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Historic, archived document

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scientific knowledge, policies, or practices.

LIBRARY

OF THE

UNITED STATES
DEPARTMENT OF AGRICULTURE

es
* 5

Mase

UNITED STATES DEPARTMENT OF AGRICULTURE

, BULLETIN No. 376 Way

Contribution from Office of Public Roads and Rural Engineering
LOGAN WALLER PAGE, Director

Washington, D. C. PROFESSIONAL PAPER November 25, 1916

THE FLOW OF WATER IN WOOD-STAVE PIPE.

By Frep. C. Scosey, Irrigation Engineer.

CONTENTS.
Page. Page.
THtToduChiOMee eee Lenten asa Seed tm 1 | A New Set of Formulas for the Flow of Water
INOMIENC]AEUIME ere ee Ma ae hl Lied oy OS Dey 3 TMNVVOOG-S tae ueipen seer eee aaa 48
Formulas for Flow of Water in Wood-Stave Comparison of the Various Formulas........ si ita
Deity ofc hs hs ea Oe UCR Oa ae pe AS Ao) 4 | Kutter’s Formula as Applied to Wood-Stave
Trend of Engineering Thought Regarding HEA OSA a MNS MOEN EM RE SUL OC ea 56

the Carrying Capacity of Wood-Stave

Effect of Age upon the Carrying Capacity

TE OY Sys Mea et a ty i SEO ON A ene TMB A u of Wood-Stave!bipe. Yona t ego 58
Necessary Field Data for Determination of Capacity of Wood-Stave Pipes............... 58

Retarding Elements of Various Formulas. . 14 | Estimate Diagrams and Table............... 66
Equipment and Methods Employed for Capacity of Wood-Stave Pipe Compared

Collecting and Interpreting Field Data... 16 with that of Cast Iron and Riveted Steel. . 72
Elements of Field Tests to Determine Fric- Conteh isions ars Wee Le rehome barre Dobe yy Lena TE 73

tion Losses and Comparison of Observed A cknowiled Sma entseenp cia 4 be ayy vga onan yas 74

Velocities with Velocities Computed from WS 0) (5) (0 Wb. EAR Rei’) SOM SANS 2 A AR 74

IWATIOMSEOUINMAS Wan ee ete cs) NU ZOHO IS CTISSIO Marceau CW ce Rea naa HOLM ece Da UE Leo 81
DescriptionioiPipest eats nse eh k es eae 40

INTRODUCTION.

During the past 10 or 15 years the use of wood pipe for the con-
veyance of water has been greatly increased. Such pipe is now quite
commonly used to convey water for the irrigation of land, the domes-
tic needs of towns and cities, and the development of power. So
long as wood pipe consisted of bored logs its carrying capacity was
limited to a small flow and its adaptation to a limited set of condi-
tions, but the conversion of clear, sound lumber into staves and the
making of stave pipe into sizes from 12 to 72 inches in diameter led
to a great expansion in both carrying capacities and uses. More
recently it has been found that stave pipe can be successfully built

Notre.—This bulletin treats of the subject of flowing water in wood-stave pipes. It is based on field
tests made on pipes in commercial operation. New formulas are developed that more accurately fit all
known data than any others now used. This publication is offered for use of engineers designing and
measuring wood-stave pipes for irrigation, power, municipal, mining, or other purposes and for courts
and attorneys at law interested in cases involving the carrying capacities of wood-stave pipes.

42463°—Bull. 376—16——1

2 BULLETIN 876, U. S. DEPARTMENT OF AGRICULTURE.

and operated in sizes up to 12 and 13 feet in diameter, the largest to
date being 134 feet. This great increase in size and carrying capac-
ity has been brought about by providing yokes or cradles which
support the lower part of the pipe and thus prevent its collapse.

Being well adapted to low heads and large diameters, such pipe
has proved one of the best and cheapest means of conducting large
volumes of water under low or medium heads from the sources of
supply to the places of use, regardless of whether the latter be a
power plant, a storage reservoir, the highest portion of an irrigated
tract, or the distributing reservoir of a municipality. Stave pipe is
also frequently used in the construction of inverted siphons, so
called, in conjunction with canals and grade pipe lines, to convey
water across gulches, ravines, or other depressions or down chute
drops to lower levels. It is likewise well adapted to rolling ground
where the building of canals on grade might be impracticable.
Finally, in the smaller sizes it is often used to convey and distribute
water to orchard tracts, manufacturing plants, and municipalities.

The present economic importance of stave pipe in this country,
which arises from its adaptation to so many diverse uses, its wide
range of capacities, the ease with which it can be laid on rough ground,
and its cheapness when compared with other pressure pipes, has led
this department to investigate and report upon its merits and de-
merits. About three years ago a study was begun which comprised
the types, materials, methods of construction, and durability of wood
pipe. The results of this study were summarized in a recent depart-
ment bulletin.t During the past two years another phase of the
same general subject has been investigated. This investigation has
included the making of tests and the collection of data on the flow of
water in wood-stave pipe, the results of which are embodied in this
report. Field work during the summer seasons of 1914 and 1915
consisted in the performance of 64 experiments on the flow of water
in wood-stave pipes ranging in diameters from 8 inches to 134 feet,
while the office work consisted in the collection and analysis of avail-
able records of all previous experiments of a similar character and
the preparation of the data herein presented. From the results of
all experiments made, which combined reach a total of 286, there
has been deduced a new set of formulas for the flow of water in stave
pipe which is here presented. (See p. 48.)

In another publication ? the writer has endeavored to show that
Kutter’s formula is applicable to the design of any open channel and
that the recommendations of the earlier writers on this subject con-
cerning the values of n (which comprises all the influences retarding

1 Wood Pipe for Conveying Water for Irrigation, by S. O. Jayne, Bulletin 155, U. S. Department of
Agricu‘ture.

2 The Flow of Water in Irrigation Channels, by Fred. C. Scobey, Bulletin 194, U. S. Department of
Agriculture.

THE FLOW OF WATER IN WOOD-STAVE PIPE. 3

the flow) were in the main correct. But a thorough study of the flow
of water in pipes, and more particularly wood-stave and concrete
pipes, has convinced him that Kutter’s formula is not best adapted
to flow through pipes running full and under pressure. The work of
recent experimenters indicates that the exponential type of formula
is best adapted to such flow. Therefore the new formula is of the
exponential type.

Much uncertainty has existed in the minds of hydraulic engineers
during the past 30 years with regard to the carrying capacities of
stave pipe. If the new formula helps to clear up former uncertain-
ties and give to those engaged in the design and operation of stave
pipes a reliable guide by which to determine flow through such con-
duits, it will have served its purpose.

NOMENCLATURE.

Unless otherwise noted, the various symbols used throughout
this publication will have the following significance:

d—The mean inside diameter of the pipe in inches.

D—The mean inside diameter of the pipe in feet.

r—The mean inside radius of the pipe, or 4D, in feet.

Q—The mean discharge of the pipe, during the test, in second-feet.

A—The mean area of the pipe bore, in square feet, =zr?.

V—The mean velocity of the water, during the test, in feet per second.

L—tThe length of reach tested, in feet.

h,;—The head of elevation lost in overcoming internal resistances within a fairly
HL

straight pipe of uniform size, in feet,=000 °°

H—The above loss (termed friction loss) per 1,000 linear feet of pipe, = — Be.

h,—The head of elevation lost in creating the mean velocity, V, in feet. Called
velocity head.

h,’—The velocity head recovered as the velocity is reduced at the pipe outlet, in feet.

h,—tThe head of elevation lost at a pipe intake due to impact and entrance resistances,
in feet, here called entry head.

P—The wetted perimeter; in a pipe under pressure, the inside circumference, =7D
or 2zr, in feet.

mI

R—The hydraulic radius,=>; in a circular pipe, under pressur2, =

?

s—The hydraulic grade or slope, in feet per foot of length of a pipe of uniferm size,
_ br,
BEF

n—The coefficient of retardation in Kutter’s formula.

C—The coeflicient of retardation in Chezy’s formula.

C,—The coefficient of retardation in the Williams-Hazen formula. Not to be con-

fused with C in the Chezy formula.

i—The coefficient of retardation in the Weisbach formula. (This formula is variously

known as Weisbach’s, Weston’s, Darcy’s, and Chezy’s.) (Seep. 6.)

H=m V?.—The general equation for the flow of water in a pipe, in which m is the
intercept on the vertical axis and z is the slope of the line, expressed as
the tangent of the angle between the line and the horizontal axis. (See |
equation 17, p. 49.)

4 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

m=K d*.—The equation for the variation in m for a series of pipes of various sizes
but with the same characteristics; K is the intercept on the vertical axis,
and x is the slope of the line, when values of m are plotted as ordinates
and values of d as abscisse. (See equation 19, p. 49.)
m’—The special values of m found for each series of pipes, by drawing lines from the
centers of gravity for the observations in each series, at a constant slope, to an
intersection with the vertical axis.
No. —.—Wherever a pipe number is given, the reference is to the corresponding
number in Tables 2 and 3, to Plate VII, afd to the description of the pipe
under that number.

FORMULAS FOR FLOW OF WATER IN WOOD-STAVE PIPE.

Water is caused to flow and velocity created by the force of gravity.
Thus the flow follows the general law of falling bodies, and the
velocity tends to become constantly accelerated. This tendency is
just balanced by the influences retarding the flow. For a pipe carry-
ing flowing water under pressure, the difference in elevation, H,

————$

-_—
—

==

Fic. 1.—Hydrauliec elements for loss of head in siphon pipe.

(fig. 1), between the surfaces of the water at the intake and outlet
is the effective head through which the force of gravity acts. The
effective or lost head is made up of several individual losses as fol-
lows (fig. 1):
V2
a
This is the head absorbed in creating the mean velocity V, at which
the water is conveyed through the pipe. This loss occurs at the
intake.
As a rule, little or none of this velocity head is recovered at the
outlet of the pipe. The conditions under which recovery may be
expected are discussed on page 61.

Velocity head =h, = (1)

Entry head, h,= S (approximately). (2)

THE FLOW OF WATER IN WOOD-STAVE PIPE. 5

The amount of loss at the entry, due to the effect of contraction
eddies and other retarding influences, is variable and uncertain, but
most authorities agree that it should be taken as half the velocity head
unless the inlet structure is especially designed to minimize this loss.
For further discussion see page 59.

Friction head, hy, is that lost in overcoming the retarding in-
fluences within a reasonably straight pipe. In pipes of great length,
the amount of this loss so far exceeds the two losses first mentioned
that they may often be neglected, especially in small pipes. This
is the loss upon which the experiments described in this paper were
concentrated. Apart from all other losses of head it must be found
in order to permit solution of the various formulas for the flow of
water in pipes with the view to securing additional values for the
factor representing the retarding influences designated as friction.

In addition to the above losses, there may be others, such as those
due to bends and valves or other obstructions; but, as a general thing,
these items do not enter the design of wood-stave pipes, especially
for irrigation purposes. In this use the pipe is laid on such gentle
curves, both horizontal and vertical, that such losses need not be
considered. Valves are seldom set across the line of the pipe,
although there are often one or more valves of various sizes leading
from the pipe. The loss in the main Ine due to these valves is
also neghgible compared with the friction and velocity head losses.

In 1775, Chezy, a French engineer, offered his now well-known
formula for the flow of water in both open channels and closed

conduits:
V=C Rs. (3)

Here C is a coefficient, originally thought to be constant, but now
known to vary with functions of the slope, the hydraulic radius, the
velocity, and with some factor representing the retarding influences
in the channel. Many of the formulas used in this country for the
design of pipes have accepted the Chezy formula as a basis and made
only such modifications as experience dictated, some of them merely
assigning definite values to the coefficient C for definite conditions of
velocity, roughness, and size of pipe.

Since the hydraulic elements secured in the field experiments fur-
nish the necessary data for the determination of the factor repre-
senting the retarding influences in all the formulas most used in this
country, this publication will show this factor as developed by field
tests for several formulas as follows:

(a) The Chezy formula, 3 on page —,

V=C/Rs = CR**s" (4)

6 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

(b) The Kutter modification of the Chezy formula,
aout 441.66 4 2200281 7

0.00281\ 2_ ie yy
S VR

in which C is elaborated so that it takes into consideration the in-
fluence of the hydraulic grade and of the mean hydraulic radius and
introduces a new variable, n, which is supposed to represent all the
retarding influences.

(c) The Weisbach formula,
LY?

eae (6)

V=
1+(41.66+

From the same field data comparison is made between the follow
ing formulas:
(d) The Tutton ! formula for flow in wood-stave pipes,

V =C,R°**s°-! with C,=129 (7)

C, in this formula is not to be confused with C in the Chezy formula.
(ec) The Williams-Hazen general formula ? for many kinds of pipes

V =C,,R-*3°-5 0,001-*-% (8)

which may be arranged in the same form as formulas 9 and 12 for
comparison, becoming, with C, = 120,

469 V8
B= pier (8a)

For wood-stave pipe a value for C,, of 120 is recommended by Wil-
liams and Hazen. This recommendation is based on their study of
pipes Nos. 20, 41, 44, 47, and 48, Tables 2 and 3. The exponents
of the formula “were selected as representing as nearly as possible
average conditions, as deduced from the best available records of
experiments upon the flow of water in such pipes and channels as
most frequently occur in waterworks practice.”

(f) The Moritz formulas:

8.6 V8 0.38 Vi

Edel Day a
V=1.72 D°? H55 (10)
Q= 1.35 D?-7 {9-555 (11)

These three formulas express the same values from different
points of view. Unlike formulas 4, 5, and 6, they were developed
1Tutton,C. H. Journal Assoc. Engin. Socs., 23 (1899), p. 151.

2 Hydraulic Tables, Williams and Hazen, 2d ed. New York, 1909.
3 Flow of water in pipes, E. A. Moritz, Eng. Rec., 68, No. 24, p. 687.

THE FLOW OF WATER IN WOOD-STAVE PIPE. neo

from an extensive series of experiments on wood-stave pipe from 4
to 552 inches in diameter and were offered for use on wood-stave
pipe only either jointed or continuous.!

In the development of formulas 9,10, and 11 Moritz used only his

own experiments on the pipes as indicated on Plate VII, rejecting
all prior tests by other experimenters.

(g) A new set of formulas is offered by the writer, based on all
experiments on round stave pipe known to him from description in
engineering literature, and supplemented by an extensive set of
experiments in which he was aided by Ernest C. Fortier. The
method used in developing these formulas is explained on page 50.
Hereafter any one of this set of formulas will be referred to as the
new formula. Arranged in the same order as the Moritz formulas for
comparison:

COSINE O41 OWES

qe ine Dan (12)
V =1.62 Ds Foss (13)
Q=1.272 D 296 To.888 (14)

It is to be noted that the exponent of V in formulas 9 and 12 is
the same, as is also the exponent of H in formulas 10-11 and 13-14.
The difference in the formulas is caused by the wide divergence in
the intercept curves shown in figure 4 (p. 56). As indicated in these
curves, the difference becomes greater as the larger pipes are ap-
proached, for the reason that all weight for large pipes in the Moritz
formulas came from his tests on the 55?-inch Mabton pressure pipe
(Nos. 45 and 46), and the position of the points representing the
intercepts for this pipe, in figure 4, indicates that this pipe was
abnormally smooth.

Referring to formula 8a, it will be seen that the exponent of D in
the new formula is almost identical with the exponent of D in the
converted Williams-Hazen formula and that it follows the sugges-

tion of Schoder:? ‘If the attempt is made to lump all pipes except —

the very smooth ones and the small tuberculated ones, giving thereby
more weight to large rough pipes and ordinary lap-riveted pipes,
then m will be found to vary inversely about as D*> to Dt°,”’

TREND OF ENGINEERING THOUGHT REGARDING THE CARRYING
CAPACITY OF WOOD-STAVE PIPES.

The ideas of the engineering profession concerning the carrying
capacity of wood pipe, expressed as direct statements or as formulas,
have varied widely during the past 20 years. Wood-stave pipe
enters into direct competition with iron and steel pipe. The claim

1 For details of these experiments see Trans. Amer. Soc. Civ. Engin., 74 (1911), p. 411.

2¥Friction Head Hydraulics and Pipe Flow Diagrams, Ernest W. Schoder, Cornell Civil Engineer, May,
1910.

8 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

has persisted that there is less friction in wood pipe than in metal
pipe. It has often been insisted that new wood pipe not only has
a higher carrying capacity than new metal pipe but that the wood
pipe becomes smoother with age, while it is a well-known fact that
metal pipe becomes rougher. (See discussion, p. 72.)

While the analysis of all the tests on wood pipe now available bears
out the above claims in a general way (excepting that wood pipe
is not shown to become smoother with age), yet the consideration
of tests on individual pipes led to hasty conclusions presently shown
to be greatly at variance with facts. The followmg ideas of hydrau-
licians have been extracted by the writer from all the hterature on
the subject known to him:

The experiments of Darcy and Bazin in 1857 and 1859 (Nos. 22
and 33) and of Clarke in 1884 (No. 49) were considered but little in
later discussions for the reason that they were made on rectangular
rather than on round pipe. Smith’s test (No. 1), made in 1877,
has also not been considered in the discussion of wood pipe, as the
test was made on a bored pipe of very small caliber; yet these four
series supplied the data upon which Tutton based his formula. (See
p. 50.)

Although none of the 81 tests considered by Kutter and his col-
league in developing the Kutter formula had been made on closed
channels running full, yet nearly all of the experimenters on wood-
stave pipe have determined for their tests the value of nm in this
formula. Kutter’s formula has undoubtedly been used a great deal
in estimating the capacity of wood pipes, but the writer will endeavor
to show (p. 56) the fallacy of employing a constant value of nm in
this formula and the advantages lying in a formula of the exponential
type.

The first experiment of public record was mentioned by the late
J. D. Schuyler’ in speaking of a test (No. 34) on the newly installed
30-inch pipe for Denver, but unfortunately he did not give sufficient
details by which the test might be weighed. Mr. Schuyler states
that “‘as low a coefficient of m as 0.0096 can be used.”’ This appeared
reasonable, as the pipe was made of planed lumber and all lists of
proper values of n then published recommended a value of 0.009 for
such material. The earlier designers adopted a value of 0.010 ‘‘in
order to be conservative.”

The next tests were made by A. L. Adams? on the Astoria, Oreg.,
18-inch pipe (No. 23). Here, too, a low value of n was found, 0.00985,
which led Adams to observe “‘that the value of 0.010 for m used by
many engineers in dealing with stave pipe, is here found to be practi-
cally correct.”” The low value of the friction factor found in this

1 Trans. Amer. Soc. Civ. Engin., 31 (1894), p. 144.
2 Trans. Amer. Soc. Civ. Engin., 36 (1896), p. 26.

THE FLOW OF WATER IN WOOD-STAVE PIPE. 9

test is the more remarkable in view of the fact that there are ‘‘in
addition to a succession of sweeping horizontal and vertical curves,
27 cast-iron bends with a radius of curvature of 5 feet, and with an
average central angle of about 31°.” (See Pl. XIV, fig. 1.)

The next test (No. 32), spoken of by F. B. Gutelius, ! was conducted
by D. C. Henny ? on the Butte, Mont., 24-inch pipe in 1892. In this
test the value of n was found to be 0.0103. Here again was a value
so close to 0.010 that it tended to establish the fact that 0.010 was,
closely, the proper value. After these three tests by three different
experimenters an extensive series of tests would naturally be required
to convince the profession that a higher value of n should be used.
Attention may here be directed to the fact, however, that in the
three last-mentioned tests but one or two runs of water, with little
or no variation in velocity, had been observed.

In 1897 Profs. Marx, Wing, and Hoskins? of Leland Stanford
Junior University, made a careful and vastly more extensive series
of tests than any previously carried through (No. 47). The values
of n varied inconsistently between 0.010 and 0.0204. (See Table 2,
column 10.) Of the 22 runs in this series, all but one showed a value
of n above 0.0123, and most of them showed it above 0.013.

The experimenters did not publish their results as values of n,
merely stating:*

In regard to the applicability of Kutter’s formula it is to be said that the experiments
on the wooden pipe herein described give values of n ranging from 0.012 to 0.015, an
average value being perhaps0.013. The difference between this value and those given
for the Denver and Butte city conduits can hardly be attributed to the greater rough.
ness of the Ogden pipe. It israther to be supposed that the Kutter formula is defec-
tive. (See p. 56.)

In correspondence relating to these tests T. A. Noble offers the
values of n for the various observations.® These have been checked
by the writer and are found in Table 2, column 10. In the same
correspondence (p. 544) A. L. Adams offers his tests on the West
Los Angeles pipe (No. 20) where the values of n range from 0.0105 to
0.0111. Mr. Adams voices the following warning:

These values * * * do not indicate 0.01 as being a safe assumed value for n
as have all previous experiments.

Various arguments were brought forward to furnish a reason for
the unprecedentedly high values of m in the Ogden pipe. These
included the following: That Kutter’s formula did not apply to pipes
as large as 6 feet in diameter; that sediment had deposited in the pipe;
that the nominal area was not the true area; that a constant reduc-
tion factor should not be used in computing the equivalent water
column from the mercury column.

1 Journal Assoc. Engin. Socs., 12 (1893), p. 219. 4Id., p. 516.

2 Journal Assoc. Engin. Socs., 21 (1898), p. 250. 5Td., p. 547.
2 Trans. Amer. Soc. Civ. Engin., 40 (1898), p. 471.

10 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

In 1899 the same experimenters made additional tests (No. 48)
upon the same pipe with improved apparatus.' Their experiments
were centered on a longer reach of pipe and a consistent set of values
of n was obtained, ranging from 0.0130 to 0.0133.

The trend of the discussion of the second Ogden tests shows that
a general belief existed to the effect that the difference in the values of
nm, when compared with n for smaller pipes, was due to defects in the
_ Kutter formula.

A graphic presentation of the data then available was made on
ordinary squared cross-section paper. In the discussion a method
was offered for testing the correctness of experimental data by the
use of this paper, ‘‘if the loss of head varies as the square of the
velocity.”? Although as long ago as 1808, Dr. Thomas Young?
suggested that the loss of head was in proportion to the 1.8 power
of the velocity, rather than the second power, many still insisted
that loss of head must vary as the square of the velocity. It is inter-
esting to note that 1.8 is the exact exponent found by both Moritz
and the writer, while Williams and Hazen use an exponent of 1.85
in their general formula for flow in many kinds of pipes.

In 1901 T. A. Noble * contributed greatly to the available knowledge
by making tests on 44}-inch and 54-inch pipes (Nos. 41 and 44),
thus bridging the gap between 30-inch and 72-inch pipes. For both
these pipes the values of n ranged from 0.0120 to 0.0136, with the
higher values in the smaller pipe, although the same water flowed
through both pipes and they were constructed at the same time.
Also, strange to say, the pipe with the lower value of n contained more
curvature and growths of Spongilla which were not present in the
smaller pipe. Noble says: °®

The writer can offer no suggestion as to why the value of C should be less and n
greater in the 44-inch than in the 54-inch pipe, when, to conform to the results of
other experiments, it should be the reverse.

In discussing the available data on this subject,’ E. W.Schoder
of Cornell University suggests the possibilities of an exponential
formula derived from a study of the straight-line curves resulting
when the losses of head are platted on logarithmic paper as ordinates
and the velocities as abscissas. This was the method used later by
Moritz in deriving his formula, and also by the writer as being the
best known form by which to study the now extensive number of
tests upon wood pipe.

1 Trans. Amer. Soc. Civ. Engin., 44 (1900), p. 34.

2Td., p. 73.

3 Philosophical Trans., Royal Society of London (1808).
4 Trans. Amer. Soc. Civ. Engin., 49 (1902), p. 112.

5Id., p. 143.
6Td., p. 145.

THE FLOW OF WATER IN WOOD-STAVE PIPE. Jidh

Gardner S. Williams! says:

One of the mcst interesting features of the investigation is the light it throws upon
the inapplicanility of the long-honored law that loss of head varies as the square of the
velocity.

He offers the deductions, based on the study of more than 80
series of tests by 13 observers, that the exponent increases from 1.80
to 2 in pipes ordinarily used by engineers; that it increases as the
roughness increases; that it decreases as curvature increases, and
that it is different for different materials, being lowest for tin and
brass.

After the Noble tests nothing was offered in engineering literature
until J. L. Campbell? made tests on the El Paso & Southwestern
Railway pipe (Nos. 15 and 21). The values of n were so low that the
results were seized upon by some wood pipe manufacturers and given
out broadcast as the values of n to apply to wood pipe. These values
showed an enormously greater carrying capacity for wood than for
iron or steel pipe. The results are unquestionably too low for the
following reasons: In the discussion G. EH. P. Smith® asks, ‘‘Was
the first appearance or the average time of appearance, accepted for
computing the velocity of flow?” to which Campbell replies (p. 188),
‘‘Referring to Mr. Smith’s question about the velocity measurements
by bran, the first appearance of the bran and the colors was taken
because the mtervals of time given thereby were in close accord
among themselves and with the weir measurements.” (Italics are
the writer’s. ) :

In the opinion of the writer, who used color for many of his experi-
ments (see p. 23), the mean of the first and last appearance of color
comes quite close to the true mean. (See also the article by E. W.
Schoder in the Cornell Civil Engineer, December, 1911.) If the
first indication of color is taken, then the maximum thread of velocity
is used; or, if diffusion in addition to mechanical mixing occurs,
a velocity in excess of the true maximum is indicated. No one would
suggest accepting as the average the velocity of a float down the
maximum current in an open channel without applying a coefficient
which varies from about 0.55 to 0.95. The fact mentioned by
Mr. Campbell, that the ‘‘intervals * * * were in close accord

among themselves,” proves nothing but consistency. Regarding the

agreement with the weir it should be remembered that this device
gives discharge; color and bran tests give velocity. To permit
comparison with the results of weir tests the velocity must be multi-
plied by the area of the bore. If the velocity as determined by the
colors were taken too high and the assumed area of the bore too low,
Cees rans. Amor. SociCiv. Engng 90)

2 Engin. News, 60 (1908), p. 225. Trans. Amer. Soc. Civ. Engin., 70 (1910), p. 178.
3 Trans. Amer. Soc. Engin., 70, p. 186. ;

12 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

the results might still agree with a weir test quite closely and yet |
include an error as to the velocity.

The writer dwells on this discussion for the reason that ne has
before him three catalogues of prominent pipe makers, each of which
claims a very high efficiency for wood pipe (to the consequent dis-
paragement of iron and steel pipe), basing this claim on one question-
able series of tests and ignoring the other tests mentioned above for
the probable reason that the most of the latter show the capacities
of wood and new iron pipe to be more nearly the same.

In 1911 E. A. Moritz! offered the results of experiments which
were quite complete between pipes 4 inches and 22 inches in diameter,
with a gap then to one pipe 55? inches in diameter. He used much

the same methods (in fact, much of the same equipment) which were
used on the Ogden tests. 7

Rejecting all previous experiments and his own series on the
22-inch pipe (No. 28), Moritz developed the formulas given on page 6.
This left a very complete set of experiments between 4 and 18 inches
but with a gap from 18 to 553 inches. The positions of platted points
for the 552-inch pipe (Nos. 45 and 46) shown on Plates VI and VII,
when compared with corresponding points for other pipes, all indi-
cate that this pipe was exceptionally smooth. So much weight was
given the tests on this pipe, being the only tests on large pipe which
were accepted, that the formulas derived from the experiments indi-
cate a greater carrying capacity for wood pipe generally and large
diameter wood pipe particularly than a study of all tests shows to be
warranted.

In the discussion of Moritz’s article, R. G. Dieck writes:

The use of the Kutter formula in pipe design has always been questionable, even
though its ease of application, in default of a more convenient formula, has commended
it * * *, Itis evident from the Sunnyside experiments that an adjustment in
the ideas of hydraulicians on this point is bound to come. * * * When the dis-
charge varies, all other conditions being the same, the value of n also varies; hence in
its present form, the Kutter formula can not be considered a true statement of condi-
tions.”

In the same discussion? Rudolph Hering states that he ‘‘recognized
as well as did Mr. Kutter himself, almost at the outset, that n was
not to be considered a precise and unvarying constant.’”’ The writer
will take up the comparison between the SESE and the new expo-
nential formula later (p. 56).

In the same discussion Gardner S. Williams objects to the incon-
sistency of the profession in introducing inches into a formula other-
wise expressed in feet and decimals. The writer agrees in this, but
the manufacture of iron, steel, clay, and wood pipe has been so long

1 Trans. Amer. Soc. Civ. Engin., 74 (1911), p. 411. 2Td., p. 452. 3Td., p. 459.

THE FLOW OF WATER IN WOOD-STAVE PIPE. 13

conducted on these units that it appears best to construct separate
formulas with terms in both inches and feet.

Also in the same discussion! J. S. Moore, who aided in the experi-
ments and computation of the Moritz data, offers tests on 48? and
31-inch pipes (Nos. 43 and 36). The 482-inch pipe appears to have
been very smooth and the tests confirm the Moritz formulas. How-
ever, it must be borne in mind that this pipe is part of the same
siphon and subject to the same conditions as those affecting the 552-
inch pipe which contributed so largely to the data from which the
Moritz formulas were derived. Advocating the use of all previous
data accepted as criteria, Moore suggests the intercept line for the
exponential formula as shown by the dash line in figure 4. This
line approaches the position of the intercept line for the new formula
which considers all reliable data.

RECAPITULATION.

The above outline indicates that 25 years ago Kutter’s formula,
with a value of n of 0.010, was accepted as accurate in the design of
wood pipes. As tests were made on larger sizes of pipe, higher values
of n were found. These results were not accepted unreservedly,
however; rather were the experiments discredited by some designers
on the grounds that conditions in the pipes were not properly ascer-
tained or that methods of making observations were erroneous.
The experimenters themselves suggest that perhaps a constant value
of nm should not be used; that is, that Kutter’s formula does not
apply if a constant value of n is to be taken. The data were too
meager to develop the variation in n with the diverse elements.

As data accumulated authorities suggested interpreting results
by exponential formulas; but not being well known this method was
not extensively accepted until used by Moritz in interpreting his own
results. He attempted to compare his formulas with the results of
other experimenters but found this “a difficult and discouraging
problem.”’ This was true because all previous data on large pipes
showed a much smaller relative capacity than the one pipe contribut-
ing so largely to his formulas. Though but tentatively offered by
Moritz, his formulas appeared to be the best available and have been
extensively accepted, in spite of the fact that Moore, who was per-
fectly familiar with the Moritz tests, suggests a formula that more
nearly fits all previous observations.

In the following pages of this publication, particularly beginning on
page 28, the writer will endeavor to show analytically the following:

1. That an exponential formula most nearly applies to the flow of
water in wood-stave pipes.

1 Trans, Amer. Soc, Civ. Engin., 74 (1911), p. 463,

14 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

2. That the mean of all reliable observations on carrying capacity
of wood-stave pipes agrees with the exponential formulas in the fol-
lowing order and per cent (see Table 2):

Per cent
ts Scobey is Bers: 2 Shh Ree ee RT te Be eee —0. 33
25 Williams-Hazen 12000: 2) Aa Ee Pee 2 Pe ee +2,4]
oo) Dutton. Sees 2 le cae 2 ee een es ene eee +2.44
4 OMORHta 6. oe. 83 Lb. Se ee ee Fe See eee eee —9. 40

3. That the mean of the capacities of the several pipes agrees with
the exponential formulas in the following order and per cent (see
Table 3):

Per cent
EL: Scobey. 3 2.5 S36 pan. 2 ee een ee Se ee +0. 66
220 Wailliams-Hazen! + i005) 15 00 Oe eee eee +3.51
yt Hutton | & 2h 35 8 css See ES SES fc A ee Se ee +5. 02
A Moritz. 2 2853250, 2 ee ee Se eee —7.64

4. That Kutter’s formula with a constant value of n does not
apply to flow in wood-stave pipes running full.

5. That n decreases with an increase in velocity in a given size of
pipe and increases with the size of pipe for a given velocity, varying
from less than 0.010 for small pipes at high velocities to more than
0.014 in large pipes.

6. That this variation in m is so marked and pomipliengal as to
render the use of Kutter’s formula inadvisable.

7. That the Ogden experiments showed the capacity of the 72-inch
pipe (Nos. 47 and 48) to be within from 5 to 8 per cent of the average.

8. That the Sunnyside experiments showed the 553-inch pipe (Nos.
45 and 46) to be abnormally smooth by 18 per cent.

NECESSARY FIELD DATA FOR DETERMINING THE RETARDATION
ELEMENTS OF VARIOUS FORMULAS.

A glance at pages 5 to 7 shows that for study of the various formu-
las the same hydraulic elements must be determined by field tests.
These are:

1. The mean velocity, V, of water in the pipe.

2. The loss of head, h;, due to retardation in a section of pipe of
uniform size, within a known distance.

3. The internal size of pipe, D or d.

The above data having been secured, the observed velocity for any
particular observation may be compared with the computed velocity
for the same-sized pipe with the observed loss of head, for any of the
formulas.

MEAN VELOCITY OF WATER.

