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"UNITED STATES DEPARTMENT OF AGRICULTURE 
BULLETIN No. 854 


Contribution from the Bureau of Public Roads 
THOS. H. MACDONALD, Chief _ 


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{| THE FLOW OF WATER IN DRAIN TILE 


By 


q D. L. YARNELL, Senior Drainage Engineer, and SHERMAN M. 
@ WOODWARD, Professor of Mechanics and Hydraulics _ 
| State University of Iowa _ 


CONTENTS 


Page Page 

NSE PIC ER IN oa = 5" nae ooo? ees eet 1°'| Necessary Data for Comparing Velocity 
z Scope of the Investigation. . . .. « 2 Formulse <= oo Se 3 2 Fa ees 
a AcaPMICLUSIONS o> eae 28S ee) = 4 Mean Velocity. . ...- .-. +. I12 
Description of Experimental Plant. . . 5 Hydraulic Grade or Slope .... 12 
¥ Pumping Plant <= oo. fo. 6 3 SB Internal Size of Drain Tile . . .. 13 
SUPMY LANES Sos -< escs ot} 5 Actual DepthofFlow ...... 14 
Weirs . . . 2 + s+ .+ «+ 6 | Methodsof ConductingTests .... 15 
RIGOR MGAVOS 2 oe 6) eso a ere 6 | Meascrement of Mean Velocity ... 17 
Flume ...e.+.-+.s.- £6] ResultsofObservations ...... 18 
Methed of Changing Grade... . 6 | Discussion of Computations . .... 34 
| Layingthe Tile .....++s.-. 7 Formule for Tile Flowing Full. . 35 
 £ Covering the Tile. . . . .. ss 7 Formulz for Tile Fiowing Partly Fall 40 
a Piezometers and Piezometer Tubes . 8 | Comparison of Various Formule ... 47 
Nomenclature ....«-.-++.-«s > 9 | Loss of Headin Catch-Basins .... 49 

Formulz for Flow of Water in Drain Tile 9 


_ WASHINGTON » 
GOVERNMENT PRINTING OFFICE 


Washington, D. C. PROFESSIONAL PAPER August 26, 1926 


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UNITED STATES DEPARTMENT OF AGRICULTURE 


Contribution from the Bureau of Public Reads 
THOS. H. MACDONALD, Chief 


Washington, D.C. PROFESSIONAL PAPER e August 26, 1920 


THE FLOW OF WATER IN DRAIN TILE. 


By D. L. YarNe.t, Senior Drainage Engineer, and SHERMAN M. Woopwarp, Pro- 
fessor of Mechanics and Hydraulics, State University of Iowa. 


CONTENTS. 
Page. Page. 
AM ITOGH ChIOMs seas o oaee occ ese canes Soleo 1 | Necessary data for comparing velocity for- 
Scope of the investigation.................... 2 mole. 2 2s Fao s) RSs Naess Sree ater 12 
Wonclusionss ties fea nese ce eeeeecnewee 4 Mean: velocityicc sesame ee aes 12 
Description of experimental plant........... 5 Hydraulic grade or slope. .-.-.-.......-.- 12 
Pumpin plant ecnccss ste s sce cee s sen sis 5 Internal size of drain tile. .-.............. 13 
SOyo gH ubinl cs See e So ae ca ene tae ose me ee 5 Aetuallidepthiochowa-sesseeeeece cae eee 14 
UYVGTIRS sa Sa oe ee ee GE oe ee ee 6 | Methods of conducting tests................. 15 
PETGO Kae aes apya seen earn ees see cee te Le 6 | Measurement of mean velocity............... 17 
ENING Sere ee ae ee acc aon Sean 6 | Results of observations................-..... 18 
Method of changing grade..............- 6 | Discussion of computations. ................- 34 
He ayilTa NO HLIG te eae oe Shon ee Los di Formule for tile flowing full............ 35 
Conerinaxthestileses ase 7 Formule for tile flowing partly full. .... 40 
Piezometers and piezometer tubes....... 8 | Comparison of various formule.............- 47 
INOTmMeN Cla LRGs so-so oe ae eee ee ece 9 | Loss of head in catch-basins...............-- 49 
Formule for flow of water in drain tile...... 9 


INTRODUCTION. 


The discharging capacity of tile drains has become a matter of. 
considerable importance in recent years, on account of the heavy 
investments being made in this kind of agricultural improvement. 
Drain tile in small sizes have been used for a long time, but recently 
much larger sizes, 2 feet and more in diameter, have come into rather 
common use in some States. Where tile 24 to 48 inches in diameter 
and larger are to be installed, at a cost of $8,000 and upward per 
mile, reducing the diameter 2 or 3 inches may mean saving $500 to 
$1,500 per mile. 

Planning the best tile-drainage system for any situation is a com- 
plicated problem of balancing many diverse and uncertain factors 
of benefit and cost. The point of largest rate of return upon the 
investment can not be determined (exactly. Obviously, a point 
may easily be reached where additional expenditure, although se- 

166597°—20—Bull. 8541 


a 
2 BULLETIN 804, U. S. DEPARTMENT OF AGRICULTURE. 


curing an enhanced degree of drainage, would not yield additional 
benefit in proportion to the increase in cost, and might not be justified. 
On the other hand, an inadequate installation might be so ineffective 
as not to justify even the small expenditure it would require. It 
is the engineer’s high duty, therefore, in planning the general scheme 
of improvement for any drainage undertaking, to determine just 
what expenditure will yield a satisfactory return, and to so propor- 
tion the details as to secure the maximum benefit from the invest- 
ment. A deficiency at one point may reduce the effectiveness of 
the whole system, while the elaboration of one part out of proportion 
to the others might add materially to the expense without obtaining 
any benefit. : 

The formule in general use for computing the velocity of flow 
in tile drains were proposed years ago, when all drain tile were small 
as compared with the larger sizes used to-day. Under the earlier 
conditions, when other considerations had relatively large weight 
in determining the size of tile to be used, accuracy in computing 
carrying capacity was relatively unimportant; but nowadays drains 
12 to 48 inches in diameter are common, al accurate knowledge 
of the capacity is essential for economical dison 

Although many experiments have been made upon fiow of water 
in iron, steel, concrete, and wood-stave pipes, the results are not 
directly applicable to tile drains. The tile usually are not nearly 
so regular in size and shape as are the other pipes mentioned, and 
specially noteworthy is the number and nature of the jomts. While 
the other conduits are either of continuous construction or in 10 to 
20 foot lengths, drain tile are in lengths of only 1 to 3 feet. Fur- 
thermore, with clay tile the nature of the materials used and the 
methods of manufacture are the causes of some distortion in cress 
section; this is particularly noticeable where two lengths abut. The 
considerable unevenness at the joints, when multiplied by the greater 
number of joints, so greatly disturbs the flow of water as to make 
formule devised for other kinds of conduit inapplicable to tile drains. 

Realizing the need for accurate knowledge regarding the flow of 
water in tile drains, plans for investigating this subject were made by 
the drainage division of the Bureau of Public Roads, early in 1915. 
The experiments so far made concern only the smaller sizes of tile, 
and this report therefore should be considered as a progress report 
of the investigation of the whole subject. 


SCOPE OF THE INVESTIGATION. 


Drain tile installed for agricultural improvement serve two some- 
what distinct purposes—as collectors of excess water and as conduits 
to convey the water to some more or less distant outlet, but usually 
both purposes are served coincidentally. The investigation herein 


od 


7 ee 


THE FLOW OF WATER IN DRAIN TILE. 5 


reported, however, deals only with the discharge or carrying capacity 
of tile drains as conduits. No tests were made on sizes smaller than 
4 inches in inside diameter, as the use of smaller sizes now is con- 
sidered generally inadvisable, the small bore greatly increasing the 
danger of obstruction by sediment or by displacement. 
Laboratory methods are essential for securing definite results 


‘In such an investigation, in order that each factor influencing the 


flow may be varied through a considerable range, yet always subject 
to control, while the other factors are maintained constant. Only 
in this manner can each influence be measured separately. The 
factors influencing the velocity of flow in a tile drain are: the inside 
diameter of the pipe, the depth of the water flowing, the slope or 
grade of the water surface (which ordinarily is that of the tile line), 
and the roughness and irregularity of the interior surface and of 
the jomts. On tile lines installed for actual use in land drainage 
the grade of each line is fixed; most of the time they are empty or 
carry but little water; the amount of flow depends upon weather 
and seasons and can not be regulated for investigation; and when 
the flow is considerable the weather is likely to be bad, the roads 
practically impassable, and the ground surface covered with water— 
conditions that make it impossible to secure satisfactorily precise 
measurements in tile several feet under ground. 

The principal feature of the equipment for making the experiments 
was a wooden flume about 570 feet long, in which the tile were laid 
in earth exactly as drains are installed in the ground. The flume 
was adjustable to any grade up to 1.50 per cent (s=0.015), without 
disturbing the tile. The depths of flow were observed by piezometer 
tubes hung on the side of the flume. Care was taken to make the 
tile lines truly representative of drains ordinarily well laid under field 
conditions. 

Experiments were made with all the usual commercial sizes of tile, 
both of clay and of concrete, from 4 to 12 inches inside diameter. 
Nine grades were used, from 0.05 to 1.50 per cent, for each size and 
kind of tile. For each size, kind, and grade it was desired to test 
depths of flow of one-fourth, three-eighths, and one-half the internal 
diameter of the tile, and other depths ranging from half full to full 
by successive increases of 5 per cent of the diameter. However, 
because of the practical difficulty of securing exactly any given depth 
of flow, the number of tests was considerably less than anticipated 
in the smaller sizes of tile. Also, the capacity of the pumping plant 
was not sufficient to fill the largest tile at the maximum grade. 
Tests were run, also, with the tile under slight internal pressure. 
In all, 824 separate tests were made, and from these a new formula 
has been devised for computing the flow in drain tile. . 


4 BULLETIN 854, U. S. DEPARTMENT OF AGRICULTURE. 
ha 


For comparison, 69 tests were made on 10 and 12 inch tile, so laid 
as closely to approximate poorly laid drains as found in the field, 
to show the results of using unskilled workmen in laying drains 
without proper supervision. Nine experiments were made upon the 
‘Joss of head in catch-basins, using 8-inch clay tile. Grades of 0.20, 
0.75, and 1.50 per cent were tested, with drops in the catch-basin of 
0.10, 0.20, and 0.30 foot for each grade. 

The investigations were made at Arlington, Va., in 1916 and 1917. 
The experimental plant was designed and constructed by S. W. 
Frescoln, drainage engineer, and the tests were made by D. L. 
Yarnell, senior drainage engineer, under the direction of S. H. 
McCrory, chief of drainage investigations. S. M. Woodward acted 
as consulting engineer for the investigation, making suggestions in 
the conduct of the experiments and collaborating in the preparation 
of the data and report. 

This report upon the investigation of flow in drain tile includes a 
detailed description of the equipment and methods used and the 
tabulated data from the experimental work. The results deduced 
from the data are shown graphically, the method of developing the 
curves being explained. The formule now in general use for com- 
puting velocity in tile are discussed and comparison is made with the 
new formula presented. A diagram is given showing discharge capaci- 
ties based upon this formula, covering sizes from 4 to 48 inch tile, 
and grades from 0.04 to 3.00 per cent. 

So far as the writers have been able to learn, only one other similar 
investigation of this subject has ever been made. This was by 
Messrs. J. F. Rightmire and M. E. Chappel and was quite limited in 
extent (see Vol. IV, No. 4, Bulletin of the Iowa State College Engineer- 
ing Experimental Station). 


CONCLUSIONS. 


The following general conclusions have been drawn after a detailed 
study of all of the experimental data: | 

(1) That the value of the coefficient of roughness, n, in the Kutter 
formula, as obtained by experiments in a drain or pipe at any depth 
of flow less than full, does not necessarily apply to that drain or pipe 
when flowing full. 

(2) That the exponent of the slope, s, is practically 0.5. In other 
words, the loss of head is in proportion to the 2.0 power of the velocity 
and not the 1.8 power, as given by many authorities. 

(3) That the exponent of the mean hydraulic radius, R, is 2/3. 

(4) The Chezy formula gives the same velocity of flow in a pipe 
fiowing one-half full as in one flowing full, with the grade constant. 
The experimental data obtained seem to disprove this commonly 
accepted theory. 


THE FLOW OF WATER IN DRAIN TILE. 5 


DESCRIPTION OF EXPERIMENTAL PLANT. 


PUMPING PLANT. 


A eomplete pumping plant was installed to supply the water 
necessary to carry on the tests. The pump used was an 8-inch 
side-suction centrifugal pump. Its economical capacity was 1,800 
gallons per minute. The suction pipe, 10 inches in diameter and 


approximately 40 feet long, was laid sloping from the pump to the 


intake ditch or sump. The discharge pipe, 8 inches in diameter, 
was so arranged that the entire capacity of the pump could be de- 
livered to the supply tank with the least frictional losses. 

The pump was run by a 30h. p. engine rated at200r.p.m. Itwas 
equipped with an oscillating-type magneto with the make-and- 
break spark. It was started on gasoline, and after becoming warm 
operated on kerosene. The engine was connected to the pump by a 
10-inch, double thickness, endless leather belt. 


SUPPLY TANKS. 


In order to maintain a constant flow through the tile line, a supply 
tank 7 feet 9 inches by 7 feet 9 inches by 10 feet 9 inches deep (A, 
Pl. I) was built to receive the pump discharge. On the side of this 
tank opposite the entrance of the pump discharge pipe, a measuring 
weir and a hook gage were installed. A baffle board extending from 
the top of the tank to within 2 feet of the bottom was constructed. 
Thus the movement of the water from the discharge of the pump 
was quieted sufficiently. to obtain a eel surface on the water at the 
hook gage and weir. 

Since the entire discharge of the pump was not required for all the 
experiments, an overflow tank (6, Pl. I) was built. Its size was 
9 feet 6 inches by 9 feet 6 inches by 5 feet 6 inches deep. A trough 
from this tank carried the overflow water back to the intake ditch. 

For regulating the flow into the supply tank, an 8-inch gate valve 
was inserted in the pump discharge pipe. This valve is shown in 
Plate I, between tank B and the pump house. The water not 
required for the experiment passed through another 8-inch gate 
valve into the overflow tank. When the entire discharge from the 
pump was used in the tile, the gate vaive in the overflow tank was 
closed. 

Another tank containing baffle board, hook gage, and weir was 
used at thé lower end of the tile line to measure the discharge from 
the tile as a check on the amount of water entering the tile. How- 
ever, the measurements from this tank, as will be explained later, 
were not used in the final computations. 

Both weir tanks were covered with boards to prevent any surface 
movement on the water being set up by winds. 


6 BULLETIN 8&4, U. S. DEPARTMENT OF AGRICULTURE. 
WEIRS. 


For use in measuring the water entering into and discharging from 
the tile line, brass, triangular-notch weirs were used, the notch angle 
being 90 degrees (Pl. II, fig. 1, and Pl. ITT, figs. i and 3). For tile 
over 4 inches in diameter, weirs with {-inch lips were used; while 
for the 4-inch tile, knife-edged weirs were deemed the most accurate. 
The weir plates, both of which were set level, were so placed that the 
nappe of each weir cut free and was fully aerated. 

To determine the discharge over the weirs, V. M. Cone’s formula, 


Q = 2.487 He 


was used in all computations. In this formula, Q=discharge in 
cubic feet per second and H =head in feet on weir notch. 


HOOK GAGES. = 


Boyden hook gages were used to determine the head on the weirs. 
On both gages the vernier plates were securely fastened and bradded 
to the gage, so as to eliminate any error due to possible charge of 
position of the plates. Each gage was set at a distance of over 2 H to 
the side of the weir so as to record the correct head on the weir. 


FLUME. 


In order to test the carrying capacity of the tile bedded in earth 
as in_actual practice, a continuous wooden fiume (Pl. IV) 570 feet 
long, 2 feet wide, and 2 feet deep was constructed of 2-inch plank. 
All joints and seams were calked with oakum and covered with pine 
pitch to make the flume water-tight. This continuous channel or 
flume was supported on yoke blocks suspended by ?-inch steel rods 
(A, Pl. V) from 6 by 6 inch caps (B, Pl. V) which rested on 4 by 4 
inch vertical posts (C, Pl. V).° Twe vertical posts with their yoke 
block formed a bent; the bents were spaced 8 feet apart. In all, 
72 bents were erected. Each bent was braced by 4 by 4 inch posts 
Gi PEW): } 

METHOD OF CHANGING GRADE. 

The upper 6 feet of the steel rods were threaded with 10 threads 
to the inch. For support on the caps, bearing plates with ogee 
washers and 2-inch hexagonal nuts were used. To raise the flume 
an inch at any bent it was necessary to turn the nuts just 10 revo- 
lutions. Ordinary wrenches were cumbersome and slow for turning 
these nuts, consequently specially-constructed socket wrenches 
(Pl. VI, fig. 1) were used, consisting of hollow pipes so shaped as to 

t over the nuts and with circular disk handles. This type of wrench 
greatly facilitated the work of changing grade. 


1 Journal of Agricultural Research, U. S. Department of Agriculture, Vol. V, No. 23, p. 1083. 


THE FLOW OF WATER IN‘ DRAIN TILE. 7 


To decrease the amount of work necessary to adjust the grade of 
this continuous channel, the flume was rotated about its longitudinal 
center. Thus, when changing grade, one half of the flume would be 
lowered while the other half would be raised. The flume could be 
set to any grade up to 1.50 feet in 100 feet. 

To enable the workmen to determine whether the flume was at the 
proper grade, graduated wooden strips (A, Pl. VI, fig. 1) 2 inches 
wide, 0.5 inch thick, and several feet long were placed on each side 
of the flume at each bent. The difference of elevation between 
various grades at each bent had been previously computed, and these 
differences were marked on the gage strips with the corresponding 
grade number. Thus, when the proper mark appeared at the cross 
board through which the gage strip ran, the workmen knew that part 
of the flume to be at the desired grade. At points where the required 
change of elevation was considerable, the flume was not raised or 
lowered the entire amount at one time, but was changed by successive 
increments of only a few inches. Thus the amount of stress on the 
flume was lessened, and the liability of leakage through the possible 
springing of the planks was eliminated. 

The grade of the flume was checked with an engineer’s level im- 
mediately before each experiment, to eliminate all possible errors 
from inaccurate adjustment or from settlement of the vertical posts. 


LAYING THE TILE. 


The tile were laid on earth in the flume as in actual practice. 
This earth in the bottom of the flume was about 7 inches deep. It 
was placed in layers, 2 inches at a time, and each layer was thoroughly 
tamped so that the bed on which the tile rested would not settle. 
At first a line was stretched along the flume immediately over its 
center and about 3 feet above the grade, and this line was used to 
grade the bed for the tile. It was soon found, however, that the gage 
line was in the way of the workmen, and another method for grading 
the tile bed wasadopted. The material for this method consisted of 
a 30-inch strip, 2 inches wide and 0.75 inch thick, and a gage stick of 
the same size but 171 inches long. The workman laid the strip 
across the top of the flume and, holding the top of this gage stick 
flush with the top of the cross arm, determined whether the invert of 
each tile was at grade (P. VI, fig. 2). 


