avoid 
confusion their papers have been therefore edited to conform to such changes. 
Throughout this discussion "the writer" will refer to the name heading that particular part of the 
discussion and "the author" will refer to the author of the paper. 
42463°— Bull. 376—16 6 