The velocity of the water flowing in a section of wood-stave pipe

may be measured in two general ways:

1 Using coefficient of 120 in Williams-Hazen formula.

THE FLOW OF WATER IN WOOD-STAVE PIPE. | 15

1. Directly, by timing a given volume of water through a known
distance. :
2. Indirectly, by measuring the discharge of the pipe, thus deter-

mining the quantity, Q, and solving the equation V = -

Where the velocity is tested by the direct method the error is
smaller than where the indirect method is used.

LOSS OF HEAD DUE TO RETARDATION.

Most of the recent experiments on the flow of water in pipes of
uniform size have been made with piezometer columns. This was the
method used by the writer. If a piezometer (fig. 1) be properly
attached to the pipe, the pressure in the latter will support a column
of water whose surface is at elevation E, on the hydraulic grade line.
In the same way the pressure at gauge No. 2 will lift a column to
elevation E,. The difference between these elevations is the head
lost, hz, due to the retarding influences.

INTERNAL SIZE OF PIPE.

It was not practicable to secure inside measurements of any of the
pipe tested in the experiments conducted by the writer. The method
used in ascertaining the inside cross-sectional area of the pipe is
recounted in the description of each test. In some cases several
joints of pipe, remaining from construction, were measured and their
mean inside cross-sectional areas accepted as the internal sizes of the
operated pipes. In other cases the external circumferences of the
reaches tested were measured in several places and the mean inside
cross-sectional areas computed, the thickness of the staves being
known. This thickness runs very uniformly, being determined at
time of manufacture by the use of the same templet.

In still other cases, especially on pipes of small diameter, the nomi-
nal diameter of the pipe was accepted. As the pipe runs very close
to nominal size the writer believes that no appreciable error is intro-
duced in accepting these areas, provided the conditions are such that
the pipe is not liable to be more or less clogged with rocks, sand, or

other débris.
SCOPE OF THE EXPERIMENTS.

The writer conducted 64 tests on 16 separate pipes, 13 of which
ranged from 8 inches to 4 feet in diameter; one was 6} feet; one, 12
feet; and one, 134 feet in diameter. Six pipes were of the machine-
banded type, put together in lengths, and 10 were of the continuous-
stave type. Mean velocities ranged from less than 1 foot per second
to more than 8 feet per second.

From other sources, listed in summary Table 3, and briefly described
in the appendix commencing on page 74, descriptions of experiments

—————————————————————————————————oooorreEeEeEeEeEOEOe—eEeEeEeee

Se

16 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

on pipes up to 6 feet in diameter were abstracted, but no other than
the writer’s records are available for pipes between 6 and 12 feet in
diameter.

EQUIPMENT AND METHODS EMPLOYED FOR COLLECTING AND INTER-
PRETING FIELD DATA.

In order to correctly weigh any new data bearing on hydraulic
formulas it is necessary to know in detail the equipment used and the
steps pursued in both the field and office. Consequently these
features are described in some detail.

EQUIPMENT.

Tapes.—High-grade steel tapes, graduated in feet and hundredths,
were used in the determination of diameters, circumferences, etc.
For distance chaining the tape was graduated to tenths.

Level.—An 18-inch Berger engineer’s wye level, equipped with a
bubble whose sensibility was rated at 10 seconds of arc for 1 division
of scale equal to one-tenth of an inch was used. The bubble vial was

6.5 inches long; the telescope power was 35 diameters. The instru-

ment was kept in excellent adjustment.

With one exception the levels in these tests were closed within the
limits suggested by the U. S. Geological Survey, the allowable error
in feet being 0.017 distance in miles.1 The exception noted occurred
in connection with the tests on pipe No. 37, where the levels were run
in high wind, over deepsand. Several trials were made, but the best
closure was to 0.023 foot, while to conform to the formula it should
have been to 0.012 foot, the distance being about 2,500 feet.

Rod.—A new Philadelphia rod, in three sections, equipped with rod
level and vernier reading to thousandths of a foot was used in the
determination of the elevations of gauge zeros with regard to an
assumed datum.

Thermometers.—Temperatures of air and water were taken with
all-glass laboratory thermometers, graduated to degrees and fifths,
Centigrade scale. The range covered in the graduations was only
that liable to be encountered in the tests, so that each degree was
represented by about three-sixteenths inch.

Hydrometer.—Specific gravity of water in the pipes was tested by
means of a laboratory hydrometer simultaneously with a like deter-
mination of the temperature of the water. The hydrometer was
afterwards tested by the U. S. Bureau of Standards. The proper
corrections were thereafter applied to readings before computation was
undertaken.

Current meter.—A small Price cup current meter of the combina-
tion type was used. This meter had been carefully rated by the U.S.

1 Precise Leveling, in Topographic Instructions of the U. S, Geological Survey, 1913, p. 100,

THE FLOW OF WATER IN WOOD-STAVE PIPE. 17

Bureau of Standards the year previous, but had been used only a few
times, and then as a standard. Its rating curve was checked by the
writer and his assistant in the channel of the hydraulic laboratory at
Cornell University, just prior to these tests. No change was found
- necessary.

Fluorescein..—Direct measurements of velocity of water in a pipe
were made by injecting solutions of fluorescein and timing the passage
of the resultant green-colored water through the reach tested.

Weirs.—Where weirs had been installed to measure the quantity
of water from pipes the writer made use of them. Each is described
in the report of the test in which it was used.

Hook gauge.—A small hook gauge of the Boyden type, with vernier
reading to thousandths of a foot, was used to determine surface
fluctuations for head on a weir. (See PI. 1, fig. 1.)

Piezometers.—Two types were used:

- Water column: This was employed’ where the pressure in the pipe
was low. A simple glass manometer-tube, engine-divided to tenths
and hundredths of a foot, was connected to the tap in the wood pipe
by a piece of rubber pressure tubing. (See PI. II, fig. 1.)

Mercury manometer: Where otherwise the pressure would have
compelled the use of a long water column, a mercury manometer of
the U-tube pattern was selected. Two of these U-tube mercury
gauges, as shown in figure 3, were provided. ‘They consisted of
wrought-iron U tubes with unequal legs. The short leg was a glass
manometer tube surmounted by a tee connection provided with the
necessary cocks for manipulation. The long leg was formed of 2-foot
units of one-eighth inch wrought-iron pipe until a length had been
attained which permitted the top of the high mercury column to
show in another glass tube.

These glass tubes were engine-divided into tenths and hundredths
of a foot, the tenths and half-tenths lines extending completely
around the tube and the other lines but half way around. By sight-
ing through the tube across the front and back of any one line, all
tendency toward parallax was removed and the mercury column
could be correctly read to thousandths of afoot. The relative vertical
positions of the two sets of graduations were of immaterial conse-
quence as the graduations on each gauge glass were brought into the
general scheme of levels above an assumed datum, as shown in
figure 2.

All abutting pipes screwed against fiber gaskets. The ends of the
gauge glasses were permanently set into sleeved couplings with sealing

1 The writer is indebted to R. B. Dole, of the U. S. Geological Survey, for suggesting the use of this won-

derful coloring matter. See ‘‘ Use of Fluorescein in the study of underground waters,” R. B. Dole, Water
Supply Paper No. 160, U. S. Geological Survey.

42463°—Bull. 376—16——2

18 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

wax. Both the couplings and attendant follow nuts were recessed
at an angle of 45° in order to effectively bind rubber gaskets. Joints
between ends of iron pipe units were made in the same way. A
cement made of equal parts of beeswax and turpentine softened the
rubber gaskets and gummed the pipe threads so that the joints were
mercury-tight. This was doubly assured by winding sewing thread
into the wax in the pipe threads.

The inside of all metal pipes and connections was japanned three
coats thick in order to prevent amalgamation with the mercury.

Color injector—The only practicable method of measuring the
velocity of water in some of the pipes tested was by timing the passage
of some color or chemical. After various tests fluorescein appeared
to offer the best results. In order to inject the color into the pipe at
the upstream gauge the ‘fluorescein gun”’
was developed (fig. 3). This is connected
to the nipple C through the T connection
D. At the downstream manometer the
nipple C connects directly to the cock E.

Mercury container.—The usual lead tor-
pedo weights for the current meter were
dispensed with and a combination mer-
cury bottle and meter weight was con-
structed (fig. 3). The details are evident in
7 Aen the illustration with the possible excep-
Fic. 2.—Hydraulic principles of mer- tion of the surge walls which divided the

cury manometer of U-tube tyPe. _ hottle into small compartments so that the

mercury gave no trouble by surging when the bottle was used as a
meter weight. Likewise the small holes in the walls at the top of
the weight offered small chance of losing all the mercury in case of
accident.

FIELD METHODS.

CHOOSING A REACH TO BE TESTED.

In order to be considered adaptable for field tests, a pipe must be
practically water-tight (or the leaks measured) and of such length,
without bends or obstructions, that the effect of errors is minimized—
the longer the better. Gentle curves, both vertical and horizontal,
were thought desirable, as their effect must be considered in the
design of practically all wood-stave pipes. No distinct bend in any
pipe was included in the reaches tested. Such a bend would cause
an appreciable loss of head aside from friction loss. Some method
of determining the mean velocity in the pipe must be available.

THE FLOW OF WATER IN WOOD-STAVE PIPE. 19

_»—Open io arr.
A
Ullliy -C./ Plog, brazed :
WS SFibre wesher-
Ze

ll

—- Ee Screw cap

Z,

= —s > By FA as as
. Surge Wall. (2°. foc.
Meter weight and Mercury-b68 le. C )

in
\

cal Open fo air.

ul al Noes, ;

fers Each glass ard iron pipe
ae 2 feet fangs P
inch Vii pipe is ra INS. OM.
Inch W.}, ype is Yt inch diam.

Bic cle Pump

in| Gradvated
git: =F Gage Glass
Lads gir cock. Sealing Wa
= xy Te F

ycle hire valve.

Bic

Yo" pipe unit.
Pressure

3‘nipple Fluorescein Gun
e . Wg*33 pres-
43 air cock. sure tubing.

Fi C.Scobey.

fic. 3.—Method of attaching mercury manometers to wood-stave pipes. Details of menometers, fluores-
cein gun, and combined current meter weight and mercury bottle.

20 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.
ATTACHMENT OF PIEZOMETERS.

As it is not often practicable to secure permission to make several
holes at each manometer in a wood pipe used commercially, the
writer accepted the discussion of Profs. Marx, Wing, and Hoskins con-
cerning the position of the point of attachment to the pipe and whether
different results will be given by multiple attachment than by attach-
ment at a single point.t Their first conclusion is:

When the pressure in the given cross section of the pipe everywhere exceeds that
of the atmosphere an open ptezometer will stand at the same height at whatever point

of the cross section it be attached, and whether it communicates with the pipe at
one point or at several.

As a rule taps were not made on the top of the pipe, as the writer
judged that more air bubbles would be in the water at this part of
the pipe than at some lower point. Care was exercised in choosing
the reach, so that guages could be set at each end of it, where the
positions of the two taps would be such that the same relationship to
velocity would hold. All taps were made on tangents. The posi-
tion on the circumference was chosen in the neutral zone where the
influence of curves would be a minimum. For instance, if the pipe
was straight in horizontal alignment, but curved vertically, the taps
were made in the side of the pipe. In experiments on pipe No. 52,
where the pipe followed a chosen gradient but was curved horizon-
tally, taps were made near the top of the pipe. (PI. V, fig. 3.)

The essential requirement in a piezometer connection is to exclude
all positive or negative influence of velocity head. The hole through
the pipe must be normal to the pipe and as clean cut as possible on
the inside. If splinters are pushed off the inner surface, then either
positive or negative influence from the velocity head must act on
the column in the gauge, whereas the pressure head alone is desired.

The gauges were attached to the pipe in a manner slightly modi-
fied from that used by Noble? and later by Moritz. They bored a
hole for the nipple with a wood bit until the tip of the bit pierced
the inner surface. In the experiments described in this paper a
seven-sixteenth-inch wood bit was used to make a hole about 1
inch deep. Then a twist drill one-eighth inch in diameter was
twisted by hand until the inner surface of the pipe was cleanly
pierced (fig. 3). Experiments made with both systems showed the
holes made by the last method to be more nearly free from splinters
which might affect the gauge tube by velocity head.

a 1 Trans. Amer. Soc. Civ. Engin., 40 (1898), p. 526.

21d., 49 (1902), p. 119.
31d., 74 (1911), p. 411.

THE FLOW OF WATER IN WOOD-STAVE PIPE. 91
OPERATION OF GAUGES.

From observations on the ground or study of the profile, the
pressure in the pipe was known roughly. In assembling the gauge
the proper number of iron-pipe units was installed in the long leg
of the U so that the two ends of the mercury column balancing the
pressure in the pipe would appear near the mid-point of the glass
gauge tubes.

The gauge, as assembled in figure 3, was set up beside the tapped
pipe, the glass tubes being made truly vertical by means of a plumb
bob. Shade was always provided for the gauges.

With the cocks I and L open and G closed, mercury was filtered
into the tube T. A paper-lined glass funnel was inserted at the top
of T. The mercury filtermg through a pin hole at the bottom of
the paper funnel was thus cleansed at each experiment and the
meniscus in each tube was made bright and clear. Mercury filtered
into a tube of small diameter in this manner will fill up without air
bubbles, but if it is poured into such a tube air bubbles will occupy
long reaches of pipe and may not be found if they occur in the iron-
pipe sections. When both legs of the gauge were filled to near the
_top of the lower glass, I was closed and G opened until the mercury
column in M was pressed well down in the gauge, when G was again
closed. Mercury was then added and G was opened from time to
time until it might be allowed to remain open, the pressure holding
the mercury column in sight on both glass gage legs.

At this time there was probably a mixture of air and water above
the mercury in M, but the air was driven out by alternately closing
G and opening I for an instant. In using the gauges L was closed
and G and I opened every few minutes, so that water and any accu-
mulated air bubles might be blown out of the pressure tube between
the gauge and the wood pipe.

Because of the use of unequal legs on the gauge there was danger
of blowing mercury out of the gauge at I unless the cocks L and G
were operated most carefully. To catch the mercury in the event
of such an accident, the tube J was discharged into the bottle K
which included a ass tube open to the air so that water was freely
discharged but the mercury caught.

Pulsations were nearly always present and as simultaneous caiees
of both low and high gauges were necessary in order to determine
the length of the mercury column, readings were made in the follow-
ing manner: :

Pulsation effect was reduced by partially closing either L or G
until the mercury was barely ‘‘alive.’”’ This assured an average
length of column. The cock was then completely closed, leaving a
‘“‘dead’”’ mercury column of the proper length. Both low and high
gauges were carefully read to thousandths after which the cock was

22 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

opened. This process was repeated every 10 minutes. All other
readings were taken by alternately reading high and low gauges
with the mercury just alive, the corresponding reading for the other
gauge being computed from the dead readings as described above.
Since the only change in the total length of mercury thread was
due to temperature changes, and since the gauges, which were made
of the highest grade of manometer tubing, were practically uniform
in diameter, no error was introduced by reading but one leg at a
time, alternately. (See p. 93.)

DETERMINATION OF LOST HEAD.

The exact amount of hy (fig. 1) must be determined. Where a
water column is used, say at gauge No. 2, the elevation E, is the
gauge reading added to the elevation of the gauge zero above an
assumed datum, with proper corrections (see p. 23). Where a
mercury manometer of the U-tube pattern is used, the reasoning is
as follows: It is desired to know the elevation E, (fig. 1) for a water
column which is the equivalent of a mercury column in a U-tube
placed as for gauge No. 1. Referring to figure 2, the mercury in
the two legs of the U-tube below c—d will be seen to balance. There-
fore the pressure of the water at ¢ is just balanced by the column of
mercury X. But the pressure at c equals that at d. If the mercury
X were replaced with water it would reach an elevation sX above
d, where s is the specific gravity of the particular mercury in the
gauge, compared with the particular water in the pipe. But the
elevation to which this water column would reach is the desired
elevation, E,. Therefore the elevation E,=sX+y above the as-
sumed datum. As applied to these experiments, referring to figures
1 and 2, the difference in elevation between the readings of the low
gauge and the high gauge multiplied by the specific gravity of the
mercury and added to the elevation of the low-gauge reading gave
the elevation of the equivalent water column when the proper cor-
rections had been applied.

tn. CORRECTIONS.

Although quite numerous, the principles involved in all of the
necessary corrections have been the subjects of such thorough inves-
tigation that appreciable errors are not liable to result from their use.

Temperature.—Corrections are necessary for the temperature
changes in both air and water. A temperature of 15° C. was adopted
as standard and the specific gravity of the mercury used in the tests
was referred to that temperature, being compared to distilled water
at the same temperature.

The mercury column balances the pressure of the water in the
pipe, but this water may be either heavier or lighter than distilled

THE FLOW OF WATER IN WOOD-STAVE PIPE. 93

water. Hydrometer tests of the water at the time of the experiment

showed the specific gravity of the water for that temperature. A
table was computed showing the proper specific gravity factor to
apply to convert the mercury column to the equivalent water column
for any observed specific gravity of water.t No additional correc-
tion is necessary for the temperature of the water as the hydrometer
takes this into consideration.

The pressure in the pipe (fig. 2) supports the mercury column X
and im addition the water column from the pipe to the elevation
ofc. If this water is of a different temperature from that in the pipe
a correction is necessary, but in these experiments the water was
kept at about the same temperature by frequently blowing off the
water in the rubber pressure tube. The length of this water column
in a Mercury gauge at no time was more than 1 or 2 feet.

However, in a water column manometer the difference in tempera-
ture must be considered. The temperature of the water in the tube
was taken as that of the air adjoining, while the temperature of the
water in the pipe was determined at the same time that its specific
gravity was tested. Water columns were not blown off but air
bubbles were driven to the glass tube by striking the rubber tubing
sharply with a stick. Siphons in the pressure tubing were carefully
prevented.

Capillarity.—W ater rises by capillarity in a small tube and mercury
is depressed. ‘Two sets of glass tubes were used for water columns.
For one, with inside diameter of 4.5 mm., water rises 0.017 foot,
while in the other set, with diameter of 5.6 mm., the water rises 0.01
foot.

MEASUREMENT OF MEAN VELOCITY.

As a rule, each pipe tested presented its own problem as to the
method to be adopted to determine the mean velocity of the water,
and in case this method digressed from one of the following standard
methods it is described.

Current meter.—Where the water entered or left the pipe in an
open channel the discharge was determined with a current meter,
and the velocity in the pipe was secured by dividing this discharge
by the area of the pipe. The two-tenths and eight-tenths depth
method was used, as the results obtained in this way, when com-.
pared with the discharge found by the multiple-point method, gen-
erally agree with it to about 1 per cent. |

Fluorescein.—About 1 teaspoonful of fluorescein (in the form of
red powder) dissolved in about a pint of water gave sufficient solution
ratory of Nutrition Investigations, U. 8. Department of Agriculture. The specific gravity was found to

be 13.575 at 15° C., compared with distilled water at 15°C. These were the temperatures adopted as basic
for the computation of results.

24 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

for four injections of color in a pipe carrying up to 60 second-feet,
while in the 134-foot pipe (No. 52) the total contents of the ‘‘fluor-
escein gun”’ (fig. 3) were injected at one time, and for the volume
of water carried in this pipe (the maximum was 871 second-feet) a
saturate solution was used. Though not measured, this consisted
of about 4 teaspoonsful of the powder for each ‘‘shot”’ of about one-
third pint. The powder dissolved readily in cold water.

In making a test the coupling W is opened and the solution ated
into the pressure tube X. The gun is again connected with the
apparatus by the coupling W. With E closed Visopened. Pressure
in the wood pipe enters the gun, making pressures in both gun and
pipe equal. In order to inject the color into the pipe the only thing
necessary is to increase the now existing pressure in the gun. After
V has been closed the gun is pumped up like a bicycle tire. While
noting the time to a second the operator opens the cock V. By
the hissing sound, it is probable that the jet passes well across the
diameter of a medium-sized pipe. If the contents of the gun are to
cover three or four injections V is opened and almost immediately
closed. If all the contents are to be used a few quick strokes of the
pump, after V has been opened, will clear the gun in a very few
seconds, the mean time being accepted in later computations.

The observer at the outlet, provided with a watch agreeing to the
second with that used in timing the start of the color, notes to the
second the first and last appearance of the color. The color is ex-
tended by the variation in the velocity throughout the section of

the pipe. This extension covers about 8 per cent of the total time

the color spends in the pipe. Comparison with carefully constructed
weirs shows that the color method is correct within about 3 per cent.
Wherever possible, a comparison between color and current meter was
also made. ‘To secure comparative results the time the color spent
in the pipe is taken as from the moment of injection to the mean
between first and last sight at the outlet. These comparative tests
are shown in Table 1.

THE FLOW OF WATER IN WOOD-STAVE PIPE. 95

TaBLE 1.— Velocities by color (fluorescein) compared with velocities by weir and current
meter.

| Velocity | Velocity | Velocity

Refer give. Crest length of Motcnmiukhod: Kpee spoon per second ond by Vo—Vm | Ve—Vw
No eter. weir. | by color. | by meter. are hao ed Ae ae
i | Ve Vn V
Ww

Inches. Feet. Feet. Feet. Fee. | Percent. | Per cent.
60 See OSMeI pera E Fo occ eae 1a ay Ie Deseo eae d WE 205 Feet san eme —3.8
GU ues Siew: UE SAE E | See an sae Ie 1736 [oe es fe 1351s 35-2 +0.1
62 Bri NDIRAact a: ee SE TE DAS ee eee Digg ie: Ba ns Dig
63 Sila aes QE Ps els ene tat se 32043 Ween Shee eee De Doi We Se See ie +2.4
64 roe) as 2 CG CT Re 8 ea | og ia Np O: 204 [Se see ena ee St (id teas ee —2.4
132 US ee kita 6-tenths 3.....- 2.08 199 eho a 3 et ee ne
(4) 36 | 10.0 CD. Tere Png Sevens 3. 48 3. 48 3. 47 0.0 +0.3
(8) Bare Os stage ce 6-tenths 3__...- 3. 48 3. 55 3.47 —2.0 +0.3
192 | cba [Ree eee, Sen 2+87, 3. 14 BB aiid sesea ieee 2.9) |noseee sere
193 ASG see Se cei ae oes é dome 3. 75 3202 cas- cee Soe Fd Ese (oe ee a
194 ASH Ps ie eee ee ee See oe dome ee 4,75 Gy df eis te ir SOS AN as se aera
263 (spt | See Ae peers 3 NA Curve 8.......- 0.911 0928 seen ad oe wl. Qiulecen-paces
264 OE Ree oe tae eeserss [ete aN (6 Lay es ake ee 0. 963 ONG74e]5- kaos ss =P esos acee
265 TEA e Se ERNE eee GOzs2 eee: 1.51 1:60 Jesus aes —=640' ke sseeet
266 (Sabai seeds aeteued Hees Gos. 2-2 2. 063 2:08) lose ace ose = a | aces Sas
(8) 1S) | a ee Jasons dos. 528 2.16 Z2E1 OME ao= Sos es AP 2 Sila Sass
269 7 ite | |ss5 See EPS Ty ani dOn noe 2. 40 PACY (eth SSE Sh eerste ee cece wees
270 | (Ones ater ee cos ass done Ree: 2. 44 DADwsoonts fae ae +0: 8 lisa soaccee
271 | Elsa itn sate emeotd San geeks dia. tas. 2.79 PE Wale |e eccee eat =F Lapa penta

1 Cipolletti weir with good conditions of contraction and velocity. Seep. 40.
2 Rectangular weir with end contractions and sharp crest. See p. 40.
3 Meter held in each vertical at 0.6 depth from surface.
4 From tests on a concrete pipe, made in 1915.
5 Velocity integrated by moving meter slowly from top to bottom and return.
6 Excluded from Table 2 because gauge data ‘lost for manometer No. 1.
7 Meter held at 0.2 and 0.8 depths in each vertical; mean accepted for vertical. See p. 44.
8 Rating curve developed by meter measurements. V elocity taken from curve. Seep. 45

FIELD PROCEDURE.

After the reach of pipe was selected, the manometers attached,
and other equipment put in readiness the method for proceeding
with the field test was in general carried out as described in the
paragraphs following. Any necessary changes are noted in the text
in connection with the description of the individual pipes tested.

The watches used at both ends of the reach were adjusted to agree
to the second, and again compared at the end of the observation.
Manometers were read every one or two minutes (depending on the
amount of pulsation in the water) for a period of 30 minutes. If a
weir was used to measure the discharge of water a hook gauge above
the weir was read every two to five minutes, depending on the varia-
tion of discharge. If a current meter measurement was necessary
to determine the discharge it was made either during or immediately
following the series of manometer readings, the manometers being:
watched for appreciable variations of discharge. Where fluorescein
was used to time the actual velocity of the water it was injected into
the pipe at approximately known intervals, say, five minutes, through-
out the time during which the manometers were read. Ordinarily
the second gauge was near enough to the outlet of the pipe so that
one observer could both read the manometer and watch for the
appearance of the color. Sometimes a third observer was necessary.

26 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.
OFFICE EQUIPMENT AND METHODS.

Original multiplication, division, and addition were performed on
mechanical devices. Checking was done by 20-inch slide rules and
graphic methods. All percentage comparisons were made on 20-inch
slide rules. Estimate diagrams were checked by proving random
examples. |

Office procedure.—Where water columns were used at both ends of
the reach of pipe tested the loss of head in the pipe for the given
velocity was the difference in elevation between the top of the mean
water column at gauge No. 1 and the top of the mean column at
gauge No. 2. Where a mercury manometer was used at one or both
of the gauges the equivalent water column for each reading of the
mercury column was computed. The mean of the elevations of the
tops of the equivalent water columns was accepted as the elevation
for that gauge. The loss of head was then computed as before.
Standard methods were employed in computing current meter data
or weir discharge. Where color was used in timing the velocity of
the water the time was computed as from the instant of injection to
the mean between first sight and last appearance of the color at the
outlet.

ELEMENTS OF FIELD TESTS TO DETERMINE FRICTION LOSSES AND
COMPARISON OF OBSERVED VELOCITIES WITH VELOCITIES COM-
PUTED FROM VARIOUS FORMULAS.

In the following pages two tables are arranged (Tables 2 and 8).
Table 2 gives the elements of nearly all known observations on wood
pipes, either round or square. The various series are arranged in
ascending sizes of pipe and within one series the observations are
arranged in ascending order of velocities.

The tests of one experimenter are omitted from these tables as
extraordinary friction values were found. ‘The writer made an inde-
pendent set of tests upon some of the same pipes and found them so
choked with ravelings from the rock cuts above the siphons that erro-
neous values were obtained. In the omitted tests the error lay in
making current meter measurements for Q and then accepting

Q

N ae where A was taken as the nominal area of the pipe when as a

matter of fact the true value of A was about 90 per cent of the nominal
A; therefore the true velocity was much higher than that found by
the erroneous assumption of A.
EXPLANATORY NOTES ON TABLE 2.
Column 1 gives the consecutive numbers of the pipes as followed in column 1, Table
3, also in the discussions in the following pages and in the appendix. The small letter
a after the numbers refers to discussion in the appendix. Experiments conducted by

this department are discussed in the text while the essential data secured from other
sources are abstracted in the appendix.

THE FLOW OF WATER IN WOOD-STAVE PIPE. Patt

Column 2 gives a consecutive reference number to each observation.

Column 3 shows the authority (see also column 8, Table 3), the series number where
such was carried, together with the date of the test.

HS refers to Hamilton Smith.

EM refers to E. A. Moritz, engineer of the United States Reclamation Service.

C refers to J. L. Campbell.

A refers to the late A. L. Adams.

DB refers to Darcy and Bazin.

H refers to D. C. Henny.

JDS refers to the late J. D. Schuyler.

JM refers to J. S. Moore, assistant engineer, United States Reclamation Service.

N refers to T. A. Noble.

MWH refers to Professors Marx, Wing, and Hoskins, of Leland Stanford, Junior,
University.

KC refers to E. C. Clarke.

S refers to the writer, Fred. C. Scobey, irrigation engineer, in charge of experiments
on the flow of water in channels and pipes.

Column 4 gives the observation number as carried by the experimenter.

Column 10 shows the value of n as computed from the observation.

Column 11 shows the value of » for a normal pipe of the same size at the observed
velocity. This value is taken by inspection of the m curves in Plate VIII. The
writer has termed this the normal value of n.

Columns 14 to 18, inclusive, show the velocities for the same size of pipe with the
given loss of head (column 9) when computed by the various formulas.

Columns 19 to 23, inclusive, show the percentage comparison of observed velocities
(column 8) to computed velocities (columns 14 to 18). This comparison is explained
on page 55, in connection with the information in Plate VII. The grand algebraic
meaus of all observations in the respective columns are given at the foot of the columns
on page 37. These means are graphed in Plate VII and shown also on page 14. The
other columns are self-explanatory.

EXPLANATORY NOTES ON TABLE 3.

Column 1 gives the same consecutive numbers of pipes as column 1, Table 2. See
discussion after ‘‘Column 1” on page 26.

Column 2 gives the inclusive reference numbers of observations on that particular
pipe, which are the same as those in column 2, Table 2.

Columns 10 to 14, inclusive, give the weights assigned to the determination of the
general value of the exponent of V in formula 12, page 7. The method of finding
these weights is explained on page 52.

_ Column 15 gives the weights assigned the various series in determining the general
equation for the intercept curve shown in figure 4.

Column 16 gives the revised values of the intercepts for individual pipes as explained
on page 53. Note that these may be quite different from the value representing the
intercept in the equations shown in column 17.

Column 17 gives the formulas of flow, as shown by the observations, for the individual
pipes. Their derivation is explained on page 53.

Columns 18 to 22, inclusive, have the same general significance as columns 19 to 23,
Table 2, respectively. For the series the figures given are the algebraic means of the
percentages for the observations. The grand algebraic means for all pipes are-shown
at the foot of the columns on page 39. These means are graphed in Plate VII, and
are also given on page 14.

The other colums are considered self-explanatory.

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40 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.
DESCRIPTION OF PIPES.

The descriptions in the following pages are to be taken as sup-
plementing Tables 2 and 3. The methods of determining the

hydraulic elements necessary for each observation are described.

The descriptions of pipes upon which previous experimenters have
made observations are given in the appendix.

No. 18, Expt. S12, 8-inch Machine-Banded Douglas Fir Pipe, French
Brothers’ Orchard, North Yakima, Wash.—From the lower end of the 10-inch
pipe discussed as No. 14a reach 1,751.5 feet long of 8-inch machine-banded pipe affords
exceptional opportunity for investigation. This pipe conveys water to a high point
in the orchard, from which it is distributed in open ditches. There are two taps in
the line within the reach between the gauges. First is a 14-inch tap for lawn sprink-
ling; second, a 4-inch valve for irrigation purposes. These were closed tightly
throughout the tests. Gauge No. 1, a mercury manometer, was placed 219 feet from
the inlet valve. Gauge No. 2 was located 1,503 feet from gauge No.1. For runs 1,
6, and 7 a water column was used. For runs 2, 3, 4, 5, and 8 a mercury manometer
was used. An 8-inch control valve is located 17:5 feet downstream from gauge No. 2.
A vertical iron pipe the same size as the wood pipe rises above the ground surface at
this valve and discharges into a wooden division box. All but one ditch leading
from this box were plugged with earth so that all the water was discharged at one end
of the division box. This was equipped with a well-made Cipolletti weir 1.05 feet
long. After run 3 this weir was removed and a rectangular weir, with end contrac-
tions suppressed, was built in its place. This weir was 2.84 feet long. Both weirs
had clean-cut, sharp crests of galvanized iron. The change in weirs was necessary
for the reason that it was desirable to run more water than could be accommodated
through the Cipolletti weir and still maintain so-called. standard conditions. The
weirs were about 7 feet from the point where the water was turbulently discharged
from the 8-inch pipe. From the place of impact to within about 2 feet of the weirs
the box was filled with fresh-cut cottonwood branches and leaves. This mass formed
an excellent screen from which the water emerged in good condition for weir measure-
ment. <A hook-gauge reading to thousandths of a foot was placed in the box above the
weir. This permitted a direct comparison between the velocity in the pipe as deter-
mined with fluorescein and the velocity as determined by dividing the weir dis-
charge by the nominal area of the pipe section. This comparison is shown in Table 1.
The reach of pipe tested was without vertical curvature and had but one bend ofabout
20° about midway in its length. According to the best information available this
pipe is about 7 years old and is used about 7 months of the year. It is buried about
3 feet below the surface and shows no signs of decay. The pipe capacity was approxi-
mately 8 per cent less than the discharge computed by the new formula.

No. 14, Expt. S-11, 10-inch Jointed Machine-Banded Douglas Fir Pipe,
Congdon Orchards, North Yakima, Wash.—lInrrigation water for the Congdon
Orchards is conveyed from the main canal of the Yakima Valley Canal Co. in a
14-inch pipe (No. 19). From the lower end of this pipe a 10-inch pipe extends about
one-half mile with a right angle bend about midway. A reach 1,297.4 feet long and
without vertical or horizontal curvature was chosen at the lower end of the pipe,
which was 7 years old at time of test and appeared to be free from leakage. The
nominal size of the pipe was accepted as correct. Velocity was measured with
fluorescein, the mean velocity shown by four batches of color for each run being
accepted. The appearance of the color was awaited at a 6-inch hydrant 55 feet
downstream from gauge No. 2. The color was injected at gauge No.1. As the intake
of this pipe line from the open canal is several miles from the river and the velocity
in the pipe is rather high, it is improbable that there was any silt in the reach tested,

TE

Bul. 376, U. S. Dept. of Agriculture. PLATE |

Fic. 1.—TYPICAL CIPOLLETTI WEIR, WITH HOOK GAUGE IN STILLING Box.
Note brush screen in foreground to reduce velocity of approach.