COVERING THE TILE. 


While blinding the tile, an engineer was constantly in the flume to 
oversee the work and prevent any tile from being pushed out of line. 
Fine earth, free from large clods, was used for blinding, the inspector 
tamping the earth on each side of the tile with his feet. Thus any 
appreciable movement or current of water through the earth on 


wee eerie ener —— 


8 BULLETIN 854, U. S. DEPARTMENT OF AGRICULTURE. 

either side of the tile in the flume was prevented. After the tile 

were covered, the remaining space in the flume was filled with earth. 
PIEZOMETERS AND PIEZOMETER TILES. 


In order to measure the depth of flow in the tile drain, piezometer 
tubes of graduated glass were placed on the side of the flume and 
connected to the lower part of the tile line. Twelve tiles of uniform 


shape, for each size and kind, were selected, and a small hole was 


drilled through the wall of each. In each hole a }-inch iron pipe, 
2 inches long, was inserted, care being taken that the tube did not 
project inside the tile bore. This tube was set in cement (Pl. II, 
fig. 2), and any unevenness on the inside wail of the tile at the en- 
trance of the tube was removed by coating the surface with a little 
cement. This method of inserting the tube was deemed the best as 
determined by Hiram F. Mills from a study of the results of some 
6,000 observations on various piezometer connections (see Trans. 
Amer. Academy of Science, 1878). Mills found that with an orifice 
whose edges are in the plane of the side of the conduit and with the 
bore of the tube normal to the plane of the wall, the piezometer 
column indicates the true height of the water surface in any open 
conduit, or the pressure in a closed conduit. 

At first these piezometer tile were so turned as to have the tube 
on the bottom of the tile in the flume. Much trouble was experienced 
from the tube openings filling up, so the piezometer tile were then 
laid with the tube leading toward the side of the flume but turned 
slightly downward. The connection was made by rubber tubing to 
a steel nipple inserted through the wall of the flume (Pl. VII). On 
the side of the flume at each piezometer tile, a frame holding the glass 
tube was set. This glass tube (Pl. VII) was graduated in tenths and 
hundredths of a foot. Its zero was set at a definite distance below 
the top of the flume. A rubber tube connected the piezometer glass 
to the nipple in the wall of the flume. 

The zero of each piezometer gage was 174 inches below the top of 
the flume. The invert of the tile in the flume was always laid 164 
inches below the top of the fume. The capillarity of the glass tubes 
used was found to be 0.01 foot. Thus, with water just entering the 
tile drain, the piezometer tube read 0.09 foot. In other words, in 
order to obtain the true depth of flow in the drain, 0.09 foot was 
subtracted from each piezometer reading. 

With the exception of the two piezometers near the tile entrance, 
which were only 8 feet apart, these tubes were distributed along the 
flume approximately 55 feet apart, the last piezometer being within 

a few feet of the outlet of the tile drain. 


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Bul. 854, U. S. Dept. of Agriculture. 


B. P. R. Reeser 

Fig. I.—CoNICAL ENTRANCE USED TO 
INCREASE ENTRANCE VELOCITY I NTO 
TILE. 


PLATE III. 


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B- P. R. D—534 


Fia. 2.—CONICAL ENTRANCE USED TO 
I NCREASE ENTRANCE VELOCITY INTO 
TILE. 


B. P. R- D-69] 
Fic. 3.—WEIR WITH 90-DEGREE NOTCH. 


Note free fall from discharge tank. 


Bul. 854, U. S. Dept. of Agriculture. 


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ONIMOHS 


JO M3IA WHANAD 


Bul. 854, U. S. Dept. of Agriculture. PLATE V. 


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B. P. R. D-700 


UPPER END OF FLUME, SHOWING I0-INCH CONCRETE TILE LAID READY FOR 
BLINDING. 


Bul. 854, U. S. Dept. of Agriculture. PLATE VI. 


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B. P. R. 0-628 
Fig. 1.—CHANGING THE GRADE OF THE FLUME. 
Note 12-inch plank laid along top of flume for men to work on while changing grade. 
¢: 
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B. P, R. D-699 


FiG. 2.—LAYING I0-INCH CONCRETE TILE IN THE FLUME. 


Bul. 854, U. S. Dept. of Agriculture. PLATE VII. 


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GRADUATED PIEZOMETER GLASS, FRAME, AND RUBBER TUBE CONNECTION TO 
PIEZOMETER TILE INSIDE OF FLUME. 


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THE FLOW OF WATER IN DRAIN TILE. 9 


NOMENCLATURE. 
The following symbols are used throughout this report: 


d=mean depth of flow in the drain, in feet. 
D=mean inside diameter of the tile, in feet. 

r=mean inside radius of the tile, in feet=4 D. 

Q=mean discharge of the tile during the test, in second-feet. 
A=mean area of the tile bore, in square feet=z7?. i 
a=average area of flow in the tile, in square feet. 

V=mean velocity of the water during the test in feet per second=“ : 


P=wetted perimeter in the tile, in feet. 


: 3 a= : : : D 
R=mean hydraulic radius=p}3 in a tile drain running full a . 


s=hydraulic gerade or slope. 
n=coefficient of roughness in Kutter’s formula. 
C=coefficient in Chezy’s velocity formula. 
Cy=coefficient in the Williams-Hazen velocity formula. 
h=total difference in elevation between ends of a main drain, in feet. 
l=length of the drain tested, in feet. 
b=summation of the amounts of excess head in the submains, in feet. 
T=number of submatnhs. 
U=depth of the soil over the main drain at its head, in feet; used only when 
main drains are 1,000 feet or more in length. 
s=miz is the general equation for the flow of water in drain tile, in which z 
is always constant and m varies only with the size of tile. 
m=eDz is the equation for the variation of m for a series of drain tile of various 
sizes but of the same material; e and x are constants. 
nv’ =the special values of m found for each series of tile. 

Whenever a test is numbered, the reference is to the correspond- 
ing numbers in Tables 3 and 4 and to Plates X and XI. 

Throughout this discussion the term “concrete tile’ is used 
instead of ‘‘cement tile.’ The American Society for Testing Mate- 
rials, in its standard specifications for drain tile, defines concrete 
tile as tile made of ‘‘a suitable mixture of Portland cement, mineral 


aggregates, and water, hardened by hydraulic chemical reaction.”’ 
FORMULA FOR FLOW OF WATER IN DRAIN TILE. 


It is common knowledge that the water enters drains at the joints 
and not through the walls of the tile. Since there is a joint either 
every foot or every 2 feet in the length of the drain, water enters the 
tile drain throughout its entire length. In tile of small sizes, this 
leads to an appreciable variation in the amount of water carried 
at different points in the tile; but in the larger sizes the amount 
entering is so small a proportion of the amount carried as to be 
unimportant in considering carrying capacity. = 

The water in any tile drain is caused to flow and velocity is set 
up by two forces, one due to the grade of the tile line, and the other 
created when there is a variation in areas of water cross-section. 


10 BULLETIN 854, U. S. DEPARTMENT OF AGRICULTURE. 


One authority ineludes a third force caused by the head due to height . 


of the water table in the soil. 

Itis in vanestns to note the variations between the different formule 
recommended for tile drainage. Some formule take into account 
only the grade or slope of the tile drain, while others include the 
additional head caused by the weight of ae water in the soil above 
the drain. Few formule distinguish between the retardation influ- 
ences in concrete and those in dese drain tile, while many treat both 
kinds of tile the same. 

One formula used by drainage engineers is the well-known Chezy 
formula, 


V= OyRs=CR™55"5 (1) 


This was introduced by Chezy, a French engineer, in 1775. In this 
formulx, Cis a coefficient, originally considered a constant but since 


discovered to vary with the retardation factors as well as with the 


mean hydraulic radius and the slope. 
- The Kutter modification of the Chezy formula, 
ie ote 6642: .00281 
V= 


1+ ( 41.66 
a Se er 


is the equation probably most widely used by drainage engineers. To 
obtain this formula, the coefficient C has been replaced by an ex- 
pression involving the hydraulic grade or slope and the mean hy- 
draulic radius, as well as a quantity, n, to represent the influence of 
the roughness of the walis of the channel or conduit. 

The Poncelet, Hawkesley,' or Eytelwein * formula 


= DY A 
S28 |e 
U [+54D (3) 


applies to drains in which the velocity is due only to the hydraulic 
grade or slope of the drain. It has been used to a great extent for 
small tile systems in close soil and for determining the size of outlet 
drains. 

According to Wollender, Wage, and John,* the mean velocity in 
drain tile is 


ih 


fies 9 oy lied eee ee 
ie 1+46.5D 4) 
. The Vincent formula is ‘ 
V5 95 2S 
V=45.95 Kk tees D (5) 


1 Sullivan’s New Hydraulics, p. 9. 
2 Hamilton Smith’s Hy araulics, poi: 
3 L. Faure, Drainage et Actaimiccenieat Agricole des Terres, Paris, 1903, p. 99. 


00281 w Ves (2). 


+ 


THE FLOW OF WATER IN DRAIN TILE. Te. 


in which Vincent gives values for the variable coefficient, K, ranging 
from 0.75 for sineh tile to 0.875 for 6-inch tile. 
Friedrich! states that Professor Gieseler’s formula, 


V =36.22-/Ds° (6) 


is the best in practice as well as the simplest. 


Formula 6 is said by Professor Luedecke to have been deduced as 
early as 1852 by the agricultural engineer Stocken, at Schweidnitz, 
from Prony’s formula, which is 


V =47.63/Ds eG) 


Beardmore’s, sometimes called Leslie’s, formula, 


00 Ree (8) 


is similar to Chezy’s, the coefficient (' being taken as a constant, 100. 
The Williams-Hazen general formula for all kinds of pipes is 


V= Oh s?=20)00 { —0-04 (9) 


This formula is of special importance in this discussion, since careful 
comparison of it with the Chezy-Kutter formula has been made. 

C. G. Elhott, a widely known drainage authority, has modified the 
Poncelet or Hawkesley formula as follows:? 


Dh+3U 


FON Gena: +54 D 


(10) 


fer use on systems where the soil is open; 


yas)? @ +p) (11) 


1+54 D 


for use on large systems in close soul; 


3 yee: 
yas)? @ +) +4 U (12) 


1+54 D 


for use on large systems in open soil. 

The last term in the numerator under the radical in formule 10 
and 12 has been added to allow for the water pressure in the soil above 
the tile drain. This additional head, however, is constantly varying, 
being greatest when the earth is ands eaematcd Itis doubtful 
whether it should be used in computing the discharge of a drain, and 
if so, then only in open, porous soils. 


1 Friedrich, Kulturtechnischer Wasserbau, vol. 1, Berlin, 1912, p. 343. 
2C. G. Elliott, Engineering for Land Drainage, New York, 2d ed., 1912, p. 93. 


‘2 BULLETIN 854, U. S. DEPARTMENT OF AGRICULTURE. . 


A new formula based on tests actually made on drain tile, derived. 
as hereinafter explained, is tentatively offered for tile flowing full. 
This formula is 

V=138 Ris? (13) 


It may seem that the exponential type of formula is inconvenient 
because logarithms must be used to calculate results from it. How- 
ever, it is comparatively simple in the case of such a formula to 
prepare a diagram or chart, composed of parallel, straight lines if on 
logarithmic scale, from which the required velocity or the required 
discharge for any size of tile at any grade can be obtained at a glance, 
the accuracy of the reading depending entirely upon the scale of the 
diagram. Plate XIII is a diagram prepared by using the formula as 
derived from the actual tests made, but applied to commercial or 
nominal sizes of tile. 

It should be noted that Elliott’s modifications of Poncelet’s or 
Hawkesley’s formula are the only ones which take into consideration 
the head caused by the water table in the soil, while the Chezy-Kutter 
formula is the only one in which the different retardation influences 
in clay and concrete drain tile may be considered. 


NECESSARY DATA FOR COMPARING VELOCITY FORMUL2. 


Jn order to test the relative accuracy of the various formule which 
have been recommended for use in determining the discharge of tile 
drains, the effect of each hydraulic element involved in the formule 
must be determined by experiment. However, in the tests made at 
the experimental plant it was impossible to determine the effect of 
the additional head caused by the water table in the soil. The ele 
ments to be determined are as follows: (1) the mean velocity of the 
water in the tile drain; (2) the grade or slope of the dram, or the 
water slope if it is different from that of the drain; (3) the internal 
size of the tile; (4) the actual depth of flow in the tile drain. 

MEAN VELOCITY. 


The mean velocity of the water flowing in the drain can be deter? 
mined by various methods. However, only the following two methods 
were used: (1) by actually measuring the quantity of water entering 
or discharging from the tile drain per second, and then solving the 


equation va ; (2) by timing a given yolume of water through a 


previously measured distance. 
: HYDRAULIC GRADE OR SLOPE. 
_ The slope of the line of tile tested at the experimental plant was 
always known, since the tile were laid in an adjustable flume which 
could be changed to the desired grade, the grade always being checked 
by a level. 


vs! 


/ 


THE FLOW OF WATER IN DRAIN TILE. re 


INTERNAL SIZE OF DRAIN TILES. 


It is generally known that drain tile are not exactly of the dimen- 
sions corresponding to the nominal size. All of the concrete tile used 
in these experiments were under the nominal size, while the clay tile 
generally were larger than the nominal size. However, the concrete 
tile more nearly averaged the nominal size than did the clay tile. 

Although in actual practice the nominal or commercial size of tile 
is invariably used in computing the discharge, yet to determine 
accurately the retardation factors it is essential to know the correct 
average diameter of the drain tile being tested. To determine the 
average diameter of all the tile tested at the experimental plant, two 
measurements were made at right angles to each other at each end of 
every tile. This task required the recording and averaging of 1,160 
measurements when tile in 2-foot lengths were used, and twice this 
number when tile in 1-foot lengths were used. 

Table 1 gives the dimensions and cross-sectional areas of each 
kind of tile tested at the experimental plant. From a study of this 
table several points are revealed. In the first place, considerable 
error would have been introduced into the final results had the 
nominal or commercial diameter—instead of the actual, measured, 
average diameter—been used in the computations. For example, 
the mean velocity for the 6-inch clay tile at a grade of 0.50 foot in 100 
feet, with a depth of flow of 0.498 foot and discharging 0.554 second- 
foot, is, when computed from the measured average diameter, 2.659 
feet per second; with the nominal or commercial diameter the 
velocity is 2.823 feet per second. As a rule the mean of the areas of 
the tile computed from the diameters varying most above and 
below the measured average diameter, with their companion diame- 
ters, varies little from the area computed from the measured aver- 
age diameter. 


TaBLeE 1.—Comparison of dimensions and areas of various kinds of tile used. 


~ = | Ps | | e 
1 2 3 aed ais 6 ) 8 Tee Sis (Yad ee 9 ian bas G2 fo 
Vari-| Diam- 1| \Diam- 
. | / bg 
|Com-| Ac- ation | eter ee eter ee 
Com-| mer- | tual in |Small-} nor- |," =| Larg-} nor- | 4. > 
> ~_ | Area} Areal ._.. = diam-| ~~~ =) |diams 
mer-| cial |meas- area} est | mal est | mal = 
° com- |} com- eters : TH eters 
Kind oftile cial | or | ured ea Nees be- | meas-| to in |meas-}_ to aS 
a aoe size |nom-| aver-|? P tween! ured |diam- pals | ured diam- pals 


diam- ever 8 diam-} eter Ths 


of | inal} age | cols. 
©” teol. 3.jcol. 4. : 
eter. | in aad eter.| in and 


tile. diam-|diam- 5 


| eter. | eter. and | col. col. 
| | 6. | | 8. a- ie ee 
| 

In. | Feet.| Feet. Sq.ft. Sq.ft.| P.ct.| Feet. | Feet. |\Sa.ft.| Feet.| Feet. |\Sq.ft 
Gencreie= =< 4:0. 3333/0. 3280/0. 0873/0. 0845} +3. 2) 0.31000. 3300/0. 0804/0. 3380/0. 3320/0. 0881 
Hard-burned clay........- 4} . 3333] . 3398] . 0873] .0907} —3.9} .3150} .3380) . 0837] .3520} .3500) . 0968 
COncrelesoaa- 8 5! . 4167] . 4127) . 1364] . 1338] +1.9} .3950} . 4100} . 1272) . 4220) . 4180} . 1385 
Hard-burned clay.......-- 5| .4167| . 4193} . 1364] . 1381} —i.2} .3780) . 4510) . 1349] . 4350) . 4310] . 1473 
COneretesS ses | 6} .5000] . 4970} . 1964] . 1940] +1.2) .4850} . 4850) . 1847} .5130} . 4950) . 1995 
Soft-burned clay.........-. 6} . 5000} . 5184} . 1964} .2111] —7. 4} .4760} .5260] .1971] .5350] .5300} . 2227 
Concrete as &| .6667] 6585] . 3491] .3406} +2.4] .6400} .6450} .3242) . 6776} . 6620) .3520 
Hard-burned clay--.-.-.-.-..-- 8} . 6667] . 6850] . 3491] . 3685} —5. 5} .6700) .6720) . 3536] . 7360} . 7030} . 4066 
Concrete. = 5 Ss 10] . 8333] . 8274) .5454} .5377] +1.4] . 8080} . 8110) .5147] . 8420) . 8410} .5562 
Netitinedion sn. ae oS e 10} . 8333] . 8360} .5454] .5489] —0.6] . 7950} . 8300] .5185] . 8650) . 8400] .5708 
Conereres so es 12)1. 0000} . 9915] . 7854] . 7721) +1. 7} . 9630] .978§ . 7398}1. 0100}1. 0000} . 7933 
MiimHOG 22 026.6 2. 28 a 12 1. 0000 - 9857] . 7854] . 7631] +2.8] .9700] . 9760] . 7436/1. 0200) - 9980} . 7996 


Ne 
1 Computed as an eliipse. 2 These tile werein 2-foot lengths; all others in 1-foot lengths. 


14 BULLETIN 854, U. S. DEPARTMENT OF AGRICULTURE. 
ACTUAL DEPTH OF FLOW. 


~ The depths of flow in the tile lines tested were measured by means 
of the 12 piezometer tubes distributed along the flume, as previously 
described. 

As first laid, the tile at the lower end of the experimental line dis- 
charged into the open air with a free drop of several inches. This 
produced a backwater curve of the drop-off type which extended 
back for a considerable distance into the tile line, decreasing the 
depth of the water near the lower end. For the steeper slopes this 
effect was much extended, and, indeed, in extreme cases reached 
throughout the length of the experimental line: Such a condition 
was objectionable for two reasons: first, the hydraulic gradient under 
such circumstances would be represented by the slope of the water 
surface, which was then somewhat greater than the grade of the tile; 
second, since the condition was not one of uniform flow, it would 
become necessary to take account of the change of velocity at differ- 
ent points in the tile, with the corresponding changes in velocity head, 
in determining the head consumed in overcoming friction. Since these 
additional complications were unnecessary and objectionable, the 
drop-off curve was eliminated by installing a low, movable dam 
(shown in Pl. VIII, fig. 1) just below the lower end of the tile line. 
By adjusting the height of this dam; the water surface at the outlet 
could be maintained in close agreement with any desired depth 
throughout the experimental line. 