Fic. 2.—WEIR AT OUTLET OF PIPE No. 30, NORFOLK COUNTY WATER Co., VIRGINIA.

The immediate bottom contraction similar to that shown at side, although water above weir
wall is several feet deep.

Fic. 3.—TANK OF BUTLER (PA.) WATER Co. USED IN MEASURING DISCHARGE OF PIPE
No. 29,

Bul. 376, U. S. Dept. of Agriculture. PLATE Il.

Fic. 1.—THUMB POINTS TO TOP OF PIEZOMETER COLUMN (GAUGE 2) SHOWING NEAR
APPROACH OF PIPE LINE TO HYDRAULIC GRADIENT. (PIPE No. 31.)

Fic. 2.—OUTLET STRUCTURE, PUMPING LINE OF PASCO RECLAMATION Co., WASHINGTON.
(No. 88.) Discharge measured by rod floats in this concrete section.

Fic. 3.—ALIGNMENT AND PROFILE OF SIPHON, BURBANK Co., WASHINGTON. (No. 39.)

THE FLOW OF WATER IN WOOD-STAVE PIPE. Ar

although the observations show that the capacity of the pipe is 10 per cent below
the discharge computed by the new formula.

No. 19, Expt. S-10, 14-inch Jointed Machine-Banded Douglas Fir Pipe,
Congdon Orchards, North Yakima, Wash.—About 1 mile of 14-inch pipe con-
veys water from the Yakima Valley Canal to the Congdon Orchards. A reach
1,251.7 feet long was chosen near the lower end. A mercury manometer was used
as gauge No. 1 and a water column as gauge No. 2. The velocity was determined
with fluorescein. The color was injected at gauge No. 1 and appeared at a 4-inch
hydrant about 1U) feet below gauge No. 2. The capacity of this pipe is about 4 per
cent less than as :omputed by the new formula.

No. 26, Expt. S-18, 18-inch Continuous-Stave Redwood Siphon Pipe,
Yakima Valley Canal Co., Washington.—lrrigation water is conveyed across two
depressions between open reaches of canal by means of a redwood siphon of the con-
tinuous-stave type, built in the winter of 1913-14. Thus the pipe had been in use
but a few months at the time of the test. It is buried about 3 feet in sandy and
gravelly soil. Blow-off valves are located at the low points, while a valve allows
the escape of air at the one summit on the line. Gauge No. 1, a mercury manometer,
was located 279.3 feet from the inlet. Gauge No. 2, a water column, was located
1,787.5 feet from gauge No. 1 and 19.7 feet from the outlet. The nominal size of the
pipe was accepted. The velocity within the pipe was determined with fluorescein.
It was not practicable to vary the velocities through the pipe, but so far as two
observations can be accepted the capacity of the pipe is 18 per cent greater than the
discharge computed by the new formula. Some excess is to be expected, as newly
_ planed redwood is very smooth and the pipe was so new that material deposits of
silt were unlikely.

No. 27, Expt. S—?7, 18-inch Jointed Machine-Banded Douglas Fir Siphon
Pipe, Burbank Co., Washington.—lrigation water from Snake River is carried
over a swale between open sections of a small ditch by means of an inverted siphon.
This pipe was laid during February, 1913. The top of the pipe is about 18 inches
below the surface of very gravelly, open soil. However, the pipe surface is protected
with a heavy coating of asphalt, so that the wood appears to be perfectly sound. The
maximum head is only about 14 feet. Water columns were used at both ends of the
reach tested. Gauge No. 1 was located 67.1 feet from the inlet while gauge No. 2 was
located 1,479.1 feet from gauge No. 1 and 7.6 feet from the outlet. The nominal size
of the pipe was accepted as correct. For each run the velocity within the pipe was
determined through fluorescein tests by taking the mean velocity of five batches of
color. The pipe is straight in horizontal alignment and has no summits in the ver-
tical plane. For all practical purposes it may be considered straight from the fact that
the low pointis but 14 feet below the hydraulic gradient, in a total distance of 1,553.8
‘feet. At no point was there any indication of leakage, but there was no way of deter-
mining the interior condition of the pipe. It is used for irrigation about seven months
of the year, but is kept full all winter. This probably accounts for the absence of
leakage. The water as pumped from Snake River contains some sand, but all of the
heavier particles have settled to the bottom of the canal before reaching the siphon,
which is some distance from the stream. For this reason there is small likelihood of —
a deposit at the low point of the siphon, although the two observations taken indicate
that the capacity is 6 per cent below the discharge computed by the new formula.

No. 29, Expt. S-2, 24-inch Jointed Machine-Banded White Pine Pipe,
Butler Water Co., Butler, Pa.—Municipal water for Butler, Pa., reaches a pumping
plant near the city by gravity flow through a 24-inch pipe line laid in 1907. This
pipe is 5 milos long from Boyds Town Reservoir to a settling tank. The maximum
static head is about 67 feet. The last half mile is a cast-iron pipe, while the rest is
a white pine machine-banded wood pipe. As there was considerable leakage through-
out most of the wood pipe a straight reach of the latter 1,357.7 feet long was chosen -

“49 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

well toward the juncture with the cast-iron pipe, which was considered tight. This
fact permitted a close determination of the. pipe’s discharge by the rise of water in
the settling tank (Pl. I, fig. 3), which is 50 feet in diameter, with vertical sides. Cor-
rections were made for baffle walls and other displacement. The surface of the water
in the tank was taken at 1-minute intervals with a plumb bob and steel tape. Mer-
cury manometers were used at both ends of the reach. During any one run of water
the mercury columns fluctuated but a few thousandths of a foot. The pipe is buried
about 2 feet deep and is slightly elliptical. The mean of the areas of 10 pieces‘of pipe
remaining from construction was taken as the area of the water section. Nothing is
known regarding the interior of this pipe, but the observations indicate that the
capacity is 5 per cent less than the discharge computed by the new formula.

No. 30, Expt. S-1, 24-inch Jointed Machine-Banded White Pine Pipe,
Norfolk County Water Co., Va.—Water for domestic use in the territory in
Norfolk County, Va., is pumped through 9 miles of 24-inch Canadian white pine
machine-banded pipe from the Cadillac Pumping Plant to the plant in Princess Anne
County. The pipe was laid during 1912 in lengths of from 3 to 12 feet. It is buried
from 18 inches to 4 feet In sandy soil. The wood where bored for the manometers was
sound, but the superintendent of the plant stated that there were several leaks in the
line. This pipe is in use throughout the year. The reach tested is free from either
horizontal or vertical curvature. It is 1,077.5 feet long, beginning about 100 feet
below a gentle curve and extending to a point near the second pumping plant, where
the pipe discharges over arectangular weir into a concrete reservoir. The absence of
moist ground indicated that there were no leaks on the reach tested, but the interior
of the pipe was partly choked by a spongy growth. The velocity of water in the
pipe was found by fluorescein tests. The discharge was determined by hook gauge
readings for head on the weir shown in Plate I, figure 2._ No correction is necessary
for velocity of approach toward the weir, but the conditions of contraction are not
quite standard. Mechanically the weir is well constructed and the discharge was not
more than 2 per cent in error, in the estimation of the writer. The mean cross-sec-
tional area of the interior of the pipe was determined by dividing the discharge as found
above by the velocity as shown by the color. This area was 2.831 square feet, while
the nominal area of a 24-inch pipe is 3.142 square feet. Loss of area was for the most
part caused by the dense blanket of spongy growth adhering to the lower third of the
circumference. As near as the writer could determine from the outlet end of the
pipe, the rest of the perimeter of the pipe was smooth. With the above assumptions
as to the true area of the pipe, the capacity is indicated by the observations to be 7
per cent greater than the discharge computed by the new formula, but if the presence
of the growth were not known and the nominal size of the pipe accepted as the true
size, then the capacity would be considered equal to the discharge computed by the
new formula.

No. 31, Expt. S-15, 24-inch Continuous-Stave Redwood Pipe, Ogden,
Utah.—Water for municipal uses is conveyed through Ogden Canyon to a reservoir
near the city in a 24-inch redwood pipe, originally laid in 1890. The use to which
this pipe is subjected, of course, requires it to be wet throughout the year, which is
a more favorable condition than that usually encountered in irrigation practice, where
a pipe is used but six to eight months. On the other hand this pipe practically
reaches the hydraulic grade line at some of the summits. (During tests by the writer
the water column at gauge No. 2 extended but 1 foot above the top of the pipe.) Thus
there is not sufficient head for thorough saturation, yet the pipe appears to be in fairly
good condition. The very rugged topography of this canyon precludes the use of
long tangents in either horizontal or vertical alignment. The reach chosen for test
commenced at the pipe bridge over Ogden River near “‘The Hermitage,’’ where a
mercury manometer was located as gauge No. 1. Gauge No. 2, a water column (Pl.
II, fig. 1), was placed 2,240.7 feet from gauge No.1. Douglas fir staves had been used

THE FLOW OF WATER IN WOOD-STAVE PIPE. 43

in replacing some deteriorated redwood staves, and both gauges had been attached
to the pipe through these because the harder fir appeared to give a tighter repair when
plugs were inserted in the tap holes after the gauges had been removed. However,
according to the superintendent of the line, that part of the pipe between the gauges
was of redwood. The nominal size of the pipe was accepted as correct. The velocity
was determined by injecting fluorescein at gauge No. 1 and timing its travel to an aux-
iliary tap on the same circumferential ring with gauge No. 2. Although the pipe was
24 years old the two observations at commercial velocities indicate its capacity to be
3 per cent greater than that computed by the new formula.

No. 37, Expt. S—4, 36-inch Continuous-Stave Douglas Fir Pipe Line, Pasco
Reclamation Co., Washington.—The rolling ground in the vicinity of Pasco,
Wash., does not furnish adequate support for an open canal. For this reason, and
because of the sandy nature of the soil, water for irrigation is conveyed in pipes after
settling in a reach of open canal where it has a very low velocity. Tests for loss of
head were made on the 36-inch pipe shown in Plate IV, figure 2. Gauge No. 1 was
placed about 800 feet from the intake and gauge No. 2 was located 2,516 feet farther
on. The line abounds in gentle curves, both horizontal and vertical. Mercury
manometers were used for both gauges. The nominal diameter of the pipe was ac-
cepted as correct. Asall the water flowing in the canal entered this pipe, it was only
necessary to measure this flow for discharge. This was done by weighted rod floats
of such lengths that any one float just cleared the bottom throughout the reach on
which it was used. This pipe was laid in the winter of 1909 and 1910. For the most
part it is buried from 1 to 3 feet in light sandy soil. Nxterior decay cf the pipe indi-
cated that it would have been better to place the pipe on the surface of the ground.
_ The two observations taken at commercial velocities indicate that the capacity of this
pipe is 15 per cent less than that computed by the new formula. The writer can not
account for this. Velocities are so low in the feed canal that all sediment should
precipitate before reaching the pipe.

No. 38, Expt. S—5, 36-inch Continuous-Stave Douglas Fir Discharge Pipe,
Pasco Reclamation Co., Washington.—Water for domestic and irrigation use 1s
lifted 107.2 feet vertically from Snake River to the canal-reservoir shown in Plate II,
figure 2. All of the pumps feed one continuous-stave wood pipe 36 inches in diam-
eter. This pipe, 893 feet in length, was built in 1909. Though at a rather sharp
incline, the pipe is practically straight. Gauge No. 1, a mercury manometer, was
located 335 feet from the pumps, while gauge No. 2, a water column, was located but
20 feet from the outlet shown in the plate and 538.1 feet from gauge No.1. The pulsa-
tion due to the pumps was evident in the mercury columns, but at gauge No. 2 their
effect was hardly noticeable, even in the water column. The nominal diameter of
the pipe was accepted as correct. The discharge was measured with weighted rod
floats in the concrete section of open canal shown in the plate. These were of such
length that they barely cleared the bottom of the channel. It was not practicable
to vary the discharges through this pipe. The two observations taken at the com-
mercial velocities indicate that the capacity of this pipe is about 13 per cent below |
the discharge computed by the new formula.

No. 39, Expt. S—8, 38.13-inch Continuous-Stave Donelas Fir Siphon Pipe, -
Burbank Co., Washington.—lIrrigation water from the Snake River is conveyed
across a wide swale in section 16, township 8 north, range 31 east, by means of a con-
tinuous-stave siphon 6,170.4 feet long, built in February, 1913 (PI. II, fig. 3). This
pipe is 38.13 inches in diameter, as determined by measurements of outer circum-
ference throughout its length and by measurements of stave thickness. It is sup-
ported on cradles on the surface of the ground and appears to be in perfect condition.
During the colder months water is withdrawn and the ends are plugged. Irrigation
continues about seven months each year. The pipe is straight in horizontal align-
ment, while the vertical curves are so gentle that for all practical purposes they are

44 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

straight. There is one summit, as shown by the view. The maximum head is 74
feet. Water columns were used for both gauges. Gauge No. 1 was located 88.8 feet
from the inlet. Gauge No. 2 was located 5,965.9 feet from gauge No. 1 and 115.7 feet
from the outlet. Velocity within the pipe was determined by fluorescein tests, the
mean time of travel of five batches of color being accepted. Levels were determined
by static head; that is, on one visit to the pipe it happened that no water was running,
so simultaneous readings at both gauges, taken 10 seconds apart for 1 minute, gave a
true water level. The extremely slow fall of the water surface throughout these
readings indicated that the leakage was negligible, which fact was also apparent to
the eye. As well as an examination of the pipe outlet would disclose, the pipe was
clean and smooth on the interior, though an examination of the long, low stretch
across the marshy bottom of the swale might have shown deposits. The writer does
not believe this likely, however, for the reason that the water flows for about 6 miles
in open channels at comparatively low velocities before reaching the intake, and in
these channels the heavier sand would have precipitated, leaving the water little
more than clouded. The one observation at the commercial velocity indicates the
capacity of this pipe to be about 10 per cent greater than that computed by the new
formula.

No. 40, Expt. S-—6, 40-inch Continuous-Stave Douglas Fir Siphon Pipe,
Burbank Co., Washington.—lIrrigation water is conveyed across a depression
between two sections of open channel by a continuous-stave siphon, built in Decem-
ber, 1912, along the west side of section 6, township 8 north, range 31 east. This pipe
was constructed on the surface of the ground and supported on cradles. At the time
of these experiments, therefore, it was in its second irrigation season. As shown by
the profile in Plate III, figure 1, there is one summit on the reach tested, but as this
is protected by a standpipe, there was probably no air accumulation at the summit
at the time of this test. Although the pipe is about 2,900 feet long, a reach 927.4 feet
long was chosen near the outlet end for the reason that there is a diversion from the
lowest point of the pipe. Gauge No. 1, a mercury manometer, was located 1,049.6
feet above the outlet and gauge No. 2, a water column, was located 122.2 feet above
the outlet. The water divided in the outlet structure, flowing in two directions, one
stream continuing in an earth channel and the other in a concrete-lined channel.
The discharge in the pipe was determined by the sum of the flows in these two chan-
nels, as measured by current meter. The nominal area of the pipe was accepted as
correct. At velocities exceeding 2 feet per second, it was noticeable that sections of
the pipe immediately following the sharpest vertical curves vibrate about 1 inch,
vertically, upon the cradles. This emphasizes the necessity for securing anchorage
at bends. The two observations taken at commercial velocities indicate the capacity
of this pipe to be about 3 per cent greater than that computed by the new formula.

No. 42, Expt. S-9, 48-inch Continuous-Stave Redwood Siphon Pipe,
Cowiche Siphon, Yakima Valley Canal Co., Washington.—Water for irrigation
is conveyed across Cowiche Canyon, about 4 miles from North Yakima, Wash., in a
redwood siphon built in January, 1914. (Pl. IV, fig. 1.) Gauge No. 1, a mercury
manometer, was located 67.3 feet from the inlet (Pl. III, fig. 2), while gauge No. 2, a
water column, was located but 7.6 feet from the outlet. The inlet to the pipe is at
the bottom of a concrete well about 10 feet deep. Subsequent tests to determine entry
losses showed that much air was entrained and carried into the pipe, but no influence
of air was apparent at gauge No. 1, which was attached to the pipe at the mid-point
of its left side. From the intake to gauge No. 1 the pipe is straight. This is likewise
true of the pipe for about 100 feet before gauge No. 2 isreached. For the balance of
the distance between gauges the pipe is virtually one long vertical curve, as it is under
a maximum head of about 100 feet and the total length is but 962.3 feet. The pipe
has but one gentle bend in horizontal alignment. For each of the several runs made
with different velocities in this pipe fluorescein was timed from inlet to outlet, the

Bul. 376, U. S. Dept. of Agriculture. PLATE III.

Fic. 1.—ALIGNMENT AND PROFILE OF SIPHON, BURBANK Co., WASHINGTON. (No. 40.)

Fic. 2.—MERCURY MANOMETER (GAUGE 1) ATTACHED TO SIDEOF COWICHE SIPHON
(No.42), YAKIMA VALLEY CANAL, WASHINGTON.

See note on figure 1, Plate IV.

Fia@. 3.—CURRENT METER STATION BELOW OUTLET TO PIPE No. 42.
A concrete slab, marked every 0.5 foot.

Bul. 376, U. S. Dept. of Agriculture.

PLATE IV.

| Fic. 1.—COWICHE SIPHON (No. 42), YAKIMA Fic. 2.—MAIN LINE, PASCO RECLAMA-
VALLEY CANAL Co., WASHINGTON. TION Co., WASHINGTON (No. 37).

TYPICAL ALIGNMENT AND PROFILE.

Fia. 3.—TRUNK LINE, MOHAWK Hypro-ELectric Co., NEW YorK (No. 50). TYPICAL
|| ALIGNMENT AND PROFILE.

‘

Bul. 376, U. S. Dept. of Agriculture. PLATE V.

Fia. 1.—TRUNK LINE, SALMON RIVER POWER Co., NEW YORK. TAKEN ON REACH TESTED.
Typical alignment. Straight in profile. o. 51.) See figure 2.

Fic. 2.—SUBMERGED WEIR BELOW POWER HOUSE, SALMON RIVER POWER Co. NEW YORK.
Discharge measured by calibrating weir. (No. 51.) See figure 1.

Fia. 3.—MERCURY MANOMETER AND FLUORESCEIN GUN (GAUGE 1) ON 1314-FooT PIPE
OF NORTHWESTERN ELECTRIC Co., WASHINGTON. (No. 52.)

THE FLOW OF WATER IN WOOD-STAVE PIPE.” 45

mean velocity of four or five batches of color being accepted as the mean velocity of
the water within the pipe for that particular run. Many of these color tests were
checked by current meter measurements made by the two-tenths and eight-tenths
depth method at the meter station shown in Plate ITI, figure 3. This station is in
the concrete flume about 70 feet below the cutlet from the siphon. The agreement
between the two methods is shown in Table 1. As this pipe had been in use but a
few months the interior was probably in excellent condition. The maximum dis-
charge of the pipe necessitates a mean velocity of about 5.5 feet per second, so that it
is probably scoured quite clean and smooth at all times. The capacity of the pipe
was about 15 per cent greater than that computed by the new formula.

No. 50, Expt. S-16, 78-inch Continuous-Stave Douglas Fir Pipe,| Mohawk
Hydro-Electric Co., Ephratah, N. ¥Y.—The power house of the Mohawk Hydro-
Electric Co., near Ephratah, is supplied with water by a trunk line of about 24 miles
of 78-inch stave pipe from the reservoir, Peck Lake, to the surge tank. (PI. IV, fig. 3.)
From the tank a stave pipe 96 inches in diameter extends to a point 1,460 feet distant,
where the pressure head is 160 feet. It here joins a steel pipe of the same diameter,
which completes the additional distance of a few hundred feet to the turbines. The
writer conducted a series of tests on a reach of the 78-inch pipe 2,650 feet long. The
lower end of this reach was about 1,000 feet above the surge tank. The whole tine
abounds in gentle curves, both horizontal and vertical. The pipe, built in 1910, was 5
years old at time of test. It is full of water throughout the year and is not protected
against freezing, being so placed that some portions are completely buried and some
completely exposed. Although extremely cold weather is experienced in this part
of New York, the wood appears to furnish sufficient insulation. The peak load
demands a velocity in this 78-inch pipe of less than 7 feet per second. This velocity

and the fact that water comes from a reservoir that should act as a settling basin prob-
_ ably guarantees a pipe free from sediment. Several minor leaks were found on the
reach tested. These are mostly at ends cf staves where no additional bands were
placed, and the pressure has bent outward the end of the stave farthest from the sup-
port of a band, the bend, of course, occurring under the last band. Whether the
elastic limit of the wood had been exceeded and the fiber torn could not be ascer-
tained, but the condition was such as to emphasize the desirability of confining all
the joints in a stave pipe to a zone a few feet in length and placing extra bands through-
out this zone. This of course does not apply to pipes under light pressures, say,
30 or 40 foot heads. Velocities within the pipes were determined directly with
fluorescein for observations 1, 2, 3, 4, 7, 8, 9, and indirectly by comparison with the
rating curve of the concrete channel forming the tailrace, for observations 5 and 6.
The tailrace was calibrated by means of six careful current-meter gaugings, and a
rating curve was plotted showing the comparison between gauge heights in the tail-
race and velocities in the 78-inch pipe. The comparison between color tests and
meter tests is shown in Table 1. The agreement between the two methods is closer
than is usually expected by experienced hydrographers. Mercury manometers were
used at both gauges. Some trouble was experienced from freezing temperatures
(tests were made the first week in April, 1915), but no trouble occurred from air in
the pipe, as the intake is deeply submerged. The color was injected at gauge No. 1
and observed at a secondary tap in the pipe 1 foot downstream from gauge No. 2, the
water flowing into a white-lined pan which reflected greenish color. The same
general procedure was followed here as on the Altmar tests (No. 51). That is, simul-
taneous readings were made over a long period of time, on both manometers and on a
hook gauge in the tailrace. When the records were brought together, periods of slight
fluctuation might be selected and each of these called an observation. Some such
method as this must be chosen when a power plant in commercial operation is tested,
as no one knows just when the changes in load, and consequent changes in velocity

1 Engin. Rec., Vol.-64, No. 22, Nov. 25, 1911, p. 627.

.
:

46 BULLETIN 316, U. S. DEPARTMENT OF AGRICULTURE.

within the pipe, are to occur. The capacity oi this pipe was 9 per cent less than the
discharge computed by the new formula. From the faci that the inlet is from a
reservoir, and because the curves are very genile, experience indicates that this
pipe should have a greater capacity for a given loss of head than the new formula
would indicate, although it is true that the interior condition .i the pipe was not
known. Two air valves ai summits and one blow-off at a low point occur within the
Teach tested. The air valves are boxed to prevent freezing.

No. 51, Expt. S-3, 144-inch Continous-Stave Douglas Fir Power Pipe
Line,* Salmon River Power Co., New YorkK.—About 4 miles irom Alimar, N. Y..
on the bank of the Salmon River, is located an hydroeleciric plant, constructed in
1913 and 1914 to carry a portion of the load formerly served by one of the big planis
ai Niagara Falls. Stillwater Reservoir is jormed by a dam across the main channel
of Salmon River about 2 miles above the power plant. A tunnel 600 ject long con-
Veys water irom the reservoir to the upper end of a continuousstave Douglas fir pipe
line 144 inches (12 ject) in diameter. (Pl. V,fig.1.) At the end of 3,450 fect a taper
transition section about 50 fect long leads into a similar pipe 132 inches (11 feet) in
diameier. Tesis were made on the 12-joot pipe. The portion of the pipe tested is
without vertical curves, being laid on an even gradient Praciically the lower third
of the pipe is buried. No leaks worthy of notice occurred throughout the pipe.
The line had been in operation bui a lew months, and since the velocities were hich
(up to more than 8 ieet per second), it probably was in periect condition on the inside,
although it was not ieasible io ascertain this. The staves are4inches thick. Taps
for the nipples were made by a-inch wood bit until the tip of the bit punctured the
inside suriace oi the pipe. The nominal area of the pipe was accepted as its true area.
Ajter making these tests the writer made careful measurements of a sill larger pipe
built by the same company and iound the true area extremely close to nominal area.
The discharge of the pipe, from which the velocity within the pipe was obiained,
was determined in the following manner: As shown in Plaie V, ficure 2, after the
water passes through the turbines it falls over a submerged weir into a tail-race
channel which in tum discharges mio Salmon River about a quarter of a mile
below the power house. , A good meier rating could be obtained, as the mean velocity
for the greatest discharge was but 3.25 feet per second. This velocity did not cause
a turbulent condition in the channel, since the latier had a hard, fiat rock bottom.
The form oi the weir and the conditions oi velocity of approach are such that the
writer did not feel justified in accepting the discharge as computed from any known
weir formula. The velocity oi approach, in particular, is an uncertaim quantity,
since the bottom of the channel slopes up from 20 ieet deep at the power house toa
mean of but 1.234 iect deep immediaiely above the weir crest, within a horizonial
distance of 220 feet. The weir is 79.6 ject long with end contractions approximately
suppressed. It is a concrete wall 18 inches thick, rounded over on top. It is not
desigcned as a measuring weir but jor the sole purpose oi drowning the drait tubes
for all discharges. This weir was calibrated by making four careful curreni-meter
measuremenis with as many discharges irom a bridge across the tailrace below the
weir; and meanwhile reading a hook gauge in a stilling box 8 feet above the weir and
a tape gauge 3 feet below the weir. The latter gauge reading had no bearing on the
calibration but was taken for the purpose of securing more information concerning
submerged weirs. The results of these measurements follow. The elevations are
based on a bench mark with an assumed elevation of 10.000 feet.

1 Eng. Rec., vol. &, No. 24, June 13, 1914, p. 67L.

THE FLOW OF WATER IN WOOD-STAVE PIPE. 47

TABLE 4.—Simultaneous discharge, elevation of water surface above weir, elevation of water
surface below weir, and head on weir.

bi eeaeiie Elevation | Head on

No. Discharge. above weir.| below weir. weir.

Second-feet. Feet. Feet. Feet.
A aN a le cl Sa Ce 3h ah ALCO a Ay Nh elle 106.6 8. 752 Teslhtl 0.515
PAA A catty toes TO MOEIEORSE Gans Ofc SES 10 2 RV AAS SEN OL a 446.1 9.539 |(not taken) 1.302
Coy AL aU TS TRN DiSa SeWN Un ALIN Es on a AG SIN RUSS NecshaU cas CC UE 724.9 10. 123 9. 62 1. 888

IEE as We Leen SN Ee eel se sega) 1 AG! Lia dS) a ea 749. 6 10.172 9. 62 1.937

The mean elevation of the weir crest, 8.237 feet, was based on readings with level
and rod taken every 5 feet throughout its length. During measurement No. 1 the
hook gauge remained constant. During No. 2 water rose 0.142 feet on the weir.
During No. 3 water fell 0.020 feet on the weir. During No. 4 water fell 0.049 feet
on the weir. The mean gauge reading was accepted were fluctuation occurred.
Current-meter measurements were made by the two and eight-tenths depth
method. As the load carried (and consequently the discharge of water at a
power house) varies throughout the day, and since the discharge is controlled
by the load (by means of governors), the following method of testing the 12-foot
pipe for loss of head was adopted: The mercury manometers and the hook and tape
gauges were read continuously throughout the morning and afternoon. A synchronous
profile was then platted showing all gauge readings. From this profile periods of
comparatively uniform flow were chosen and each of these periods was designated as
an observation. These would necessarily vary in length of time. From the calibra-
tion curve of the weir the discharge for each reading of the hook gauge was taken
and the mean of these discharges was assumed as the discharge which held throughout
the observation. The capacity of this pipe was 2.4 per cent less than that computed
by the new formula. Since the pipe was new, joints smooth, and the curvature
gentle, the writer would estimate the capacity of this pipe to be greater than that
computed by the new formula. Tests by all experimenters show similar cases where
the observations indicate far different results than the conditions appear to warrant.

No. 52, Expt. S—14, 162-inch Continuous-Stave Douglas Fir Power Line,
Northwestern Electric Co., Condit Plant! on White Salmon River, Wash-
ington.—About 2 miles above the mouth of White Salmon River is located the
Condit Plant of the Northwestern Electric Co. Some 6,000 feet upstream a high
diversion dam raises the water above the intake to the supply pipe line. This, said to
be the largest wood-stave pipe in the world, 162 inches or 134 feet in diameter, is used
to convey the waters of White Salmon River from the diversion dam to the surge tank,
a distance of 1 mile. Within the surge tank is a structure that divides the water from
the 134-foot pipe between two 9-foot pipes with very little loss of head. Each of the
9-foot pipes serves 1 electrical unit in the power house. (PI. XI, fig.1.) About mid-
way of the large pipe, upon which tests were made, is a bend of 83° with a radius of but
40 feet (less than 3 diameters). In the opinion of the writer, such a bend would cause
an appreciable loss of head independent of the friction loss, and for this reason a
reach of pipe was chosen between this bend and the surge tank. Mercury manometers.
were used for both gauges, the equivalent water column being just too high to be
feasible. (PI. V, fig. 3.) Gauge No. 1 was located on the zone of neutral velocities
209.9 feet from the bend. Gauge No. 2 was located 2,378.9 feet from gauge No. 1 and
about 40 feet above the dividing tongue in the surge tank. During all of the runs the
load carried by the unit served by the right-hand 9-foot pipe was held constant, all the
fluctuation being thrown to the other 9-foot pipe. The time necessary for fluroescein
to travel from gauge No. 2 through the constant-velocity pipe was determined by

1 Eng. Rec., Oct. 11, 1913; Eng. News., vol. 70, No. 15, p. 685.

A8 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

accepting the mean time of four batches of color traveling from that gauge to the outlet
of this particular pipe in the tailrace at the power house. For each of the tests for loss
of head for differing velocities, color was injected at gauge No. 1 and timed to the outlet
of the constant-velocity 9-foot pipe. To determine the time necessary for the color to _
travel between gauges for any particular run the time it spent in the 9-foot pipe
was deducted from the total. For each run of water two batches of color were timed
immediately before and aiter the gauge readings, and the mean time obtained was
accepted.

A NEW SET OF FORMULAS FOR THE FLOW OF WATER IN WOOD-STAVE
PIPE.

So far as the writer has been able to ascertain, there have been two
suggested modifications of existing formulas and three sets of formulas
which were intended solely for use in the design of wood-stave pipes.

With the experiments before them, which have been underscored in
Plate VII, Williams and Hazen in 1903 suggested the coefficient 120
in their general formula‘ given on page 6. .

In 1915 Andrew Swickard,? after writing, “‘It is quite apparent
that m [in Kutter’s formula] is not a constant for wooden pipe but a
variable that varies directly with the size of the pipe,” offered the
following formula representing this variation of n,

d

= 30,000

0.0105 (15)
This formula ascribes all variation in n to the change in diameter of
- the pipe, while the present paper shows quite clearly in column 10 of
Table 2 and in Plate VI that this variation is also a function of the
velocity. This latter fact has also been noted by Moritz and by

The first formula proposed for sole use in design of wood-stave pipe
(see p. 6) was offered by C. H. Tutton * in 1899. Although not given
wide publicity in this country and apparently not used to any extent
here, Parker regards it with much favor, stating * in regard to gen-
eral formulas for the flow of water in pipes that “the most useful
formula seems to be the one given by Tutton.”

In this work Parker unfortunately misquotes Tutton’s data from
that journal, giving as Tutton’s formula for flow in wood pipes, V=
140 Reo instead (of V — 129 Roa") (See mega.)

In October, 1910, T. A. Noble published his own formula,® .

Q= 1.28 D8 He (16)

which may be compared with formulas 11 and 14, pages6 and 7. This
formula was not given the publicity it deserved and does not appear

1 Hydraulic Tables, Williams and Hazen, New York, 2d ed., 1909, p. 8.

2 The Design of Wooden Stave Pipe, Engin. and Contracting, Vol. XLIII, No. 1, p. 10.
3 Journal Assoc. Engin. Socs., 23 (1899), p. 151.

4 The Control of Water, P.& M. Parker, New York, 1913, p. 427.

> Wood Pipe, T. A. Noble, Pro. Pac. Northwest Soc. Engin., Vol. IX, No. 1, Oct., 1910.

THE FLOW OF WATER IN WOOD-STAVE PIPE. — 49

to have been used to any great extent, probably for the reason that it
was based on tests covering only a few pipes, namely, a 4-inch pipe
tested by Noble and Harris, Adams’s 14-inch and 18-inch pipes,
Noble’s 44 and 54-inch pipes, and the Ogden tests of 1899 on the
72-inch pipe (Nos. 20, 23, 41, 44, and 48, Tables 2 and 3, and PI. VII).