The water. entered the upper end of the tile through a conical 
entrance pipe (PI. Il], figs. 1 and 2) designed to give an entrance 
velocity approximating that of the steady, uniform flow im the tile 
line. But it was found impracticable to adjust the entrance Velocity 
exactly to that of the line, with the result that the upper 50 feet 

f tile were required to bring the velocity to the condition of uniform 
flow, and the piezometers at the upper end would not aiways agree 
with the others along the tile. With this exception, the readings of 
depth in the various piezometers along the tile line could generally 
be brought into satisfactory agreement. 

With the tile only partly full, there were occasional quite erratic 
readings on some piezometers. These indicated unusual disturb- 
ances within the tile lme. When through the warped or elliptical 
shape of the tile the jomts do not fit ciosely, a portion of one tile 
at the joint may project inward in such a way as to present a square 
obstruction against the edge of the moving stream of water. Violent 
impact of the water against such an obstruction produces a marked 
_ disturbance of the stream, and is indicated by extensive ripples and 
foam on the water surface which may persist for several feet down- 
stream. Several such cases were carefully examined by uncovering 
the tile and inspecting the water surface within, gs well as by measur- 


THE FLOW OF WATER IN DRAIN TILE. 1a 


ing the height of the water surface outside of the tile at the joint. 
In some cases the water level outside the tile would remain steadily 
0.1 or 0.2 foot higher on one side of the tile than on the other, and the 
surface inside the tile wauld be very turbulent and would seem to 
bear no relation to the elevation of the water surface outside the tile 
joint. Such phenomena were most conspicuous when the depth of 
flow was between half and full depth, and with the high velocities due 


' to the steeper slopes. The phenomena seemed to depend upon the 


presence of air in the tile, as they disappeared largely when the tile 
were completely filled, so that all air was excluded. 


METHODS OF CONDUCTING TESTS. 


A test was always begun at the least depth of flow. Six men were 
needed to conduct a complete experiment at one grade, which required 
from 3 to 6 hours, depending upon the number of depths of flow 
tested. One man cared for the pump and engine, one read the upper 
hook gage, a third was stationed midway the length of the flume at 
a piezometer tube, another was stationed at the outlet to adjust the 
height of the movable dam, and a fifth man read the lower hook gage. 
The engineer in charge usually operated the valve controlling the 
supply of water to the upper weir tank, and watched the upper 
piezometer tubes. 

The engineer announced the depth of flow he desired to obtain to 
the man stationed at the dam. The gate valve in the supply pipe 
was partly opened and the piezometer readings noted, The dam was 
then raised or lowered to secure the correct depth of flow at the 
piezometer tube near the outlet, special care being taken not to get a 
greater depth than desired there. The observer at the upper hook 
gage called out the various gage heights at short intervals, that the 
water supply might be regulated properly, and when the desired depth 
in the tile was obtained, sufficient time was allowed to determine that 
the depth over the weir was constant. The observations at the 
upper, middle, and lower piezometers indicated when the flow was 
steady throughout the tile lme. When the flow was steady at the 
proper depth, the signal was given and each of the two hook-gage 
readers made record of the readings at his station every 30 seconds. 
Meanwhile, the engineer in charge passed along the flume, recording 
the readings of all piezometers in succession; the observer at the 
lower end of the flume went to the upper end and then recorded the 
piezometer readings in order, following just 2 minutes behind the 
engineer’s readings; the observer at the middle of the flume watched 


_ the piezometer there to report if any considerable fluctuation indi- 


cated that the test should be run again. If the depth over the upper 
weir remained constant throughout the test, the engineer proceeded 
to obtain the next depth of flow; if the weir readings varied, the test 


16 BULLETIN 854, U. S. DEPARTMENT OF AGRICULTURE. 


for the same depth of flow was run again. About 20 minutes were 
required to obtain the data for each depth of flow, the amount of time 
depending upon the grade of the flume. 

The readings for the first two and the last piezometers. were not 
included to obtain the depth of flow in the drain. It should be 
remembered that water as it enters the drain has not the velocity it 
will acquire after traveling some distance; therefore the first two 
piezometers usually recorded a depth slightly different from that of — 
the piezometer 60 feet from the tile entrance or those of the succeed- 
ing piezometers. Even with a gradual, conical entrance to the tile 
drain (PI. III, figs. 1 and 2), the entrance velocity could not be easily 
regulated to be the same as the uniform velocity through the main 
portion of the tile. The average of the readings of the intermediate 
nine piezometers, less 0.09 foot, usually was taken as the true depth 
of flow, although at times very erratic individual piezometer readings 
were obtained which were not used in obtaining the average. 

Only the upper weir readings were used in the final computations. 
It was found in the earlier experiments that after waiting some time 
for the lower weir box to fill to a steady height, the lower weir would 
read practically the same as the upper weir, proving that there was 
no measurable loss of flow in passing through the tile line. Hence, to 
save time in performing the experiments, it was decided not to wait 
for the lower weir to reach a steady reading. It may appear that, 
in using only the upper weir readings to obtain the carrying capacity 
of the dram, too great a quantity of water was recorded due to. 
seepage into the earth adjacent to the drain, which would credit the 
tile with carrying more water than it actually did carry. However’ 
observation of the condition of the soil indicated clearly that the 
soil became sufficiently saturated by the time steady flow was 
obtained in the tile, that there was no such loss, at least not in 
quantity that could have affected the results of this mvestigation. _ 

The use of the dam at the tile outlet did not affect the carrying 
capacity of the drain, for special care was taken not to allow any 
piezometer readings at the lower end of the flume to exceed the 
readings near the upper end. The dam merely assisted in obtaining 
a uniform depth of flow throughout the length of the drain. Thus 
the necessity of corrections for changing velocity heads due to 
decrease in the water cross-sectional area at succeeding piezometers 
near the outlet was eliminated. Without the dam and with a con- 
stant flow over the upper weir, the successive piezometers showed a 
continuous decrease in depth, and therefore increase in velocity, 
toward the outlet of the tile line. In other words, the hydraulic 
gradient or water slope was greater than the grade of the tile. With 
no change in the amount of water passing over the weir, the height 
of the dam could be raised until the piezometer near the outlet re- 


*SSANHONOY AO LN3AIOIsAS 


-O9O SHL NO SLINIOP YVINDAYY] AO LOS4dASy AHL “ANIL NI MOV AO Hidag 
SANINYSLAG OL CIV] SV ATIL AVIO HON] -GI—'S “SI WHOJINAM NIVLEO OL SLNAWIYSAdxXy NI Gas¢q, WV¥q—"|] "SI 
goge—d "u ‘d ‘a feo-a "uy ‘d*g 


PLATE VIII. 


Bul. 854, U. S. Dept. of Agriculture. 


ae ae ¢ a . t 
ASSL LEW SCI 


a 
Pere ee 


Ji Se AN 


i FPR 


tat poms 


Pat 


mae 


i 
were Abe atone BG | 


a 


aie 


e 
. 
i 
e 


Bul 654, U.S. Dest of Agrcuirure Pate IX 


4" HARD BURNED CLAY TILE) 


Mean Velocity in Feet per Second. 


! 
-7. Fig 7 
CONGRETE 


L Velocity in eet per Second 
,—s]— 
-+ 
DOVE IC : 
y fv VV As 
Tig? y oy 1 Fip8 =a 
5" HARD BURNED CLAY TILE™ | 


ai 


Moan Velocity in Feet pur Second 
“i ee Pe 


y | 
al 5’ CONCRETE TILE 
) 


T T 
‘Mean Velocity. in Feat par Second 


Fig3 


BURNED CLAY TILE 


SOFT ILE 


e 
4 


Mean Velociyy In Feel par Second 


et 


Feet per 


2 


* yo 
S 
b GS Wy sy 
4 1 
Fig 10 | 
ria CONCRETE TILE 


8” HARD BURNED CLAY TILE 


Ia] Mean Velocity in Feet per Secord 
4 


Mean Velocity in Feet per Second 
i 3 4 5 


ars =e 
i] 
rs 
+ 


— 
Sa z 
: | 
48 ihe g y ¥ by, ay Ry 
is A Y | 
* A! 
| & 7 
By 
f? * 5 o> = 
7 
0 a 
kt 4 i =e 
Ae Fig. 


10” CONCRETE TILE | 


} By lx 2 
2 Figs fz 
JE JO"VITRIFIED CLAY TILE 


} Mean Velocity in Feet per Second = 
Vex 
a “ ies ‘ 


Velocity in Feet per Second 
ri 


Le ee 


7. 
Ie 
> 6s 
$ 
< oo ” 
I ten 
& Is [P° 
° 
4 
* cy 
3 
E 7 
rig.6 Fig. 2 
I2" VITRIFIED CLAY TILE ey 12” CONCRETE TILE 
ia = = 
Mean Velocity in Feet per Second Mean Velocily in Feet per Second 
f ¢ 6 ! H ss | rf See 


Tem 
CURVES SHOWING RELATION BETWEEN DEPTH OF FLOW, VELOCITY, AND SLOPE. 


~ GHSaN 


bf 


tit ble ak ba 


atin 
Oi ee Fen TPO 
4 


ot i Mal iabiveeeh Arras san a vnebre M bee Asp aia ak 
i 


‘ 


2 aan 


7 a 


“he fo orheepainrt een thle 


Aa ihe emealtone hep. 0 


| aw NON seh 


, _— 


“| 
sesh 


j 


THE FLOW OF WATER IN DRAIN TILE. a7, 


corded the same depth as that shown by the piezometer 60 feet from 
the tile entrance, without affecting the latter piezometer but caus- 


. ing the intermediate piezometers to register the same depth. 


MEASUREMENT OF MEAN VELOCITY. 


As stated before, the mean velocities obtained during the experi- 
ments were determined by dividing the quantity of water passing 
over the upper weir by the average cross-sectional area of the water 
in the tile. For checking these results, velocities were determined 
also by coloring matter and by the use of a voltmeter. Both potas- 
sium permanganate and dyes were used. For injecting the colored 
solution into the tile, the use of a large hard-rubber syringe proved a 
satisfactory method. The voltmeter was of the portable Weston 
type (model 45) with a range of scale from zero to 14 volts; carbon 
and zinc electrodes were used. To complete the circuit, a saturated 
salt solution was inserted by the method employed in the color 
tests. When the water saturated with salt passed the point where 
the electrodes were placed in the tile, a current was set up whose 
intensity was indicated by the voltmeter. When the volume of 
saturated water had all passed, the needle of the voltmeter would 
return to its original position. 

An observer noted the time the color was injected and also ob- 
tained the times when the first and the last color passed the outlet. 
The time the color spent in the tile was taken as from the instant of 
injection to the mean between the first and the last of the appearance 
at the outlet. This same method was used in the voltmeter tests, 
the time being taken as from the instant of injection of the salt 
solution to the mean between the time the needle of the voltmeter 


y began to register and the time when it returned to its original posi- 


tion. Table 2 shows part of the results obtained in comparing the 
values of the mean velocity as found by the weir, with those deter- 
mined by color and voltmeter. 


TABLE 2.—Comparison of mean velocities as determined by various methods. 


Tile ey by| Velocity by | Velocity by ee. VV 


: color voltmeter 
per ey). |, (re). |e (Yes Y v 
Set ie Ft. po: ae: | Ft. per sec.| Ft. per sec.| Per ncn: Per cent. 
Pas Dap Sail IEEE US aoe || 8 BBY one ees SEE eres - 
4 5. 133 Dh Gif ae les soe cone S162) jason saoeeaee 
4 1. 866 TBS OG eid Reese ee es I Ney Pel las Beare 
12 1. 236 1298 Se ee ctee oer = 4°56) ci aero eee 
12 1.124 SUD VEN | Sere torches a (OW eae ee ea 
12 4.551 A182)— Nee ee Ses o soe — Osh teen eee 
12 3.711 SS ae ae ue neat ONS. at 265 eee 
12 2. 251 2.320 291 —3.1 —1.8 
12 2.493 2.656 2.500 —6.5 —0.3 
12 2.769 2. 723 2.764 | +1.7 + 0.2 
| 12 2.104 2.272 2.235 —8.0 —6.2 


166597 °—20— Bull. 8542 


18 BULLETIN 854, U. S. DEPARTMENT OF AGRICULTURE. 


For determining the velocity, coloring matter can be used success- 
fully only in clear water. Potassium permanganate as well as dyes 
of all colors were tried in muddy water having a large velocity and 
it was found practically impossible to detect the colors. However, 
the voltmeter method may be used equally well in muddy and in 
clear water for determining the velocity. It is believed that veloc- 
ities obtained by the use of either color or voltmeter will be quite 
accurate if the mean of several readings is taken. 


RESULTS OF OBSERVATIONS. 


Tables 3, 4, and 5 give the results of the tests. The various series 
are arranged in ascending sizes of tile and ascending grades. Table 
3 gives the results of observations on clay tile; Table 4, the results of 
observations on concrete tile; and Table 5, the results of observa- 
tions on clay tile poorly laid. The Kutter coefficient of roughness, 
n, given in column 10, was determined from a large diagram specially 
drawn for this investigation. The variation and irregularity of 
the joints of the tile in the lines poorly laid can be seen in Plate 
VIII, figure 2. 

The tests summarized in Tables 3 and 4 were plotted on coordinate 
paper, with velocities as abscisse and depths of flow as ordinates. 
Mean curves were drawn for each grade through the points repre- 
senting the tests for each size and kind of tile. These curves are 
shown on Plate IX. A study of the curves reveals some interesting 
facts. For the flatter slopes the curves more nearly approximate a 
straight line; as the slopes increase the lines become more curved, 
until at the steepest grade there is considerable bulge to the curve. 
The velocity at any depth of flow over half full is shown at a glance. 
It will be noted that the velocities at half full and at full are seldom 
the same, as they would be according to the Chezy formula. The 
sreatest velocity seems to be approximately at the 0.8 depth. The 
curves were not extended below the half-full point on account of the 
insufficiency of data. In the largest sizes of tile, where symbols are 
shown but no curves have been drawn, incompleteness of data has 
prevented the development of accurate curves through these points. 
It will be seen that with some of the curves the points le practically 
on the lines, while with other curves some points vary greatly, show- 
ing probable error in the experiments. 


THE FLOW OF WATER IN DRAIN TILE. 


TaBLE 3.—Elements of experiments for clay tile. 


19 


4-INCH TILE. 
1 2 3 4 5 6 7 8 9 10 11 

Depth Area Hy- é Kutter! Chez 

Test No. of a of * | draulie aise 1 ie Slope. | coeffi- eoaiiie 

flow D | flow A | radius TSC-5) JOCIvY. cient. | cient. 

(d) (a) (Rk) (Q) CA) (s) (n) (C) 

Cu. fi. Feet 
Feet. Sq.ft. Feet. | per sec. | per sec. fs 
Aileen edna 8 Doe yi 0.332 | 0.98 | 0.0901 | 0.99 | 0.0935 | 0.0547 | 0.607 | 0.0005 | 0.0101 88.8 
Deri neve vel ea pence. .309 | .91] .0866) .96] .1007 . 0562 .649 ; .0005) .0100 91,4 
3} cae eee .298 | .88] .0843] .93] .1023 . 0487 -578 | .0005 |] .0110 80.8 
[Rares en eee mS ROAST 7307008) - 78s Ols . 0404 -570 | .0005] .O111 79.9 
USSU cb stp 2a ge a are ee BO14s 632) ~ 060211: 366 1) 20905 . 0274 -456 | .0005 | .0126 65.6 
Gee ee en ee .159 | .47] .0416] .46] .0813 .0177 424 0005 | .0120 66.5 
Oe en ins PS .131 | .39] .0322} .36| .0708 . 0098 . 304 0005 | .0139 51.1 
Biles So eee Sa ES .331 | .97] .0900] .99}| .0940 . 0703 . 780 0010 | .0110 80.5 
O}leeger soa oe So .327| .96] .0896] .99] .0958 0744 . 831 0010 | .0106 84,9 
AQ eee ne ere) os BOR Sh 84a | OST ae 89) e032 . 0580 .714 | .0010 | .0123 70.3 
1 nk See ae a a ee .228 | .67| .0647] .71 |] .0992 . 0568 -878 | .0010] .0104 88.2 
rene ieee oe an a ae .160 | .47| .0420] .46] .0817 . 0235 .560 | .0010] .0128 62.0 
eS aaa ae ae ae eit .136 | .40] .0339] .37] .0728 - 0166 490 | .0010| .0131 57.4 
LC Sey ee ree .329 | .97 | .0898] .99] .0950 .0969 | 1.079 0020 | .0113 78,3 
lope ere ee eh .321 | .95] .0887] .98]| .0979 .1019 | 1.148 0020} .0111 82,1 
GE eens ae: .283 | .83] .0807] .89]| .1033 .0940 | 1.165} .0020] .0113 81.0 
Wis ee Ste age 1971 | .80.| .0775 | .86 | - 1034 .0904 | 1.166 | .0020] .0112 81.1 
UR ete pea ee -223 | .66] .0631/. .70 | .0983 -0710 | 1.125 | .0020] .0113 80. 2 
Oe ee ea .173 | .51 | .0464| .51 1] .0859 0414 . 892 0020 | .0122 68.1 
OA Ue Sint ioe aah Sees eget PIQ9F|F 288) =. 0316-12 35-1- ..0700 . 0187 592 0020 | .0145 50. 0 
PN IS a a eo ee eee 313 | .92] .0874] .96]| .1000 .1230 | 1.408 0030 | .0112 81.3 
7 Sa ee ik ae BDA eel SOG9 7 |= sits LOLS .0864 | 1.240 0030 | .0123 Tet 
UP rs Scie 5G Oe eg ae a .213 | .63] .0598] .66] .0963 .0685 | 1.145 0030 | .0127 67.4 
Dae ee .166 | .49] .0440] .49] .0837 . 0361 820 0030 | .0148 51.8 
PANS SERS aE eee .123 | .36| .0296| .33] .0675 . 0180 608 0030 | .0161 42.7 
Mec noes eae ene .317 | .93] .0881] .97] .0990 .1578 | 1.792] .0050 | .0113 80.5 
OA Seip cic eer S28 7a le cs 1 ROS 90s. 1032 .1494 | 1.829] .0050| .0114 80.5 
ants Gosae oe aes SIS |} ol. co OVER Pecks} | oilsyl .1327 | 1.762] .0050 | .0117 77.6 
PASE Ei one eg oe D033 5668 e 063 | 27071 109083 .0978 | 1.550] .0050 | .0125 69.9 
GL ate Somes mem Meine .170 | .50] .0454] .50] .0850 .0517 | 1.139 | .0050 | .0142 55.3 
Gio OE ek ane are eee wigs 5128"! 2.38 -|- 50313 | .35-| ..0696 . 0256 .819 | .0050 | .0159 43.9 
S71 Sas TUN ae ete aa Ea .382 | .98| .0901| .99} .0935 .1931 | 2.142 | .0075] .0111 80.9 
8 ince: SOS ee eee ee .320 | .94] .0886] .98 | .0982} .1905|) 2.151] .0075| .0114 79.3 
BS reese ees ts ee .288 | .85| .0819] .90] .1031 .1756 | 2.143} .0075] .0118 vite 
eee ee Genet Sie 5958s 2141-2 072441. 80:| . 1023 .1482 | 2.047 | .0075| 0121 73.9 
BOI ee ee .209 | .62] .0585| .65| .0954 .0996 | 1.702} .0075] .0133 63. 6 
SES ces eis cree eee ten eee Seed .164| .48] .0434] .48] .0830 .0654 | 1.508 | .0075 | .0133 60. 4 
le Soe: Sa aaa Sepeeiee ae C1345 ee SO 2 (03325 | 2597. |. OT20 .0425 | 1.279] .0075 | .0137 55.0 
DOM ee ee eee .312 | .92] .0872] .96/ .1002 .2159 | 2.477 0100 | .0116 78.3 
Bs erence ae en aa .298 | .88] .0843] .93) .1023 .2068 | 2.453 0100 | .0118 76.7 
Mil Reese aco Se SORSS |e S3s|—> AORN Gs 2589.1) 21033 .1984 | 2.459 0100 | .0118 76.5 
LOTTE Rice eer oe we i ~233 | .69 | .0663 | .73 | .1000 .1476 | 2.227 0100 | .0125 70.4 
A eee ea ete esa Gi .205 | .60] .0572 |] .63] .0946 1140 | 1.994 0100 | .0131 64.8 
PL aero Se eae 151 | .44 1 .0389 | 143 .0785 0615 | 1.579 0100 | .0138 56. 4 
Ay Lee reneged oy ear .331 | .97] .¢6900 99 | .0940 . 2640 | 2.932 0125 | .0107 85.5 
Gee cee see eS .304 | .90; .0856] .94)] .1016 . 2472 | 2.888 0125; .0113 81.1 
Aen 2 Seats fae Me .270 | .80] .0773| .85] .1033 SOA TE OX, 7/0) 0125 | .0120 76.5 
LS SoS ROR Sx Meee ae AD st AO SO oy! .1951 | 2.683 0125 | .0120 75.0 
AO Meee ae ce oe tae A SBP le SOS OSB aOeval SLOSQEe 2G 0125 | .0127 65. 5 
Ee Baie eee ak re es .148 | .44] .0379| .42/| .0774 .0736 | 1.941 0125 | .0128 62. 4 
Migr se .329 | .97/] .0898] .99]| .0950 .2890 | 3.218 0150 | .0108 85.3 
Ey Dalat ete oe RE arate .313 | .92] .0874] .96] .1000 .2907 | 3.328 |} .0150] .0168 85.9 
27ers .298 | .88] .0843] .93] .1023 .2814 | 3.338 0150 | .0110 85. 2 
GES Sie ose Caain ee Sega SI || SG CORO Ge = Sly . 2318 | 3.150 0150 | .0114 80. 2 
Rieke ase es ee een BDISHle wba le 20647.) . al |e 0992 . 2026 | 3.132 0150 | .0113 81.2 
DOs era ae te et es .168| .49| .0447] .49/] .0843 .1322'| 2.957 0150 | .0107 83.1 
i Pen Ae ee ae .126 | .37] .0306| .34] .0688 .0720 | 2.353 0150 | .O111 73.3 
5-INCH TILE. 

ote: Ree seo, eee 0. 404 | 0.96 | 0.1364 | 0.99 | 0.1180] 0.0868} 0.636 | 0.0005 | 0.0111 82.8 
Ops ai ee he eae SS90n en 9Setealoosy |. Ore) al 225 . 0848 .634 | .0005 | .0114 81.0 
Oe AO ee SB | ce esate) herds . 0832 .676 | .0005} .0112 84.6 


1 These tests used in deriving formule 27 and 29. 


20 BULLETIN 854, U. S. DEPARTMENT OF AGRICULTURE. 


TaBLE 3.—Elements of experiments for clay tile—Continued. 
5-INCH TILE—Continued. 


1 2 Bera 4 5) 6 7 8 9 10 ili 
Depth Area Hy- : ; Kutter} Chez 
Test No. of @ of — | draulic = Die 1 Nc Slope. | coeffi- cose 
flow D flow y radius. Bee OCtE Me cient. | cient. 
(d) (2) (Rf) (Q) (V) (s) (n) (C) 
Cu. ft. Feet 
Feet. Sq.ft. Feet. | per sec. | per sec. 
Geek ee see eae 0.314 | 0.75 | 0.1109 | 0.80 | 0.1265 0. 0699 0.630 | 0.0005 | 0.0116 79.3 
CARN SOA eS IIe 3 745 .61 - 0879 . 64 1171 - 0547 . 623 . 0005 .0113 81.3 
Goa tes Se eae - 221 568 . 0738 54 . L083 SQ386sli e523 . 0005 0122 ist 
Se eat Ae . 162 39 . 0492 . 36 . O875 . 0150 . 305 - 0005 0157 46.2 
(DE OSes a Eee eee ete .119 28 - 0323 592} . 0684 | . 0074 . 201 - 0005 0165 39.4 
GG fas eh SS Mam ANGI OG |e toOSh| =a OO nee liz -1415 | 1.035] .0010 0102 95.6 
(Gy iilessed <) Spsaed tar er -402] .96| .13861] .99] .1189 . 1366 | 1.003 | .0010 0105 92.0 
GSE eae reht a ees s . 350 - 83 . 1231 . 89 5753 . 1230 . 999 . 0010 . 0110 88.5 
GQ po eo Pe Sets Rolain LIOOR Is 2807s ~ L264 . 1065 -960 | .0010] .0112 85. 4 
AU seat da a ee .273 | .65| .0952| .69]| .1209 - 0824 .866 | .0010} .0118 73.7 
Se Ae ener one. 2 3215 aii . 0713 On . 1065 . 0532 . 746 . 0010 . 0122 vey 
Lie ie LR eo .155 5au/ 0464 -o4 - 0847 . 0231 497 . 0010 0142 54.0 
UB Ser Bee a ea «5 MIG SPR] oO | RBS CORD . 0165 531 | .0010 0119 | 64.9 
ARLE: Bis eens Ns Ni a 411 .98 1374 =99 . 1146 . 1905 1. 386 . 0020 0105 91.6 
Re oe OR Oh oC .410 | .98 13378} | ok) Shiay .1892 | 1.378 | .0020 0106 90.8 
LG ee ae ee oe ee . 348 - 83 . 1225 - 89 31275 . 1827 1.491 . 0020 0106 93. 4 
(li eR es Bee Been eee 315 a 73) poles -8l.| .1265 . 1686 1.515 - 0020 0105 95.3 
Violette Se eS ee e en . 279 . 67 . 0976 = fA . 1220 = aii 1. 405 . 0020 -0108 ; 90.0 
Oe ee eo ce = AUP e51 0700 =i . 1056 . 0840 1. 200 - 0020 . 0112 | 82.6 
SO or ae neo See ee . 164 .39 . 0501 . 36 - 0883 . 0481 . 961 . 0020 O118 | ee 
fo been a enna ere eee ears . 129 33! . 0361 - 26 . 0732 . 0291 . 807 . 0020 0120 | 66.7 
Soo catia Smee egos ae tae . 399 95 1356 - 98 . 1199 . 2408 1 7c . 0030 0105 93.6 
RS Bh aph seers Ras cals .392 | .94 13437) 229% |) 51220 .2370 | 1.765} .0030 0106 | 92.3 
SAR Me Uae es ahs oe Sey? . 84 1238 - 90 . 1274 . 2208 1.784 . 0030 O108 | 91.3 
SE as Say hea Sc SaPAll eit/ . 1134 - 82 . 1270 . 1998 1.761 . 0030 0109 90.3 
SORE tre See hy ee seen aae te SAS . 65 . 0952 . 69 . 1209 . 1566 1.645 . 0030 ONS 86. 4 
BY (oe eee SRO een A SPU) 4 EY OSM ol. Sz -0987 | 1.368] .0030 | .0119 | 76.4 
BB ee reno cine te . 165 .39 . 0505 soir . O887 . 0544 1.078 . 0030 0126 66.1 
RO Bere ae eee Se ene ats maltGy toe 5 0308 | .22 | .0665 . 0231 (ok 920030 0137 | 53.1 
(A) PVT ee ed 5 nce a ls 397 | .95 1352} .98 | .1205 . 3026 | 2.237 .0050 0107 91.1 
QU aie are teeony sk. israrsp Na. BO . 90 1308 .95 . 1250 . 3096 2. 367 . 0050 0106 94.7 
US Oe Sree a ee Siete cele . 347 . 83 1222 . 89 QD . 2958 2.421 . 0050 0105 95.9 
ORS ae be On en ASE . 298 a Hfit . 1050 . 76 . 1247 . 2464 2. 347 - 0050 0106 94.0 
Oo ar Che Mees eee SEE AL OES |) GB S1blee .1892 | 2.162} .0050 0109 89. 4 
Oi Se SR aie ea retorts . 220 any? 0734 = 583 . 1080 . 1448 1. 973 . 0050 OL 84.9 
GO eee ene ee . 154 os 0460 5383 . 0842 . 0784 1.705 . 0050 0107 | 83.1 
C8 (idee ee te aN rea CAP er .118 . 28 . 0319 oe . 0680 . 0381 1.194 . 0050 .0121 64.8 
ORE eee) eee tears hens Saket fal, OP I SBR 1) aOy yo ge .o0%0 | 2.682'|} .0075 | . 0111 88. 2 
QO VIS Be rane ai hte raja 8 ~ 383 91 . 1823 - 96 . 1240 «3582 2.708 . 0075 0110 88.8 
WOO Rae tes esas nae .325 . 718 1148 - 83 5 WPT . 3326 2.896 . 0075 0107 93.7 
OPS et aot ee eas . 281 - 67 . 0984 Sil 5 WOE} . 2746 2. 790 . 0075 0107 92.1 
Pe ie ae She Semin nae oee ear . 249 . 59 . 0855 . 62 . 1158 . 2215 2. 592 . 0075 0110 88. 0 
LVS tae fe Desh ees pees ea . 197 47 0637 - 46 - 1006 . 1404 2. 203 . 0075 . 0114 80. 2 
0 Pesos eae Sone oe ee een e142 34 0412030) | 0791 0816 |} 1.981 | .0075 0108 81.4 
TIC Oops reste an ts eine ere SATS |e 2Se lee OSLOR Rees n | eeOGSO 0445 | 1.396 |} .0075 0126 | 61.8 
NOG a We ets eee - 402 . 96 Sao .99 . 1189 . 4009 2.945 0100 .0113 | 85.4 
VDC ah ees eps meet ape! - 383 -91 1323 - 96 . 1240 - 4051 3. 063 0100 . 0112 | 87.0 
IO sears Aer ee ee a - 326 Sis: 1152 eo 5 LO 18% - 3740 3. 247 0100 0109 91 0 
1100 oe ies Pes cca ee ar ean en . 282 - 67 - 0988 5 a W745) . 3096 3.135 0100 0110 89.6 
LN OSes ee eee ae S202 . 60 - 0867 . 63 . 1165 . 2648 3. 055 0100 0109 89.5 
TI eae eee apr ae . 216 shy - 0717 aby? . LO68 . 2096 | 2.923 0100 0107 89. 4 
HOLD alin 5 ewes Se Ps orc Se re . 154 .3o7 0460 BOS . 0842 . 1255 2. 730 OLOO 0098 94.1 
WWE Se ore Newoct eee She - 26 0293 PAL . 0646 - 0640 2.185 0100 0098 86.0 
VTE yaa eA Da en ce. -402 | .96 PSG GPa OOF ee lS .4749 | 3.488 0125} .0108 90. 5 
1S US eS a nee Bae nae . 386 . 92 1330 - 96 - 1234 - 4703 3. 537 0125 . 0109 90. 1 
il Grete ee a ee mates BOLT .78 1155 . 84 SiS . 4272 3. 698 0125 . 0107 92.7 
V7 (eee eee eee as 2945 0 10384} .75 | .1242 . 3862 | 3.734 0125 | .0105 94,7 
1S Rese at a haste ae Sale le e204: .63 . 0916 . 66 . 1190 . 3392 3. 704 0125 . 0103 96. 0 
Cal PR 2h aya eae oe Beatin 7A = 58° 0738 53) . 1083 . 2624 3. 556 0125 . 0101 96.7 
QE eee A Seana hs eeliies Al . 0538 .39 . 0919 . 1698 3.158 0125 . 0100 93. 2 
AAS 2 hak ea ee ANG) 5 il - 0308 x22, . 0665 . 0836 2.718 0125 . 0092 94.3 
Me Pa aN ee ae . 399 95 1356 98 . 1199 . 5415 3. 993 0150 0105 94, 2 
18} te eae eee . 394 . 94 1347 -98 eL2T5 . 5428 4. 030 0150 0105 94. 4 
10. SSC Sa eee . 043 . 82 1209 - 88 . 1276 . 5066 4.190 0150 . 0105 95.8 
Mea ee a EU -319 . 76 1127 . 82 . 1269 - 4738 4, 203 0150 . 0104 96. 4 
2G Seca, eae 2 OE bee ee a = 200 . 60 . O871 . 63 . 1167 - 3582 4.113 0150 . 0102 98.3 
1 feta ae ra A .209 |} .50] .0688] .50] .1046 .2704 | 3.932 0150 | .0099 99. 3 
Pas SOCIO EHD O DOA EEE . 158 -38 . 0476 se) . 0859 . 1674 3. 516 0150 . 0095 98. 0 
NG See ats E52 sed anh ee -118 - 28 . 0319 oe . 0680 . 0969 3. 041 0150 . 0093 95. 2 


1 These tests used in deriving formule 27 an d 29. 


Z 


THE FLOW OF WATER IN DRAIN TILE. 


TABLE 3.—Elements of experiments for clay tile—Continued. 


21 


6-INCH TILE. 
¢ 
1 2 3 4 5) 6 7 8, 9 
Depth d Area y- Di Vv 

Test No. of = of £ | draulie ISS < | Slope. 

flow D flow. A | radius. charge. | locity- 

(d) | (q) | (R) (Q) (V) (s) 
= seer 

Cu.ft. | Feet 

Feet. Sq.ft. Feet. | per sec. | per sec 
SURE gees eee ns 0.517 | 1.00 | 0.2110 | 1.00 | 0.1319 | 0.1614 | 0.765 | 0.0005 
Pee ee Ne ee - 402 .78 .1756 .83 . 1573 . 1464 . 800 . 0005 
RD Repete aig ieee me BO 2 2300; 5 2583) 21266) 2605) 21412 0724 .572 | .0005 
SR So See eee . 223 -43 -0868 | .41 . 1170 . 0397 -457 . 0005 
[RU ee Be ene ee ae BESS3| ger obs eesUG02eleesoon peelOSE .0225 825 0005 
TY) Te? 5 ta ppg i Re Na .510 -98 . 2108 .99 . 1404 . 2229 | 1.060 . 0010 
GUS Sane es eee aoa SSO65 |: ecOah sel a0dls 482=)iee 1569 . 1578 .912 | .0010 
SY. Se Se ey eee ee . 304 -09 . 1286 -61 . 1422 21255 .976 . 0010 
TORE ee eee wae . 221 .43 . 0858 -41 . 1168 . 0706 823 . 0010 
1G) So Sa AR oe a eee Site easel es OGO Msi e429 4h en 0958 . 0372 613 | .0010 
MA Quisenmetee Pas Se a Ser -498 | .96} -2083 | .99]| .1465 .3563 | 1.710} .0020 
Tel Eee he Os teen AND (Oat SS60l) 85 |—at5 26 - 2680 | 1.500 | .0020 
ADE e ee erie cee = = SHEN Gey |) ele Gee |) ie -1801 | 1.569 | .0020 
PA ees Oe bees one eee . 216 -42 . 0832 .39 . 1144 -1090 | 1.310 . 0020 
Te ee nce -157 |} .30| .0540 | .26 | .0893 .0559 | 1.036 | .0020 
[ZF Sa a es eae .508 | .98| .2100} .99] .1418 -4282 | 2.039 | .0030 
AG er a esa aee -414 . 80 . 1807 . 86 .1577 .3620 | _ 2.003 . 0030 
ieee eee ee ee - 302 .58 . 1276 .61 . 1417 . 2194 1.719 . 0030 
VARS Sos ot ee eee ee e227 | eas . 0863 .41 . 1167 -1382 | 1.601 . 0030 
1 Os Sees ae a .167 | .32| .0588) .28}| .0939 .0685 | 1.165 | .0030 
PS) SL et See ae se .498 . 96 . 2083 .99 . 1465 .5940 | 2.659 . 0050 
i) a ey ae ees -318 aie . 1649 .78 | .1552 -4440 | 2.692 . 0050 
Ae Doe rg See tee eA . 276 =88 .1143 04 . 1347 ATA 2.425 . 0050 
TERIA oS ae ie eae ean ee, SIS Bee ls ee OSTallh Ixoos| cells -1512 | 1.850 | .0050 
1 Bs Oe eee Sees .152 . 29 .0516 . 24 . 0870 .0664 | 1.287 . 0050 
UD Se ie de eae .473 91 -2020 | .96 . 1534 -6804 | 3.368 | .0075 
1G Series es RRS .389 | .74} .1681} .80]| .1560 -0390 | 3.206 | .0075 
ED pera a a ene . 258 - 50 - 1049 .00 . 1292 -2771 2.641 . 0075 
TS Serge ca eee a ee 199 -38 . 0746 .30 .1077 -1692 | 2.268 . 0075 
a en ee - 147 . 28 . 0493 220 . 0846 . 0969 1. 967 . 0075 
Ge een ea eee -461 | .89 | .1983 .94 | -1554 . 7630 | 3.847 0100 
GTS a Ne he es -336 .65 . 1448 .69 1491 .9174 3.575 0100 
1 a pc . 222 -43 - 0863 41 1167 . 2560 2.966 0100 
NGS a See ae 2 a .191 8x7 . 0706 .33 . 1044 -1608 |} 2.278 0100 
GA ae ee ee eS -141 svt . 0465 -22 0817 . 0864 1. 860 0100 
GWE See See ece See ee -405 |} .78} .1769}| .84 1574 .8028 | 4.538 0125 
EG Gs ee ee -343 . 66 - 1482 7 1505 . 6346 | 4.281 . 0125 
TOTES ene ee eS - 260 - 50 - L060 - 50 . 1299 -3894 | 3.674 . 0125 
5 She Se are ore eee ee . 204 BGt) 0771 sa. . 1097 -2600 | 3.371 . 0125 
GORA ee eres ee . 147 22800492, 23 . 0846 .1185 | 2.409 - 0125 
LO eae ere ee RS OZ a6 SLEDS SS 1567 RO dco Dat 220 ee OL50 
fy A Seep en Seri SS LET -333 . 64 - 1433 - 68 . 1485 .6650 | 4.641 . 0150 
NY aa 6 ee eee eae . 233 -45 . 0920 -44 . 1207 .3592 | 3.904 . 0150 
AS See aayecin ees ee . 175 .34 . 0627 .30 .0975 -2243 | 3.579 . 0150 
ICE Se ae and ree og a - 140 .27 | .0460 22 | .0812 -0872 | 1.896 . 0150 