In 1911 E. A. Moritz proposed the fourth set of formulas! (sce
p. 6) with the following qualification: “This formula is not recom-
mended for adoption until more data are available and some of the
uncertain points have been cleared up.”

A fifth set of formulas is now offered by the writer, who has fully
appreciated the inadvisability of extending the number of formulas
already existing except as must be required by continued investigation.
His own experiments, especially those on large pipes, when studied in
connection with all previous data, would seem to supply convincing
proof that a new formula is needed.

With the exception of formula 15 all of the formulas referred to
are of the exponential type; that is, they are based on the fact that
for any particular series of observations, if losses of head are plotted
logarithmically as one set of ordinates and velocities as the other,
the resulting points will le more or less along a straight line. Such
-a straight line on logarithmic paper represents an equation of the
form

isi Sm We (17)
which, expressed for logarithmic study, may be stated
log H=log m+z log V (18)

where m is the intercept on the axis of H, for V=1 foot per second
and z measures the inclination of the line, being the tangent of the
angle which it makes with the axis of V.

For a series of pipes of the same general characteristics but of
varying diameters the values of m follow the general equation

m=K d= (19)
Substituting in formula (17)
Ke d= V2 (20)
This expressed logarithmically becomes
log H=log K+x log d+z log V | (21)

Smith’s tests (No. 1) were made on a pipe too small for any irri-
gation usage and the graphic representation of the results, while

1 Trans. Amer. Soc. Civ. Engin., 74 (1911), p. 442.
42463°—Bull. 376—16——4

50 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

adding no significant information, would have required a far larger
diagram than that presented here. With the exception of these
tests, therefore, data were plotted for all known observations where
records were sufficiently complete. The writer agrees with J. S.
Moore? that—

In preparing a tentative formula for general use all complete data, which can be
accepted as criteria for the loss of head in wood pipe, should be recognized in arriving
at a conclusion.

However, in deriving the new formula, tests made on round wood-
stave pipe only were considered, in view of the proposed use of such
a formula. The comparatively close agreement between results
by use of the new formula and by the Tutton formula, as shown by
Tables 2 and 3, indicates that had the excluded tests been used they
would not have materially changed the new formula, inasmuch as
Tutton used only four series, all of which were excluded by the
writer because they were on other than wood-stave pipes. The
close application of Tutton’s formula to stave pipe, as shown by the
consistent agreement in pipes all the way from 4 inches to 144 inches
in diameter, is a remarkable coincidence, since his base data included
no stave pipes whatever and but one round pipe.

In deriving the new formula the following methods were used:
After the observations had been plotted the diagram was used
merely as asketch, all slopes and intercepts being determined analytic-
ally. Where the test on any one reach of pipe included several
observations the procedure observed was that used in the following
example:

Take the writer’s series 3 (Nos. 272-281, inclusive) on the 144-inch
Altmar pipe. The center of gravity of all the points was first deter-
mined. The antilogarithm of the mean value of the logarithms of
the respective velocities gave the velocity ordinate of the center of
gravity. The slope ordinate of the center of gravity was found
similarly. This point, c, shown by a dot within two circles (Pl. VI),
divides all the plotted observations into two parts. The center of
gravity of each of these parts was found by using only the observa-
tions within the zone of the part. These points, a and b, are shown
by dots within single circles. Thus three points are found, all of
which lie on the straight line representing the equation for that
particular reach of pipe.

Let c=center of gravity of whole group; a=center of gravity of the
part of the group above c; b =center of gravity of the part of the group
below c; and let c,,-a,, by, and Cg, ag, bg, be, respectively, the V
and H coordinates of the above centers of gravity.

1 Trans. Amer. Soc. Civ. Engin., 74 (1911), p. 470,

ee

Woop PIPES.

PLATE VI.

in feet.

~ Le)
| XS 2 Sane
a VEX CN AS 2 ce :
| S Fear Ah ota Gee CAL Tinh
\“" S

99

NUMBERS CORRESPOND WITH

Bul. 376, U. S. Dopt. of Agricultura
PLaTe VI.

fen
Ss

\ a an

o

\ Moritz 6 In-F)

= : p 9 8 Mori? N8 17. 1909)

. ¢ —
* >Scobey 8 in. y X : oe — . S : 7
Bo Morr#378 in. oN we Y- 5 8 qo One FIN-(BOY% % ,

>

pa Moris 1217. 73 \ x A * Xi gindvio0)
» ; "axie 15120 Wy Ke Re Equiv.

9 i 45

5 & Moritz 14 in' Z Z

Morit L oe § \ a =o

® Moritz I41n. S27 ote Tes ;
ZZ 2% \8 % Ae &

Oo 4.
Y

Ul ‘SOLLOO[AA,

64. Lg
2.62164 g90

{139 Adams 18.8)
O0re 3/ine oo

ad 4ea3

S

Marx = Wing- Hoskins

uocoes J

P

LocariTHMIc Diagram SHOWING OBSERVATIONS FoR Loss OF HEAD IN Woop Pipes. NUMBERS CORRESPOND WITH COLUMN 2, TABLE 2s

“Ge

Ava l
shes in seed ty Misditcsenin

THE FLOW OF WATER IN WOOD-STAVE PIPE. 51

No. V EPP los Viti log H
272 5.942 0.5144 0.7739 Oe ilao
273 6.127 .6426 .7873| (Sum=4. 7756 9.8079| (Sum=58. 8637
274 6.190 .6154 .7917||Mean=.7959=b, 9. 7892| | Mean= 9. 8106=by
275 6.312 .6938 .8001{)Anti-log mean 9. 8412/) Anti-log mean
276 6.436 .7237 .8086 =6. 250 9. 8595 =0. 6466
277 6.516 .7155 .8140 9. 8546
278 6.693 .7700 .8256) (Sum=3. 4915 9. 8865) (Sum=39. 8249
279 6.852 .7490 .8358\|}Mean= .8729=ay 9.8745||Mean= 9. 9562=ag
280 8.222 1.061 .9150{)Anti-log mean 10. 0257 {) Anti-log mean
28085223 0.0925, 9lol =7.463 10. 0382 =0. 9040
Sum==8. 2671 Sum=98. 6886
Mean= .8267=cy Mean= 9.8689=cy
Anti-log mean=6. 710 Anti-log mean=0. 7393

The center of gravity of the whole series thus comes at such a point
that there are 4 points below and 6 points above c. Then

ay — Cv = .0462, and apg — Ce= 0873 ;

Cy — by = .0308, and cy — by =.0583;

whence:
0.0462 0.0873 6
0.0308 0.0583 4

p>

When the above ratios are in inverse proportion to the number of
observations in the respective zones the three points found lie in the
same straight line and approve the mathematical operations.

The exponent of V in formula 17 is the inclination of the line acb
and is equal to the tangent of the angle formed by the curve and the
axisof V. Thus

on Pe — 1.891=z. (See No. 51, column 17, Table 3.)
The intercept m is found as follows: Since log m=log H—z log V
(from formula 18, p. 49), by using the coordinates of the center of
gravity c
log m=9.8689.—1.891 xX 0.8267
log m= 8.3056, therefore m=0.02021

In the same manner the exponent of V for each of the pipes
underscored in Plate VII was determined, being found to vary from
1.53 for No. 36 to 2.31 for No. 42. Any general law of variation in
this exponent was not considered in their formulas by Moritz, Wil-
hams and Hazen, or the writer, although Hazen sees a tendency for
the exponent to increase with the size of the pipe,! while Williams
later offered the deductions mentioned on page 11. Simultaneous
values of diameter and exponent were plotted on logarithmic paper.

1 Trans. Amer. Soc. Civ. Engin., 51 (1903), p. 320.

52 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

As the exponent did not appear to vary in accordance with any
particular law, but depended upon each individual pipe, the writer
followed the authorities name above and derived one general value
for this exponent. The method employed was as follows:

Obviously one observation on a particular pipe gave no data of
value in determining the slope of a line. Two observations at about
the same velocity contributed little more, but two observations at
widely separated velocities gave enough information to indicate at
least a tendency. Ten observations over a very short range of
velocities did not give results as dependable as the same number over
a greater range. Likewise ten observations, eight of which were
close together and the other two well apart, did not contribute as
much as the same number of observations evenly distributed through-
out the range of velocities. With these general arguments and Plate
VI as a basis, three men outlined a system for weighting the various
exponents in the individual pipe formulas.

Four factors entered into this process: First, the number of obser-
vations; second, the distribution of the observations as shown by
the distance between the centers of gravity of the upper and lower
zones of observations; third, the extreme range of the observations
on the chart; fourth, the actual range of the velocities. Usually
the weight factor for the number of observations equaled the total
number of observations, but some of the series showed an excessive
evidence in restricted zones with fewer data in other zones. As an
example of this, see No. 41. One observation within each half-
second of velocity range received full weight. Each additional
observation within the same half-second of range received an addi-
tional weight of half a unit. Thus the 11 observations in this series
received a total rating of 8 for the number of observations. (See
column 10, Table 3.)

The study of the data was made on 10-inch base logarithmic paper.
Each inch of distance between centers of gravity of the upper and
lower zones received a weight of 1 in the second factor. Thus, No.
41 was rated 1.6 in this factor. (See column 11, Table 3.)

Each inch of distance between the extreme observations also
received a weight of 1 in the third factor. Thus, No. 41 was rated
2.8 in this factor. (See column 12, Table 3.)

Each one-half foot per second of velocity between the extreme
observations also received a weight of 1 in the fourth factor. Thus
No. 41 was rated 3 in this factor as the range of velocities extended
from 3.5 to 4.8 feet per second, a difference of approximately 1.5 feet
or the equivalent of 3x 0.5 feet per second. The total weight for this
pipe was the product of these four factors, the equivalent of

8x 1.6xX2.8X3.5=125. (See column 14, Table 3.)

THE FLOW OF WATER IN WOOD-STAVE PIPE. 583

No pipe was permitted a greater weight than 1,000 in determining
the exponent of V. If the product of the four factors exceeded
1,000 no additional weight over the 1,000 was assigned.

The writer is aware of the arbitrary character of this method of
determining the exponent, but it was obvious that some system of
rating must be assigned and the one used appears to give about
the right weight to the various pipes when Plate VI is studied. The
proof of the relative accuracy of this method is shown in Tables 2
and 3 where the mean of all observations entering into the derivation
of the general value of the exponent agrees with the formula to
within —0.33 per cent. (See foot of column 19, Table 2). The
mean value for all the pipes entering into the derivation of the
exponent agrees with the formula to within +0.66 per cent. (See
foot of column 18, Table 3.)

Letting W., W,, W;, etc., be the weights for Nos. 2, 4, 5, etc., in
column 14, Table 3, and E,, E,, E;, etc., be the exponents of V in
formulas for Nos. 2, 4, 5, etc. (column 17, Table 3), then

W,E, + W,B,+ W,E, +... Wak

52 —Z—= 1.803
Neca le Weta oe Ete Gs

In deriving the values of the coefficient K and the exponent x,
the writer has not pursued the usual practice. This is to plot and
study logarithmically the various values of m (found in a similar
manner to m on p. 51) and corresponding values of d as ordinates
and abscissas, respectively.

The exponents of V in column 17, Table 3, vary within rather wide
limits. The new general formula accepts a weighted mean value
of this exponent, 1.803. Instead of using the values for m as taken
from column 17, Table 3, the writer drew lines at the constant inclina-
tion 1.803 from the center of gravity of all the points in one series
to the line where V equals 1 foot per second (the line for pipe No.
51 being shown in dot-dash in Pl]. VI). This revised value of m for
each series shown in Plate VI is found by the equation

log m’ = log H—1.803 log V (22)

(substituting 1.803 for z and transposing equation 18).
Again, taking No. 51 as an example:

log m’ = 9.8689 — 1.803 X 0.8267
log m’ = 8.3784
m’ =0.0239

By the method usually employed the value of m (0.0202) shown
in the formula for No. 51, column 17, Table 3, would have been

54 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

used as derived on page 51. The reasoning which recommended
revising the usual method follows:

In Plate VI the curves for the pipes of small diameters intersect
the V=1 line. These intercepts give the values of m. Likewise,
the lines drawn from the centers of gravity for these curves at the
constant slope 1.803 give intercepts m’ not far, as a rule, from m.
Thus not very much difference appears for the smaller pipes; but
_ out in the zones of curves for the larger pipes the average velocities
are so much higher, and consequently the centers of gravity are so
far from V = 1, that the difference between m and m’ is very marked.
The revised method places all curves on the same footing; that, is,
the intercepts for the large pipes will have no more influence on
the general formula than the intercepts for the small pipes. Using
this method a line at the constant inclination 1.803 may be drawn
through the point representing but one observation and a value
of m’ found that is of weight in determining the general formula,
whereas this same point contributes nothing toward the determina-
tion of the exponent 1.803.

The values of m’ for the various series are shown in column 16,
Table 38. In order to derive the term Kd* (formula 19), figure 4
was platted logarithmically with values of m’ as ordinates and of
d as abscissas.

The center of gravity of all the points is shown by the dot within
two circles while the centers of gravity of the zones above and below
this point are shown as dots within single circles. These three
dots lie in the same straight line represented by the equation

m’ =7.68 d-!7=0.419 D-7 (23)

where 7.68 is the intercept on the line d=1 and —1.17 is the inclina-
tion of the curve to the horizontal axis.

Substituting in the general formula (20, p. 49), the general equation
is now evolved for wood-stave pipes, either jointed or of continuous-
stave construction, based on the weighted average condition of all
round stave pipe upon which accepted experiments have been made.
This formula is |

= 7 168'd 3 SUL aves
becoming
H— “68 Vie Og Wee

qi-17 hi p17

(12)

which is shown, with the related formulas, on page 7.

B PLATE VII.

Marx,Wing and Hoskins Scobe ara
1899" TS SoS

wins NO ‘
NARS:

TH Hi Rrormuls Signs and Formulas.

inne
CSAIL it HHUATTTULAAGL 62 D°S5HOSSS hina
ea HER rer Na Beason ee MUL 20
a HCH Hill ; = 479 DOTOHO.S55 Th ae
HEUTEICHTUPICE LITEM Merit, # VeureD aa
HUE ETT Tatton v Vets
tT] TTT Weisbach wo
Hie ERR HUTT TTT 20g
SOOT ALE HOHE
HVAT STPMHNAESATANFOATOOTNGNPOOTAGATUHNOHNGDHAGHIG ttt
TEAUTCSURACSETAAUUCAUUATOUAGEUAUGQGLAL ACTUATE ee
HEEL EEE AEE
MME ELE EERE Ht
HEE SU LULU EE
Sad ANNA EES HATHNAT HSI ETY 2H |
STATE HE EAETEEA ELE EERE PERL AWERVEAE EERE
nin STR HLT pu HT
SURO Mt
HAbANAYAPANONE AD ATNOOOOTT HUTTTTEUGTIUL MINA
TSH HEHE EET
aN VEEUUSUAVAONNCS4UPSUSNVORPOORONGTSONOAINDIGY

FT TTT
TRUM aun
UOUAURAOLEAD ONL UN

Hl Hitt

HHAATAAUATUUNAGTUNUEAARUP*4QGai ir MMA: STITH APONMHATVAITAO A AAAT ET W

OT TT TT TT TTT TU TTT tet

ATTA RA ARRAN Hcsia hat TT TI

I U3 TTT et ig,
PTPALCTTT DELUCA

BURUEURHUUTUREEOARREDGP PORATED AREOUERERD OO ORRROOOO REPS

aR a I PEERAGE ET

TTT MADOC IEA VAESNUI
TR TE
TT PUSTPRU TTA eedP APT ST TST TT TTT

=
S555 Sr5Es

A
ALT ST ae
| EH TEEE CHEECH CHEE THER Cre HH

RH aan tte HTT
TLL HOUDUORAEUAA ttt!

ii Aa AEA

FC. Scobey.

AMS-HAZEN (Cw=120), MORITZ, TUTTON, AND WEISBACH FORMULAS.

Bul. 376, U. S. Dopt. of Agriculture, Plate VII.

Experimenter, year and reference numbers.

Moritz Scobe Morit Scy]_ Adams | Moritz [Sc Moritz | Scobey Scobe
[istoT f905 [ter T 1319 Tata isio | 1e09"{ isio isi i698 T 1910 iia {Tee i914 1914 Jia
call aalaealaeaass] 9]$3a5] 95] Hace] 8 ferea| gesg] agg] a [88e sls & RES Pale) SoS PS ASSP IE ; SN RSE 88 [E SIREN RRR] SS
TTT T NIT MNT
125+ y UL UI i eer
i2sf tit mu AON ONOUNIT i i | :
LAT ATT STITT | I
SSTLERRAARRAGAE M set Hitt | 7 ESATA Formula Signs and Formulas. L
HY | | ig i {| i + ni HUATTATTUGHT Scobey #V=1.62D°SS 2555 |
42120 t I ne r tT aH STITT r| +! 1 Stites Ht Wins-Hageno Y= 120s >hooro ty 120
& HTT mM rt LTT 1 Moritz, Vei72D970H05S6 q
8 AIT Ht i it ut H i HEAHUTUGUQUN GGSHTATOQTESUUNGATURUUOQUAIAIUUIUNVON RRC ae ee He
5 UAUUDONNOOECIBNGOIE rl t TT Ul Ct il HOTUHVAGUC (eT | Weisbach # hp=fLV2 rn
a bin I II Ea | bit 20g
au) 1 a t sit | fl 1 q it i l nT % AOVAVATAT 1
fi AED AAANOUEA ITT He ii nn LIT FET! | | 1H min I] Hit
8 SATA TTA Eat i ; wa ITT Te | Tt I TET
3 NG H im STATI UT
Ejto iM tl { Paul - i [ |
C HEH tl Wl tt O {| it |
io) y, i # | I rl
3 i ci oF i He rN
§ HTT kd kd Me | (| Lhe Sy mnt i 4 tl Ith || II II a. 1
€ i 1] 1 CFs il 4 i b IT & | 5
a al] ial i 4 it t iT SAETURESAU CoTATTNE Hat | I " nt t i 10
£ i si TeiT|
a HI tN ka I i i iit it aL at RE i AUTHLULUTTH efile AU
E a hi anne FY aie | fa Ai lI
8 yoo Lite CTT U Wan as Hil i Mt
wv th nt NUESUUD I
wr bd 11} \ LI Peel IL 1 l9 {|
5 ALTA Te tit ¢ call tl Ea i vat if
7 i Iatith Pau i te SUS ILI 7 i *
o TI 2
= gail TERT HI ¢ ANSI ig CAE ETU VISIT fy Sain
ad Ht HM Ki 4 1 Hf PANG huahil
= 8) | iT af Pg it Peay
e TI ae TU i ll $ Cone
8 ALT rs i hi
£ STATES H uy i I
8 || elt Hl ry + fa ntnd La
2 RA UUIIE | Fst | 4 4 1! H | i Ma
I 2 tt HII Py # ATS I] ‘| ty er I] ro
z | id | + ATTN tt =| Jas
$ ¥ nM 1 TONITE TT Te l +] $
3 il fi) Tit f + tle
way tt CUPSSaNG ancy I] i] MTF rar
© poll Hi i t Ut l Hat BE
° LI {II If ¢ he 4 >
S eof ATR tH na ee tH HH BE
a a 3 [tee i i
8 | tt i t i i ! :
E IT q | tL ft t i =
15 — LH 11 +H Hittite —-L.
es il il f HN ul
Sit
Pipe No, 2-3 [ 4 | s[ 6 [rel o fiof 1 Jiz[ i [ta] te 20 [23 al 2s [as[e7]_ 28 | 29]30|31] 35 [| 36 |s7|zepq4o] 41 42 |43| 44 [45 t 46 AT 52 |
Diam.-ins. 4. 5 6 8 10 12 + 18 22 24 3) 36 [B|40 442 | 48 +h 54+ 5534 72%
Scobe = —S
> 1S _——— 7 ————
——— —t
Basic observations for Williams-Hazen coefficient of 120 and Moritz and Scobey formulas; also assigned weights for Jaffer: FC. Scobey.

= Zz WEISBACH FORMULAS.
CHaRT SHOWING DEGREE OF CONFORMITY OF OBSERVED VELOCITIES OF WATER IN WoOD-STAVE PIPES TO CALCULATED VELOCITIES FOR GIVEN Loss OF HEAD, BY ScoBEY, WILLIAMS-HAZEN (Gw=120), Moritz, TUTTON, AND

A a Pee a Psy oe
1 aD AL SN PUNE OEE ETN Ne wtenes ren Carnnnenina
in cay } ond = Ph : y 4

mera ntop agente teagnT ae NAN L O TT
ye Me ts =<
t dh i

tay mee we eee ae - Serer y

4 Be
ie

eal ad

es 7 5
M Pee ee Oe
. ‘ Nance eee Pay ee cheetah
Bap ey Ata et A! TATE deny . é , F - — “
ees tee 2 - ~+ re - } . foreervents ar meee Pas ee
6 aed i) al a [a fae x | .
ee Ae ee en a emrememibinea

ores eens

Re en il

THE FLOW OF WATER IN WOOD-STAVE PIPE. 55

COMPARISON OF THE VARIOUS FORMULAS.

The comparison of the various formulas is shown in columns 19 to
23 and 18 to 22, inclusive, Tables 2 and 3, respectively, and graphically
in Plate VII, which presents the following information:

First, a comparison in per cent of observed velocities to velocities
computed by the Williams-Hazen formula (with C,=120), the
Moritz, Tutton, Weisbach, and the new formulas, for all accepted
experiments on wood-stave pipes known to the writer where sufficient
data are given.

Second, the mean of the various percentages, awarding each

_ observation the same weight; also the mean of the various percentages,

awarding the average percentage for each reach of pipe the same
weight. These items correspond with the footings under columns
19 to 23, inclusive, Table 2, and columns 18 to 22, Table 3.

Third, lines underscoring the observations used in deriving their
formulas by Moritz and Scobey, and the observations leading Wiliams
and Hazen to recommend a value of 120 as the coefficient to be used
jn their formula in the design of wood-stave pipe. (The Weisbach
formula was derived from tests on metal pipes.)

Tutton apparently assigned the same weight to each series of tests,
although he had but one observation on the Moon Island Conduit
(No. 49) against five for No. 1, and eight for each of the other two
(Nos. 22 to 33).

For the new formula double lines are used, the upper line denoting
the observations used and the weight assigned (1, 2, or 3) in determin-
ing the general equation for m’, and the lower line denoting the
observations used and the weights assigned in determining the
exponent of V. (These lines correspond to the figures in columns
15 and 14, respectively, Table 3.)

As an example of the use of this chart, take observation No. 274
(run 9 on pipe No. 51). Near the top of the plate above the figures
274 (the reference number), Scobey is given for the experimenter and
1914 as the year. Under 274 it will be noted (as indicated by the
cross) that the observed velocity (column 8, Table 2, 6.19 feet per
second), is 0.1 per cent less (column 19, Table 2) than the velocity
(6.20 feet per second, column 14, Table 2), as computed by the new
formula for the same sized pipe with the same loss of head. Similarly
the open circle shows that it is 5.9 per cent more than the velocity
(5.83 feet per second) as computed by the Williams-Hazen formula
(column 20, Table 2); the black dot shows it to be 17.2 per cent less
than the velocity (7.48 feet per second) computed by the Moritz
formula (column 21, Table 2); the winged circle shows it to be 0.8
per cent more than the velocity (6.14 feet per second) computed by
the Tutton formula (column 22, Table 2); the fact that there are no

56 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

triangles (see other observations on Pl. VII) shows that listed tables
of fin the Weisbach formula do not extend
to 144-inch pipes; hence comparison was
not made with the Weisbach formula
(column 23, Table 2).

At the bottom of the chart the reason
for the blank opposite ‘‘Moritz”’ is quite
obvious, since this observation was made
subsequent to his own tests. Opposite
Scobey’s name the heavy upper line
indicates that all the observations in this
series received a weight of 3 in determin-
ing the general value of the intercept
equation (fig. 4). The light line under
the heavy one indicates that these obser-
vations did not receive much weight in
determining the general value of the
exponent of V (see p. 51, and column 14
Table 8).

At the extreme right of the chart the
same symbols are used to show the relative
positions of the mean of all observation
percentages (see foot of columns 19 to 23,
inclusive, Table 2) and also the means of
the average percentages by pipes (see foot
of columns 18 to 22, inclusive, Table 3).

The new formulas and the Moritz form-
ulas agree for a 4-inch pipe, diverging as
the diameters increase exactly as do the
curves in figure 4. Thus by the time a
pipe 144 inches in diameter is reached the
Moritz formula shows 20 per cent greater
capacity than that shown by the new
formulas while a glance at the larger
sizes of pipes (Pl. VIL) shows that even
the new formulas give a greater carrying
capacity than observations on most pipes
larger than 24 inches would promise.

6

4

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Fia. 4.—Logarithmic diagram developing curve for equation m’/=7.68 d -1.17. Small circles show values of m before revising to mn’.

KUTTER’S FORMULA AS APPLIED TO
WOOD-STAVE PIPE.

In discussing the Moritz experiments
with reference to the value of n in Kutter’s
formula, Hering states! that he ‘‘recog-

1 Trans. Amer. Soc. Civ. Engin., 74 (1911), p. 459.

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LOGARITHMIC DIAGRAM FOR FLOW OF WATER IN WooD-STAVE PIPE, BASED ON FORMULA
V=1.62D°©F°>, SIMULTANEOUS VALUES OF 7 IN THE KUTTER FORMULA ARE GIVEN
FOR COMPARISON.

PiaTe VIII.

FORMULA ARE GIVEN

UTTER

K

U, S, Dept. of Agriculture,

Bul. 376,

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ses

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Ni

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-STAVE PIPE, BASED ON FORMULA

SIMULTANEOUS VALUES OF 7 IN THE

1.62D°SHos,
FOR COMPARISON.

LoGaRrITHMIC DIAGRAM FoR FLOW OF WATER IN Woop
Vv

THE FLOW OF WATER IN WOOD‘STAVE PIPE. S17

nized as well as did Mr. Kutter himself, almost at the outset, that n —
was not to be considered a precise and unvarying constant, although
it was more nearly so than any other constant before proposed.’’ +

The fact that n does vary has been understood by hydraulicians
specializing in work involving the Kutter formula, but notwithstand-
ing this the tables and charts which have been accepted as standard
have assigned values of n to certain degrees of roughness without
reference to other conditions. The usual understanding regarding
variation occurring in the value for nm has been that n is less in large
channels than in small ones, although the writer has not been able to
show from a study of all available data that this variation is as great
as suggested by Johnston and Goodrich?.

In the case of wood-stave pipes an opposite effect is noted; that is,
the value of n becomes greater as the value of R (which is directly
proportional to the diameter) becomes greater. Referring to Plate
VIII it will be noted that all of the straight lines are based on the new
formula (13), page 7, while the n curves are determined in the fol-
lowing manner: To determine the curve for n=0.012, the inter-
sections of the n curve with the diameter curves for various pipes are
found and these give the locus for all pipes and velocities with
n=(0.012.

Each intersection is found by solving formulas 5 and 13 (pp. 6 and
7) as simultaneous equations, eliminating V, substituting a known

value for D (from which the known value of R is found, as R=7)

and solving for H, which is equal to 1000s in the Kutter formula.
Note that the value of n increases for a given velocity as the size
of pipe increases and that the value of n decreases for a given size
of pipe as the velocity increases. These last two statements are
borne out by a glance at the general trend of column 10, Table 2.
Assume that Plate VIII, which is a graph of formula 13, page 7,
correctly represents the flow of water in an average wood-stave pipe.
This assumption is supported by the figures at the foot of columns
19 and 18 in Tables 2 and 3 respectively. Assume also that the n
curves represent the simultaneous values of n for any position on the
graph. Then the variations in the proper value of n to assume
in the design of wood-stave pipe become so complicated that the
Kutter formula had better be abandoned in favor of the exponential
type of formula. This would leave the Kutter formula for its
originally intended purpose, that of design of open channels, for
which it is eminently fitted.’

1E. Ganguillet and W. R. Kutter, translated by Rudolph Hering and John C. Trautwine, jr. A General
Formula for the Uniform Flow of Water in Rivers and other Channels, New York, 1907, 2d ed.

2C. T. Johnston and R. D. Gocdrich. A Formula and Diagram for Determining the Velocity of Flow

in Ditches and Canals. Eng. Rec., 64 (1911), No. 19, p. 542.
3 The Flow of Water in Irrigation Channels. Fred. C. Scobey, U.S. Dept. Agr. Bul. 194, p. 60.

58 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

EFFECT OF AGE UPON THE CARRYING CAPACITY OF WOOD-STAVE PIPE.

Some manufacturers and hydraulicians have contended that wood-
stave pipe becomes smoother with length of use, and that therefore
the capacity of the pipe increases with its age.

In order to study this question the writer prepared figure 5. This
chart shows that, judging by available experimental data, there is
no definite law between age and change in capacity, but unfor-
tunately the results of but one test are accessible on any pipe older
than 7 years. That pipe (No. 31, Ogden, Utah), ney 24 years

paci er cent :
aay ay -~below overage ie P GD big mohneae overage
Te)

EE RET RIMES PTI MT Me ea

BRERA eee Aes ease)

PEN PES SATS PeT ePIC BS TP ame SY a EP PL

PEL ete Wee Poe oh SL 1: Aral O se | epec Tee eae: Chee [Le ease a
srtenttenttsstessts

eaten a me

Fig. 5.—Diagram showing lack of relationship between age and carrying capacity. Numbers correspond
with those in column 1, Tables 2and 3. Ages taken from column 4, Table3. Relative capacities taken
from column 18, Table 3.

old at time of test, shows a capacity only about 3 per cent greater

than the discharge computed by the new formula.

CAPACITY OF WOOD-STAVE PIPES.

In the following pages the design of wood-stave pipes is con-
sidered with reference to carrying capacityalone. Such structural
features as thickness of staves, banding, cradles, etc., do not come
within the scope of this paper.

The total loss of head necessary in the conveyance of a given
quantity of water will be the sum of the velocity head, h,; the entry
head, h,; and the friction head, hy, or its equivalent per unit length;

THE FLOW OF WATER IN WOOD-STAVE PIPE. 59

less any velocity head, h,’, that may be recovered as the water
approaches the pipe outlet at a velocity relatively high compared
with the velocity in the open water below the outlet chamber. This
total may be expressed by the formula

He=h,+h,.+hr—hy’ (21)

where Hz has the significance shown in figure 1 and hy, hg, hry, and
h,’ have the significance defined on page 3. The influence of
gentle curves was included in the data upon which the formulas were
based, so that an additional loss for slight bends or curves need not
be considered in the design of the usual pipe on irrigation systems.
If sharp bends can not be avoided then an additional loss of head
must be anticipated. The results of such tests as have been made
on bends in pipes are given in standard works on hydraulics.

VELOCITY AND ENTRY LOSSES.

In designing pipes of small diameter and great length, the losses
due to velocity and entry heads, h, and h,, are so small compared
with the friction loss that they may be neglected. Otherwise they
_ should be included in the allowance for total lost head.

As a rule a wood-stave pipe line begins under one of four general
conditions:

1. Intake chamber located in a reservoir, where the velocity of the
water is practically zero. No taper or transition section between
intake and pipe.

2. Intake chamber located on an open channel where there is an
appreciable velocity toward the structure but where this velocity
is not available because a bend or weil at the intake practically
dissipates the velocity head.

3. Intake chamber followed by a transition section in which the

velocity is increased over that existing in the leading channel or
reservoir. The outlet end of a pipe beginning under this condition
is usually provided with a similar transition section.
_ 4, The wood pipe but a continuation of another pipe of the same
size but of concrete, steel, or other material. In this case there is
little or no loss due to entry or velocity, the only factor introduced —
being the change in friction head due to change of material.

In conditions 1 and 2 it is best to consider the water above the
intake as at rest. From this state of rest velocity must be created and
increased to the mean velocity, V, existing in the pipe. The head,
h,, necessary to create a given velocity is shown in column 2, Table 5.
The entry loss will be from 0.5 h, where the pipe of standard size
begins at a headwall and is without bell or taper mouth, to about
0.25 h, for a rounded intake, and 0.05 h, for a bell-mouth intake.
Many of the structures built by the United States Reclamation

60 BULLETIN 376, U: S. DEPARTMENT OF AGRICULTURE.

Service were designed with the entry loss taken as half the velocity
head, even though there were more or less rounding and taper in the
intake structures. In Table 5, column 3, is shown the amount of
entry loss when taken as half the velocity head (column 2); and the
sum of the entry and velocity losses is shown in column 4.

TABLE 5.— Mean velocity in pipe, V, in feet per second; and head of elevation lost creating
this velocity and overcoming entrance conditions, hy+he, in feet.