8-INCH TILE 

AZO be ese es | 0.673 | 0.98 | 0.3670 | 0.99 | 0.1862 | 0.3240} 0.883 | 0.0005 
EGS ee oe. 664 | .97 3692 | .99 tObt . 3260 - 893 - 0005 
RE Coe re SR 3 = 515 Se PATINA stik . 2067 . 2540 . 885 . 0005 
ERS eee oe 342 - 50 1839 .00 sient . 1370 . 745 . 0005 
LIT Res es Soe aes en 259 .38 1277 .30 - 1406 . 0840 . 658 - 0005 
SO rere a ee Se ee 166 . 24 0689 -19 . 0978 .0363 -027 | .0005 
if) LESS ee eer eres 656 | .96 3631 | .99 1944 -4570 | 1.259 | .0010 
Lge a a ee ee 656 - 96 3631 .99 1944 -4670 | 1.286 - 0010 
Cae Sin eee 509 | .74 2936 | .80 - 2061 -3740 | 1.274 . 0010 
oe ee eae 348 ol 1881 ol 1730 -2060 | 1.095 | .0010 
PRO eee eee ie 271 -40 1357 sai 1456 1380 1.017 - 0010 
j tol Se Seo See 192 . 28 0846 | .23 1106 0720 -851 . 0016 


1 These tests used in deriving formule 27 and 29. 


10 il 

Kutter | Chezy 

coeffi- | coeffi- 

cient. | cient. 
(7) (C) 

0. 0103 94.2 
.O111 90.1 
. 0134 68.0 
.0141 59.7 
. 0165 45.3 
-0111 89.5 
. 0132 72.8 
.0119 31.8 
. 0120 76.3 
. 0132 62.6 
. 0104 99.9 
.0119 84.5 
. 0105 95.5 
.0110 86 6 
.0112 Geo 
. 0104 98.8 
.0112 92.1 
.0118 83.4 
.0112 85.6 
.0123 60.4 
. 0106 98.2 
.0108 96.6 
. 0108 93.5 
.0119 TUT 
.0131 61.7 
. 0106 99.3 
.0111 93.7 
.0115 84.9 
.0116 79.8 
. 0112 78.1 
. 0107 97.6 
.0111 92.6 
.0111 86.8 
. 0126 70.5 
. 0126 65.1 
. 0104 102.3 
. 0106 98.7 
. 0109 91.2 
. 0105 91.0 
.0116 74.1 
. 0102 105.7 
. 0106 98.3 
. 0107 91.7 
.0101 93.6 
. 0142 54.3 

0. 0114 91.5 
-0115 91.3 
.0122 84.1 

0123 80.6 
.0120 78.5 
.0114 75.4 
.0118 90.3 
.0116 92.2 
.0121 88.7 

0122 83.3 
.9118 84.4 
.0114 80.9 


22 BULLETIN 854, U. S. DEPARTMENT OF AGRICULTURE. 


TaBLE 3.—Elements of experiments for clay tile—Continued. 
8-INCH TILE—Continued. 


<< 4 aie at: 7 8 9 


1 10 11 
Depth Area Hy- = = Kutter} Chez 
Test N' of a of — | draulic eee 1 ae Slope. | coeffi- panes 
flow D flow + radius. [os y- cient. | cient. 
(d) (a) (Rk) (Q) CV 65) (n) (C) 
— es | ———____| 
Cu. ft. Feet Bea 
Feet. Sq.ft Feet. | per sec. | per sec. | 
Gt fee Bc peat rege 0.669 | 0.98 | 0.3663 | 0.99 | 0.1885 | 0.6750 | 1.842 | 0.0020 | 0.0113 94.9 
VSG ieee ee ase 661 | .96| .3644|) .99| .1924 .6720 | 1.844 | .0020} .0115 | 94.0 
Ce Ween ad, See wei .509 | .74] .2936| .80] .2061 -5220 | 1.778! .0020} .0123 87.6 
(OO Sasa 2 ee ABUSE, |= 2H) |= SURE) | eS h lin SAL -2805 | 1.439! .0020] .0130 76.8 
1G] es ee eS .267 | .39 1329 | .36] .1439 -1540 | 1.159 | .0020] .0138 68.4 
ODS oo Sete oes el mt Goalie. 24: 0684 | .19 | .0973 . 0540 .790 | .0020| .0144 56.6 
LR SL es ceeea Reet oe -670 | .98| .3664| .99] .1880 .7996 | 2.182} .0030| .0117 91.9 
L$ atk Se .663 | .97| .3649]| .99| .1915 -7870 | 2.157 | .0030; .0119 90.1 
TOWes oe Sees Nee -510 | .74] .2942|_ .80.| .2062 .6390 | 2.172} .0030: .0122 87.5 
OG IR ee hs Pe 364 | .53 . 1990 04 1778 .3392 { 1.705 . 0030 .0136 73.8 
dO ee | .280; .41} .1417| .39] .1490| .2054 | 1.449 | .0030 | .0139 68.7 
10h tee te 2 etn oe -196 | .29] -O871} .24 1126 .0920 | 1.057 |~ .0030 | .0149 57.6 
ROO NO = terete meee ue -676 | .99 -3675 .99 . 1840 1.0800 2.939 . 0050 .0112 96.9 
DM Sees eso see ress Sea ee |) 558?) S828 82105)" 2.87 2085 .9210 | 2.870} .0050] .0121 88.9 
CAINE aaeibee tie Cae gee ee | .427 |; .62] .2415 | .66| .1935| .5660 | 2.344 | .0050 | .0137 75.4 
Danses Sees emo pt sebiee It = pues 1949 | .53 |; .1760 .3950 | 2.030 | .0050 | .0143 68.4 
18 Gee ana aus Re oe | Sole eral) (PS IRGR} |) = 8 7/ 1459 .2360 | 1.730] .0050 | .0145 64.0 
Oi gt ee ang en ER cae SALTZ | -2267(= 207558|2 2228 1033 .0946 | 1.250! .0050 |] .0149 55.0 
2 at Sad See .662 | .97 3647 | .99 | .1919) 1.2840] 3.522] .0075 | .0117 92.8 
Gi Sete = .642 | .94 3588 | .97| .1989] 1.3000 | 3.623 | .0075 | .0117 93.8 
NY esate = Pe .503 St . 2900 .79 . 2055 9480 | 3.270 .0075 .0129 83.3 
CB Nek > Sitaet atin Sp os = Zale .356 BZ . 1935 208 .1754 5590 2.889 .0075 .0128 79.7 
SOO gees ae a -270 | .39 PS50nE Od tees 45 3392 | 2.513 | .0075 | .0127 76.2 
F1) ae .180 | .26 0773 | .21 | .1048 1481 | 1.915 | .0075 | .0129 68.3 
i ee ee 667 | .97| .3658| .99| .1886| 1.4920! 4.079| .010 | .o116| 93.7 
SI) epee Ho 2 Sa eae Spe -661 | .96| .3644|] .99] .1924] 1.4650} 4.021 010 .0118 91.7 
SSE ee ees .657 | .96 | -.3635 |} .99- .1940 |) 1.4475 | 3.982 010 . 0120 90.4 
SU Vii hein ae Sn Rael riety .473 | .69| .2714 l .74 | .2021 | 1.1580 | 4.267 010 0116 94.9 
i 5) gern = Whee coe he etic tea a a 47 gies 47 . 1654 5980 3.471 010 .0120 85.4 
TANG SOU SS + os ee eet is B2bOD | cal bom bolwele oo 1369 3760 | 3.089 010 .0118 83.5 
DAL? | 53 ne OR apa ee se 57) 0731 . 20 1013 . 1814 2.483 010 .0116 78.0 
| 
DUR Die es wht eee | 673 .98 . 3670 | .99 . 1861 1.6200 | 4.414 0125 .0118 91.5 
DEO ee a . 669 98 . 3663 .99 . 1885 1.6200 | 4.423 0125 0118 91.1 
Dh. nme See ee eee . 490 She . 2821 Stil . 2040 1.3475 | 4.778 0125 .0117 94.6 
DPD Vee oa oe cep HN I OM . 346 .51 . 1867 SOL 1723 a( Gres 4.031 0125 . 0120 86.9 
DI) Tee a Sp aR nae Oe EDG0E| cena Salm coon leno elmer ako .4430 | 3.453 0125 | .0120 82.3 
DA Be oS EEE See eM .173 a2 .0731 . 20 . 1013 . 2096 2.869 0125 .0113 80.6 
OI Deca ee ar ~ODa 81 . 3187 87 . 2085 1.7675 5.546 0150 .0112 99.2 
DO ead wer SS ee . 540 .79 .3116 . 85 . 2082 1.7375 5.576 0150 .O111 99.8 
De ae ia earn a S5O1S |) 2-735) 2 52888. | = 782|-— = 2053) |) 1553508 phe S16 0150 | .0114 95.8 
Pid (zaiai eae at ey ee ea Be aeeasS .49 . 1812 -49 . 1698 . 7932 4.378 0150 .0119 86.7 
doy anaes Sane eaten cages SDF 2Syi A sere ay/ || Shee .4772 | 3.798 0150 | .0119 83.1 
DDO EE cme ear. teenies | es l66 .24 . 0689 .19 . 0978 2138 | 3.102 0150 .0112 81.0 
10-INCH TILE. 
Fea 9) 1S Aelia Rata a Seen ae 0.821 | 0.98 | 0.5467 | 0.99 | 0.2275 | 0.6386 1.168 | 0.0005 | 0.0104 109.5 
TAYE 5 Sa yey nee es - 812 SOF . 5444 -99} .2324 . 5874 1.079 | .0005 . 0112 100.1 
FAT): | Th ee ee ee ee ee ee - 783 . 94 - 5343 .97 . 2429 .5770 T7080 . 0005 0114 98.0 
E335 SES RES Ie ar -749 | .90] .5186 -95 . 2497 -5640 } 1.088] .0005 . 0116 97.3 
Date Se en ae Poe .697 | .83]-.4890| .89] .2541 .5578 | 1.141 | .0005] .0112 101.2 
Da eeiees Ree enge Sin. Send .666 | .80}] .4689| .85] .2542 .5503 | 1.174] .0005| .0110 104.1 
Se Neen te Spee ad -626:| 2 75-} ~4408 | .80°}> .2521 .5366 | 1.217} .0005| .0107 108. 4 
DE | I aes A len . 567 -68 | .3963 aiPe . 2451 - 4982 1s / - 0005 . 0102 113.6 
aaa ee ee ee ee eid .546 | .65] .3798| .69| .2413 -4611 |] 1.214] .0005} .0104 110.8 
DB QUaiae Se ae ale .473 | .57] .3203 58 | .2250 -3967 | 1.239] .0005] .0098 116.5 
DAVEE Ee a, OL the: - 421 -50 . 2770 . 50 . 2099 . 3078 ieihial . 0005 - 0103 108. 4 
DA re ates x -310 537/ - 1852 - 34 - 1692 . 1998 1.079 . 0005 . 0093 117.3 
GH EB SON RE ie . 214 .26 -1110 . 20 ~1 PAM - 1005 -906 1 .0005 . 0089 114.5 


1 These tests used in deriving formule 27 and 29, 


he 


Test No. 


THE FLOW OF WATER IN DRAIN TILE. 23 
Taste 3.—Elements of experiments for clay tile—Continued. 
10-INCH TILE—Continued. 
| 

2 3 4 5 | 6 7 8 9 10 11 
Depth Area Hy- = 7 Kutter | Chezy 
of a of £ | draulie Gi a : vee Slope. | coeffi- | coefti- 
flow. | D flow 4 radius...) oat 8e: roety.: cient. | cient. 

(d) | | (a) | (fk) (Q) | Cyets7G) (n) (C) 

| | { 
Cu.ft. | Feet 

Feet. Sq.ft. Feet. | per sec. | per sec. 

0.782 | 0.94 | 0.5339 | 0.97 | 0.2431 | 0.8870] 1.661 | 0.0010 | 0.0109 106.6 
SANS eee O04 One SO 2ae a2020 - 8837 | 1.752} .0010} .0107 110.2 
-681] .82] .4788] .87| .2544 8722 | 1.822} .0010; .0104 114.2 
- 625 -75 | .4401 .80} .2520 -7996 | 1.817} .0010} .0103 114.5 
OZ le NOSaine 400 Daou fo . 2459 - 7120 | 1.780} .0010 - 0104 113.5 
-542}] .65] .3766] .69] .2406 -6748 | 1.792] .0010} .0102 115.6 
-466] .56] .3145 250 | 2231 -0378 | 1.710} .0010; .0101 114.5 
425] .51] - 2803 ol SA -4726 | 1.686} .0010} .0099 116.1 
SSUIB be SS Si/4 pep clave  aeee es ilyAnlet -2788 | 1.486] .0010) .0097 113.8 
-205 | .25] .1044] .19] .1206 -1240 | 1.188] .0010} .0094 108. 2 
-823 | .99] .5471 -99 | .2260} 1.2680] 2.318} .0020] .0106 109.0 
797] .95]} -5397} .98] .2385] 1.2680] 2.350} .0020] -0108 107.6 

778 93 5322} .97 2441 1.2520 | 2.353} .0020} .0110 106.5 
694 83 4871 . 89 2542 | 1.2300) 2.525 -0020] .0106 112.0 
667 80 4696 . 86 2543 | 1.1840 | 2.521 .0020 | .0106 111.8 
623 75 4386 | .80 2518 | 1.1380] 2.595 .0020 | .0104 115.6 
- 963 .67 | .3932 | .72} .2444] 1.0090} 2.566; .0020) .0102 116.1 
-925 -63-| -3629 | .66] .2370 .9380 | 2.585 -0020} .0100 118.8 
-472} .56} .3195 .58 | .2248 . 7964 | 2.493; .0020!] .0100 117.6 
- 428 = OL - 2828 -o2 PAPAL - 6832 | 2.416 . 0020 . 0099 Ines 
-318 | .38}) .1917 SOD foe 24: -3841 | 2.004) .0020} .0101 107.9 
2203. | ee O4e | oL0305|) 05) 1196 1614 | 1.567 .0020 } .0099 101.4 
827 99 5479 99 2232} 1.5300} 2.793 .0030 | .0107 107.9 
814 97} .5449 99 2314 | 1.5350 | 2.817] .0030} .0109 106.9 
810 97 5438 99 523384.) 71-5350) }2 -2..8232)—. 0030 . 0109 106.7 
804 96 5421 99 2360] 1.5250} 2.813; .0030] .0110 105.8 
796 95 5393 98 2388 } 1.5180 | 2.815 .0030 | .0111 105.2 
777 93 0318 97 2444] 1.5140} 2.847| .0030] .0111 105.1 
756 90 5221 95 2485 1.5020} 2.877} .0030] .0112 105.4 
689 82] .4840 88 2543 | 1.4960] 3.091 -0030 | .0107 111.9 
684 82} .4808] .88 2544 | 1.4800] 3.078] .0030} .0107 111.4 
631 76 4444) 8] 2525 | 1.3960} 3.141 -0030 | .0105 114.1 
563 $7 3932 | .72 2444} 1.2100; 3.077} .0030] .0104 1B) 
542 65 3766 | .69 2406 | 1.1240] 2.985 0030 | .0106 GE 
484 58 3294 | .60 2278 - 9227) 2.801 0030 | .0108 107.2 
431 Sy = GyAclas |) gu 2130 7450 | 2.611 0030} .0110 103.3 
328 39 1998} .36| .1765 4542 | 2.274] .0030{] .0109 98.8 
224 27 PiSSal eee? 1301 2173 | 1.8386} .0030] .0107 93.0 
801 96 5410 99 2371 | 1.9900] 3.678} .0050] .0110 106.8 
801 96 5410 99 2371 | 1.9700} 3.641 -0050 } .0110 105.8 
Tol 90 5197 95 2494} 1.9575 | 3.767 | .005 . 0110 106.7 
701 84 4915 90 2540 | 1.9300] 3.927] .0050] .0108 110.2 
665 80 4682 Sd 2542 | 1.8400} 3.930] .0050 .0108 110.2 
647 77 4558 | .83 2536 | 1.7975 | 3.944} .0050 . 0107 110.7 
618 74 4350 | .79 2512.) 156575 S20! . 0050 . 0110 107.5 
565 68 3948 | .72 2448 | 1.4700 | 3.724] .0050}] .0110 106.5 
534 64 3701 .67 | .2389-| 1.3625] 3.681 -0050 } .0110 106.5 
470 56 3178 | .58 2242 | 1.0980] 3.455 .0050 | .O111 103. 2 
426 ig) SexslD El Say 2115 9261 | 3.294] .0050) .0112 101.3 
307 37 1828{ .33 1679 5306 | 2.903 | .0050] .0107 108. 2 
213 25 1102} .20 1246 2568 | 2.330} .0050] .0106 93.3 
801 96 5410 | .99 2371 | 2.3850 | 4.409 | .0075} .0111 104.5 
796 95 5393 | .98 2388 | 2.4120 | 4.473 | .0075 {| .0110 105.7 
782 94 9339 -97 2431 2.37€0 | 4.450 . 0075 - 0112 104. 2 
748 90 5181 . 94 2498 | 2.3760 | 4.586 . 0075 -O111 106.0 
726 87 5063 | .92{ .2524] 2.3400] 4.623] .0075 O11 106.3 
684 82 4808 -88 -2544 | 2.2590 | 4.699} .0075 - 0110 107.6 
646 hd. 4551 | .83.| .2536| 2.13830] 4.687] .0075| .0110 107.5 
564 68 3939 | .72| .2446] 1.8150] 4.608| .0075]) .0109 107.5 
540 65 3749 . 68 - 2401 1.6925 | 4.515 - 0075 - 0110 106. 4 
487 58 3318 | .61] .2286|] 1.4850] 4.325) .0075}  :0110 104.5 
409 49 2669 |} .49} .2060 |] 1.0820} 4.054} .0075 . 0109 103.1 
311 37 1860 . 34 - 1696 6440 | 3.462} .0075 . 0110 97.9 

: Sal 


i) 
[o2) 
~I 
Ne) 


1 These tests used in deriving formule 27 and 29. 


.0075 | ».0109 


24 


BULLETIN 854, U. S. DEPARTMENT OF AGRICULTURE. 


TABLE 3.—Elements of experiments for clay tile—Continued. 
10-INCH TILE—Continued. 