1 2 1
Vi hy he hy+he Vi hy he hy+he
Ft.persec.| Feet. Feet. Feet. ||Ft.persec.| Feet. Fee. Feet.
1.0 0.016 0. 008 0.024 5.0 0. 389 0.195 0. 584
2 022 011 - 033 .2 . 210 630
4 030 015 045 4 453 ~ 227 680
6 040 . 020 060 6 488 . 244 732
xe 050 . 025 075 8 523 . 262 785
2.0 062 . 031 093 6.0 560 . 280 840
2 075 - 037 112 2 598 . 299 897
4 090 . 045 135 4 637 319 956
-6 105 . 053 158 -6 677 339 1.016
-8 122 . 061 183 8 719 359 1.078
3.0 140 . 070 216 7.0 762 381 1.143
2 159 . 080 239 2 806 - 403 1.209
4 180 . 090 270 4 851 . 426 1.277
-6 202 .101 303 6 898 449 1.347
8 224 112 336 -8 946 473 1.419
4.0 249 125 374 8.0 995 . 498 1, 493
-2 274 . 137 411 2 1.045 523 1. 568
4 301 151 452 4 1.097 . 549 1. 646
6 329 - 165 494 6 1.150 .575 1.725
8 358 .179 537 8 1. 204 . 602 1. 806

Where the usual types of inlet and outlet structures are employed,
with but little construction and consequent expense incurred for con-
servation of entry and velocity heads it is recommended that the
figures in Table 5 be used. In that case any influence on the total
loss of head, derived from the rate of flow toward the intake as in
condition 2, where water enters the pipe from an open channel, will
introduce a small factor of safety for conservative construction.
The same may be said of any slight recovered velocity head where
the pipe discharges into an open channel.

In figure 1, Plate XII, probably the most common form of con-
struction for both inlet and outlet of a wood-stave siphon is shown.
In some cases taper staves are used in both inlet and outlet, so that
the velocity is gradually increased in entering the pipe, thus reduc-
ing the entry loss. This construction classes the pipe under
condition 3. The velocity is gradually decreased at the outlet,
preserving the velocity head. The usual practice in this type of con-
struction is to place the center of the pipe opening for the inlet cham-
ber at or below the bottom of the leading canal. The pipe at the
outlet is usually placed so that the top of the opening is slightly
below the high-water line at full capacity.

Bul. 376, U. S. Dept. of Agriculture.

SUGGES"

ti

Bul, 376, U. S. Dept. of Agriculture.
PLaTe IX.

Scale of BCDE.

SUGGESTIVE INLET AND OUTLET STRUCTURES FOR INVERTED SIPHONS.

Maen

sovnihaenton on pete comet
+5 . : wa, ' ’ ' . ‘ ( it ate

bee :

‘ Hi
}

bie
peat yy

iA *
4 |

euamnammnenenaaeaincmmmniaid

THE FLOW OF WATER IN WOOD-STAVE PIPE. 61

The type of construction with a well having a rounded intake is
shown in C, Plate IX. This type is generally used where the hillside
is very steep just at the pipe intake or where a drop in grade line is
included in the well structure.

In D, Plate IX, is shown a type of entrance structure for both
round and square pipes quite frequently used by the United States
Reclamation Service where moderate velocities (5 or 6 feet per sec-
ond) only are to be considered.

The west Okanogan irrigation district (Washington) uses a general
type like E, Plate IX, for both inlet and outlet structures. In the
inlet structure shown the concrete rounds into the pipe opening, the
center of which is level with the bottom of the canal.

The forms, reinforcement, and final entrance of a large siphon in
Wyoming are shown in Plate XIII.

A pipe with both inlet and outlet tapering, such as condition 3,
will have the maximum efficiency as it approaches a ‘‘ Venturi tube
with elongated throat,” as described to the writer by D.C. Henny.
Such a structure would have the sides of the inlet converge at the
rate of about 1 in 5, while the transition section at the outlet would
diverge at the rate of about 1 in 24. On such a pipe less than 5 per
cent of the velocity head will be unrecovered, charging all losses
other than friction to entry head.

The transition section usually includes part of the intake or out-
let structure proper and also a short length of the wood pipe. On
the Arkansas Valley conduit of the Colorado Fuel & Iron Co. there
are 25 siphons of wood, incased in concrete.1 The intake ends of
these siphons taper at the rate of 1 inch per foot of pipe until the
diameter at the opening is 1 foot greater than that of the main pipe:
The inlet to one of these siphons is shown in figure 8, Plate XII.

This argument regarding conservation of velocity head and reduc-
tion of entry head is exemplified in the recently completed designs
for a large siphon carrying water at a very high velocity at the Sun
River crossing on the Sun River project of the United States Recla-
mation Service. The outlet structure is shown as A in Plate IX.

The water section in the leading canal has an area of 928 square feet
with a velocity of 1.08 feet per second. By tapering wing walls and
concrete intake structure the area at the upper end of the wood-stave |
pipe has been reduced to 50.3 square feet (96-inch pipe) and the
velocity increased to 19.9 feet per second. By this time 6.14 feet of
head of elevation has been devoted to building up a high velocity.
Of course it is important that as much as possible of this velocity
head be recovered at the outlet end.

1 Frictional Resistance in Artificial Waterways, V, M. Cone, R, E. Trimble, and P. S. Jones, Colorado
Sta. Bul, 194 (1914).

62 -« BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

Throughout approximately the last 100 feet of wood pipe ending at
a, Plate 1X, tapering staves are inserted in the pipe until an elliptical
section 12 feet wide and 9 feet high isreached ata. The area has been
increased so gradually up to 84.82 square feet that, it is computed,
3.99 feet of velocity head have been recovered, the velocity meanwhile
being reduced to 11.8 feet per second. Between b and c the transition
section changes from an elliptical to a rectangular shape 132 feet wide
by 10.6 feet high, with an area of 153.12 square feet. In this transi--
tion section the vertical walls and flat floor and roof begin at b with
zero width, increasing to full width at c, the corners being rounded
out in the concrete. The velocity is further diminished to 6.54 feet
per second and the computations show an additional velocity head
of 1.51 feet recovered. At the upper end of the canal leading from
the structure the velocity is further reduced to 2.10 feet per second by
enlarging the section, the additional recovered velocity head being
computed as 0.59 feet. Thus of the 6.14 feet devoted at the inlet end
to increasing the velocity, the computations show the recovery of all
but the 0.05 foot, which is due to the difference in velocities in the
channels above and below the structure. However, even with care-
fully designed transition sections the computations show an aggregate
of 1.80 feet devoted to ‘‘entry head”’ at the various changes in cross
section.

The outlet structure of the Similkameen Siphon of the West Okano-
gan Irrigation District, Washington, is also designed with a view to
conservation of velocity head. This structure (B, Pl. TX) consists
of a 46-inch stave pipe tapered in a length of 12 feet to a diameter of
57.5 inches, the pipe then discharging into a wooden flume. The
most noticeable feature of the structure is the use of guide wings
extending into the flume. These prevent a sudden enlargement of
the cross section at the end of the pipe and tend to recover the veloc-
ity head. The floor of the flume is extended into the pipe to the point
where the taper section begins, thus preventing contraction and con-
sequent loss of head due to extension of the segment of the pipe below
the floor line at the bulkhead. No attempt is made to secure water-
tightness in these guide wings, but the water is allowed to enter
between the wings and the flume proper so that no pressure may be
brought against the ight wings. All] tightness is secured at the bulk-
head and in the flume proper.

Where a change is made in the size of pipe a long taper transition
section is usually installed. In the Altmar pipe (No. 51) the diameter
is changed from 12 to 11 feet. This change is so gradual that it can
hardly be detected by the eye. Inasimilar way the Mabton pressure
pipe (Nos. 43, 45, and 46) is reduced from 55? inches to 48} inches.
Where changes in sectional area are made in this manner probably

THE FLOW OF WATER IN: WOOD-STAVE PIPE. 63

the loss of head due to such change is negligible, the change in velocity
head alone being appreciable.

Unless a tapered outlet structure is installed it will be best to
consider all of the velocity head within the pipe as dissipated in impact
and eddies due to the sudden enlargement of the sectional area in the
outlet chamber. That is, for purposes of design recovered velocity
head should not be counted upon.

During the season of 1915 the writer endeavored to secure informa-
tion as to the amount of head lost between the surface of the water
at the intake and a point 3 diameters down the pipe, charging such
loss of: head to velocity and entry losses jointly. Some of the pipes
tested were of concrete and some of wood, but this difference did not
alter the value of the information secured. The latter was meager,
however, for the reason that designers have been ultraconservative
in allowing for friction losses of head in the pipe; consequently the
entrance in most cases is not submerged. The water from the canal
rushes down the first reaches of pipe and in a very turbulent and air-
charged condition finally fills the pipe.

Table 6 shows the results of such tests as could be made. These
were incident to those made for the determination of friction losses
in the pipe.

TaBLE 6.—Tests for loss of head at inlet of wood and concrete pipes.

1 2 3 4 5 6 7 8 9 10 Vi

Mean | Loss of | Loss of | Length} Total | Loss hy=
veloc- | head, | head |ofpipe,| loss be- veloc- |} he=
Diam- | ityin | intake |perfoot] 3D to | from | tween | ity entry
eter. pipe to ofpipe,| gauge | 3D to |intake| head | head
per | gauge | gauge i gauge |. and | for V, | =4hy.
if:

Test. hy+h..

| second. 1-2: il, 3D. | col. 3.
|
Inches.| Feet. Foot. Foot. Feet. Foot. Foot Foot. Foot. Foot.

Piet cig Se age Aaa 8 3.51 | 0.039 |0. 0108 3.8] 0.041 |—0.002 | 0.191] 0.095 0. 286
De Fan les IC TR tiny Ca 8 3. 56 .014 | .0108 3.8 041 |— .027 .197 . 097 . 294
Cie AE See ob Rea Seat i 12 1. 60 .021 | . 00126 7.0 009 |+ .012 . 040 . 020 069
2 pe eree e ee 12 1. 60 . 047 | . 00146 7.0 .010 |+ .037 . 040 . 020 060
Eth, $e ALA ei ie ae 60 3.08 . 125 | . 00054 65. 0 035 |-+ .090 150 .075 225
Geer ciin seen ene: 60 3.03 .098 | . 00056 65. 0 .036 |+ .062 14. . 072 216
fag a gh ES ee es eee 54 4.03 .498 | .0015 12.8 .019 |+ .479 . 254 ay 381
Soh dutta eee Bae aie 54 4.02 .431 | .0016 12.8 .021 |+ .410 . 252 . 126 378

It is appreciated that this table is of but little assistance in the
design of intakes, but it is offered as a start toward the collection of |
information on this subject. Except in the case of tests 1 and 2 the
velocity of approach was indeterminate, due to changes in channel
section and to eddying conditions. It will have served its purpose
if it brings out the fact that close computations on entry and velocity
head losses can be but approximate.

A hook gauge in a stilling box in the intake gave the water surface
at that point, while the elevation of the top of the equivalent water
column (see p. 22) at gauge No. 1, deducted from the elevation of

64 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

the water surface at the intake, gave the loss of head between the
intake and gauge No. 1. These losses are shown in column 4.
Column 7 gives the friction loss between a point 3 diameters down
the pipe from the intake and gauge No. 1. This column is based
upon the friction loss per foot within the pipe (column 5) multiplied
by the number of feet (column 6) back from gauge No. 1 to the
3-diameter point. Column 4 less column 7 gives the computed loss
of head (column 8) due to velocity and entry heads combined be-
tween the intake and the 3-diameter point. Theoretically column 8
should approximate column 11, which is the sum of columns 9 and
10, but in most cases the velocity of approach was sufficient to make
the entries in column 8 much smaller than those in column 11.

Referring to these two columns: Tests 1 and 2 were conducted on
a concrete pipe where the water entered a 16-inch standpipe from an
8-inch pipe and left the opposite side in an 8-inch pipe. The obser-
vations show that no head was lost within the standpipe. ‘Tests 3
and 4 were on pipes in an installation similar except that the water
left the standpipe in a 12-inch pipe at right angles to an 8-inch pipe
through which it entered. Tests 5 and 6 were on the pipe shown in
Plate XII, figure 3. Here the velocity of approach in the canal
acted directly on the intake opening, greatly reducing the loss of
head. Tests 7 and 8 were on a similar pipe, but in this instance the
canal turned an abrupt right angle just before entering the pipe,
causing a violently turbulent condition which probably introduced a
large error in the observed head at the intake.

AIR IN PIPE.

In speaking of a pipe that did not show sufficient carrying capacity
Moritz states: !

Examination showed that air imprisoned in the pipe was.causing the difficulty.
This was overcome by inserting a $-inch wrought-iron standpipe in the top of the pipe
about 15 feet below the intake. In this way the air was, to all appearances, entirely
removed, and the carrying capacity was raised to 1.54 cubic feet per second, an
increase of about 60 per cent.

Pipes taking water directly from reservoirs are, of course, not sub-
ject to these troubles, the depth above the intake being, as a rule,
sufficient to insure filling of the pipe with water alone.

Siphon pipes and, in even greater degree, pipe chutes are often
reduced in carrying capacity by entrained air. In his investigations
on wood-stave pipes the writer has observed that air troubles are
minimized under the following conditions: (a) Low velocity in
channel approaching inlet; (b) inlet end set well below the hy-
draulic gradient, as a rule with top of pipe at about same elevation
as bottom of the canal above the inlet; (c) intake chamber designed
to minimize eddies.

1 Trans, Amer. Soc. Civ. Engin., 74 (1911), p. 435,

THE FLOW OF WATER IN WOOD-STAVE PIPE. 65

Moritz suggests the extensive use of air valves in some form. The
| best air outlet is probably a “chimney” rising above the hydraulic
| gradient. There should be several connections to the siphon, either
normal to the pipe or, better, pointing slightly upstream. These
| may be independent of each other or all may connect to a common
|. pipe extending along the top of the siphon, the upper end passing
through the head wall of the intake chamber so that any water that
blows out with the air will fall back into the pipe. The last connec-
tion should be at a lower elevation than the water surface in the out-
let chamber so that, with a small discharge, the air entrained will be
collected and passed off. As a rule low discharges entrain more air
than does a full discharge, since the water rushes down the initial
reaches of pipe in a turbulent condition. On the other hand, the
upper air vents are necessary to care for air entrained and compressed
during discharges approaching maximum capacity. These vents
may be from 1 to 12 inches in diameter, depending on the size of the
wood pipe, and should be so assembled that they may be taken
apart, as débris collects in such vents and must be periodically
removed. If excessive air troubles are present, a collecting chamber
may be attached to the siphon at each vent, the air pipe being at-
tached to the top of the chamber rather than directly to the siphon

pipe.
FRICTION LOSSES.

The loss of head necessary to overcome internal resistances within
the pipe is proportional to the length of the pipe but is independent
of the static pressure in the pipe. That is, the loss necessary in the
conveyance of a given quantity of water through a siphon pipe will
be the same whether the low point is, say, 10 feet or 150 feet, below
the hydraulic grade line, the other factors remaining unchanged. The
influence of temperature upon the frictional resistances was found
_ by Saph and Schoder to be considerable in small brass pipes but has
_ not been studied in connection with tests on large wood pipes. It is
_ doubtful whether the influence of temperature could be differen-
_ tiated from that of friction alone in tests on large pipes in commercial
| service.

_ In order to determine the size of pipe and the loss of head neces-
| sary to overcome the frictional resistances in the conveyance of a
_ given quantity of water, two estimate diagrams and a table have
| been prepared. Two examples of typical pipe problems are given.
In these the use of the diagrams only is explained, as the table is
| considered self-explanatory. The factors of safety given below
should be considered in each problem, as a study of Plate VII shows
that an averaging formula, accepted literally, can not assure the
desired discharge for a given loss of head.

42463°—Bull. 376—16——5

66 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.
FACTORS OF SAFETY.

A study of Plate VII shows that a general formula may be often
10 per cent, sometimes as much as 15 per cent, and in isolated cases
25 per cent, at variance with observed capacities for given losses of
head. Likewise a study of the conditions holding in various pipes
fails to disclose just when high or low relative carrying capacities are
to be expected. However, the following factors of safety ee to
be warranted:

Five per cent when only a.rough approximation to the actual needs
of the pipe is possible; when water enters the pipe from a settling
reservoir and velocities in the pipe are so high that a clean-scoured
condition will always be present inside the pipe; and also where con-
ditions of operation are such that no penalties are attached to a
slight insufficiency of carrying capacity.

Ten per cent when the above conditions for a very clean pipe are
assured, but where penalties are attached to lack of capacity; or
where no direct penalties are attached but silted waters and low
velocities may permit deposits and growths of Spongilla or other
vegetable life.

Fifteen per cent where rock ravelings may reduce the interior area
of the pipe, or when penalties are attached and silted water or vege-
table growth are likely to cause excess retardation of flow.

The designer may safely assume that the capacity of wood pipe will
not change unless the pipe is subject to Sunes ravelings, or vegetable
erowth. (See fig. 5, p. 58.)

ESTIMATE DIAGRAMS AND TABLE; SOLUTIONS FOR TYPICAL PIPE
PROBLEMS.

1. An inverted siphon is required to convey 60 second-feet of
water a length of 2,800 feet with an allowable total loss of head of
1.8 feet. Water has settled in a reservoir before entering the canal.
No direct penalty has been attached for lack of capacity. Required,
diameter of the pipe.

Allowing a 5 per cent overload as a factor of safety, the rated
capacity will be 60+3=63 second-feet. Since the velocity is not
known, the entry and velocity head combined can not be determined
at present. For preliminary figures, 2,800 feet=2.8x1,000 feet;

therefore 5S =0.642=H. Referring to Plate X,' enter diagram at

63 second-feet. Intersection of Q=63 with H=0.642 is about on
the diameter line for 58 inches and at a velocity point of about 3.6
feet per second. Referring to Table 5, opposite V =3.6 the combined

1 Plate X was prepared by the writer from the new formula (No. 14, p. 7) in a manner similar to that
first used by Schoder in Engineering Record, Sept. 3, 1904.

;

eal
sl
=a
a
5
=
ct
a)
io)
©
B
=
5 Teen}
a
<
e-
cal
io)
ca
>)
a
ey
&
ea
H

/
ts

U. §. Deph. of Agriculture

BASED ON FORMULA: Q= 1.272D'°H?~
+ 1,000 feet H; and velocity. V. For probleis involving velocities less than 0.7 foot per second or
ot per reconil, ee Plate V:

LOGARITHMIC DIAGRAM FOR USE IN Desianinc Woon-STAVE PIPE.

Any point on the diagram gives slinuttancous values of qnantity, Qs dlameter of pipe, Mi loss of heal pe
Inore than 9,0 Hee

weet pee

oh i

= aa
aye

tae oe eee aaah Va

‘

ae eS ee Oe

ee ee eee
ne, Pa :

>-- ~ >

. ae And lee eRe, it,
Ae er ee etn etl nae ae a Se
x,

J ° i> } \
ue am all Vie
Pak wie & chee Mat
% . he

vat |

+

wt

SNe AC 0 Pee ELIE st | NLM OL LAGE MS EOE IEL SOE!

Mn NBI220 “11+ F0kb RO ME MORIT COIMH TRO me ena ruccre meant

r

CELT EERE | uoonelinrl. sewed Wrraii

THE FLOW OF WATER IN WOOD-STAVE PIPE. 67

velocity and entry head is found to be 0.303 feet. Therefore, the final

figures are pee 0.536 = H.

Again, referring to Plate X, at the intersection of Q=63 and
H=0.536 the diameter of the required pipe.is found to be 60 inches
and the peak-load velocity to be 3.3 feet per second. The difference
between the preliminary figure for combined velocity and entry heads
and the final figure is not sufficient to warrant more trials.

2. A power trunk line from a reservoir to a surge tank to convey
a peak load of 700 second-feet is required. The length of pipe will
be 11.3 miles, the total loss of head under peak load shall not exceed
20 feet, and the value of head shall be sufficient to warrant a factor
of safety of 15 per cent in designing. Required for comparison, the
size of pipe for both a single and a double pipe line with the same loss
of head.

The length of pipe is so great that velocity and entry head may be
ignored. :

One hundred and fifteen per cent of 700 =805 second-feet.

Eleven and three-tenths miles=11.3 x 5,280 = 59.664 x 1,000 feet.

ae = 0.335 feet per 1,000 feet =H.

Enter Plate X at Q=805. Intersection of Q=805 with H=0.335
is at D=14.5 feet and at V=5 feet per second. Thus a single pipe
line 14.5 feet in diameter will convey the peak load at a velocity of
about 5 feet per second.

To study the possibilities of a double pipe line, turn to figure 6.
Enter at intersection of diameter 14.5 feet and relative capacity 1.
From this point the left slanting line intersects relative capacity
line 4 on diameter line 135 inches or diameter line 11.25 feet. Thus
twin lines each 114 feet in diameter will convey the given quantity
of water with the same loss of head as will a single line 143 feet in
diameter.

Pipe problems involving velocities less than 0.7 foot per second or
more than 9 feet per second may be solved by the use of Plate VIII.
With a straightedge join the two discharge scales at the given dis-
charge. All points on the straightedge will now give simultaneous
values of diameter, loss of head, and velocity. For instance, the
dash-dot line representing 100 second-feet intersects the 84-inch pipe
line on the H-line of 0.237 foot per 1,000 feet and on the V-line of
2.58 feet per second. Thus an 84-inch pipe will convey 100 second-
feet of water at a velocity of 2.58 feet per second with a loss of head
of 0.237 foot per thousand feet of pipe.

D=Diameter- fee!
Pa ° 9) al ?

2° ART
POLINADA ANAS OBRK T
AANA He ca NN ya Wi
AAA Aan vaya AAS | Hh KW ik a
AERA PANNE
SAS RR Wr

hye A na WU

MN ony Nh Hh Ry AR HNN nnn

NN nM na a Ny uh MAN Mi Ha ue ie

a vi PE a Me HA

in ah Mp aN

a AN UN )
eee VENEI LA al MW
EEA SAW 7.07 A eR, pu
DEN VO

15.

J

N @ VO

Ol-

Hh
il
Mi
A
na
/|

WW
Mi
/
Hi)
Ui
NY
My
AV

Bs S35 PS aS
— a
. yi fo>)

SSS
C=

es for left slants
= “ ui,

eT

eran ANAK AN TN LEA kK \A VARMA NK

AN KAAAANY mt Kh Naval XAKY nt Av HEN an
RAIA Hi ne HN ONY ua th j HAAN CW ONAN rN
Biviceenarivise ns, y ANNE RNR ne He i RW YVAN} HON xX
TAIZ AI ZATATALXIXIYIVIY Vy My) yyy NON A ue ANNI OO x
Vy

AAA AAA SRR
nr 0 OW = v3 co

on MTN OW
a timate hehen a

Relive: Ascent for right slants.

Relative Sane

BULLETIN 37 y LUIS DEPARTMENT OF AGRICULTURE.
lw vp

68

/3,

ght slant from 12

This intersection is approxi-

=

senting 1

For the first problem, enter
the ri

second problem follow

for the

y

For instance, an 8-inch pipe will carry one-third as much as a 12-inch
gram. Similar]

m (as noted) on the left slanting line leading from 12inchesasabase. Theinter-

s at left of dia

gure

n by fi
as a base to the intersection of this slant with the vertical line from 18.

section of this slant with the verticalline above 8 is approximately on the horizontal line repre

given hydraulic gradient.
pipe, and an 18-inch pipe will carry three times as much as a 12-inch pipe.

the diazram at the botto

mately on the horizontal line representing 3 as shown by figures at right of diagram.

as show

Fic. 6.—Logarithmic diagram showing relative capacities of wood-stave pipe of various diameters for
any

Bul. 376, U.S. Dept. of Agriculture. . PLATE Xl. |

Fic. 1.—PIPES FROM SURGE TANK TO POWER House. |
Right-hand pipe held at constant velocity. 131-foot pipe in

Fia. 3.—WINTER FLow Is RETARDED BY SLUSH ICE. i
Note rings for grating remoyed to prevent ice accumulation.

Bul. 376, U. S. Dept. of Agriculture. PLATE XII.

Fic. 1.—TYPICAL OUTLET STRUCTURE. WILL PARTIALLY RECOVER VELOCITY HEAD.
Pipe is one-half diameter too high forinlet structure. Too much air would enter.

Fic. 2.—VIEW TAKEN FROM STRUCTURE IN FIGURE 3.
Hillside cut ravelings enter pipe and reduce capacity. A condition to be avoided.

Fic. 3.—ENTRANCE WELL SUBMERGED, REDUCING AMOUNT OF AIR CARRIED INTO PIPE.

Bul. 376, U. S. Dept. of Agriculture. PLATE XIII.

SOIT AO RE 2 SS ESSE

4
|
il
|

Fic. 1.—SIPHON UNDER UNION PACIFIC RAILROAD, ROCK CREEK CONSERVATION Co.,
WYOoMING.

Form for inlet bowl to rcduce entry loss. Bee under construction in distance. See figures
2 and 3.

a

{
f

Fi@. 2.—FORM FOR BOWL, FLoor REINFORCEMENT, AND CAST-IRON PIPE FOR INLET SECTION
FOR STRUCTURE IN FIGURES 1 AND 8.

Fia. 3.—SIPHON INLET MADE FROM FORM SHOWN IN FIGURES 1 AND 2. ENTRANCE WELL |
SUBMERGED, PREVENTING AIR BEING CARRIED INTO PIPE.

Bul. 376, U. S. Dept. of Agriculture. PLATE XIV.

Fic. 1.—EVEN WITH 27 Cé=T-IRON BENDS LIKE THIS THE ASTORIA, WASH., PIPE SHOWS
A CAPACITY 17 FER CENT MORE THAN THE AVERAGE. (No. 23.)

Fic. 2.—PIPE FOR BUTTE, MONT., MUNICIPAL SupPLy. (No. 32.) SPRINGING INA BUCKLE
JOINT.

-

THE FLOW OF WATER IN WOOD-STAVE PIPE. 69

TABLE 7.—Velocity V in feet per second and loss of head H in feet per thousand feet of
pipe, necessary to the conveyance of a given quantity of water, Q, in second-feet and in
millions of U.S. gallons per day through wood-stave pipe, based on formula H=

1.8
oo For instance, 5 second-feet will be carried by a 16-inch pipe at a velocity of

3.58 feet per second with a loss of head of 2.98 feet per thousand feet of pipe.

Inside diameter, in inches, and corresponding area, A, in square feet. Quan-
Chit pa Ie 0 a ee ia La ul Pc ce ly,
tity. 4 5 6 7 8 9 10 mil-
A=0.0873. | A=0.1364. | A=0.1963. | A=0.2673. | A=0.3491.) A=0.4418.| A=0.5454.| lions
ff oper
Q Veer eV eV) Eee | | a vy | ay
Sec.-ft. | Feet.| Feet.| Feet.| Feet.| Feet.| Feet.| Feet.| Feet.| Feet.| Feet.| Feet.| Feet.| Feet.| Feet.| Gals. :
Soe meo a Gra) Leah 2YS3) (O27 0298) Oral, O14 10 O:57]* 0225)... Lele. 2 ect [os - 2 ae 0. 129 |
-4| 4.58) 23.4! 2.93] 8.10) 2.04) 3.40} 1.50) 1.63) 1.15 86] 0.90) 0.49) 0.73} 0.29) .259 “i
.6|. 6.87] 48.7] 4.40) 16.8] 3.06) 7.05) 2.24) 3.38] 1.72) 1.79) 1.36} 1.02) 1.10 60} .388 k
-8| 9.16] 81.7} 5.86] 28.2) 4.08) 11.8] 2.99] 5.67) 2.29) 3.00} 1.81] 1.71) 1.47} 1.02) .517 4
1.0} 11.4 | 121 7.33| 40.6) 5.10) 17.7 | 3.74) 8.47) 2.87) 4.42) 2.26) 2.56] 1.83] 1.52) .646 :
1.2) 13.7 | 169 8.80| 58.5) 6.11) 24.6} 4.49) 11.7] 3.44) 6.22) 2.72) 3.55) 2.20) 2.10] .776 |
1.4] 16.0 | 224 | 10.3 | 77.1) 7.13) 32.4] 5.24) 15.5] 4.01) 8.21) 3.17) 4.68) 2.57] 2.78) .905 7
1. 6].18.3 | 285 | 11.7 | 110 8.15] 41.3 | 5.99) 19.7] 4.58) 10.4] 3.62) 5.95) 2.93] 3.54] 1.034 a
1.8) 20.6 | 352 | 13.2 | 121 9.17) 51.0 | 6.73) 24.4] 5.16) 12.9] 4.07) 7.35) 3.30) 4.37) 1.163 el
Fe Vo 2) see 5 14.7 | 147 | 10.2] 61.6] 7.48] 29.5] 5.72] 15.6| 4.53] 8.89] 3.67] 5.28] 1.293 ||
RG ee A eee 18.3 | 219 | 12.7] 92.1 | 9.35) 44.1] 7.16) 23.3 | 5.66) 183.6] 4.58] 7.89) 1.616 z]
SaQie cae. oe 22.0 | 304 | 15.3 |128 11.2 | 61.2} 8.60} 32.4] 6.79) 18.9] 5.50} 11.0 } 1.939 ;
BSL GB 8 Hee es | ee Ce 17.8 169 | 13.1 | 80.6 | 10.0 | 42.7 | 7.02| 25.2| 6.42) 14.5 | 2.262 ina
AOE Sees SaeE NS Sok (es 20. 4 |215 15.0 |103 11.5 | 53.7} 9.05) 31.9] 7.33) 18.6 | 2.585 §
5 | Fee acts | Se = cl |e Sooke eee | Sis oe] eos 16.8 |127 12.9 | 67.1 | 10.2.| 39.4] 8.25) 22.7 | 2.908 ry
Fo OI As Lis MR eu re | gear Lea eS 18.7 |155 14.3 | 81.2 | 11.3 | 47.7 | 9.17) 27.5 | 3.232
Lis He heath bec Ree freee icy [ma ae Ml bea a en 20.6 |182 15.8 | 96.4 | 12.4 | 56.6 | 10.1 | 32.6 | 3.555
Oe 35.58) Sassen eared hae eAeee ae eases] eer oes aerate 17.2 |113 13.6 | 65.4 | 11.0 | 38.2 | 3.878
Bo Tics ch Lene a en A Al | 2 ee Le 18. 6 |130 14.7 | 76.5 | 11.9 | 44.1 | 4.201
(OU eco 4 (aes 4 eae ee Sa eee a SL me als a ---| 20.1 |149 15.8 | 87.3 | 12.8 | 50.3 | 4.524
12 14 16 18 20 22 24
A=0.7854. | A=1.069. | A=1.396. | A=1.767. | A=2.182. | A=2.640. | A=3.142.
Vv H V H Vv H Vv H Vv H Vv H Vv H
THO) pels 27) = ON Ga|mrOL OA O5 31/2 OL 721220. 162/057)" O09. 2 cle o-s -- |. 2-5 | eee snd (A Mee a 0. 646
Me eee le | Wes GO| moka ba meosAS ie ea SOc a ect sOS|au a 's|n Onde Ondo sean a ee ae ale csecte|sooeee - 776
EAE 78119 esl = sor} 12 00|"— 530 TN) oe cA foes STD) Ob G81) SOLOS Secea lsdacee - 905
1,6] 2.04) 1.51) 1.50) .72) 1.15) .38 91] .22 73 113) beans O) 9 Seatar US} bapa | abi aeaey 1.034
1.8] 2.29] 1.87] 1.68) .90) 1.29) .47) 1.02) £27) .88 16h, S68 S10 e eees | es. aS: 1.163
2.0) 2.55) 2.26} 1.87) 1.08) 1.43) .57| 1.13 33} .92) .20) .76) .12) 0.64) 0.08] 1.293
2.5) 3:18) -d.37, 2-34 1.62)" 1579) 285) 1.42 49 1.15) .29| .95) .19) .80 12| 1.616
3.0) 3.82] 4.67) 2.81) 2.24) 2.15) 1.19} 1.70 68] 1.37) .41) 1.14 .26] .95 17| 1.989
3.5} 4.46] 6.17) 3.27] 2.96) 2.51) 1.57) 1.98 89) 1.60 54; 1.33) .34) 1.11 23] 2.262
4.0} 5.09) 7.86} 3.74) 3.76) 2.87} 1.99) 2.23) 1.14) 1.83 69} 1.52) .44) 1.27 29] 2.585
4.5) 5.73) 9.69} 4.21) 4.65} 3.22} 2.46) 2.55) 1.40) 2.06 85} 1.70) .54) 1.48 36] 2.908
5.0} 6.37] 11.7) 4.68] 5.63) 3.58] 2.98) 2.83) 1.70) 2.29) 1.03) 1.89) .65| 1.59 43] 3.232
5.5} 7.00) 18.9) 5.15} 6.67) 3.94) 3.49) 3.11] 2.02] 2.52) 1.22) 2.08) .78] 1.75 §1| 3.555
6.0) 7.64] 16.3 | 5.61] 7.80) 4.30} 4.13} 3.40} 2.32) 2.75} 1.42) 2.27) .90} 1.91 60} 3.878 eT
6.5} 8.27) 18.8] 6.08] 9.02} 4.66] 4.77) 3.68) 2.72) 2.98) 1.65] 2.46) 1.04! 2.07 69] 4.201 i
7.0} 8.91) 21.5 | 6.55) 10.3] 5.01] 5.45) 3.96) 3.11) 3.21) 1.88] 2.65) 1.19} 2.23) .79| 4.524 H
7.5| 9.55) 24.4] 7.02! 11.7] 5.37) 6.16) 4.24! 3.52) 3.44) 2.13] 2.84] 1.35} 2.39) .89) 4.847 >|
8.0] 10.2 | 27.3 | 7.48} 13.1 | 5.73) -6.94) 4.53) 3.96) 3.67} 2.39] 3.03) 1.52} 2.55) 1.00) 5.171 oa)
8.5) 10.8 | 30.5 | 7.95} 14.6] 6.09} 7.73] 4.81} 4.41) 3.90} 2.67] 3.22} 1.69) 2.71] 1.12) 5.494 i
9.0} 11.5 | 33.7 | 8.42) 16.4 | 6.45) 8.40) 5.10) 4.89) 4.12) 2.96) 3.41) 1.87) 2.86) 1.24) 5.817 ~ |
9.5) 12.1 | 37.2} 8.89) 17.9 | 6.80] 9.45) 5.38) 5.39) 4.35] 3.27] 3.60] 2.06) 3.02] 1.37) 6.140 i
10 | 12.7 { 40.8} 9.35) 19.6} 7.16) 10.4 | 5.66) 5.91) 4.58) 3.59) 3.79) 2.27) 3.18) 1.49) 6.463 bs
11 | 14.0} 48.5} 10.3 | 23.2] 7.88) 12.3 | 6.22) 7.01) 5.04) 4.28) 4.17) 2.68) 3.50) 1.78) 7.109 ‘
12 | 15.3 | 56.8 | 11.2] 27.3 | 8.60) 14.4] 6.79) 8.21] 5.50) 4.97) 4.55} 3.16) 3.82] 2.08) 7.756 ah
13 | 16.6 | 65.6 | 12.2 | 31.4] 9.31) 16.6 | 7.36) 9.48) 5.96) 5.74] 4.92) 3.63] 4.14) 2.41) 8.402 )
14 | 17.8 | 74.8 | 13.1 | 35.9 | 10.0 | 19.0} 7.92] 10.8 | 6.42) 6.55) 5.30) 4.15] 4.46) 2.74) 9.048 4 |
15 | 19.1 | 84:7 | 14.0 | 40.8} 10.7 | 21.5 | 8.49) 12.3 | 6.87) 7.43) 5.60] 4.70} 4.77) 3.11) 9.695 a
16 | 20.4 | 95.2 | 15.0 | 45.7 | 11.5 | 24.2 | 9.06) 13.8] 7.33) 8.33} 6.06) 5.28]. 5.09) 3.49/10. 341 :
il Beads eeebes 15.9 | 51.0 | 12.2 | 27.0 | 9.62) 15.4 | 7.79) 9.30) 6.44) 5.74]! 5.41] 3.90)10.987 ie
1d need ene 16.8 | 56.6 | 12.9 | 29.8 | 10.2 | 17.0 | 8.25) 10.3 | 6.82) 6.54) 5.73] 4.31/11. 634 ‘i
hy Reread ee 17.8 | 62.2 | 13.6 | 32.9 | 10.7] 18.8] 8.71] 11.4] 7.20) 7.20] 6.05] 4.76/12. 280 re
7A} eet Lerten. 18.7 | 68.1 | 14.3 | 36.1 | 11.3 | 20.6) 9.17) 12.4] 7.58). 7.90) 6.37) 5.22)12.926
PALS 7 SANS boca 19.6 | 74.5 | 15.0 | 39.4] 11.9 | 22.5] 9.62) 13.6] 7.96} 8.63} 6.68) 5.70/13.573
Poe Ne ss Se ee be i 20.6 | 81.1 | 15.8 | 42.9 | 12.4 | 24.4) 10.1] 14.8] 8.33). 9.37} 7.00] 6.19/14.219
723 ed Seog Ce et ee 16.5 | 46.4 | 13.0 | 26.5 | 10.5 | 16.0] 8.71] 10.2 | 7.32) 6.71)14. 865
2) 4 les Grieg Bene Aeeee| Smee 17.2 | 50.1 | 13.6 | 28.5 | 11.0 | 17.3 | 9.09) 11.0] 7.64) 7. 25)15. 512
POSTE Ne ge ec ieee te] ee ea es 17.9 | 54.0} 14.1 | 30.9 | 11.5] 18.6] 9.47) 11.8] 7.96) 7.79/16. 158
140: Jl Ge Shee paces eae beaeee 18.6 | 57.9 | 14.7 | 33.0 | 11.9 }.19.9 | 9.85) 12.7 | 8.27] 8.37/16. 804
ZA fc eset ack eel eee! pace ras 19.3 | 61.9 | 15.3 | 35.3 | 12.4 | 21.3 | 10.2] 138.6] 8.59) 8.95/17. 451
758) a ee arte ea eae 20.1 | 66.1 | 15.8 | 37.7 | 12.8 | 22.8] 10.6 | 14.5 8.91) 9.56/18. 097