1 Foe, heya | 5 6 7 8 9 Teg ae 
Depth d Area - Hy- Dis- ie Kutter| Chezy 
Test No. of = of = |draulic] Gharce. | locity. | S!ope- | coeffi- | coefh- 
flow. |- D--|. flows | A> radius. | ©1T2" =| °Chy- cient. | cient. 
| r 
(d) (z) (Rk) (Q) (V) (s) (n) | (C) 
Cu. ft. Feet 
| Feet. Sq.ft. Feet. | per sec. |per sec. 
SO fee eae Na ee nee ene. -809 | 0.97 | 0.5435 | 0.99 | 0.2338 | 2.7715 5.099 | 0.0100 | 0.0110 105.5 
SUS oe ears ae eee ae Sid ees -5389 | .98] .2391 2.7645 5.130} .0075 -O111 105.0 
BUY ee eee eh et eee -744}] .89 -5161 -94) .2505| 2.7070]. 5.245 0160} .0112 104. 8 
SOR Sone ah Sess - 741 -89} .5145 ~94) -.2508 |) 2.7505 5. 347 . 0100 -Oi11 106.8 
Gi bas cee Nee ie eee -708 | .85 - 4957 . 90 . 2537 | 2.6695 5.385 . 0100 -O111 106.9 
DD a eee oe ee See - 705 - 84 - 4939 - 90 - 2538 2. 6485 5. 363 . 0100 -O111 106. 4 
SIG Ses Sse ee eke Ss . 676 - Sl - 4755 87 . 2545 2.5980 | 5.464 . 0100 . 0110 108.3 
SLA SS So eae I oe Renee . 642 Sill - 4523 . 82 2534 | 2.5050] 5.538 | .0100 . 0108 110.0 
Blo eee Ss Ee 577 . 69 - 404 .74 24607} 2.1960} 5.435 . 0100 . 0108 109.5 
DIG Se eg ea ae - 545 . 69 - 3790 . 69 . 2411 2. 0075 5. 297 . 0100 . 0109 107.9 
le se end thet oe . 489 .59 3339 .61 . 2291 1.7325 | 5.196 . 0100 . 0107 108. 6 
Bo SS See eas eet eee . 414 -50 2711 .49 . 2077 1. 2920 4.766 . 0100 . 90108 104.6 
BA cee eee eee . 299 - 36 . 1764 = Bee . 1645 . 7270 4.122 - 0100 . 9106 101.6 
SOA oe Sega eee st . 212 SD 1095 . 20 1241 - 3831 3. 498 . 0106 . 0102 99.3 
2 DA Ba ae ese ea . 819 - 98 5462 .99 . 2288 3. 1220 SETA: - 0125 . 0109 106.9 
2 DA el ae le nga ae 752 . 90 5202 - 95 . 2492 3.0380 5. S41 . 0125 . 0112 104.7 
S75 es ee ei Seen . 697 . 83 4890 - 89 . 2541 2.9750 | 6.085 . 0125 . 0119 107.9 
DIA ge eee ee See Sas 657} .79 4628 | .84]{ .2541] 2.8430] 6.144] .0125 . 0109 109.0 
Doe a sees peg = Sales . 636 .76 4480 - 82 .2529 | 2.7715 6. 187 . 0125 . 0109 110.0 
SLA ae ora ee eek 563 .67 3932 Si .2444 | 2.4030] 6.112 . 0125 . 0107 110.6 
2 eee eee Se En . 928 . 63 - 3653 . 67 .2376 | 2.2080} 6.045 . 0125 . 0106 110.9 
ae eee -4G1 oe 3104 ar) . 2218 1.7950 5.78 . 0125 . 0106 109.8 
SUAS Oe es ee eee ae - 418 . 50 745 . 00 . 2090 1.5120 |} 5.509 . 0125 . 0106 107.8 
Ba Rs see es eee ae HOUSE wed 1836 .34}] .1683 8804 | 4.796} .0125 . 0104 104.5 
Ba Se ee er ee ee eer a 208e rae 1066 -19 . 1221 - 4303 | 4.038 . 0125 . 0099 103.4 
Ba 2 tery eee ee ee 618 74 4350 .79 .2512 | 2.8580 | 6.569 . 0150 . 0110 107.0 
BOOS ED ae See Shee s wees 557 -67 3885 Ok . 2433 2.5380 | 6.53: . 0150 . 0109 108.1 
3525 eee eee eee . 926 . 63 3637 . 66 . 2372 | 2.3670} 6.509 .0150 | .0108 109.1 
OO es ep eee oe | 457 So 3070 - 56 . 2206 1. 8480 6.018 . 0150 . 0110 104.6 
BOO! wae eso eee | 3392 47 2527 . 46 . 2003 1.4120 | 5.587 . 0150 . 0110 101.9 
Shes oes ee ye A . 300 .30 1772 ey. . 1650 . 8854 4. 997 . 0150 . 0107 100.5 
De Ona tte see ty ene te - 215 . 26 1117 . 20 . 1256 -4462 | 3.995 . 0150 . 0108 92.0 
12INC H TILE. 
Boe | a eae ee ee 0.986 | 1.00 | 0.7631 | 1.00 | 0.2464 0. 8972 1.176 | 0.0003 | 0.0108 105.9 
is (YE a a een Ne oe ey - 896 -91 . 7286 -96 . 2922 +. 9006 1. 236 - 0005 -0115 102.3 
37 LP ieee Ses oe ease ae Aaa - 856 - 87 - 7037 .92 . 2975 -8540 } 1.214 - 0005 -0118 99.5 
ee tpt FOS SR ee - 803 81 - 6657 -87 - 3000 - 8380 | 1.259 - 0005 -0115 102.8 
Bi Eid Serie eC aoe ee oe - 754 -76 . 6263 82 - 2985 -7360 | 1.175 - 0005 -0121 96.2 
Soe ae ee ah Ne - 694 - 70 - 5743 ~75 . 2924 -6762 | 1.178 - 0005 - 0120 97.4 
ab Re ee Se ee aa . 650 - 66 - 5338 .70 - 2857 - 6496 1.217 - 0005 -0115 101.8 
AO Set ee be teint 592 . 60 - 4786 . 63 2738 . 5390 |. 1.126 - 0005 -0119 $6.3 
31 (a ae ee eee pe a | 558 -57 - 4456 .58 . 2654 - 5006 1.124 - 0005 -O117 97.6 
By tod SS ee eee 2 eee ee | . 502 -51 . 3906 21 2493, - 4261 1.091 . 0005 -0115 97.7 
DAD aan ene -412 -42 - 3022} .40 2181 - 2754 -911 - 0005 - 0122 87.3 
EU si Rene Misc Oe ii |. 3067] )-3Es|" ©2019 27 | 21732 Fe S1aI8h -S752 V5 O00 aa ane Gos 80.8 
SO Ree shes ee Seep 2931 -95 . 7464 -98 -2841 | 1.4350 |- 1.923 -0010 | .v107 114.1 
Bs ee ee ee es ag - 846 -86 . 6970 91 -2984 |} 1.3430 1.927 - 0010 - 0109 PACS 
Ss ea aCe Salm ae - 194 -81 - 6587 -86 . 2999 1.2660 | 1.922 - 0010 -0110 | 111.0 
A ie Ee ee be spertoo 74 . 6060 79 . 2964 1.1320 | 1 868 - 0010 -O114 108.5 
Sepa eye Seok fe nie pe a } 697 -71 - 5769 7 2927 | 10500; 1 820 - 0010 - 0113 106.4 
OR eee eas or ee ae - 046 - 66 - 5300 -70 - 2850 -9516-| 1 795 -0010 | .0112 106.3 
SER me es a ep ese ee ab ah - 601 -61 - 4873 - 64 . 2756 . 8508 1.746 - 0010 - O12 6. Oba 
Oy Mareen wR at oy eee EES | 555 -56 - 4427 -58 - 2646 .7360 | 1.663 -0010 -0114 | ©1022 
SOM igs eee ya 501 | .51 | .3896} -51 | .2490 .6170 | 1.584} -0010| .0115 | 100. 
215 |e ee ete ee Dene ae ee -390 -40 - 2809 33% - 2094 a Yi) ee Be Pe) . 0010 -0118 91.7 
Sid Be of alge a ete eee eee . 296 -30 - 1928 Boe) - 1686 .2026 | 1.051 . 0010 . 0124 80.9 
Og a a Cole et ee ee 974 .99 . 7614 .99 -2640 | 1.9080} 2506] .0020 .0109 | 109.1 
Oe heres eter MY 3 .853 | .87 - 7017 - 92 .2978 | 1.7200 2.451 . 0020 .0120 100.4 
SO eae Be ee . 807 .82 - 6687 -88 . 3000 1.6900 ATPL - 0020 .0117 103.2 
Ae eee ae ae ee . 764 | -78 - 6346 -83 . 2991 1.5550 2.450 . 0020 .0120 100.2 
SOO Me ree ee eS -701 -71 - 5805 .76 -2932 | 1.3900} 2.394 . 0020 -Q121 | 98.9 
SOP am wee oe Pos SN. 4 | 646 - 66 - 5300 .70 2850 | 1.1960 | 2.256 . 0020 . 0124 94.5 
Bee eer os eee aE ee -590 . 60 - 4767 - 63 2733 1.0160 2.133 . 0020 .0127 91.2 
OD ary ee ee ye A 549 -56 - 4368 =O | -26380 . 8904 2.038 . 0020 -0128 88.9 
SAO Resins ee ee ee) ae I= o2504. = -3925 ~-51 | .2499 . 7450 1.898 0020 -0131 84.9 
Sy Let Fo ee ey DN - 406 -41 - 2964 -39 | .2157 S4650e)) Leon . 0020 -Q140 75.6 
31 (PAS Re eh eat sn 2 PR [ex 298 -30 - 1947 ~26 1 .1695 .2340 ' 1.202 - 0020 - 0148 5.36 


1 These tests used in deriving formule 27 and 29. 


e 


THE FLOW OF WATER IN DRAIN TILE. 


29 


TABLE 3.—EHlements of experiments for clay tile—Continued. 


12-INCH TILE—Continued. 


1 2 3 4 5 6 a 8 i) 10 11 

Depth Area Hy- P Kutter} Chezy 

Test No. of w of © | draulie eae 1 ate Slope. | cceffi- | coefii- 

fiow. | P | fiow radius. Be y cient. | cient. 

(d) (a) (Rk) (Q) (V) (s) (n) (C) 
Cu. ft. | Feet 
Feet. Sq. ft Feet. | per sec. | per sec, 

UO Mees ne ane oe eins 0.887 | 0.90 | 0.7234 | 0.95 | 0.2938 2.2320 | 3.086 | 0.0030 | 0.0116 103.9 
ase eta sr seen a eee a . 853 87 - 7017 -92 .2978 | 2.1840] 3.113 . 0030 . 0116 104.1 
OM Daae Sa eee een . 809 -82 .6702 | .88 -3000 | 2.0800 | 3.103 . 0030 .O117 103. 4 
SOS eee ee ed Se e008} .78 -6420 | .84 .2995 | 1.9450 | 3.030 - 0030 .0119 10:.1 
SU Sa ets RES as . 7124 ode - 6007 -79 -2957 | 1.7980 | 2.992 . 0030 . 0120 100.5 
SUSAR eis Sr Stor . 693 .70 5734 275 - 2923 | 1.6100] 2.809 . 0030 . 0124 94.9 
BD) a ses Sivas a NN ee eat - 646 . 66 - 5300 -70 -2850 | 1.4400 | 2.717 - 0030 . 0126 92.9 
SO eee ie eis sare . 603 61 - 4893 - 64 -2761 | 1.2560} 2.567 - 0030 - 0129 89.2 
Patol eee Oe el ee ee seme 547 56 - 4349 57 . 2624 1.0260 2.360 . 0030 - 0134 84.1 
Don Me een ne eee Ss oe 500 51 - 3886 -51 . 2487 -8440 | 2.173 - 0030 - 0138 79.6 
BOOrE eee eee eae - 402 41 . 2925 -38 - 2142 -5222 | 1.785 - 0030 -0147 70.4 
Coes Gel be aa maces e - 303 -3l 1992 - 26 -1718 sloie| ole OTe . 0030 .0158 60.5 
Bie See Seer eee ere -974 99 . 7614 .99 . 2640 | 3.0380 | 3.990 . 0050 . 0109 109.8 
SO OMe ie Near ae - 940 95 7504 98 - 2811 3.0030 | 4.002 . 0050 .0113 106.8 
BANC ice aa) i as rec aa -878 89 - 7179 94 -2952 | 2.8400} 3.956 . 0050 . 0117 103.0 
OSS eee ees Erber a 817 83 . 6763 89 -2998 | 2.5440} 3.762 . 0050 0124 97.2 
BOO Re eee abies Cora oars 741 75 . 6154 81 -2975 | 2.1300] 3.461 . 0050 0131 89.7 
BAU) Biss ni ee es eee Oe -696 | .71 5760 | .76 | %2927| 1.8400] 3.195} .0050| .0138 83.5 
OO aE poe oe ie Se - 644 - 65 - 5282 - 69 -2846 | 1.5650 | 2.963 - 0050 . 0144 78.6 
SACS es SE Be eet eas .597 61 4835 - 63 2748 | 1.3550 | 2.803 . 0050 .0147 75.6 
BOB Aye rer ee eae - 552 - 56 - 4398 -58 - 2638 | 1.1660 | 2.651 - 9058 . 0150 73.0 
ODA et es eRe Waa - 509 52 -3975 - 52 . 2514 .9838 | 2.475 . 0050 0154 69.8 
OOD REN en patos cnr Serer - 409 42 . 2993 39 . 2169 - 5981 1.998 . 0050 . 0165 60.7 
BOO eee bee ed ne -313 7102 - 2083 27 -1765 -3259 | 1.564 . 0050 0175 5225.7 
Ope eee gents Re La .723 | .73 | .5998] .79] .2956} 2.9890} 4.983] .0075 | .0114 105.8 
DO See ee ae eset . 688 - 65 ~ 5225 - 69 - 2834 2.5440 4.869 0075 0114 105.6 
OO ee mircnee tiie eae ee ol - 584 59 4708 - 62 . 2719 2.1480 4.563 - 0075 0117 101.0 
AQ 2 ee eee Sa se ee - 563 57 4505 59 - 2667 | 2.0500 | 4.551 -0075 | .0117 101.8 
A (ese ioe eek eee -512 52 4004 . 83 -2523 | 1.7400 | 4.346 .0075 | .0117 99°.9 
QD ie aes Sena be. clei . 388 -39 2790 30 -2086 |} 1.0180} 3.651 - 0075 - 0120 92.3 
A () Biya Seat Se sea io Se .302} .31 1983 26} .1714 6250 | 3.153 -0075 .0119 87.9 
404 ee ees Se eee ae ee .651 | .66} .53847] .70} .2858] 2.9400] 5.498] .0100} .0117 102.8 
CA iS eee ene eta ars . 598 61 - 4844 . 64 -2750 | 2.6170 | 5.403 . 0100 .0116 103.0 
AG ae aes ere a - 546 -55 - 4339 JONG . 2622 | 2.2980 | 5.297 . 0100 -0114 103.5 
ATES eae She aaa - 494 50 -3827 50 .2468 | 1.8400 | 4.809 - 1000 . 0119 96.8 
ASS ene es oa aan aaa -413 -42 . 3031 -40 .2184 | 1.2960] 4.276 - 0100 -0121 91.5 
GNU Sire see ear, One er eres .307 | .381 | .2028] .27) .1787 .6972 | 3.488 | .0100 |} .1026 82.5 
AN OB ape R Ges eyo se eee he -496 | .50 3847 50 .2474 | 2.0150 | 5.239 .0125 .0122 94.2 
HUG bese ee See ere ate a oer ee -419 - 43 3090 41 . 2207 1.5400 4.984 0125 0118 94.9 
A Dre oe ioe ae ees es 321 -33 2157 28 -1801 .9694 | 4.495 0125} .0114 94.7 
2 PB Nes areas eet ca are - 459 -47 3482 -46 . 2351 1.9600 | 5.630 -0150 | .0120 94.8 
Co MAS erage es enn ts Se ne ee -444 -45 - 3335 ~44 .2299 | 1.8575 5.570 - 0150 0119 94.9 
EU eee one eee eye - 403 41 - 2935 39 -2145 | 1.6150 | 5.525 - 0150 -0116 97.0 
SQ ie epee ee ee . 284 29 1820 24 . 1629 -8639 | 4.747 | .0150 |] .O111 96.0 


1 These tests used in deriving formule 27 and 29. 


26 BULLETIN 854, U. S. DEPARTMENT OF AGRICULTURE. 


TAPLE 4.—Elements of experiments for concrete tile. 
4INCH TILE. 


1 2 3 4 5 6 af 8 9 
Depth; gq Area a Hy- Di Vv. 
Test No. of = of =z |draulic aS | Slope. 
flow. | P| flow. | 4 |radins.| Chatee: | locity. P 
| - (d) (a) (R) (Q) EB) (s) 
Cu. ft. Feet 
Feet. Sq.ft. Feet. | per sec. |\per sec. 