70

BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

TABLE 7 (Continued).— Velocity V in feet per second and loss of head H in feet per thou-

sand feet of prpe, necessary to the conveyance of a given quantity of water, Q, in second-
For instance,
160 second-feet will be carried by a 42-inch pipe at a velocity of 16.6 feet per second with
a loss of head of 15.3 feet per thousand feet of pipe.

feet and in millions of U.S. gallons per day through wood-stave pipe.

Quan-
tity. 26 28 30 32 34
A=3.687. A=4.276. A=4.909. A=5.585. A=6.305.
Q V H V H Vv H V H V H
Sec.-ft. | Feet. | Feet.| Feet. | Feet.| Feet.| Feet.| Feet.| Feet.| Feet.| Feet.
8} 2.17] 0.68} 1.87) 0.48) 1.63} 0.34! 1.43) 0.25) 1.27} 0.19
PAC ee PL IO AGO ede GeBi Gb Sabir ae eas 528)
LOW 2270 VOD 25341 ae eiZi* 2104 ee eo2| es deel eosin 159i es
DN 2598) SST 2257 paso ee lave meee mele tn e14 | needs] tens 4
12) 3.25) 1.42) 2.81] 1.00) 2.45) .72| 2.15) .53) 1.90) .39
13] 3.53) 1.64] 3.04) 1.15) 2:65) | .82) 2:33) <61) 2:06) 246
14} 3.80) 1.87) 3.27) 1.32) 2.85) .95) 2.51 70) 2:22) 352
16) 4.34) 2.38) 3.74) 1.67} 3.26] 1.20; 2.87) .89' 2.54) .67
18} 4.88) 2.94] 4.21) 2.07} 3.67) 1.49) 3.22) 1.09) 2.86) .82
20| 5.42) 3.56) 4.68} 2.50) 4.07) 1.80} 3.58) 1.32) 3.17} .99
22| 5.97) 4.23] 5.15) 2.96) 4.48) 2.14) 3.94) 1.57) 3.49] 1.18
24) 6.51} 4.94] 5.61) 3.47) 4.89) 2.50) 4.30) 1.84) 3.81) 1.38
26] 7.05} 5.70} 6.08) 4.02} 5.30) 2.89) 4.66) 2.12) 4.12) 1.59
28| 7.59) 6.55) 6.55} 4.58! 5.70) 3.30! 5.01} 2.42) 4.44) 1.82
30} 8.14) 7.40) 7.02} 5.18) 6.11] 3.73! 5.37| 2.74) 4.76) 2.05
32| 8.68} 8.30) 7.48] 5.82) 6.52) 4.19} 5.73) 3.08] 5.08) 2.29
36| 9.76] 10.25} 8.42) 7.19} 7.33) 5.18) 6.45) 3.81) 5.71] 2.85
40] 10.8 | 12.4 | 9.35] 8.72) 8.15] 6.26] 7.16) 4.61) 6.34) 3.45
45| 12.2 | 15.3 | 10.5 | 10.8 | 9.17) 7.74) 8.06) 5.70) 7.14) 4.27
50] 18.6 | 18.5 | 11.71 18.0 | 10.2} 9.36) 8.95! 6.90) 7.93! 5.16
55| 14.9 | 22.0 | 12.9 | 15.5 | 11.2} 11.1] 9.85} 8.15) 8.72) 6.11
60] 16.3 | 25.6 | 14.0 | 18.1 | 12.2 | 13.0] 10.7 | 9.56) 9.52) 7.16
65| 17.6 | 29.6 | 15.2 | 20.9 | 18.2 | 15.0} 11.6 | 11.0 | 10.3 | 8.27
70} 19.0 | 33.9 | 16.4 | 23.8 | 14.3 | 17.1 | 12.5 | 12.6 | 11.1 |} 9.44
75| 20.3 | 38.2 | 17.5 | 26.9 | 15.3 | 19.4 | 13.4 | 14.3 | 11.9 | 10.7
SOE actrees ecm 18.7 | 30.2 | 16.3 | 21.8 | 14.3 | 16.0 | 12.7 | 12.0
AN ESS ee ce 19.9 | 33.9 | 17.3 | 24.3 | 15.2 | 17.9 | 13.5 | 13.4
QO eeeras| eee ene 21.0 | 37.4 | 18.3 | 28.4 | 16.1 | 19.8 | 14.3 | 14.8
Obl secu inceee aliases oles eee 19.4 | 29.7 |.17.0 | 21.8 | 15.1 | 16.4
LOO Pass8 al SES Sea | eae 20.4 | 32.6 | 17.9 | 24.0 | 15.9 | 17.9
40 42 44 46 48
A=8.727 | A=9.621. A=10.56 A=11.54. A=12.57
V H V H V H V H V H
30} 3.44) 0.95} 3.12) 0.75) 2.85) 0.60) 2.60} 0.49) 2.39) 0.40
B5l| 450 26) ) e641) 99 VOSS 219!) Ss O3ls. 504m 2aiale vee
40| 4.58] 1.59] 4.16) 1.26) 3.79) 1.00) 3.47) .82) 3.18) .67
45] 5.16} 1.97 | 4.68) 1.56) 4.26] 1.25) 3.90} 1.01) 3.58) .82
50) 5.57) 2.26) 5.20) 1.88) 4.74) 1.50). 4.38) 1:22) 3:98), .99
55| 6.30} 2.82} 5.72) 2.24) 5.21) 1.79} 4.77) 1.45) 4.38] 1.18
60} 6.88) 3.29 | 6.24] 2.62) 5.68) 2.09) 5.20} 1.69) 4.77] 1.38
65} 7.45} 3.8 6.76} 3.01! 6.16) 2.42, 5.63} 1.95] 5.17) 1.59
70| 8.02} 4.36] 7.28) 3.44] 6.63) 2.76) 6.07) 2.23) 5.57) 1.82
75| 8.59} 4.92} 7.8] 38.89} 7.10) 3.12) 6.50) 2.53) 5.97) 2.06
80; 9.17) 5.538 | 8.32) 4.37) 7.58) 3.51) 6.93) 2.84] 6.36) 2.31
85| 9.74] 6.16} 8.84) 4.88} 8.05) 3.92) 7.37) 3.17] 6.76) 2.58
90| 10.3 | 6.84] 9.36] 5.41] 8.52} 4.34) 7.8] 3.53) 7.16) 2.87
95} 10.9 | 7.55 | 9.87] 5.96] 9.00} 4.78) 8.23) 3.87] 7.56] 3.16
100) 11.5 | 8.380} 10:4 | 6.55) 9.47) 5.24) 8.67) 4.25) 7.96) 3.46
110) 12.6 | 9.79 | 11.4 | 7.77) 10.4 | 6.24) 9.53) 5.04) 8.75} 4.11
120) 13.8 |11.5 | 12.5 | 9.09) 11.4 | 7.23) 10.4} 5.89) 9.55) 4.81
130} 14.9 |18.3 | 13.5 | 10.5 | 12.3 | 8.41) 11.3] 6.81) 10.34) 5.55
140) 16.0 }15.1 | 14.6 | 12.0 | 13.3] 9.60) 12.1} 8.64) 11.1] 6.35
150) 17.2 |17.1 | 15.6} 13.6 | 14.2 | 10.9] 13.0! 8.81] 11.9! 7.18
160) 18.3 |19.3 | 16.6 | 15.3 | 15.2 | 12.2] 13.9} 9.89) 12.7] 8.07
170) 19.5 |21.4 | 17.7} 17.0 | 16.1 | 13.6 | 14.7] 11.0] 13.5] 8.98
180} 20.6 |23.8 | 18.7 | 18.9 | 17.0 | 15.1 | 15.6 | 12.2) 14.3 | 9.96
15210) eats Ness a 19.8 | 20.8 | 18.0 | 16.7 | 16.5 | 13.5 | 15.1 | 11.0
200) 26 oe Salers ae 20.8 | 22.8 | 18.9 | 18.3 | 17.3 | 14.8 | 15.9 | 12.1
PAM) ees Oe o Aleem eral Beep 19.8 | 20.0 | 18.2 | 16.1 | 16.7 | 13.2
Z20)| cbccrctcl tres een Mee zeae lies Sera 20F8 21.7 a| LOSI oy eledron| al aud
DO) rs s\shieca (ahs old erel| Spe aber ates has | neko Soret seetoonee 19.9 | 19.0 | 18.3 | 15.5
YAU 30 Salloogee||eobsocboar ocllesasucligedcoe 20.8.) 20.5 | 19.1 | 16.8
250) on Sera) Sie. tog | emia arctan spate racle eepids oil coe heel ere tees 19.9 | 18.0

Inside diameter, in inches and corresponding area, A, in square feet.

36
A=7.069.

Feet.

1.27
1.41
1.56
1.70

1. 84
1.98

TIS Orory
~I “I

_

FO SIDES: S59 So ees

NOPNTOFP MOON LA CWD
ooo Co

i

Feet.
1.13] 0.14

18

3.77

Cor COOrh © Oot Ricks

ROS SMO GNS Soro or Pe
WIE POHRMO NORDWO Te

ad

Quan-
tity,
38 mil-
A=7.876. | lions
per
V H day.
Feet. | Feet | Gals.
1.02} 0.11} 5.17
1.14) .14) 5.817
1.27] .17| 6.463
1.40} .20) 7.109
1.52] .23) 7.756
1.65) .927) 8.402
1.78] [33] 9.048
2.03} * 39] 10.341
2.29] = 4s} 11.634
2.54} | 58] 12.926
2.79] _ 69] 14.219
3.05] "gy! 15.512
3.30] _ 93) 16.804
3. 56] 1, 97| 18.097
3.81] 1. 91| 19.389
4.06 20. 682
4.57| 4° 38) 93.267
5. 08) 9. 94] 25. 853
Eval 9.51) 29-084
6.35! 3°94] 32.316
6.98 35. 547
7,62| $27] 38.779
8.25] 4° 87| 42.010
8. 89} 5.55 45. 242
9.52) 8! 99| 48.474
10.2 ~| 51.705
10.8 | #°07| 54.937
11.4 | 9° 79| 58.168
12.1 | 9° | 61.400
12.7 110.6 | 64-632
60
A=19.64
V H
1.53} 0.14) 19.389
eSineslomocsGal
2.04] .23) 25.853
2.29] .28) 29.084
2.55! .34| 32.316
2.80) .41) 35.547
3.06] .48) 38.779
3.31} .55) 42.010
3. 56] 63) 45.242
3.82] .73) 48.474
4.07} .80! 51.705
4.33] .89) 54.937
4.58} .99) 58.168
4. 84] 1.09) 61.400
5.09] 1.19) 64.631
5.6 | 1.42] 71.095
6.11) 1.65) 77.558
6. 62} 1.91] 84.021
7.13) 2.19) 90.484
7. 64! 2.48) 96.947
8.15} 2. 78/103. 41
8. 66} 3. 12)109. 87
9.17} 3. 43)116.34
9. 67) 3. 79/122. 80
10.2 | 4.16/129. 26
10.7 | 4.54/135. 73
11.2 | 4.94)142.19
11.7 | 5. 34/148. 65
WIZ EDs 78/155. 12
1254 41 6. 22| kG os

THE FLOW OF WATER IN WOOD-STAVE PIPE. ral

TasLE 7 (Continued).— Velocity V in feet per second and less of head H in feet per

thousand feet of pipe, necessary to the conveyance of a gwen quantity of water, Q, in
second-feet and in millions of U. S. gallons per day through wood-stave pipe. For in-
stance, 550 second-feet will be carried by a 120-inch pipe at a velocity of 7 feet per second
with a loss of head of 0.94 foot per thousand feet of pipe.

Inside diameter, in inches and corresponding area, A, in square feet. Quan-
Quan eos oe eI tity,
tity. 66 72 78 84 90 96 102 mil-
A=23.76 A= 28.27 A=33.18 A=38.48 A=44,18 A=650.26 | A=56.74 | lions
eee ee OE
Q V H V H V H V H V H V H V H | day

Sec.-ft. | Feet.| Feet.| Feet.| Feet.| Feet.| Feet.| Feet.| Feet.| Feet.| Feet.| Feet.| Feet.| Feet.| Feet.| Gals.

60} 2.53) 0.30} 2.12} 0.20) 1.81} 0.14) 1.56} 0.10) 1.36} 0.07| 1.19} 0.05) 1.05} 0.04) 38.78

70| 2.95) .40) 2.48 26; 2.11; ,18) 1.82 -13} 1.58 09} 1.39) .07; 1.23) .05} 45.24

80) 3.37) .51) 2.83 33] 2.41 23) 2.08} .16) 1.81 12} 1.59; .09) 1.41) .06) 51.70
90| 3.79) .63) 3.18 41} 2.71). .28) 2.34 20} 2.04 14| 1.79 11} 1.59) .08) 58.17
100} 4.21) .76) 3.54 50} 3.01 34, 2.60 24) 2.26 17; 1.99 13} 1.76} .09} 64.63
110} 4.63} .90} 3.89} .59| 3.32 41} 2.86 28) 2.49 20} 2.19 15} 1.94) .11) 71.09
120} 5.05) 1.05] 4.25) .69/ 3.62 47| 3.12 33] 2.72 24) 2.39 18} 2.10) ©. 13). 77256
130) 5.47) 1.21) 4.60) .80) 3.92 55} 3.38 38) 2.94 28) 2.59 20) 2.29) .15) 84.02
140} 5.89) 1.39) 4.95 -91| 4.22 63) 3.64 44, 3.17 32} 2.79 23} 2.47 17; 90.48
150} 6.31) 1.57) 5.31) 1.04) 4.52 71) 3.90 50) 3.39 36] 2.98 26} 2.64) .20) 96.95
160} 6.73) 1.77) 5.66) 1.17) 4.82} .80) 4.16 56} 3.62 40} 3.18} .30) 2.82) .22) 103.41
170| 7.16) 1.97; 6.01) 1.30) 5.12 -89| 4.42 62) 3.85 45| 3.38 33] 3.00) .25) 109.87
180) 7.58) 2.18) 6.37) 1.44) 5.43 -99| 4.68 69) 4.07 50} 3.58 37| 3.17) .27| 116.34
190} 8.00} 2.41) 6.72] 1.59) 5.73} 1.08) 4.94 76) 4.30 55] 3.78 40) 3.35} .30} 122.80
200} 8.42) 2.64) 7.08) 1.74; 6.03) 1.19) 5.20 84) 4.53 60) 3.98 44) 3.53} .33] 129.26
220) 9.26) 3.14] 7.78] 2.06} 6.63) 1.41) 5.72 -99) 4.98} .71} 4.38 53} 3.88} .39] 142.19
240) 10.1 | 3.67} 8.49} 2.42) 7.23] 1.65) 6.24) 1.16) 5.43 .83| 4.78 62| 4.23) .46} 155.12
260) 10.9) 4.23} 9.20) 2.79) 7.84; 1.91) 6.76) 1.34) 5.88 395) 5.17 71); 4.58) .53) 168.04
280} 11.8} 4.86} 9.90] 3.20} 8.44) 2.18) 7.28) 1.53) 6.34] 1.11) 5.57 81} 4.94) .61) 180.97
300} 12.6} 5.48} 10.6} 3.61} 9.04), 2.47) 7.80) 1.74) 6.79) 1.25) 5.96} .92) 5.29} .69) 193.89
320) 138.5] 6.17) 11.3 |] 4.06} 9.64) 2.78) 8.32) 1.95) 7.24) 1.40} 6.37) 1.03) 5.64] .77] 206.82
340] 14.3 | 6.86] 12.0] 4.53] 10.3 | 3.09} 8.84] 2.17) 7.70) 1.56) 6.77} 1.15) 5.99} .86] 219.75
360} 15.2 |. 7.60) 12.7] 5.01] 10.9] 3.48) 9.36) 2.41) 8.15) 1.74] 7.16] 1.27] 6.35) .95)] 232.67
380) 16.0} 8.39) 138.4] 5.53] 11.5] 3.78) 9.88] 2.66] 8.60) 1.91) 7.56) 1.40} 6.70} 1.05} 245.60
400} 16.8} 9.19) 14.2 | 6.05} 12.1} 4.14) 10.4] 2.91) 9.05) 2.10) 7.96} 1.54) 7.05) 1.15) 258.53
450) 18.9 | 11.4] 15.9] 7.52] 13.6] 5.12) 11.7] 3.60) 10.2} 2.59) 8.95) 1.91) 7.93] 1.42] 290.84
500} 21.0 | 18.7 | 17.7 | 9.06) 15.1] 6.20) 13.0} 4.35) 11.3] 3.13) 9.95) 2.32) 8.81) 1.72] 323.16
SO odesocisseuod 19.5} 10.8 | 16.6} 7.37) 14.3} 5.17) 12.5] 3.71] 10.9 |. 2.74] 9.69) 2.04) 355.47
GOO Asses 21.2 | 12.6) 18.1] 8.59) 15.6] 6.03) 18.6] 4.33] 11.9] 3.20) 10.6 | 2.39] 387.79
CYL 0 by a Sat a | Pes eA 19.6 | 9.90) 16.9} 6.98) 14.7] 5.02} 12.9 | 3.76) 11.5 | 2.76} 420.10

108 114 120 132 144 156 168
A= 63.62 A=70.88 A=78.54 A= 95.03 A= 113.1 A=132.7 | A=153.94
V H V H V lal V H Vv H V H V H

200] 3.14) 0.25) 2.82) 0.19) 2.55} 0.15) 2.10) 0.10) 1.77} 0.06) 1.51) 0.04) 1.30] 0.03] 129.26
250) 3.93 -38] 3.53 .24| 3.18 -23| 2.63 14) 2.21 -10) 1.88 -07| 1.62) .05) 161.58
300) 4.72) .52| 4.23 40) 3.82 32] 3.16 20) 2.65) .13) 2.26 09) 1.95] .06] 193.89
350} 5.50) .68! 4.94 53) 4.46 42; 3.68 26) 3.09} .17| 2.64 12} 2.27) .08] 226.21
400} 6.29) .88] 5.64 67) 5.09 53) 4.21 34; 3.54) .22) 3.01): .15) 2.60] .11) 258.53
450} 7.07} 1.09} 6.35) .83) 5.73) .66) 4.74 42} 3.98) .27) 3.39 19) 2.92 13] 290. 84
500} 7.86) 1.31) 7.05) 1.01} 6.37) .79) 5.26 50} 4.42) .33) 3.77 23) 3.25| .16) 323.16
550] 8.65) 1.56) 7.76) 1.21) 7.00} .94| 5.79 60} 4.86) .39) 4.15 27| 3.57) .19) 355.47
600} 9.43} 1.82; 8.46] 1.42) 7.64) 1.10' 6.31 70, 5.31 -46, 4.52 31; 3.90] .22] 387.79
650; 10.2} 2.11) 9.17) 1.63) 8.28] 1.27) 6.84 81| 5.75 53) 4.90 36| 4.22] .26) 420.10
700] 11.0} 2.40} 9.88) 1.86) 8.91) 1.45) 7.37} .92! 6.19} .61] 5.28 42| 4.55) .29| 452.42
750| 11.8} 2.72} 10.6] 2.11) 9.55) 1.65) 7.89) 1.04) 6.63) .69] 5.65 47| 4.87| .33) 484.74
800} 12.6} 3.04] 11.3} 2.37) 10.2} 1.85) 8.42) 1.17) 7.07) .77] 6.03 53} 5.20) .37) 517.05
850} 13.4 | 3.41] 12.0] 2.65) 10.8} 2.06) 8.94} 1.31] 7.52) .86| 6.41 59} 5.52] .41) 549.37
900} 14.2 | 3.79) 12.7] 2.94) 11.5] 2.29} 9.47] 1.45] 7.96) .96| 6.78 65| 5.85) .45) 581.68
950; 14.9 | 4.17) 18.4] 3.23] 12.1] 2.52) 10.0] 1.60) 8.40] 1.06] 7.16] .73| 6.17] .51| 614.00
1,000) 15:7 | 4.57) 14.1} 3.54) 12.7] 2.76) 10.5] 1.75) 8.84) 1.15] 7.54) .79) 6.50] ..56] 646.31
1,050) 16.5} 5.00} 14.8] 3.86) 13.4} 3.02) 11.1] 1.91] 9.28) 1.26) 7.91] .86) 6.82] .61] 678.63
1,100) 17.3 | 5.42) 15.5 | 4.20) 14.0} 3.28) 11.6] 2.08! 9.73] 1.37] 8.29) .94) 7.15] .66] 710.95
1,150) 18.1! 5.88) 16.2! 4.55) 14.6) 3.55) 12.1! 2.25) 10.2] 1.49) 8.67! 1.00] 7.47! .71] 743.26
1,200) 18.9 | 6.34) 16.9) 4.90) 15.4] 3.84) 12.6] 2.43) 10.6] 1.61] 9.04! 1.10) 7.80) .77| 775.58
1,250) 19.7 | 6.83} 17.6] 5.30) 15.9 | 4.13) 13.1} 2.62} 11.1] 1.73] 9.42] 1.18] 8.12] .83! 807.90
1,300) 20.4) 7.32) 18.3 | 5.70) 16.6] 4.43) 13.7; 2.81] 11.5] 1.86] 9.80] 1.27] 8.45] .89) 840.21
1,400|..-...]-.-.-- 19.8 | 6.50) 17.8} 5.06; 14.7} 3.21) 12.4] 2,12] 10.6] 1.45) 9.09! 1.02} 904.84
Ves occs|dosace 21.2) 7.34) 19.1} 5.73) 15.8] 3.66) 13.3] 2.31] 11.3] 1.64} 9.74! 1.15) 969.47
ROU (essere Niet Green, <a eal te 3s 20.4 | 6.44) 16.8} 4.09] 14.2] 2.70] 12.1] 1.84) 10.4 | 1.29/1,034.1
LEC) Spices Rise SE ee ol eee Seetese ees 17.9} 4.56} 15.0} 3.01) 12.8] 2.05] 11.0] 1.44/1,008.7
AA SOO Seem eae ot Rice Sere aol ee Sey (Be ae 18.9] 5.05] 15.9] 3.34] 13.6] 2.28) 11.7 | 1.58/1,163.4
i, (ON 2 Pica PO (A | eo PI 20.0] 5.57] 16.8] 3.68] 14.3] 2.51) 12.3 | 1.76|1,228.0
Ph VOD a ae caer Me ua La eel Dee RUS 21.1) 6.11) 17.7] 4.02] 15.1] 2.75) 13.0] 1.93)1,292.6

BRE a RS ag SO CS

Saaee

eae oa Pace

28

fe BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

CAPACITY OF WOOD-STAVE PIPE COMPARED WITH THAT OF CAST-
IRON AND RIVETED STEEL.

Table 8 gives the relative carrying capacities of wood, steel, and
cast-iron pipes. The table is based on velocities of about 1, 3, and 7
feet per second in the steel and cast-iron pipes of diameters ranging
from 4 to 144 inches. For a given velocity the loss of head for new
cast-iron, new riveted steel, 10-year-old cast-iron, 20-year-old cast-
iron, and 10-year-old-riveted steel is based on values of C, in the
Williams-Hazen formula (No. 8, p. 6) of 130, 110, 110, 100 and 100,
respectively, these conservative values being recommended by
Williams and Hazen. (See Mr. Williams’s discussion, p. 82.)

TABLE 8.—Relative capacity, in per cent, of wood-stave pipe, compared with new cast
iron, new riveted, 10-year-old cast iron, 20-year-old cast iron, and 10-year-old riveted
steel or iron pipe; based on Williams and Hazen recommendation for values of C, in
their formula, of 130 for new cast iron, 110 for new riveted and 10-year-old cast iron,
and 100 for 20-year-old cast iron and 10-year-old riveted steel or iron pipe.

Cast-iron ivet ipes. ood-stave pipes.
ast-iron and riveted pipes W ood-stave pipes Per leant of aelecteneme
is. wood pipe over eat
- 2 n x
ees - 1.2: | Loss of head for velocity. (H) | Velocities correspond- 2) oe pee
Velocity eeEO A : 1 » corresp g to
Ce ing <3 Bans as pee 6, 7, 8, Te-
second. | ¢,—130.| C,=110.} C,=100.| tively.’ 7” octane ti
Inches Feet Feet Feet. Feet. Feet Feet. Feet
1.02 EST Us ee ee ag 2.230 0.94} of. Be 24). —7.8 |s2---.-% +22
= 3. 06 TOSSOO ee aes 17. 100 Pe ees Redipne 3.90}. Si 2s oe +26
= 6.64 AA OUD (oe ne ee = ee 72.000 (is ipl A eee S203) 3 Ash [eee +31
12 -99 . 360 0.480 - 080 -92 1.08 1.25; —7.1] + 9.1 +21
12 2.96 2.730 3.710 4. 430 2.83 Base Spi —4.4 |} 412.0} +25
12 6.89 13. 200 17. 900 21.300 6.80 8. 60 8.80} —1.3] 416.0} +28
36 1.09 - 121 - 164 196 1.02 $925 1.34) —6.4|) +15.0] +23
36 3. 06 - 810 1.110 1.320 2.90 3.50 3.80} —5.2| +14.0} +24
36 7.00 3.740 5. 100 6.100 6.90 8.10 9.00; —1.4] +16.0} +29
72 -98 - 044 - 060 072 - 92 1.10 1.20} —6.4] +12.0| +22
72 3.01 349 -476 o7 2.90 3. 50 3.80 | —3.6] +16.0] +24
72 7.11 1.720 2.340 2.790 7.00 8.30 9.10 —1.4| +17.0| +28
108 1.10 034 . 046 055 1.00 1.20| 1.35) —8.0| 411.0] +23
108 3.14 237 321 382 3. 00 3.60} 4.00) —4.5|) +15.0| +27
108 6.92 1.020 1.380 1.650 6.90} 8.00 9.00; — .3) +16.0} +30
144 1.06 023 - 031 - 037 1.00) “£20 1.35 | —5.7 | +18.0; +21
144 3.01 156 -211 252 | - 2.90} 3.40 3.80} —3.7 | +138.0| +26
144 | 7.07 760 1.030 1.230! 7.00} 8.30 9.10} —1.0 | +17.0|} +29

For the same sized pipe and the various losses of head the corre-
sponding velocities in wood-stave pipe (as shown by the new formula)
are compared with the velocities in the metal pipes. This comparison
is on a percentage basis, with the velocity of the metal pipe as the
base. As an example: The loss of head in a new cast-iron pipe
(C,,=130), 12 inches in diameter, for a velocity of 2.96 feet per
second, is 2.73 feet per 1,000 feet of pipe. For the same velocity in
new riveted steel or 10-year-old cast iron (Cy=110) the loss of head
in a 12-inch pipe is 3.71 feet. For the same velocity in 10-year-old
riveted steel or 20-year-old cast iron (C,,=100) the loss of head is
4.43 feet.

THE FLOW OF WATER IN WOOD-STAVE PIPE. 73

The velocity in a 12-inch wood-stave pipe for a loss of head of 2.73
feet per 1,000 feet of pipe is 2.83 feet per second or 4.4 per cent less
than that in a new cast-iron pipe for the same loss of head.

The velocity in a 12-inch wood-stave pipe for a loss of head of 3.71
feet per 1,000 feet is 3.33 feet per second or 12.5 per cent more than
that in a new riveted steel or 10-year-old cast-iron pipe for the same
loss of head.

The velocity in a 12-inch wood-stave pipe for a loss of head of 4.48
feet per 1,000 feet is 3.7 feet per second, or 25 per cent more than that
in a 10-year-old riveted steel or eae cast-iron pipe, for the
same loss of head.

As shown by the table, the relative cupeaael change for various
sizes of pipe and various velocities, but, speaking broadly, it is also
shown that the capacity of “reed stuns Aine is about 5 per cent less
than that of new cast iron, 15 per cent more than that of new riveted
steel or 10-year-old cast iron, and 25 per cent more than that of 10-
year-old riveted steel or 20-year-old cast-iron pipe. ;

CONCLUSIONS.

A study of the previous pages appears to warrant the following
- general conclusions concerning the capacity of wood-stave pipes:

1. That the new formula herein offered is the best now available
for use in the design of wood-stave pipes, as its application meets
(within 1 per cent) the mean of all observations and the mean capacity
of all wood pipes upon which experiments have been made.

2. That a very conservative factor of safety should be used where
a guaranteed capacity is to be attained.

3. That the Kutter modification of the Chezy fourm Be is not well
adapted to the design of wood-stave pipes.

4. That the data now existing do not show that the capacity of
wood-stave pipe either increases or decreases with age. This state-
ment, of course, does not consider sedimentation, a buy mechanical
process.