SS ae RS oe 0.328 | 1.00 | 0.0845 | 1.00 | 0.0820 |} 0.0426] 0.504 | 0.0005 
oT Be tay atleast) A Aare ceca ze F 48 tell Pe UP BI hese ean DEER - 0386 -499 | .0005 
CATA Sa gee ee -247 |} .75 | .0683 81} .0990 - 0335 -491 - 0005 
1 UE Sate ag Ses Ree NONE oe -206 } .63-1 .0559'] .66 7 -0930 . 0196 -315 | .0005 
ASIEN SEES 2S Ba key 7 Nesey | -0432 | .51 - 0829 - 0120 -278 | .0005 
TD NS I apn Ee -118 | .36] .0274] .32{| .0649| 2.0020] 2.075] -.0005 
AD See e ees tiaie we ee -o11 | .95 | 50828 | .98.4- .0941 . 0650 -785 | .0010 
7) nal eee a een Pee -274 | .841 0754) .894 .0997 - 0550 .730 | .0010 
Ze Sars oo ee epee tee 239 73 0660 78} .0982 0450 682 0010 
AGH as eee eS See 210 64 0571 68 | .0938 0375 656 0010 
GY Ee Sore Nie een Never ares aes - 163 50 0419 50 | .0817 0218 519 0010 
AOS ea encase en se SS SES -118 36} .0274 32} .0649 0083 301 0010 
ESS Se ea ee 323 99 0842 99} .0890 0832 988 0020 
ies eae a a ae 271 83 0747 88 | .0998 0800 | 1.071 0020 
AS es ane ee ee 243 74 0671 79 | .0986 0650 968 0020 
BB eR ag ee re SS 215 66 0587 70} .0948 0544 927 0020 
PS ee. hy ee A 162 49 0416 49} .0814 0280 673 0020 
ADA ee ean = Oa See see 124 38 0293 | 35] .0674 0127 434 0020 
ZS ba SCPE cap aiaeeerball opera 323 99; .0842 99 0886 1014 | 1.204] .0030 
114 theses yas een reece 295 90 | .0801 95 0978 1041 1.300 | .0030 
AST eee om ae ae aS 271 83 0747 88} .0998 0969 | 1.298 | .0030 
A Ree sre Met ents oe a Sts ae 243 74 0671 79} .0986 0848 | 1.263 | .0030 
LENS eee Sy ae eC 211 64 0575 68} .0940 0591 1.028 | .0030 
BA eee ee oe Se mere 160 49 0409 48 | .O807 0298 727 | .0030 
LT eee, peg eee 118 36 0274 382| .0649 0130 475 | .0030 
2 ae ee ea ae | I 315 96 - 0834 99 0928 1415 | 1.697 | .0050 
A Ae Pn ape oe Sonik 276 84 0759 90 0996 1235 | 1.627 - 0050 
ob Ee ees ee ee eg era 243 74 0671 79} .0986 0996 | 1.484 .0050 
AA Ee Ee ea eee 2 212 65 0578 68} .0943 0788 | 1.364} .0050 
DAG ee eens Reg Ps ae 170 52 0442 52+ .0838 0478 | 1.081 - 0050 
LY RE ere oan ene 121 37 0283 34] .0661 0200 706} .0050 
AA RH a2 ere see 305 93 | .0819 97 0959 1775 | 2.168 | .0075 
7 Se a ee ea a 290 88 0790 94 0985 1686 | 2.133 - 0075 
40s ose ee Eee 269 82 0742 88 | .0998 1459 | 1.968] .0075 
2 ee a ine ee Be 252 77 0697 83 | .0994 1299 | 1.866 | .0075 
SI as Te NRE eae 222 68 0609 72 0961 0956} 1.571 - 0075 
1 Ee iin 5 Ae NS Seta ge aes 191 58 0511 61 0897 -0696 | 1.362} .0075 
AOA Ras se a eet 173 53 0452 44] 20847 0594 | 1.314] .0075 
SA ta ee ts Ts 296 90} .0803] .95 0976 1931 | 2.406} .0100 
vl Cyberspace 291 89 0792 94 0984 1905 | 2.404} .0100 
SLY (ok es ale cea ee a 278 85 0764 $0 0995 1686 | 2.208 | .0100 
ZL PSSn ais  e 2t a Re 249 76 0688 81 0992 1382 | 2.008 | .0100 
EU a irae Mine se rae aia a 209 | .64 0568 67 0936 1046 | 1.840} .0100 
21 @ Uap ea I ei Ee earn oe 165 50 0426 50 0823 0622 | 1.461 - 0100 
A et irae leh oe ae -301 OF OSI 2H as 0 . 0967 2200 42a - 0125 
Ze) fy eT Ee eS ee as .287 | .88] .0784} .93] .0988 3212444 22709) | 0125 
AG ite een ree ee Serer 3242:1 . 744-0668) 79-4 >. 0985 .1656 | 2.478 | .0125 
AGA = (SES Sees ae S204 45 6221 e-Odo2te--bo th 0geb 21377 | - 2-492.) 0125 
AG DSS hd Beene eR -196 | ~.60 | .03896}] .47 7} .0793 -0760 | 1.918] .0125 
AGG <2 ee ero eee ae - 133 -41 | .03822] .38] -0710 -0416 | 1.293 | .0125 
ay ine 5 ae eee ee 314} .96 | .0833 .99} .0931 -2544 | 3.056] .0150 
AGS Ee Samo Nr eh eee - 302 . 92 - 0814 - 96 . 0965 - 2456 | 3.018 . 0150 
ARG rises. eee eet -274| .84] .0754] .89] .0997 - 2236 | 2.965] .0150 
TA pe eke 3 RL Je es fe SDR5 i aS 1a OV Obule 3605 meoUG . 1892} 2.684] .0150 
Af APN te P Soer a a os oe . 224 . 68 - 0615 Sides . 0964 -1506 | 2.449 - 0150 
Ae Se aS eer ee -159 | .49] .0406}] .48} .0804 -O848 | 2.088 | .0150 
TANS ios eee ae ean a .123 -38 . 0290 .34 . 0669 - 0438 1.511 - 0150 


10 


Kutter 
coeffi- 
cient. 


t 
ee ry 


| 


11 
Chezy 


coeffi- 
cient. 


(C) 


i) 
fat De HS > ST ST 
wes SS oo 


SNBSNG FSRWHA AVISE ATASHS 


SUISIOO OO ROW DR AT OR MODO HUNOIWOUDO OnMDDNHNOO RPNNRODO BOWDOH PROD RO RR wnTON 


BS8SNS SSESIN CVSBISS 


1 ~100 
BO 


69. 


1 These tests used in deriving formule 26 and 28. 
2 Evidently an incorrect hook-gage reading. 


THE FLOW OF WATER IN DRAIN TILE. De i} 


TABLE 4.—Elements of experiments for concrete tile—Continued. 
5-INCH TILE. | 


1 2 3 4 5 6 7 8 9 10 1 | 
Depth Area : Kutter | Chezy | 
Test No. of 5s of 4 draulic ee 1 he Slope. | coeffi- | coeffi- i 
flow. flow radins json y- cient. | cient. \ | 
(d) ©) (F) (Q) (V) (s) (n) (C) 
ay fameaeietneet Fe meee Bt a ce De eae ese if 
Cu.ft. | Feet 
Feet. Sq. ft. Feet. | per sec. | per sec. 
ATA Ma Sees Bi ie 0.396 | 0.96 | 0.1319 | 0.99 | 0.1169 | 0.0844 | 0.640 | 0.0005 | 0.0110 83.7 
AONE Saracen Seine 3808 | .75|, .1071) .80] .1243 - 0671 -627 | .0005} .0116 79.5 
IASI Sales) Nas acpi Ce ae ne 221 | .54) .0729) .55] .1076 - 0346 -475 | .0005) .0131 64.7 
AUT a poets ge eae IA -405 | .98] .1882] .99 | .1125 . 1305 -980 | .0010} .0103 92. 4 
A Biers eee ee Bema -293:' | 71} 21016 |). 76) 2 1227 . 0969 954} .0010} .O111 86. 1 
CNA igs re tl gS anal -206) .50] .0667) .50] .1031 . 0448 G71} .0010 4) .0130 66. 1 
480......- eae eee .184 |) .382]) .0377) .28{ .0752 . 0196 -521 } .0010 | .0130 60. 1 
ASI Rie sete) ese a ene ~093 |° .95 | .1314 7) 2987 1179 .1840 |} 1.40 -0020] .0106 91.2 
AS DRS Ria sean oA ya -317 | .77 4 .1102) .82] .12051 -1608 | 1.459} .0020] .0107 92. 2 
AS eiegey ee eae eed es ee .223 | .54] .07388 | .55] .1082 .0848 | 1.150} .0020] .0117 78. 2 
Ae eae ees ees 171 | .41{ .0524{ .39] .0907 . 0466 -890 | .0020} .0127 66.1 
AS Re ee Sree eee wen eb .126 | .31| .0846] .26) .0715 . 0256 -740 | .0020} .0126 61.9 
ARGU erase ees eee 404] .98} .18381 ) .99} .1181 - 2303 | 1.730 | .0030] .0104 93.9 
AS (Pees eerie ES -310 | .75{ .1078| .81] .1246 .1853 | 1.719 | .0030] .0110 88.9 
AS Sitemap pence Sirs 209} .51] .0680]) .51} .1040 0828 | 1.218) .0030] .0127 69.0 
NS Ore gees in le SSE 159 | .88] .0475 | .36] .0859 . 0404 - 851 .0030 | .0146 53.0 
AO Reh ee See 119) .29] .0319} .24] .0683 - 0150 -470 | .0030} .O191 32.9 
AO Beton Ges oie ease O08 |) 96:| 323) 13994 . 1160 .3052 | 2.307 | .0050] .0103 95.8 
AD Degas oes Se ~218 | -..00)) 209597)" 72). 1207 2020 | 2.107} .0050} .O0113 85.8 
Ls eels eo ees ee 193 | .47] .0613 | .46] .0987 .1023 |} 1.668} .0050] .0119 75. 1 
A OA a mie cee ee 159] .38) .0475| .36) .0859 . 0622} 1.310) .0050] .0130. 63.2 
AQ OR a eateries san 114} .27] .0301 23} .0659 . 0283 940) .0050}] .0139 52.2 
AD Geter ere ar ne 893 |e Oo ioe IBIAS. 08s 1179 .3563 | 2.711} .0075 | .0107 91.2 
AO [ete ypree mre ee .316 |] .77 | .1099) .82]| .1250 .2814 | 2.560) .0075; .0116 83.6 
de ene, es ee eae 196 | .47 | .0626) .47] .0997 -1349 | 2.154 | .0075] .0115 78.8 
AO esis SEGA s ols 146] .385] .0423 | .32] .0805 .0748 | 1.767 | .0075} .0117 diss9 
DOOM tee Pee ee Se ek .126 | .31] .0846] .26] .0715 . 0439 | 1.270 0075 | .0138 54. 8 
RUN) Bo Sew gee -404| .98| .13381}] .99] .1131 - 4282 | 3.218} .0100] .0103 95.7 
Bass Asienceia ener eens 298) .72] .10384] .77 | .1233 8105 | 3.003 | .0100] -.0114 85. 5 | 
OUD Ses mia eee ae 224) .54}] .0742) .56] .1085 - 2318 | 3.124} .0100} .0102 94.9 i 
DOLE eee cee ene -195 | .47} .0614| .46] .0987 .1644 | 2.680} .0100} .0109 85.3 | 
OU OES a ea ene os .1385 | .33! .0380] .28) .0757 -07386 | 1.935; .0100 | .0117 70.3 | 
DUG rete tee ee -396 | .96} .1319) .99] .1169 -4669 | 3.538 | .0125] .0106 92.6 | 
DU psec ee eee -312] .76} .1085] .81 . 1247 -3660 | 3.374] .0125)] .0114 85, 4 
DU Sseae srs ee eee - 231 . 06 0771 -58 | .1104 -2688 | 3.489 {| .0125) .0104 93.9 H 
Os ets Re ee -188 | .46] .0593 {| .44] .0970 1892 | 3.189} .0125} .0102 91.6 ] 
OL OMe cee eset see as ie -129} .31] .0357| .27] .0729 -0920 | 2.574] .0125) .0101 85.3 
GL esse Re es Sa -401} .97| .13827{ .99]) .1147 -5162 | 3.891 | .0150}; .0104 93.8 | 
OUD se ae ate Sa 823 | .78| .1123 | .84] .1254] -.4565| 4.065] .0150}| .0107 93.8 
Og ee as asec ee peer ee -261 | .63] .0892] .67) .1174 -3150 | 3.533 | .0150 | .0114 84. 2 } 
OU set gee a Ne oes sen -176 | .43 | .0544]) .41}) .0926 1548} 2.846] .0150}] .0116 76.4 
| 
6-INCH TILE. 
z 
Ose iS as pee Sees ase 0.492 | 0.99 | 0.1937 | 0.99 | 0.1325 | 0.1366 | 0.705 | 0.0005 | 0.0111 86. 6 | 
DIO Spee ace ee ce sia -o91 |} .79| .1637] .84] .1510 - 0888 -542] .0005 | .0145 62. 4 
OMe SS psenis: o hace the -282 | .57) .1186] .59] .1340 . 0463 -408 | .0005 | .0164 49.8 
OMe atv a oan ages 225) .45] .0853}] .44] 1163 . 0343 -401 -0005 | .0154 52.6 
Ue ee tea se eee 173) .35] .0601} .31)| .0958 . 0206 .343 | .0005 | .0152 49.6 : 
SYA) ii as encima erm 484) .97] .1926} .99]| .1375 .2187 | 1.136} .0010/} .0104 96.8 
GD ES ese te oop nT so845| oud | 16081 288 | 1508 |) .1795.| 1-116 | +0010) 0110 90.9 | 
BY ia Pe Saar ia res Sse 298; .60} .1214] .63] .1379 - L070 -881 | .0010 | .0126 75.0 | 
OO ee Sea eee .222| .45] .0838{ .43] .1152 . 0535 .638 | .0010 | .0142 59.5 
ODA pa ee ar pie Te oh 176] .35] .0615} .382| .0971 0295 -480 | .0010 |) .0159 48.7 
oO ses rene eset eee -481 | .97 | .1921} .99) .1390 -3026 | 1.575 | .0020 | .0107 94.5 | 
OVA Rea Wi cise esa eeete mes dtl -75 | .1553} .80] .1498 .2378 | 1.531] .0020) .0115 88.5 | 
OD ose see eee SS -293 | .59} .1190] .61 | .1368 -1578 | 1.326] .0020} .0121 80. 2 
eae pare ha tS a eee -216| .43] .0809}] .42] .1130 -0880 | 1.088} .0020 | .0124 72.4 | 
DOOM a a ee oe -170 | .34| .0587{ .30] .0944 - 0459 .783 | .0020] .0142 57.0 
1These tests used in deriving formule 26 and 28. | 


28 BULLETIN 854, U. S. DEPARTMENT OF AGRICULTURE. 


TABLE 4.—Elements of experiments for concrete tile—Continued. 


6-INCH TILE—Continued. 


1 2 3 4 5 6 | 7 | 8 9 10 | iB 
Depth | Area | Hy- : = Kutter} Chezy 
Test No. pit Rese cae © | draulic DS 1 we Slope. | coeffil- | coeffi- 
flow D | flow. | A |radius.| ©12t8e- | 70etty. cient. | cient. ' 
} | | 
(d@) | (a) | (R) | (Q) | (*Y) | @& | ® | ©} 
| 
| Cu.ft.| Feet | 
Feet. Sq. ft. | Feet. | per sec. | per sec. 
a Re Sa ao eee 0.489 | 0.98 | 0.1933 | 0.99 | 0.1346 | 0.3831 | 1.983 | 0.0030 | 0.0103} 98.7 
spies eens ree -383 | .77-| .1604| 83] .1507 .3177 | 1.981 | .0030] .0111 93.1 
Fo Sere Ree a a Se od 273) .55 1091 | .56] .1315 | .1795| 1.644] .0030|] .0117 §2.8 
eo eels nee Ee a te .222} .45| .0839| .43| .1152] .1190|] 1.419] .0030| -.0121 76.3 
Sa St oe SOEs fea a 164] .33]| .0558] .29] .0919] -.0550| .985| .0030 | -0137| 59.4 
Ta GSW S| ot Be Bee na ee -480| .97]| .1919| .99| .1394] 74335 | 2.259] .0050| .0116 85.6 
See et ee ae 385] -77| -1612| .83] .1508| .3915| 2.428] .0050) .0115 88.4 
ie aoe: Denne ely eee 970| .541 1077]. .56| 1307] .2082] 1.93 .0050 | .0126 75.7 
Rie beets Paha cles = Te 210| .42| .0779| .40| .1108] .1250| 1.6041 .0050| .0129 68.2 
ye See Ree | .151] .30] .0498| .26] .0858| .0615| 1.234] .0050] .0135| 59.6 
Bye AEE > ae 480 | .97| .1919| .99] .1394| .5874| 3.061] .0075| .0108; 94.7 ; 
Rie Seas; See ee 384] .77| .1608| -.83}] .1508| .4691 | 2.917] -0075| 20117} 7 Sas p 2 
ROMY Oe ee sees 272| .55| .1087| .56]| .1813| .2680| 2.466| .0075| .0121] 78:6 
GP inl See he 5 eae | .212] .43] 0789] 41] .1115]| .1602] 2.030] .0075| -0126| 70-2 
(Foe oe Ogi os Seen [P5149 |e 20) OSTA ae 4 0633 | 1.383] .0075| .0139| 55.9 
ade eee eeee ee |. .473| 95 | <1905 |~ .98 | - 1491 6238 | 3.274] .0100| .0116 86.9 
ee poeeeees resee are "365: | oy Biya Peay .1491 .4807 | 3.148 | .0100| .0123 81.5 
ea, Se 278 1 a5Gil) =. MAGI ASB 1929 .3186 | 2.854] .0100} ~.0123 78.3 
Pinseye eer tee: S .212| .43] .0789] .41] .1115 -1991 | 2.523] .0100| .0122 75.5 
He, age ote -144] .29| .0466] .24] .0825 .0904 | 1.939] .0100] .0128 7.5 
ff Epa At ee .440| .89} .1816] .94| .1492] .6874| 3.785] .0125] 0116 87.7 
ng ltee yee es See Hebe > Lal Uae fd Rae Uy ps7 9) leaes ye bak Tt) - 6818 | 3.815} .0125 | .O114 88.1 
ATP eet a ae oan Jecae 35 7 -1460| .75| .1474| .5306] 3.635] .0125]| .0118 84.7 
Gs ie a pees 41 5 .1047 | .54| . 1289 .3402 | 3.249] .0125] .0119 80.9 
ATL seege Oh Se ee eee -202 | .41|° .0740| .38| .1077 .2096 | 2.832] .0125} .0119 Tee 
Sp RACES DERE Ie ihe -132| .97| .0413 | .21] .0767) .0706 | 1.709] .0125) .0139 55.2 
| 
Soies eae os! 2 .485 | .88| .1800| .93| .1497 7705 | 4.280] 0150] .0113 90.3 
CAF (eee oe ge ee Se Bd oma 1469 | .7 1477 5941 | 4.043] .0150| .0117 85.9 
Gal ar ee eg ee eo D581 1 bod AOUZ | oe lant 3630 | 3.569} .0150| .0118 81.7 
BQ ele iste cas -193 | .39| .0696| .36] .1041 2325 | 3.339] .0150| .O111 84.5 
3 el = Oo eee ss eee | 123 25 0874 19 0723 0936 | 2.504] .0150] .0110 76.1 
sINCH TILE = 
| [ 
Bhi ae Se 1645 170.9810. 2a89 0.99 | 0.1803 0.3096 | 0.914 | 0.0005 | 0.0109 96. 2 
RGQi)< swh nee a | Sige | .642] .98| .3383| .99] .1818 3096 915 | .0005| .0109 96.0 
Efsie Pie a = abe | 1547] .83| .3024| -89| 2002] - -2873] 950] .0005| .0113| 94.9 
Bete ON eee ae | ":479:| 73 | 226551 178 1 1970 2187 824} .0005| .0124 83.0 
7 i neh bs sae cane [=a |) Gil ESB GS | EROS 1957 840 | .0005] .0120 86.3 
EG tale re 319d 481 < 1635 48 | .1612 1105 676 | .0003 | .0128 75.3 
i 77 OE Ge Ra ee Tie | PER A. a8 ho 21237) | 236i ert ano 0720 582 | .0005| .0134 69.8 
PERU ere Se oe 2 ets0el 27 S0Tss | 2a tere 0323} .428| .0005| .0137 59.3 
i 
Df Sa tarde ee hese te | 1654] .99] .3402] .99| .1720]- .4440|] 1.305] .0010| .0107 99.5 
(Tune a Sg ae aa 625] .95| .3341] .98| .1888 .4261 | 1.276} .0010} .0116 92.9 
Byles Ved soe ee 554] .84| .3058| .90| .2000| .4104] 1.342] .0010] .0115 64.9° 
ipa ah ene eee ARTA Se .2666 | .78| .1972] .3278| 1.227]. .0010] .012% 87.6 
7 ik er ees ee PON a ee 428] .65| .2343] .69] .1897| 2839] 1.212] .0010| .0120 88.0 
By Ce on eee eg SU age ASR 7 1585 | .1638 | 1.036] .0010| .0121 82.3 
Te ee octet ec 253 | .38| .1205| .35] .1368| 1130 .937 | .0010 | .0120 80.1 
RaGriee tes. Se Ni dacess 7A Weg fs PN YO eee [ee Lr 0463 628 | .0010| .0136 62.0 F 
77 Ween ee eee ee 648 | .98| .3394] .99]| .1782|} .6373} 1.882] .0020] .0109 99.7 
771 is ae a, oe Sie .640} .97| .337 .99| .1828/ .6496] 1.923] .0020] .0108] 100.5 
Bp adie ae TRG > ake | 2565s a2 SE SIMO ed 1994} .6035] 1.940] .0020| .0113 97.2 
LS a oe RS es | .496-| .75.|- .2752) 84 1988 |  .5090} 1.850] .0020| .0117 92. 4 
Cis fan a Oe a ene SIO 3 | e441 268-2467 1: Te as .4387 | 1.778] .0020| .0119 90.7 
Mpegs ais ate. <7 ee | .335| .51 | .1741| .51] .1664| .2616] 1.503] .0020 |> .0124 82.4 
Faience Seat. > ag l I 26s 40 1270} .37] .1409| .1602] 1.260] .0020! .0128 75.1 
Gee Pen air = Barns, } .180 27 0735 | .22| .1042} 0664 -879 | .0020 0139 60.9 


1 These tests used in deriving formule 26 and 28, 


THE FLOW OF WATER IN DRAIN TILE. 29 


TaBLe 4.—Elements of experiments for concrete tile—Continued. 
8-INCH TILE—Continued. 