5. That if silted waters are to be conveyed the pipe should be
designed for a working velocity of from 5 to 10 feet per second.

6. That if sand is present in the water, the design should be for a —

velocity of about 5 feet per second, which will be high enough to

carry out a large part of the sand and at the same time not so high as |

to seriously erode the pipe. The better method, of course, is to
remove the sand by sumps or other means.

7. That air should be removed from the intake end of every pipe
line, especially when the capacity load is approached.

8. That wood pipe will convey about 15 per cent more water than
a 10-year-old cast-iron pipe or a new riveted pipe, and about 25 per
cent more than a cast-iron pipe 20 years old or a riveted pipe 10
years old.

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74. BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.
ACKNOWLEDGMENTS.

The writer desires to acknowledge indebtedness to the various
engineers and managers of irrigation, municipal, and power systems
who permitted and aided in tests upon the pipes in their charge.
Acknowledgment is also made to the engineers of the United States
Reclamation Service for suggestions and drawings. Where data
have been secured from other sources footnotes give the necessary

references.
APPENDIX.

The following pages are devoted to abstracts of descriptions of
experiments made by agencies other than the division of Irrigation -
Investigations, Office of Public Roads and Rural Engineering. The
number before each description refers to the corresponding numbers
in columns 1, Tables 2 and 3.

No. 1. Expt. HS—X, 14-inch Jointed (Bored) Redwood Pipe,! New Almaden,
Cal.—In 1877 Hamilton Smith, jr., made tests for loss of head in a straight pipe of
eight joints, made of heart redwood, bored by a pipeauger. The pipeswere new and
uncoated. Connections were made by driving one joint into another, an outer iron
band preventing splitting during this process. The area of the pipe was determined
by weighing the water contained in each joint. The total loss of head was determined
from the difference in elevation of the water surface over the inlet and at the mid-
point of outlet (discharge being into openair). To ascertain friction head the velocity
and entry heads were deducted from the effective head. The discharge was meas-
ured accurately in a rectangular wooden tank having a total capacity of 15.2 cubic
feet. In this series of tests the pipe and water discharges were so small that labora-
tory accuracy was practicable. This series was used by Tutton but not by Williams-
Hazen, Moritz, nor the writer in derivation of formulas. The line is not a stave pipe.

Nos. 2-3. 4-inch Jointed (Machine-Banded) Wood-Stave Pipe, Sunnyside
Project, U. S. Reclamation Service, Washington.?—This pipe had been used for
three years for irrigation purposes when tested by Moritz. It is straight in horizontal
alignment, on a continuous down grade. Discharge was measured over a 12-inch
Cipolletti weir. A fungous growth was noted at the inlet, being from one-eighth to
three-sixteenthsinch thick. The condition of the interior of the pipe was not known.
The short reach (No. 2) was included in the longer reach (No. 3). The capacity of
this pipe is 12 per cent less than the discharge computed by the new formula, prob-
ably due to the fungous growth. This conclusion is reached by taking the mean of
observations on reaches 2 and 3 together.

No. 4. 5-inch Jointed (Machine-Banded) Wood-Stave Pipe, Sunnyside
Project, U. S. Reclamation Service, Washington.—This line had been used for
about two years at the time of the tests, for conveying irrigation water across a wide,
shallow depression. Horizonta! alignment was straight. Discharge was measured
over an 8-inch sharp-crested Cipolletti weir. Water columns were used for gauge
No. 1 for all runs except 3 and 4, and for gauge No. 2. For runs 3 and 4 a mercury
manometer was used at gauge No. 1. Some trouble with air in the pipe was experi-
enced in these tests. The capacity of the pipe was about 5 per cent less than the
discharge computed by the new formula.

1 Hydraulics. Hamilton Smith, jr., John Wiley & Sons, N. Y. (1886), p. 297.
2 All tests made on the Sunnyside project were by E. A. Moritz and associates. Trans. Amer. Soc. Civ.
Engin., 74 (1911), p. 411.

THE FLOW OF WATER IN WOOD-STAVE PIPE. 75

No. 5. 6-inch Jointed (Machine-Banded) Wood-Stave Pipe, Sunnyside
Project, U. S. Reclamation Service, Washington.—This pipe was built for
irrigation purposes about five months before the tests. It is practically straight in
both horizontal and vertical planes. Water cclumns were used for both gauges.
Discharge was measured over a 12-inch Cipolletti weir. The capacity of this pipe
was about 4% per cent greater than the discharge computed by the new formula.

Nos. 6, 7, 8. 6-inch Jointed (Machine-Banded) Wood-Stave Pipe, Sunny-
side Project, U. S. Reclamation Service, Washington.—This new pipe had
been used for irrigation purposes about four months at the time of tests. Alignment
and profile were as described for the 8-inch pipe in abstracts for Nos. 9, 10, 11, and
12. Water columns were used at both gauges. Discharge was measured over a 12-
inch Cipolletti weir. Usual velocity was about 3 feet per second. Three reaches on
the one pipe were tested. The capacity appeared to be about that computed by
the new formula.

Nos. 9, 10, 11, 12. 8-inch Jointed (Machine-Banded) Wood-Stave Siphon
Pipe, Sunnyside Project, U. S. Reclamation Service, Washington.—This
pipe, built for irrigation purposes, had been in use about five months at the time of
tests in 1909. Approximately the same reaches were again tested in 1910. Nos. 9
and 11 consist of two tangents intersecting at an angle of 16° 40’ made by a gentle bend
with short lengths of pipe. They include the dip in the profile, No. 11 is 120 feet
longer than No. 9. Reach No. 12 includes No. 11 with an additional 540 feet of
straight pipe on the upstream end. Reach No. 10 is the final 2,002 feet of Nos. 9, 11,
and 12, is straight in horizontal alignment, but includes the dip. A remarkable con-
trastappearsinthesetests. In 1909 the capacity was about7 per centless than that com-
puted by the new formula. 1In1910 the testson the same pipe indicated an apparent
increase in capacity to about 20 per cent more than the discharge computed by the
new formula, when reach 11 was considered; but reach 12 (which includes No. 1land is
but 15 per cent longer) showed the capacity to have increased to but 5 per cent more than
the average. It should be noted that velocities in No. 11 were far greater than those
in No. 12. A study of figure 5 fails to show a general tendency toward increase in
capacity with age of pipe. The tests on reach No. 11 plot (see Pl. VI) in the zone
normally occupied by those on a 10-inch pipe.

No. 15. 10.12-inch Jointed (Machine-Banded) White Pine Pipe,' Bonito
Pipe Line, El Paso & Southwestern Railway, New Mexico.—This pipe line,
part of which is 10-inch and part 16-inch, is more than 100 miles in length and is used in
connection with a railway water-supply project. In 1908, 1909, and 1911, J. L.
Campbell made tests on both sections. The larger pipe joins the lower end of the
smaller pipe at an open standpipe. In measuring velocities the experimenter
used bran and colors, accepting the first appearance of the bran or color in
computing the period elapsed between the time of their injection and their
later appearance. The fact is well known that the velocities near the center of
the pipe are higher than those near the perimeter, and thus higher than the mean
velocity. Hence if the first appearance of the color is accepted then a velocity in
excess of the mean isindicated. In the opinion of the writer this fact accounts for
the low friction factor found, and for this reason he did not use these tests in the deriva-
tion of the new formula. For additional discussion of these tests see page 11. Had
the elapsed time been considered as from the moment of color injection to the mean
of its first and last appearance at the outlet, a highly satisfactory series of tests would
have resulted. The latter method was employed by the writer and is mentioned by
Roy Taylor in connection with tests on the Altmar pipe,? No. 51.

No. 16. 12-inch Jointed (Machine-Banded) Wood-Stave Pipe, Sunnyside
Project, U. S. Reclamation Service, Washington.—This pipe was built for

1 Engin. News, 60 (1908), p. 225; Trans. Amer. Soc. Civ. Engin., 70 (1910), p. 178; 74 (1911), p. 455.
2 Engin. News, Sept. 23, 1915.

PE, LE SIE EE.

i Sie 2 LASS

i en «= I-A SB a eg

76 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

irrigation purposes in 1910 and had been in use but three months at the time of tests,
The line supplements and parallels the pipe described as No. 28. However, the
vertical curve at the low point is not so sharp as in the 22-inch pipe. A water column
was used for gauge No. | and amercury manometer for gauge No.2. The diameter was
measured at the intake and found to average 12 inches. Discharge was taken over a
Cipolletti weir at the intake. The loss of head was abnormally great, capacity being
about 15 per cent below the discharge computed by the new formula. Moritz suggests
the possible presence of silt in the lower portions of the pipe, as the normal velocity is
but 0.8 foot per second and the water is silt-laden.

Nos. 17, 18. 14-inch Jointed (Machine-Banded) Wood-Stave Pipe, Sunny-
side Project, U. S. Reclamation Service, Washington.—This pipe for carrying
irrigation water had been in use five consecutive seasons when tested in 1909. The
reach included in the tests consists of two tangents intersecting at an angle of 32° 12’,
whereagentle bend of short lengthsof pipeismade. Thesamereach wastested in both
1909 and 1910. Loss of head appeared less in 1910 than in 1909. This may have been
partially due to less friction in the pipe at the later date and partially to mere difference
in experimental results. Mercury manometers were used for both gauges. Ata place
where a stave blew out opportunity was afforded for an examination of the interior of
the pipe and for measurement for area in addition to inlet and outlet. At this hole the
soiter portions of the fir wood had worn away, leaving longitudinal ridges of harder
wood. The frictional influence of this condition was problematical. Discharge
measurements in 1909 were made over a round-crested weir; those in 1910 were made
over sharp-crested weir. In general the 1910 tests should be given more weight than
those of 1909. The profile of the line is wavy but without pronounced vertical curve

or bends. Three summits are indicated by a ground line profile, but their actual

existence in the pipe is questionable. The capacity of the pipe in 1909 was about 9
per cent greater than the discharge computed by the new formula, while in 1910 it was
less than 3 per cent greater than that discharge.

No. 20. 14-inch Redwood Stave Pipe, West Los Angeles Water Co., Cali-
fornia.'—Arthur L. Adams conducted a series of seven tests upon reaches of various
lengths of a 14-inch redwood pipe supplying the Pacific Branch of National Soldiers’
Home, in California. Throughout the length of the pipe line vertical curves were
quite numerous, but all were made without the use of “‘specials” and with radii of not
less than approximately 40 feet. Horizontal curves were few, and 286 feet was the
minimum radius. The size of the pipe was determined by numerous measurements
of external circumference, the thickness of the staves being known to be constant.
The discharge was measured with a 4-foot weir whose coefficient was determined by a
volumetric measurement. The head on the weir was read on a hook gauge. The loss
of head was observed in open standpipes and other designated structures. Points of
observation were connected by wye levels. Taking the mean of’all the observations
on this pipe, the capacity is shown to be about 9 per cent less than as computed by
the new formula. This series was used by Williams and Hazen in determining their
suggested coefficient of 120. It was also used by the writer in deriving his formulas
but was rejected by Moritz.

No. 21. Bonito Pipe Line, New Mexico.—This series is digehieea under No. 15
on page 75.

No. 22. Rectangular Unplaned Poplar Pipe.—Tests on an experimental pipe
1.574 feet wide and 0.984 foot deep were made in France in 1859 by Darcy and Bazin.?
The discharge was determined by weir measurement and the loss of head by piezo-
meters. This series was used by Tutton in deriving his formula, but was rejected by
Moritz and the writer, both of whom considered only round-stave pipes in deriving
their formulas.

1 Trans. Amer. Soc. Civ. Engin., 40 (1898), p. 542.
2 Recherches Hydrauliques, Henry Darcy and H. Bazin, Paris, 1865.

THE FLOW OF WATER IN WOOD-STAVE PIPE. Wk

No. 28. 18-inch Yellow Fir Continuous-Stave Pipe, Astoria Waterworks,
_ Oregon.1—A. L. Adams made two tests on long reaches of new yellow (Douglas) fir
continuous-stave pipe. The gravity line supplying Astoria consists of 74 miles of 18-
inch wood-stave, 3 miles of 16-inch and 1 mile of 14-inch steel pipe. The maximum
head on the stave pipe is 172 feet. The pipe is buried from 4 to 22 feet deep. Loss of
head was observed at standpipes, when the pipe line was carrying maximum ca-
pacity. Discharge was measured by the rise of water in a concrete reservoir. Leak-
age was tested and found to be negligible. The low friction factor found in this test is
the more remarkable in view of the fact that there are ‘‘in addition to a succession of
sweeping horizontal and vertical curves, 27 cast-iron bends, with a radius of curvature
of 5 feet, and with an average central angle of about 31°.”’ (Pl. XIV, fig.1.) If but
two tests at the same velocity are to be accepted as a criterion for the capacity, then
the pipe will carry about 17 per cent more than as computed by the new formula.
According to Henny this pipe was replaced with redwood in 1911. It had lasted 16
years.

Nos. 24-25. 18-inch Jointed (Machine-Banded) Wood-Stave Pipe, Sunny-
side Project, U. S. Reclamation Service, Washington.—This pipe was built in
1908 for conveyance of irrigation water. The reach tested is straight except for one
gentle curve through an angle of about 18°. In profile the pipe dips between gauges
1 and 2 about 20 feet in the reach 2,803 feet long. There are three minor summits in
the reach. Water columns were used at both gauges. Air pulsations made tests
difficult and but one measurement for internal area was possible, this being at the
outlet where a distortion of about one-half inch was noted. Discharge was measured
over a 6-foot Cipolletti weir and was corrected for leakage through another gate in the
outlet structure. The two reaches cover approximately the same stretch of pipe.
The capacity of the pipe was about 11 per cent greater than the discharge computed
by the new formula.

No. 28. 22-inch Jointed (Machine-Banded) Wood-Stave Pipe, Sunnyside
Project, U. S. Reclamation Service, Washington.—This pipe, built in 1906 to
convey water for irrigation, had been used four seasons of seven. months each at the
time of tests. The horizontal alignment consists of two tangents intersecting at an
angle of about 5°. The low point of the pipe is about 75 feet below the hydraulic
gradient. There are probably no summits. The circumference of the pipe appears
to be distorted about 1 inch. Water columns were used for both gauges. Measure-
ments of diameter made at inlet and outlet gavea mean of 22inches. Discharge was
measured for runs | and 2 over an 8-foot round-crested weir. The discharge for re-
maining runs was taken over a 4-foot sharp-crested weir. Seven small leaks were
measured volumetrically. Four irrigation hydrants are attached to this pipe. Re-
ferring to Plate VI it is seen that some unusual condition must be present in this pipe.
Although the mean of all the observations indicates that the capacity is 3 per cent
greater than that computed by the new formula, the individual observations indicate
that the lowest velocity is 25 per cent greater than the discharge computed by formula,
while the highest velocity is 12 per cent less than that discharge, for their respective
losses of head. The intermediate velocities show the same trend through the above
range. This series was rejected by Moritz, because of the unusual exponent of V.
As no really definite reason was given for the rejection, and since other series of various
experimenters show nearly as great peculiarities, the writer has retained the series.

No. 32. Experiment H, 24-inch Continuous-Stave Redwood Pipe, Butte
City, Mont.—Water for the city of Butte, Mont., is conveyed from a reservoir about
9 miles distant in a redwood pipe laid in 1892 (Pl. XIV, fig. 2), which was designed
as a low-pressure line following just under the hydraulic grade line as nearly as topog-
raphy would permit. However, insome places a head of 200 feet is developed and a
great deal of curvature, both horizontal and vertical, occurs throughout the length of

1 Trans. Amer. Soc. Civ. Engin., 36 (1896), p. 26.

a

78 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

the line. Henny states ! that too much reliance should not be placed on this test as
‘‘ the only method at hand to determine the flow was from frequent determination of
velocity by means of vertical floats in a semicircular flume at the upper end of the
pipe.’”? This test was not used by Williams-Hazen, Moritz, or the writer in the deriva-
tion of their formulas. The friction factor found indicates a capacity greater than the
average. According to Henny’s report in the Reclamation Record for August, 1915,
this pipe is still sound ‘‘except some deterioration where covered with loose rock only.”

No. 33. Rectangular Unplaned Poplar Pipe.—Tests on an experimental pipe
2.624 feet wide and 1.64 feet deep were made in France by Darcy and Bazin. As the
pipe is similar to that described as No. 22 the same discussion applies to both. (See
page 76.)

No. 35. 31-inch Continuous-Stave Douglas Fir Siphon Pipe, ieSsier Pipe
Line, Sunnyside Project, U. S. Reclamation Service, Washington.—In the
discussion of the Moritz tests J. 8S. Moore gives the details of experiments conducted
by him on the Prosser pressure pipe. Irrigation water is conveyed across the Yakima
Valley over the Yakima River in a pressure pipe of combination type. A concrete
pipe 30% inches in diameter is used until the head reaches about 45 feet, at which
point the line is changed to a 31-inch stave pipe. The reach tested has but one 5-
degree curve, for about 19 degrees of central angle, located near the outlet end. At
the river the maximum head is about 105 feet. The tests were conducted in August
and October of the first irrigation season after the pipe was finished, the highest
velocity being obtained only in August. Before backfilling, but following recinching
of bands, external diameters were measured every 50 feet. The discharge was ob-
tained from the rating curve of a 6-foot Cipolletti weir, the curve having been ob-
tained by calibrating the weir against current-meter measurements from a meter sta-
tion near the weir. The capacity of this pipe was about 6 per cent less than the dis-
charge computed by the new formula. From the fact that the feed canal is down a
very steep grade in a natural channel for part of the distance it appears to the writer
that the pipe might very easily contain sufficient débris to account for any deficiency
in capacity.

No. 36.—This is another reach of the same pipe as that last described. These
tests covered a shorter piece, included in the long reach tested as No. 35. The two .
runs made at the highest velocity, in August, showed the same loss of head per unit of
length in both reaches of pipe, but the other runs, made in October, gave divergent
results, as shown on Plate VI. Mr. Moore states that he is not prepared to explain
this divergence. This series of tests indicate that the capacity is 10 per cent less than
the discharge computed by the new formula. (See discussion of No. 35.)

No. 41. 444-inch Continuous-Stave Douglas Fir Pipe, Municipal Water
Supply, Seattle, Wash.?—T. A. Noble conducted a series of tests on a 44-inch pipe
at the time the tests on the 54-inch pipe (discussed as No. 44, p. 79) were carried on.
With the exceptions noted below the same general methods were used on both pipes.
The horizontal curves in the 44-inch pipe were so flat that for all practical purposes
the pipe may be considered straight. For about one half the total reach the pipe
follows an even gradient. For the other half it crosses a depression about 10 feet in
maximum depth in a distance of about 2,000 feet. ‘Thus, practically, the pipe is with-
out curvature in either plane. After passing through the reach of 54-inch pipe dis-
cussed as No. 44 the water enters a settling basin. From this basin it is conveyed in
the 44-inch pipe now under discussion. Water columns were used for both gauges.
Gauge No. 1 was located 150.6 feet downstream from the inside wall of the basin.
Gauge No. 2 was located 4,041 feet farther down the pipe line. No growth appeared
within the 44-inch pipe; according to Noble the higher velocities in the 44-inch pipe

1 Journal Assoc. Engin. Socs., 21 (1898), p. 250.
2 Trans. Amer. Soc. Civ. Engin., 49 (1902), p. 113.

THE FLOW OF WATER IN WOOD-STAVE PIPE. 719

prevent the attachment of growths. The capacity of this pipe was about 11 per cent
less than the discharge computed by the new formula.

No. 43. 482-inch Continuous-Stave Douglas Fir Siphon Pipe, Mabton
Pressure Pipe, Sunnyside Project, U. S. Reclamation Service, Washington.—
Under and adjacent to the Yakima River the Mabton pressure pipe is reduced in size
from the 553-inch pipe tested by Moritz and described as Nos. 45 and 46, page 79, toa
483-inch pipe of similar construction. At the time of the test the pipe had been in
operation two and one-half irrigation seasons. During this time the mean velocity
had been about 5.4 feet per second. The discharge was measured during the tests in
the same way as that used for Nos. 45 and 46. Several diameters were measured at
the time similar measurements were made on the 553-inch pipe. Mercury manometers
were used for both gauges. The mean of these three observations indicates that the
capacity of this pipe was about 20 per cent greater than the discharge computed by
the new formula. This same excess of capacity is shown in the other portions of this
siphon, discussed as Nos. 45 and 46. Subsequent to the tests described by Moritz,
J. S. Moore experimented upon the portion of the Mabton pressure pipe below the point
where the reduction from 552 inches to 48? inchesin diameter wasmade. These tests
are all described in the same publication. (See footnote under Nos. 2-3.)

No. 44. 54,3,-inch Continuous-Stave Douglas Fir Pipe, Municipal Water
Supply, Seattle, Wash.'—T. A. Noble conducted a series of tests for loss of head by
friction in the reach of 54-inch pipe between the intake at the dam and the settling
basin. As the line follows the sinuosities of Cedar River, it consists of gentle curves
joined by short tangents. The minimum radius of curvature is 289 feet. From the
_ appearance of the profile the pipe is laid on an even gradient, with the exception of
one slight depression, where a blow-off is located. As a summit is reached after this
depression, a 3-inch standpipe is carried above the hydraulic gradient. Holes for
the attachment of the piezometers were made by boring with an ordinary wood bit
until the tip of the bit pierced the inside of the pipe, making a hole about three-six-
teenths inch in diameter. This method was afterwards adopted by Moritz for his
experiments. The pipe had been in use about 10 months at the time of test. Gauge
No. 1, a water column, was locatéd 232 feet from the intake, while gauge No. 2 was a
hook gauge in a well at the outlet of the pipe near the settling basin, 2,446.7 feet below
gauge No.1. The zero points of the various gauges were connected by lines of levels
run by three different observers, the mean of the two nearest together being accepted
as correct. Noble states that the probable error does not exceed 0.007 foot. The
discharge was very carefully measured by an elaborate series of current-meter tests.
For this purpose the area of the pipe was divided into four concentric zones, and each
zone was covered with a sufficient number of meter readings to develop fully the mean
velocity within that zone. In all, the meter was held at 50 points. The interior size
of the pipe was carefully measured some two months after the tests. Vertical and
horizontal diameters were taken every 100 feet. The resulting figures indicate that
the pipe was badly distorted in several places. Growths of Spongilla in scattered
bunches, each about one-fourth square inch in area and projecting about three-six-
teenths inch, were distributed over the inside of the pipe, except along the bottom.

The capacity of this pipe was about 2 per cent less than average, probably accounted —

for by the growth within the pipe; but the 44-inch pipe downstream from this one
lacked an average capacity by 11 per cent, with no growth inside.
Nos. 45 and 46. 5534-inch Continuous-Stave Douglas Fir Siphon Pipe,

Mabton Pressure Pipe, Sunnyside Project, U. S. Reclamation Service, Wash-'

ington.—Irrigation water is conveyed across the valley of the Yakima River by a
siphon pipe carried under the river. At the intake end water in an open channel
passes over an 18-foot rectangular weir into a 54-inch reinforced-concrete pipe. At

1 Trans. Amer. Soc. Civ. Engin., 49 (1902), p. 112.

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80 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

the end of about 3,000 feet a head of nearly 60 feet is attained and the pipe changed
to a 55$-inch continuous-stave pipe of Douglas fir. A reach of this pipe 2,848.2 feet
long was tested in 1909 and again in 1910. At the time of the first series of tests the
pipe had been in operation about five months. It was new, well rounded, and con-
tained but minor distortions. There was no deposit or growth inside. Cross-sec-
tional areas of pipe interior were determined by taking four diameters every 200 feet
throughout the reach tested. Velocity in the pipe was determined by dividing the
discharge, as found by the 18-foot weir, by the mean inside cross-sectional area of the
pipe. Mercury manometers were used at both ends of the reach. A comparison of
the capacities of this pipe and nearly all other large pipes shows that this siphon is
remarkably smooth. ‘This fact is also borne out by the tests on the 48}-inch pipe dis-
cussed as No. 43, which is part of thissame siphon. This fact is also clearly shown by
the relative positions of the points for this pipe in Plate VI. The two series of tests
on this pipe were the only ones on any pipe of greater diameter than 18 inches not
rejected by Moritz in deriving his formula. This accounts for the difference between
the Moritz formula and those of Williams-Hazen, Tutton, and the writer. Giving all
weight for large pipes to these two series develops a formula indicating a far greater
capacity for large wood-stave pipes than a study of all available tests on such pipes
will warrant. Ii the new formula represents the flow in an average pipe, shown in
Tables 2 and 3 to be true, then this pipe will carry more than 18 per cent more water
than the average pipe. While conducting tests for the Department of Agriculture the
writer visited this pipe after a lapse of four years with a view to securing additional
information, but the pipe leaked so badly that tests were not feasible. The pipe was
rebuilt in the winter of 1914-15.

No. 49. Moon Island Conduit, Boston, Mass.'—In October, 1884, E. C. Clarke
made one test on a rectangular conduit, flowing full; that is, asa pipe. This conduit
is a tight wooden flume 6 by 6 feet, made of planed plank, laid lengthwise. The ex-
perimental section was straight, 2,486.5 feet in length. During this test the flow con-
sisted of about one-fourth sewage and about three-fourths salt water. The sides of
the conduit were covered with from one-eighth to one-fourth inch of slime below the
ordinary flow line.. Above this line, on the sides and top, there was some slime but
not so much as below the line. Discharge was measured with approximate accuracy
by the strokes of the pump pistons. This test was used by Tutton in deriving his
formula but rejected by other authorities as the conditions did not parallel those for
which the usual pipe is designed.

Nos. 47-48. 7214-inch Continuous-Stave Douglas Fir Power Trunk Line,
Pioneer Electric Power Co., Ogden, Utah.?—Soon after the construction of the
Ogden Canyon pipe line supplying the Pioneer Electric Power Co. plant, near Ogden,
Utah, tests were made by Profs. Marx, Wing, and Hoskins, of Leland Stanford
Junior University. These tests covered loss of head in the 6-foot wood-stave pipe
and the riveted-steel pipe leading from the stave pipe to the power house. Experi-
ments were first made in 1897 3 but were supplemented by a second series of tests in
1899.4 In both series the discharge was measured through the Venturi meter installed
at the plant. The loss of head was measured by the mercury manometers afterwards
used by Moritz in the Sunnyside experiments. The relative elevations of the gauges
were determined by the static head in the piezometers with the valves closed so that
there was no velocity in the pipe. A constant reduction factor was used in converting
the mercury column to the equivalent water column. These experiments have been
criticized for this reason, but the writer is of the opinion that no error of moment was
thus introduced since, in the tests conducted by him, hydrometer readings were taken

1E.C. Clarke. Main Drainage Works of the City of Boston, Mass., 2d ed., 1886.
2 Trans. Amer. Soc. Civ. Engin., 38 (1897), p. 246.

3Td., 40 (1898), p. 471.

4Id.. 44 (1900), p. 34.

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. Asit was not practicable to make an examination
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. WittiaMs, Consulting Engineer, Ann Arbor, Mich.; THrRoN A. NOBLE,
Consulting Engineer, North Yakima, Wash.; D. C. Henny, Consulting Engineer,
U. S. Reclamation Service, Portland, Oreg.; E. A. Morirz, Engineer, U. 8.
Reclamation Service, Denver, Colo.; E. W. ScHopEer, Professor in Charge of
Hydraulic Laboratory, Cornell University; L. M. Hosxtins, 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 Vi:8
Saeco

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 Vi.87
ee

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.

1 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

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82 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

The reference of the author (p. 25) to the watches being exactly set together leads
one to infer that a comparison was made at the conclusion of the experiment to deter-
mine how closely they had continued to run together. If this was not done there is
a possibility of a small error in time due to the varying rate of the watches. It is not
an uncommon thing to find two watches to run several seconds apart in the course
an hour, although in the course of a day the difference may be inappreciable.

It would add materially to the value of the paper as a record of experimentation if
the author would give some details as to the general measurement of the water and
also a sketch of the weir used, showing the method of attachment and location of the
stilling box. The measurement of the quantity of water is fully as important as the
measurement of the loss of head, and it depends upon the precision of the measure-
ment of the head, and upon the accuracy with which the weir is constructed in con-
formity with previously used experimental examples. 3

With the information as it stands in the paper it is impossible for one to determine
whether the weir measurements are to be relied upon within 2 per cent or within 10
per cent.

The rating of the submerged weit by means of a current meter in a tailrace is per-
haps the least accurate experimentation recorded in the paper. The use of a current
meter ‘in a tailrace is very unsatisfactory and its indications are liable to be in error
anywhere from 10 to 20 per cent. If the wheels in question were reaction turbines it
would be possible to get a considerably more accurate determination of the flow by
reference to the gate openings and head on the wheels during the test in question.
If this were compared with Holyoke tests on similar wheels a determination of the
water could probably be arrived at within 3 or 4 per cent.

The investigation of inlet losses described by the author (p. 63) may be subject to
error because the distance from the inlet to the place of measuring the head is prob-
ably too short. Had the measurement of head been taken 4 or 5 diameters down the
pipe it is quite probable that the apparent loss would have been less than that shown
at the point where the author observed, by reason of the fact that a contraction of the
stream is formed at the entrance which causes an eddy to lie along the wall and this
in experiments by the writer was found to’extend for some 12 to 15 diameters down-
stream. The distance to which this might extend, in a large pipe is probably less
than that in a smaller one, but it seems questionable if the length of 3 diameters was
sufficient to eliminate it even in the large pipes considered.

A statement is made (p. 65) that low discharges entrain more air. This statement
is apparently in error. The lower discharges release more air from the water which is
flowing through the pipe and hence more air is apparent along the top of the stream
and at places where it may accumulate, but rapidly flowing water will absorb and carry
with it more air than the more slowly flowing, and this is the reason that the air does
not appear at high discharges.

As to the author’s comparisons of carrying capacity of wooden-stave and cast-iron
pipe it is to be said that the values of the coefficient recommended for different ages |
in the Williams and Hazen formula are believed by its authors to be very conservative.
With the modern coated cast-iron pipe, if well laid, it is doubtful if a coefficient less
than 115 will be found at any age unless the coating has been damaged.

In closing it gives the writer pleasure to express his appreciation for the very work-
manlike manner in which the observations reported by the author have been
conducted.

Mr. Noble: Page 58, line 16, and page 60, line 17. The velocity head and the
entry head at the entrance may or may not be lost head, depending upon the shape of
the approach to and the exit from the pipe line. This loss may be entirely eliminated
by making the first section and the last section of the pipe funnel-shaped, the small
end being joined to the pipe in each case. The large end must be sufficiently large’
that the velocity at the entrance will produce a negligible velocity head (see Francis’,

THE FLOW OF WATER IN WOOD-STAVE PIPE. 83

Lowell Hydraulic Experiments, and Clemens Herschel on Venturi Water Meter, pub- —

lished in Trans. Amer. Soc. Civ. Engin., vol. 26, p. 452). This form of entrance and
exit also has the advantage of furnishing an accurate and convenient means of meas-
uring the quantity of flow and of keeping track of the gauge height which will not be
affected by the condition of the ditch.

Page 5, line 15. In small pipe, from 4 to 12 inches, used for irrigation and water-
works purposes, valves are always used at least in one place, and often a large number
of fittings and valves whose effect on the flow is similar to the ordinary gate valve.

In such tests as the writer has made he has found no appreciable loss in any single
valve or fitting, but where there are many, as in waterworks systems, the loss on this
account is a matter for serious consideration. There does not seem to be much infor-
mation published that would throw light on this subject.

Page 3, line 5, and page 48, line 35. Attention is directed to the fact that the
writer in 1909 first devised this type of formula from suggestions of Messrs. Saph and
Schoder. This formula is as follows [Formula 16, p. 48]:

Q=1.28D?-58H.9-585

Since that date he has been using this in all his calculations as to the flow in wood
pipe. It isin the same form as the one devised by Mr. Moritz and the author. This
formula gives results from 0 to 15 per cent less than the author’s formula, being about
the same for smaller sizes of pipe and 15 per cent less discharge for the larger sizes of
pipe. It was the writer’s intention in devising this formula to so select the coeffi-
cients of D and H that the calculated flow would more nearly approach the quantities
of flow determined from tests that were lowest instead of those that were the average.
- Page 15, line 27. Itis not atall impossible thatin a number of the tests on which
the formula is based the real average diameter is different from the nominal diameter
assumed, due to the following causes:

(a) Swelling of the wood by saturation.
(6) Distortion due to imperfect backfilling or settlement where the pipe may have
been laid on more or less of a fill, or where there has been more or less leakage.
(c) Inaccuracy of manufacture. The writer in his examination of a 54-inch pipe
found an average of one-half inch larger than the nominal diameter, making
a difference of 1.8 per cent increase in the area. This pipe was measured every
100 feet throughout its entire length, from one manometer to the other. In
-making these measurements considerable distortion was found to exist, and the
writer is not certain that these measurements revealed the exact diameter.

Page 46, line 42. It is the experience of most engineers who have had much to do
with current-meter measurements that they can not be depended upon to give
satisfactory results where the water is at all turbulent or where the cross section of any
stretch of the channel is uneven, thus causing considerable turbulence. The greatest

care in rating a meter will not help this very large source of error. The error due to

turbulence is greater with the Price meter than with the Haskell meter, which latter
was used in the writer’s experiments on the 54-inch and 44-inch pipe-line tests. The
measurements were taken by inserting the meter into the exit end of the 54-inch
pipe, being held in exact position by a templet and a pin fastened through the upper
end of the meter rod.

Page 47, line 37. The line of maximum velocity within the pipe would be shifted
from the center of the pipe to a line close to that portion of the outside of the pipe on
which the convex side of the curve occurs. This line of maximum velocity would
retain its position for a long distance from the curve and would occur within the
length of the pipe tested.

The writer doubts if this abnormal condition would affect the results, particularly
if the manometers were attached in the neutral zone of velocity, as the author states
was done.

ST ee nN oa

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84 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

Page 79, line 27. The writer would here call attention to the importance of deter-
mining accurately the average diameter at each point of manometer attachment. A
very slight difference between the areas at the two points will make a very considera-
ble difference in the results, particularly if the total difference in head between the
two points is relatively small. An examination of the data relating to the test of the
54-inch pipe, No. 44 (Trans. Amer. Soc. Civ. Engin., vol. 49, 1902) will show a very
considerable change in area throughout the length of the pipe. It was found that the
velocity head at any point was exactly proportional to the calculated velocity head.

Page 64, line 40. Same reference is made as for page 60, line 17, as the best
means of preventing loss at the entrance and exit. This funnel-shaped entrance pre-
vents the trapping of air at the entrance caused by excessive suction and cross cur-
rents, but does not prevent the minute particles of air flowing with the water, or the
air that is absorbed by the water, and does not leave it until under a greater pressure
from entering the pipe line. Accumulation of air from these causes must be taken
care of either by standpipes or automatic relief valves. To leave it in the pipe when
there are high points in the pipe line and low velocities is to seriously diminish the
flow. It is the writer’s opinion that many of the inconsistent results from various
tests are due to this cause.

Page 73, line 35. In the case of pipe used for irrigation purposes where the entrance
is direct from a ditch, with no adequate settling basin, a considerable quantity of silt,
moss, and other débris traveling along the bottom of the ditch finds its way into the
pipe line and accumulates in the low points of the pipe, even at velocities higher
than 5 feet per second. It becomes settled and packed and slimed over at times
when the velocity in the pipe is low. The moss and other vegetable matter tend to
bind the silt together into a solid mass, which is not washed out by the higher veloc-
ity. This is probably what happened to the pipe line in question.

Page 79, line 31. There were three gauges used in these experiments:

(a) A hook gauge located at the settling basin or discharge end of the pipe.

(6) A water manometer attached to the top of the pipe about 150 feet upstream from
the outlet end. Sufficient readings were taken at manometer B to make a check
on accuracy of using the hook gauge.

(c) A water manometer located 232 feet downstream from the intake. The area of
the pipe at the exit was slightly larger than at manometer B. The head of
water at manometer B, less the friction in the pipe line between manometer B
and the settling basin, less the difference in velocity head, equaled the head
at the settling basin or exit end within the limits of possible error from other
causes.

Page 79, line 36. The velocity measurements at the exit of the 54-inch pipe revealed
some interesting facts regarding the flow in pipe lines as follows:

First. That the line of maximum flow of water in a pipe line beyond a bend is not
in the center of the pipe, but near the outer circumference, and on the same side as
the convex side of the curve in the pipe. This would seem to be due to the action
of centrifugal force of the water in going around the curve, tending to crowd the max-
imum velocity toward the outer edge of the curved portion of the pipe.

Second. The average velocity as determined from a number of points distributed
systematically throughout the area of the circle of the pipe is the same as the average
velocity along either the vertical or horizontal diameter.

Third. The curve of velocity, as near as the writer could determine, is an ellipse
where the maximum velocity is in the center of the pipe.

Mr. Henny: The results of the experiments on flow in wood pipe made by the
author, under the direction of Mr. Fortier,! constitute much needed addition to the

1 Author’s footnote —Samuel Fortier, Chief of Irrigation Investigations, Office of Public Roads and Rural
Engineering, U. S. Department of Agriculture.

ee

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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 VIT.

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.

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THE FLOW OF WATER IN WOOD-STAVE PIPE. | QT

The causes of the large deviations in the constants of any formula so far proposed
have been the subject of frequent discussion. The varying amount of curvature is
undoubtedly one of these causes, and its separate effect upon resistance may well
engage the attention of experimenters. Age appears generally to have little effect
on carrying capacity of wood pipe. Errors in the experiments themselves are becom-
ing smaller with greater refinement and the use of coloring matter in determining
the velocity directly may be considered as a distinct advance. The main reason for
the apparently arbitrary variations probably lies in the difference in smoothness of
the interior surface, which may be due to vegetable growth, effect of wear, variability
of the wood, and in some measure to workmanship. So long as it is not practicable
to specify and insure a known degree of smoothness, so long will the application of
judgment be necessary in the use of any formula.

Entry head is due to eddy currents above and below the point of entry. The loss
due to eddy currents in the intake basin is very variable, depending upon the lines
of approach which at times favor the formation of whirls and vortexes. This item of
loss is, however, relatively small and may generally be neglected. The loss below
the point of entry is due to an uneven distribution of velocity throughout the section
immediately below the point of entrance.

The area so far as it is occupied by rapidly forward-moving water is contracted as in
the case of open-air discharge, although under conditions of counterpressure probably
to a smaller extent. The area between the contracted section and the pipe shell
is a cavitation space which may be filled with eddying water or may become under
high-velocity discharge a complete vacuum. The energy of the moving water in the
contracted area is greater, due to higher average velocity, than in the moving water
farther down the pipe, the difference being destroyed by internal friction and con-
stituting the principal part of entry head.

Where the assumption is made by the author that h,=4 h,, it is equivalent to assign-
ing a constant value of 0.82 to the coefficient of contraction. While this assumption
is not unusual it must be evident that this coefficient must be largely affected by con-
ditions of velocity, depth of pipe entrance below water surface, shape of intake basin
and elevation of floor with reference to pipe invert.

Table 6, presented by the author on this subject, yields no positive information.
The influence of velocity of approach is neglected, which may be permissible in
cases such as tests 7 and 8 where the outlet is at right angles to the direction of approach,
but is not correct in tests 5 and 6 where the flow is straight toward the entrance. The
table gives results which are erratic, as might be expected. For tests 7 and 8 it indi-
cates that the entry head equaled 0.89 h, and 0.63 h,, respectively, instead of 0.50 hy,
equivalent to coefficients of contraction 0.73 and 0.78, respectively, instead of 0.82,

The usual assumption of 0.82 as the coefficient of contraction, or 4 h, as the entry
head, may be justified in some cases, but will at times lead to serious error. (See
also, Merriman’s Hydraulics, 9th ed., p. 214.)

Mr. Moritz: It will generally be conceded on the basis of the showing made in |
this paper that the new formulas proposed fit all observations so far made on wood-
stave pipe better than any other formula heretofore offered. The problem is, how-
ever, not susceptible of cold-blooded scientific analysis and the personal equation of
the analyst must necessarily affect the ultimate result. The present paper can not
be considered as the final answer to the problem of flow of water in wood-stave pipes
and in view of the close agreement between the author’s formula and others that have
been used, the writer is not satisfied that there is sufficient justification for a radical
departure from formula constants that have been well established and accepted. The
writer has in mind especially the exponent of d which for upward of 10 years or more

_ has stood unchallenged at 1.25 and this figure has been accepted by such well-known

hydraulicians and experimenters as Dr. E. W. Schoder, of Cornell University, and

I}
'

88 BULLETIN 3876, U. S. DEPARTMENT OF AGRICULTURE.

Gardner S. Williams, formerly of Cornell and Michigan Universities, as representing
the best average value. They inclined rather toward varying the exponent of V within
the range of about 1.75 to 1.95 and they also varied the coefficient m for different kinds
and conditions of pipes from about 0.30 to 0.50.

The exponent 1.25 was determined by Schoder from a plotting of all known observa-
tions on pipes covering the entire field from very small drawn-brass pipes to very
large tuberculated riveted-steel pipes, and is therefore not based on estimate nor
opinion, but on actual facts.!. The writer’s observations on wood-stave pipes developed
a value of 1.26, which he has since reduced in the formula for practice to 1.25 to con-
form to the generally accepted figure.

In the matter of proposing a new formula, the writer lives in a glass house and can
therefore not afford to throw stones. However, there were extenuating circumstances
in this case, which need not be discussed here, that ultimately led to a rather wide
acceptance of the writer’s formula, although he originally offered it with reservations
because there were a number of points not satisfactorily explained, and experiments
on very large pipes were notably lacking. Thanks to the author’s careful experiments
the deficiency has now been supplied to a considerable extent and we are closer to the
ultimate solution.

It is interesting to note that the author has arrived at the same figure for exponent of
V, namely 1.8, that developed from the writer’s experiments. Unfortunately, he
had not time to check the author’s analysis on this point, nor to make an independent
analysis of the data in this paper, but the evidence in support of this average figure
may now be fairly considered as having been greatly extended. The evidence in
support of 1.25 as the exponent of d is in the writer’s opinion equally as good if not
better, since its derivation was based on observations on all kinds and sizesof pipes.!
If we could, therefore, now agree on these two figures and throw the variation in
formula for different classes of pipe into the factor m, a much longer step will have been
made toward the general acceptance by engineers and courts of an exponential formula
for flow of water in pipes.

It must be conceded that additional experiments that may be made in the future,
especially in the field of diameters between 60 and 160, may have a marked effect on
the exponent of d and we will then no doubt be confronted by another formula. More-
over, as has already been pointed out, the personal equation of the analyst, especially
in the application of weights and methods of reasoning, must be taken into account
and another person with the same data as a basis would no doubt arrive at somewhat
different conclusions than those given in the present paper. No doubt this factor has
been eliminated to the greatest possible degree in the present paper, but complete

1 Author’s footnote (the italics are his).—A study of original sources does not bear out thisstatement. In
Trans. Amer. Soc. Civ. Engin., vol. 51, Messrs. Saph and Schoder, on page 305, state: “‘ First of all, the line
best fitting the points for the writers’ brass pipes has been drawn,” which line, as they say on page 306,
“forms the lower limit of the zone in which all the plotted points lie. This is another way of stating that
these pipes represent the extreme of smoothness and ideal conditions.”” The exponent of d for this line
was found to be 1.25. (This line is A, fig. 7.) The values of m for all kinds of pipes were then platted and
Saph and Schoder state (id., p. 308): ‘‘It will be seen that a line parallel to the one already drawn will
represent fairly the other limit” ofthezone. (This line isshown as B, fig.7.) Thus it will be seen that this
exponent was derived from a study of smooth brass pipes and then applied to all kinds of pipes by drawing a
line parallel, i. e., with the same slope, hence indicating the same exponent of d, or 1.25. In discussing the
exponent as derived by Saph and Schoder, Mr. Allen Hazen states (id., p. 321), ‘It is, unfortunately, a
fact that probably none of the large pipe has as smooth surfaces as the brass pipe used by the authors (Saph
and Schoder) and some allowances must be made for this fact in the comparisons, and, while the line drawn
as a general average would be a matter of individual judgment, the writer (Hazen) would hardly give it
an inclination greater than that corresponding to an exponent of 1.20. If the matter were carried further the
exponent would probably be lower.’’ It is interesting to again note that the exponent of d is 1.17 in the
formula derived from a study of these same pipes of all kinds by Williams and Hazen, and that this is the
same exponent found in this study of the flow in wood-stave pipes. (Line E, fig. 7. This question is
further discussed on page 94.)

.
a

THE FLOW OF 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 0.48. Ifthis be accepted,

= 1.8
the formula becomes a ce ee gives velocities and consequently discharges

a: 1,8
that are about 7.6 per cent smaller than those given by the writer’s formulas
Tf the figures in column 20 of Table 3 are now corrected by the addition of 7.6, the
‘‘orand 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.! 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.
PASS) | a5 to ||. 10ito)| 1 5it |ee oO tole soa) genes tl, Less
roy) +10. +15. +20. +25. 425 +10 nats
SGODGY 2a ens Sass Se eats tas Se 30 24 19 20 8 5 54 73
Wialliams-Hazens 2. 3-2 se 44 30 24 16 14 8 74 98
IM OnE Z eee ee le ee ee 43 12 5 6 it 0 55 60
IROELONEE ee ee ee 42 39 36 20 4 Ak 81 117
Weisbach 254 6 ee 37 20 6 4 5 1 57 63
Less More Less Less
Author of formula. than mek wie te Siar eI as than than than
—5d. 3 : awe ; —25. —10. —15.
SCODGY aso et eee none Meee 46 48 39 12 1 2 92 131
Williams-Hazen.... Ee 49 40 16 9 1 2 89 105
Moritz? 92.2. ee 29 18 42 49 41 8 47 89
PREG bOMe pee eat ees ec Ae 46 40 13 11 1 5 86 99
RVVIGIS DaGreek 29 36 30 39 14 11 65 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

_ 1Author’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 zeroas 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
lineis 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.

SS OSS er eee. - ee

ee

Tr

a ee ee COC
= a Sr ews >

NN

ee ee

90 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

reduced from 1. 25to1.17 until the field of larger pipes has been more fully covered.
= 71.8 :

The formula ge — gives practically as correct results as the author’s formula

and conforms much better with the results developed by previous experimenters.

It is conceded that the arguments presented herein are rather unscientific, but we
are dealing with a problem that is more practical than scientific, and expediency
should be given as much weight therein as science. The engineer should not strive
for an impossible accuracy or an artificial consistency in his essentially practical
operations. The writer feels that the author would be doing the engineering profession
a greater good if he would depart to a smaller extent in his formula from the factors
that have been developed by other experimenters before him.

Dr. Schoder: After the first reading of the paper the writer is inclined toward a
somewhat detailed discussion of numerous points that seem open to reasonable differ-
ences of opinion. However, after again reading the paper, most of these points seem
to be aside from the main argument that is advanced somewhat directly and some-
what by implication in the paper. Consequently the writer’s comments will deal
rather with the question it seems proper to ask: ‘“‘ Does the paper sufficiently empha-

size the relations of the facts therein established for wood-stave pipes to the facts for ©

pipes of all materials?”’

This suggests the query: ‘“‘Is a special formula for wood-stave or any other particular
material proper or practically desirable in the light of information now before the engi-
neering public?”’ The author’s paper is a very important contribution toward such
information. It remains to make the general examination and comparison suggested.

Concerning the new data gathered by the author, the writer would sum up his esti-
mate and appreciation: (1) The field difficulties were many and serious. (2) The
measurements, in the main, appear to be reliable.

Comparison of the data on wood-stave pipes with the data on pipes of all materials.
The author states (p. 51) that the exponent of the velocity ranges front 1.56 to 2.31
and that he is unable to find any law for this variation for the wood stave pipe data.
It is interesting to examine these exponents as given in the nicely arranged Table 3.

vag” | 1a-2¥ | 307-162” |

1. 723 1. 738 1.56
1. 895 1. 730 1. 67
1. 808 1. 870 1.70
1.877 1. 703 2.31
1. 847 2.176 1.719
1.724 1. 696
1. 590 1. 747
1. 766 1.618
1. 875 1.973
1. 690
1. 891
2. 143

|

It seems to the writer that ‘“‘confusion will be worse confounded” by the apparent
sanction of a United States governmental department to a formula and diagrams or
tables based thereon, particularly applicable to wood-stave pipes, when the data,
according to the author’s own statements of factors of safety on page 66, and particularly
in column 19 of Table 2, show such large departures from the results by the formula,
and when there is nothing in the data on weod-stave pipes that distinguishes such
pipes from the data on iron, steel, brick, concrete, or other pipes.

In other words, if all the data presented on wood-stave pipes are plotted on Plate
XI, Trans. Amer. Soc. Civ. Engin., vol. 51, or on figure 2, Cornell Civil Engineer,
May, 1910, or even if the data for all steel and iron pipes be added to the author’s
figure 4, the conclusion seems to be irresistible that the pipes used in engineering
practice for the conveyance of water can not be segregated, as to hydraulic resistance

|
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,

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eS we

—— es eT

THE FLOW OF WATER IN WOOD-STAVE PIPE. OQ]

to flow, into the particular materials of which the pipes are constructed, except in
sharply limited cases where the material is a meas-
ure of the roughness.

The writer considers the author’s formula as good
and as safe as any, if its limitations as shown by
column 19, Table 2, be taken into account and if
the velocity in the pipe under design is not much
ereater than in the data presented in Table 2.

This suggests the difficulty in getting the engineer-
ing public to recognize the average quality of an
averaging formula. Thus the significance of the
formulas on page 309, Trans. Amer. Soc. Civ. Engin.,
vol. 51 (1903), is very liable to be overlooked when
presented in the form given on page 281, Eng. Rec.,
September 3, 1904.

Unless these general interrelations of all pipe flow
data are specifically emphasized, it seems that a
good opportunity will be lost. The author states
on page 50, ‘‘However, in deriving the new for-
mula, tests made on round, wood-stave pipe only
were considered, in view of the proposed use of such
a formula.” The inference that data on other pipes
are not relevant will be drawn from this by the
ereat body of readers. Thus the error so long per-
petuated by hydraulic texts will be given apparent
sanction.

From a purely selfish viewpoint the writer would
not be eager to see the author’s paper broadened as
suggested. It furnishes data to drive home maiters
about which there have been great uncertainty in
the minds of a few, and general ignorance in the
minds of the many who place a halo about text-
book formulas. If the author does not, others will
do it.

The value of the paper asit stands isgreat. Itis
in the hope that the author may be persuaded to
make the shift in viewpoint necessary to add much
to the permanent value of his deductions that the
writer ventures these comments.

In The Cornell Civil Engineer of December, 1911,
page 127, there are some data that may be found of
interest in connection with the author’s method of
finding velocities by injecting a colored solution into
_the pipes and timing the interval from the instant
of injection to midway between the first and last
appearances of color downstream.

’ for experiments on wood pipe, shown by circles (also see fig. 4). Dotted lines suggested

of pipes, for which values of m are shown as dots.

iu
13)
ce
oO
oS
rs
as
(
VU
—_—
Vv
1 0
ia

-

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>

IES INE 5 ye Na A a in Od tO cin oe het

by Saph and Schoder for many kinds

genera it pes te gs

tai eet oe

Prof. Hoskins: The experimental work described
in “The Flow of Water in Wood-Stave Pipe” isa
valuable addition to knowledge on the subject, and
the author’s summary of conclusions appears to
merit confidence as embodying present knowledge
on the hydraulics of wood-stave pipe. The expo-
nential formula adopted as the result of the discussion is probably as reliable a

owt hee

Fig. 7.—Comparison of curves for exponent of d. Line E based on values of m

CEE DN PEK PE A owe

2 ew om oe

CE I AF ll = ae tn ol

£

weer ae 5

OS CEL TOE GS MTD POM, i
.

92 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

guide as the present state of knowledge makes possible. The writer thinks all

- who have been concerned in experimental work of this character must recognize

that a close approach to exact agreement among results is not to be expected. The
author’s analysis of the conditions affecting the reliability of the experiments is very
thorough and his work seems to merit acceptance equally with the best previous
results. Nothing occurs to the writer by way of criticism or discussion worthy of
publication.

Author’s closure.—The apparent lack of conformity in results of hydraulic
experiments has discouraged many observers. It would appear that carefully con-
ducted experiments, made with the best of apparatus, should give results of extreme
consistency. It is more than likely that results that should be consistent are so and
that variations are due to influences that can not be seen or guarded against. The
best that may be done is to anticipate all known abnormal conditions and either elimi-
nate them or make corrections for them.

Discussions of some experiments mentioned appreciated field difficulties. There
is a vast difference between testing small pipes, weirs, or other devices in a hydraulic
laboratory, where all of the factors are assuredly in the control of the observer, and
testing large commercial structures in the field under varying weather conditions with
unavoidable fluctuation in discharge of water and other difficulties that may or may
not come to the knowledge of the experimenter during the tests. Seldom it is thata
field layout approaches ideal conditions for experimentation. Except in rare cases
tests of commercial plants must be foregone if laboratory conditions are to be met.
When apparatus is set up for test in a laboratory, minute measurements of diameters,
water volumes, and other factors may be made. Both interior and exterior may be
examined with microscopic care. In field tests of pipes, on the other hand, it is not
often that water may be withdrawn for sufficient time to enable the experimenter to
fully acquaint himself with conditions that are ordinarily hidden.

Probably the most accurate series of tests of record are those conducted by Saph and
Schoder on brass pipes. The largest of these was slightly more than 2 inches in diam-
eter. With all the accuracy the experimenters could bring to bear upon these tests in
a hydraulic laboratory, the results were such that they qualified their derived formula
with a factor of +7 per cent.!

When the above qualification is necessary for a formula based on laboratory tests on
pipes having uniform structural characteristics which have never been subjected to
deposits, growths, or tuberculations, what is to be expected of a formula for use in the
design of wood-stave pipes based on pipes taken as they come in the field? Cansucha
formula show more than the new formula shows in Table 2 and on Plate VII? Except
in isolated cases this agrees within +15 per cent with more than 250 observations on
52 pipes from 1 to 162 inches in diameter. Furthermore, more than half of these pipes
are siphons on irrigation projects; that is, pipes inserted between open sections of canal
from which all manner of trash, silt, and rock ravelings may enter the pipe and retard
the flow. These are unavoidable conditions in the operation of such pipes, and the
author would not confine his tests to pipes under more nearly ideal conditions, even
if such might be chosen. These conditions must be anticipated by the designer and
some suitable factor of safety introduced as is suggested on page 66.

The above is not offered by way of apology for the new formula but to make clear
the fact that the actual discharges from pipes designed on the basis of the new formula
are not to be expected to agree with the formula values exactly but only to a reasonable
degree.

The author agrees with Mr. Williams and Mr. Noble that experimental errors, due
to erroneous assumptions of pipe diameter, may creep into the results. These errors

1 Trans. Amer. Soc. Civ. Engin., vol. 51 (1903), p. 306.

THE FLOW OF WATER IN WOOD-STAVE PIPE. 938

may involve a change in velocity head or be due to an incorrect mean area of the pipe
being taken, and consequently an incorrect velocity used in a given test, if the indirect
method of measuring the velocity is employéd. The fact that the interior of most
pipes tested in commercial service can not be examined means that the nominal
diameter of a pipe must in many cases be accepted or that no experiments be made.
The reverse of this problem confronts the designer. He must make computations on
the basis of a given size of pipe, whereas the pipe when actually built may vary slightly
from the designed size.

No appreciable error was introduced by reading but one gauge glass of a U-tube
manometer at atime. It must be remembered that before reading the pressure was so
throttled that the mercury was barely ‘‘alive.”’ This means that in either gauge glass
the ‘“‘breathing” of the mercury did not extend over more than two or three thou-
sandths of afoot. Any error of reading due to a difference in the size of the tubing, as
questioned by Mr. Williams, would be so small a part of these two or three thousandths
of a foot as to be negligible. Reading alternate legs of the manometer and computing
the leg not read would tend to neutralize any error that did exist, remembering, of
course, that both legs were ‘“‘dead”’ columns of mercury, at intervals of approximately
10 minutes.

In answer to Mr. Williams’s question as to comparing watches after the tests, the
author would say that this was done and any necessary corrections of a few seconds
was immediately noted in the field notes. Many experimenters are very careful to
conduct all work with a stop watch. These watches may be read to a nicety but can
still be inaccurate unless most carefully adjusted with a chronometer. This is quite
evident if several of them be started together and compared at the end of an hour.

Additional information on the weirs used has been written into the original text or
shown in the views in conformity to Mr. Williams’s suggestion.

The accuracy of the meter calibration of the Altmar weir in connection with the
tests on pipe No. 51 is questioned by both Mr. Noble and Mr. Williams, for the reason
that the meter measurements must be made in the tailrace. As shown by figure 2,
Plate V, the water downstream from the weir was not turbulent. When the gaging
bridge was reached several hundred feet downstream from the weir, the water was
flowing evenly and smoothly. The channel is excavated in flat, rather level strata
of rock, and the four meter gaugings conform so closely with an even curve that the
author does not believe any undue error was made. The verticals in which the meter
was held were sufficient in number so that the section was well covered. The mean
velocity of the channel was but 3.25 feet per second for the greatest discharge meas-
ured. Such a velocity in a relatively smooth channel will not produce turbulence.

Regarding the experiments on loss of head at entrance to pipes, Mr. Williams appar-
ently misunderstands the author. The loss of head was not observed at a point three
diameters down the pipe but at a point several diameters down the pipe, and the loss
between the inlet and the 3-diameter point was computed by deducting the friction
loss per foot for the number of feet back from the point of observation to the 3-diameter
point; thus finally the net loss from the intake to the end of a short tube 3 diameters
long was deduced.

Regarding the entrainment of air: A large proportion of the wood pipes used in
irrigation practice are on inverted siphons between sections of open channel. When
such a pipe is running at full capacity the inlet is usually well submerged and but a
moderate amount of air is caught and carried into the pipe. When the pipe is carry-
ing but a small part of its capacity the water rushes down the intake end and generates
a violently turbulent condition just where the pipe is filled. The impact of the
water rushing down the intake at high velocity causes many air bubbles to be carried
into the pipe. Obviously, as suggested by Mr. Williams, a pipe at full capacity

94 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

would carry more air were the same opportunity offered at the intake for its entrain-
ment. ; :

Concerning the various factors of the new formula: From the discussion it appears
to be granted that this formula fits the basic observations better than any other for-
mula. It should, of course, do this as it is an averaging formula based on all known
observations. Two questions now arise: Should an average formula be used and should
factors in new formulas be allowed to digress from time-honored factors in accepted
formulas? If we do not accept an average formula we must do one of two things. The
first 1s to accept a formula that will give the most conservative results. Such a for-
mula for wood-stave pipe would be probably 25 per cent more conservative than the
new formula or 40 per cent more than the Moritz formula, if all observations on wood-
stave pipe are to be included. If we exclude any tests as abnormal we find it hard
to draw the line—hard to find any tenable intermediate ground between the aver-
age and the extreme. The other method that may be pursued is to follow Schoder?
and Moore,” and give the bounding limits for any particular factor, stating these
limits as a variable feature of the formula.

Unfortunately the practice of the average engineer is so general that he does not
become qualified, nor has he the time, to properly choose the correct figure between
the varying limits. He would rather that the one most familiar with the variables
give him one formula without varying coefficients or exponents and with a statement
as to its approximate accuracy. This was recognized by Moritz.? In the opinion
of the author the averaging formula appeared best when used in connection with the
suggested factors of safety. (See p. 66.)

Mr. Moritz’s suggestion that the exponent of d or D in the new formula violates
accepted exponents in parallel formulas does not appear to the author to be well
taken when studied in connection with figure 7, which shows the same plotted points
for wood pipe experiments as figure 4, and which in addition shows by small round
dots the values of m for all the experiments given on Plate XI, Trans. Amer. Soc.
Civ. Engin., vol. 51, ‘‘The Flow of Water in Pipes,’’ by Saph and Schoder. These
additional experiments are on various kinds of pipe, including brass, galvanized-
iron, wrought, sheet, and cast-iron, brick, glass, lead, and riveted pipes. In figure 7,
line A, isSaph and Schoder’s limiting line for ‘‘very straight and very smooth pipes’’

; : 0.296 ‘ 3 anki : : .
with the equation M—=i25;° Line Bis their limiting line for tuberculated pipes, with
0.68 Ae tiatog
the equation m=>yj25' These writers then state that most pipes in commercial use

: : ; 0.46
will plot between lines A and C, the equation of the latter being me As the

values of the exponent of V vary from 1.74 to 2.00 the general equation showing the
0.296 to 0.469

variation between the lines A and C becomes H= Di25 VATE ter 2 Uns
: 0.38 V1-8" : ati tara: ©
Note that equation Ela zon mentioned near the beginning of Mr. William’s

discussion on page 81 takes the average of these variants, m=line D, figure 7, while
Dr. Schoder+ in 1904 suggested exactly the same formula except that the exponent
of V was given as 1.86 instead of 1.87. (See column 6, Table 10.)

Again referring to figure 7, line E shows the author’s curve, m/’ Sa or oe Sa
Note how closely this line on a slope of —1,17 conforms to the plotted points for all

1 Trans. Amer. Soc. Civ. Engin., 51 (1903), p. 308.
2Td., 74 (1911), p. 471.

31d., p. 478.

4 Eng. Rec., Sept. 3, 1904, p. 281.

THE FLOW OF WATER IN WOOD-STAVE PIPE. 95

kinds of pipe, and note also that Williams and Hazen found this slope for all kinds of
pipe to be —1.167 (practically —1.17) as shown in formula 8a, page 6. Furthermore,
by reference to pages 4 to 7 of their tables ! and to the plotted points in figure 7, or
to Plate XI in volume 51 of the Transactions of the American Society of Civil Engi-
neers, it will be seen that Williams and Hazen found this exponent of d and D to
be 1.167 from exactly the same experiments, except for a few additions, as those that
were included in a zone bounded by two lines (A and B, fig. 7) at a slope of, and indi-
cating an exponent of, 1.25 by Messrs. Saph and Schoder, while the author found
a value of 1.17 when experiments on circular wood pipe alone were considered. As
shown in the author’s note on page 88, the exponent of 1.25 was determined from a
study of smooth brass pipes.

Summing up, it does not appear from the above study that a value of 1.17 for this
exponent of the pipe diameter based on_.a line plotted through the centers of gravity
for all values of m’ in wood-stave pipe experiments is at variance with accepted
values of this exponent for flow in all kinds of pipe, as typified by the Williams-
Hazen general formula.

Dr. Schoder suggests that this paper be broadened to compare ‘“‘the facts herein
established for wood pipes to the facts for pipes of all materials.’’

In the author’s opinion, however, the structural characteristics and the methods of
making joints in pipes of the various materials are so different that it will be extraor-
dinary indeed if any one formula can be found to even approximately fit all kinds
of pipes. The author believes that such a comparison and conclusions therefrom
would be premature at this time, especially in view of the meager information now
available concerning the flow in pipes of cement and concrete materials, which are
being used more and more for permanent pipe construction.

In order that a final comparison may be made of various formulas, as suggested in
the discussion, the writer has prepared Table 11, which shows the computed veloci-
ties by various formulas for given sizes of pipe and given losses of head. The general
deduction may be made from a study of this table that it makes little difference
which of these formulas is used in the design of pipes up to 12 inches in diameter,
with velocities up to 4 feet per second. As larger pipes and higher velocities are
involved, the divergence between velocities as computed by various formulas becomes
greater and greater. For instance, a loss of head of 1 foot per 1,000 feet of 12-foot
pipe will generate a velocity of 9.74 feet per second, according to the Moritz formula,
or 50 per cent more than the velocity computed by the Swickard formula, although
the latter was developed for the most part from a study of the Moritz data.

1 Hydraulic Tables. Williamsand Hazen. New York, 1909.

| 96 BULLETIN 376, U. S. DEPARTMENT OF AGRICULTURE.

i : Eas

1 TaBLE 11.—Comparison of velocities, in feet per second, as computed by various formu-

’ las, for given sizes of pipe with given friction heads.

il

| oe

\ Velocity per second by formulas.

| Diame- | Friction | |

ii ter. | head, H. “115 +

iI : Williams - F Swick-

! Scobey. Eon Moritz. | Schoder. ae Noble.

| 4

I Inches. | Feet. Feet Feet Feet. Feet Feet Feet.
6 2.0 1.52 1. 48 1.58 1.54 1.49 1.63
6 5.0 2.52 2. 45 2. 60 2. 52 2.35 2. 80
6 9.0 3. 50 3.39 3.57 3. 46 3. 20 3.97
12 1.0 1.62 1.60 172 1.67 1.65 1.63
12 5.0 3.95 3.78 4. 20 3.98 3. 85 4.19
12 9.0 5.48 5.16 5.82 ‘| 5.50 5.10 5.90
36 @ 1.35 1.32 1.52 1. 48 1.50 1. 20
36 1.0 3. 30 3.15 3.71 3. 50 3.45 3.06
36 5.0 8.05 7.50 9. 06 8.30 7.80 7.90
72 oo) 2.12 2.06 2. 46 2.34 2. 25 1.79
72 1.0 5.18 4.89 6.02 5.55 5.00 4.62
72 2.0 7. 60 7.14 8. 85 8.00 7.20 6.91
96 Ao 2. 56 2. 46 3.02 2. 86 2. 55 9.138.
96 .6 4.70 4. 46 5.55 5.15 4.45 4.04

' 96 1.0 6.25 5. 82 7.37 6. 70 5. 60 5.44

120 Av 2. 96 2. 84 3.53 3.30 2. 80 2.42

| 120 .6 5.44 5.14 6. 49 6.00 4.85 4.60

! 120 1.0 7.25 6.73 8. 62 7.90 6.00 6.20

| 144 2 3.32 3.18 3.97 3.75 2.95 2. 69

| 144 .6 6. 10 5.75 7.35 6. 70 5. 10 5. 10

, 144 1.0 8.15 7.58 9.74 8.95 6. 40 6. 89

i

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