1 2 3 4 5 6 7 8 9 aelhG 11 

Depth| 4 Area _ Hy- Di Vv Kutter | Chezy 

Test No. of we of = |draulic is -°- | Slope. | coeffi- | coeffi- 

flow | D | flow radius.| Charge. | locity. cient. | cient. 

(d) | (a) (RF) (Q) V6 (s) (n) | (C) 

Cu. ft. Feet 
Feet. Sq. ft. Feet. | per sec. | per sec. 
Ey ppb yap icone eisai ee ra 0.643 | 0.98 | 0.3385 | 0.99 | 0.1813 | 0.7870 } 02.325 | 0.0030 | 0.0109 99.7 
TRS Gil eee, Meter tang gait carrey - 623 -95 . 3334 -98 - 1894 . 7750 2.324 - 0030 -O112 97.5 
yO ieee peat apace ae ay ee - 003 - 84 - 3053 -90 - 2001 . 7240 2.301 . 0030 .O114 96.8 
ENC YS Sli, Stone oi ee oe - 489 .74 . 2712 - 80 .1981 . 6224 2.295 - 0030 . 0116 94.1 
ES RO en ie rrr rg nt eo - 445 -68 . 2449 57 . 1928 . 5440 Za22M - 0030 .O118 92.4 
GON es oe Seer . 341 Auiy? . 1780 202 . 1682 . 3304 1. 884 . 0030 . 0123 83.9 
Ey GiM pamper ee GE tay ee - 262 -40 . 1263 Sei! . 1405 . 1886 1.492 . 0030 .0131 Patt 
IO Ase eke Races oe eree - 182 28 . 0767 -23 . 1051 . 0824 1.075 - 0030 .0140 60.8 
EC 2 es See ee . 647 -98 . 3392 -99 . 1789 1.0105 2.979 . 0050 . 0109 99.6 
OAR ie oars ee oe -628 | .95 - 3349 .98 1877 1.6164 3.035 . 0050 - 0110 99.1 
SOS 5s ose, aS See eee - 623 95 . 3384 -98 . 1894 .9930 | 2.978 . 0050 -0113 96.8 
BOD Sau Sat See ae ee - 566 . 86 -3115 .92 . 1993 .9108 2.924 - 0056 . 0117 92.7 
BO Leese ekeeeeaese -512 -78 . 2841 -83 . 1999 . 8028 2. 825 - 0050 .0121 89.4 
5O Ooo ats ae eae ee - 443 . 67 . 2437 ol . 1924 . 6440 2.642 - 0050 - 0124 85. 2 
SOG eae 2 eee ot aes -318 .48 . 1629 .48 . 1609 . 3610 2.216 - 0050 - 0128 78.1 
TOD a Ge aa eee ee eee - 270 -41 . 1315 .39 . 1436 . 2608 1.983 . 0050 .0130 74.0 
GO ee eee cee . 189 -29 - 0808 SoA: . 1085 - 1140 1.411 . 0050 -O141 60.6 
GU) Due ee see cere SS . 647 -98 ~ 3092 .99 . 1790 1.1900 3.508 .0075 . 0112 95.8 
GOST reat Mere se ero - 63 .96 - 3362 -99 . 1860 1. 2280 3.652 - 0075 .0112 97.0 
GO eon eee Sate . 546 - 83 - 3019 . 89 . 2003 1. 0880 3.603 . 0075 - 0117 93.0 
Gi ees a eee eee - 495 wD . 2746 81 . 1988 -9658 | 3.517 . 0078 - 0118 91.1 
GOUGH ees recone = - 442 . 67 . 2431 mil! . 1922 8204 | 3.375 . 0075 .0120 88.9 
GU/(SsS een Soe eee - 300 2OL - 1741 soul . 1664 . 5042 2.896 - 0075 . 0122 82.0 
GOS are ek ee eee: . 260 .39 . 1250 RO . 1397 . 3096 2.476 0075 .0125 76.5 
GOQ Eee steerer .170 .26} .0697 s7yt . 0992 51 PAIS 1.743 - 0075 . 0132 63.9 
GON Sener Se eee ce . 645 .98 . 3389 .99 . 1803 1. 3580 4.007 . 0100 - 0114 94.4 
COE La Pa Ss le ae ee . 642 .98 . 3383 .99 -1818 1. 3630 4.030 . 0100 .0114 94.5 
Ges ete ees Sas - 909 . 85 . 3082 91 . 1998 1. 2680 4.114 . 0100 . 0117 92.1 
(0 IB epee Sats ees eee - 464 aiid! . 2565 who . 1954 1.0470 4.082 . 0100 .0117 92.3 
GRE ea se aa -415 . 63 . 2261 . 66 . 1870 . 8788 3. 886 - 0100 .O118 89.9 
Oe oa a Seen ee - 309 -47 . 1570 .46 . 1579 . 5318 3.388 . 0100 . 0119 85.3 
GUO Wee So es = . 220 34 . 1028 .30 . 1250 . 2899 2.820 . 0100 - 0120 79.8 
Uc eee eseSee eee . 153 320 - 0601 -18 . 0906 . 1283 2.136 .0100 - 0120 71.0 
On ee SS eee Sena . 642 -98 . 3383 .99 . 1818 1.5120 4.470 . 0125 .0115 93.8 
OS Ses ne sees termee . 600 91 3207 .96 . 1950 1. 4880 4. 569 .0125 -0118 92.5 
C2 ae eee ea . 593 -90 - 3229 95 . 1962 1.4700 4.553 . 0125 -O118 91.9 
G2 Ss eee eee oe -553 . 84 . 3054 - 90 . 2001 1. 4080 4.611 .0125 .O118 92.2 
(OE See ee en eee ee - 487 .74 . 2701 eu . 1979 1. 2040 4.459 .0125 .0120 89.6 
OP oe at oe ea aera on - 426 .65 . 2331 . 68 . 1893 - 9928 4. 260 .0125 . 0121 87.6 
(GP), ee eee ea eee . 324 - 49 . 1668 .49 . 1629 - 6224 3.731 . 0125 . 0122 82.7 
(Sas cea ame . 244 Sel! . 1148 34 . 1332 . 3620 3.153 .0125 . 0123 77.3 
GAG Bea ee ee . 163 ~20 . 0656 .19 . 0957 - 1602 2.441 -0125 . 0122 70.6 
ODE ae ae es Nee ee . 634 . 96 . 38365 .99 . 1856 1. 6450 4.889 . 0150 .0116 92.7 
Si ee os Gee ees . 616 94 . 3313 .97 .1915 1. 6425 4.959 .0150 -0115 92.5 
G2OR ES ar eas or Sse 545 - 83 - 3015 . 89 . 2003 1.5060 4.996 . 0150 -0118 Oiled 
O30 eee ss ee .482 oti . 2671 78 .1974 1. 2900 4.829 - 0150 - 0120 88.7 
(OB Ge ee ee Sea -414 . 63 . 2255 . 66 . 1868 1.0140 4.500 - 0150 . 0122 85.0 
OS Dee Pe ee eee es . 323 -49 . 1662 -49 . 1626 .6524 | 3.926 . 0150 . 0126 79.5 
OS ace seboahce saan - 245 -ot . 1155 04 . 1336 . 9925 3.399 . 0150 . 0123 75.9 
G3 ae te rte are acs . 165 20 . 0668 .19 - 0967 . 1879 2.813 - 0150 .0120 73.9 
10-INCH. TILE. 

G35 eer See eee 0.818 | 0.99 | 0.5366 | 0.99 | 0.2213 | 0.4818] 0.898 | 0.0005 | 0.0125] 85.4 
GS aeons oa ae Se eee - 183 -95 - 9265 . 98 . 2379 - 5150 .978 - 0005 . 0122 89.7 
GS eee ae . 739 - 89 - 9068 . 94 . 2475 5114 1.009 . 0005 . 0122 90. 7 
OS 0h Shas eee -706 | .85 | .4887 91 . 2508 4910 | 1.005} .0005 | .0123 89.7 
GSORr eae See ete . 666 -8l - 4638 . 86 . 2518 . 4429 . 955 . 0005 - 0128 8.1 
OAS a ea Se Se -616 | .75 | .4293 | .80'| .2491 .4324 | 1.007} .0005 | .0122 90.3 
OARS eens sees .579 . 70 . 4018 sta . 2451 . 4188 1.042 - 0005 0118 94.1 
3 On eS oo ree ee ee BODE . 67 - 8803 a(t . 2408 . 3668 . 962 - 0005 . 0124 87.7 
GAS RES ase ae ee DATA 00 | -ol86) 090 2240 . 2780 . 873 0005 | .0129 82.4 
GAdES ee Hee ee es SALGT | es DON 2 OSs 008s 2016 . 2408 . 889 »0005 | .0122 87.3 
GA ae Re See -323 .39 . 1944 ° 80 - 1741 . 1470 - 756 > 0005 . 0123 81.1 
64622 ate ace Tasos - 241 . 29 . 1302 o 24 . 1380 . 0832 - 639 »0005 | .0122 77.0 


1 These tests used in deriving formule 26 and 28. 


30 BULLETIN 854, U. S. DEPARTMENT OF AGRICULTURE. 


Tapir 4.—Elements of experiments for concrete tile—Continued. 


10-INCH TILE—Continued. 


1 2 3 4 5 6 7 8 9 10 11 

Depth} @ Area @ Hy- Di Vv Kutter Chezy 

Test No. of = of > |draulic iS © | Slope. | coeT- | coeffi- 

fiow. | ? | fiow A | radius. | Charge. | locity. cient. | cient. 

(d) (a) (R) (Q) (V) (8) (n) (C) 
Cu. fé. Feet 
feet. Sq. ft. Feet. | per sec. | per sec. 

Ga eI ae 0. 814 | 0.98 | 0.5357 | 0.99 | 0. 2241 0.7240 ; 1.351 | 0.0010 | 0.0121 90. 3 
G18 eee ae . Sil BOSE paso! . 99 . 2262 7510 | 1.403 -0010 | .0119 93.3 
GAGE eee te .789 | .95 | .5286|] .98]| .2360 .7780 | 1.472 | .0010 | .O117 95. 8. 
G50) Sees a eet . 139 | .89 | .5068 | .94 | .2475)  .7615] 1.503) -0010} .0119 95.5 
Galassi ee ees -710-). 86} 4910) |= 90)" 2.2505 .7360 | 1.499 | .0010 | .0120 94.8 
Gigs eee ek ee ee .670 | .81 | .4664] .87] .2519 .6930 | 1.486} .0010 |] .0121 93.6 
eee erin neta eel waa eee .617 | .75] .4800| .80] .2493 . 627 1.460 | .0010} .0121 92.5 
G5 ae ee ee ene . 993 ~ 12 - 4124 51 . 2466 . 5954 | - 1.444 . 0010 . 0122 91.9 
Ob5 ets he ae Sanayi . 67 - 3850 ~ 12 . 2419 | .o304 | 1.391 -6010 | .0124 | 89.4 
GDB Eee Pee eres Pe -486 | .59| .3283 | .61 | .2273 .4462 | 1.359) .0010 | .0122 90.1 
OB Bee esis Se Pelee - 423 aol . 2766 OL . 2097 . 3650 1.320 | .C010 . 0119 91.1 
GoSE ates rae ee SERRE Beso) 5 WORT | tb | aXe .1998 | 1.032] .0010 |; .0128 78.3 
GSO Ber teenies ee ee ja * D3Rel 220) | SAg8OL Ot Pe I1866 . 1110 .868 | .0010 | .0126 74.3 
God rate en. nee .813 | .98| .5855} .99 | .2248) 1.1160] 2.084] .0020| .0114 98. 3 
COS Fee es 19819 =< 97; 3162/5995) =.2326 |= 1102081 2.0731 00202] =. Oleg 96.1 
GOD poe ee ee . 797 . 96 . 5313 . 99 . 2330 11360") 2138 - 0020 - 0115 99. 1 
GO3ta ee ees .738 | .89 | .5063 | .94) .2476] 1.0960 | 2.165} .0020; .0118 97.3 
66 Te ee eee .108 | .&86 . 4899 91 . 2506 1. 0600 2.164 - 9020 - 0119 96.7 
GOB ieee eee . 667 .8l . 4644 . 86 .2518 | 1.0105 | 2.176 - 0020 . 0119 97.0 
GOGEEE eee hee . 621 5 fh . 4329 .8l . 2497 9448 | 2.183 . 0020 . 0118 97.7 
OO (eerste eee es . 594 ~t2 . 4132 5 ef . 2467 . 8639 2.091 -0020-| . 0121 94.1 
GOS ee seen eee . 561 . 68 . 3881 si} . 2425 . 1996 2. 069 - 0020 . 0121 93. 6 
G69 cee eer eee . 483 . 58 - 9259 61 . 2265 . 6251 1.918 - 0020 | .0123 $0. 2 
Gi Ose se ee . 439 5 is - 2898 . 54 . 2145 . 5186 1.790 - 0020 . 0125 85. 4 
Giles eee ae es . 429 . 52 . 2815 sO2 . 2115 -4982 | 1.770} .0020 | .0125 &6. 0 
OQUDEE ee Sen a Pees he | =, 843 41 . 2106 .39 . 1819 - 3250 1. 543 - 0020 - 0127 | 80.9 
Clos soe es or eee ee | . 248 . 30 . 1355 25 . 1413 . 1487 1. 060 - 0020 - 0145 63.1 
G(s oe eee ee He 8131 2 98) 8 2.5356) | =e 99 | .2248 | 1.3400 | 2.502; .0030 | .0117 | 96.3 
OSS ies ae eee Seas iene . 810 . 98 - 0349 . 99 . 2267 1.3380 2. 502 . 0030 -O117 95. 9 
OL Gas ees ces ee . 790 95 . 9290 - 98 - 2356 1.3800 2. 609 - 0030 . 0116 98.1 
Oia eee ae ee . 740 . 89 . 5073 94 . 2473 1.3450 | 2.651 | .0030 |] .O0118 97.3 
GIs carers ak ees lS . 86 . 4939 . 92 . 2501 1.3280 | 2.689 .0030 | .0117 98. 2 
Oise ees Sip Reena . 663 . 80 - 4619 . 86 . 2517 1.2360 | 2.676 . 0030 . 0118 97.4 
GSO Sse eee en . 636 Sty . 4435 . 83 . 2508 | 1.1800 | 2.661 | .0030 . 0119 97.0 
foil Laerer ce a) eaeiey at een .598 | .72 | .4161] .77| .2472) 1.0760] 2.584] .0030| .0120 95. 0 
OS Dees os erie a Saar eae SSA ROE bee oye = Se -9586 | 2.505 | .0030 | .0122 93. 1 
OSS Bass sree ane ee . 498 . 60 . 3381 . 63 . 2300 . 8092 | 2.393 . 0030 . 0123 91.1 
OSS ee eee ee eS ee . 436 BOS . 2873 - 53 . 2136 . 6332 2. 205 . 0030 . 0125 87.1 
O52 eae eee al . 339 41 . 2074 239 . 1804 . 3/91 1.828 |} .0030 . 0130 78.6 
GOERS ieee ee . 243 . 29 al Sils Zo . 1390 . 1853 1.407 . 0030 . 0136 68.9 
GSTS Eee a eee eae . 805 . 97 . 5336 .99 . 2294 | 1.7650 | 3.308 . 0050 . 0116 97.7 
G88 le area pee eee ee . 804 97 . 0333 .99 . 2299 1.7350 | 3.253 - 0050 -O118 96.0 
GSO US eile oes See oe . 789 .95 . 5287 -98 PAO Mesa) Sy . 0050 . 0119 95.6 
OOO Rees aa ae eae . 741 . 90 . 5078 .95 . 2471 1.7300 | 3.407 . 0050 - 0119 96. 9 
GOI teste erry se . 704 . 85 . 4875 91 . 2509 1.6825 , 3.451 - 0050 . 0119 97.5 
O92 EE een ene se ee . 678 . 82 . 4716 - 88 - 2518 1.6250 | 3.446 - 0050 - 0119 97.2 
003 Fe eee we ae .623 | .75 | .4843 |) .81] .2498) 1.4800] 3.408) .0050; .0120 96. 4 
i Reece eI AS es ER AL . 586 ail -4072 | .76 2458 ; 1.3450 | 3.303 -0050 | .0121 | 94. 2 
O95 eee eee eee . 562 . 68 . 3889 A . 2427 1.2480 | 3.209 0050 | .0123 92.1 
GOO mies eee eo ee eer - 492 . 60 . 002 . 62 . 2286 . 9930 2.980 | .0050 | .0126 88. 1 
OOS ee eee eee . 420 . dl . 2741 as! . 2088 . 7345 2. 680 . 0050 . 0129 82.9 
i Seta here oie rte .338 41 . 2066 -38 . 1800 .4934 |} 2.388} .0050 . 0129 79.6 
O99 Bac ee es ce ee SPAN 5743) |e Oy 5 . 1332 . 2222 1.810 0050 | .01383 70. 2 
OUI eaten Oo re ae oe . 793 . 96 - 5300 . 99 . 2346 1.7600 | 3.321 . 0050 .O117 97.0 
pO aS apseer ae eee eer a . 785 .95 . 9272 -98 awote 1.7400 | 3.300 . 0050 . O119 95.8 
(Eas Soe Sa a ae eee didi . 93 5O222 97 . 2411 1.7175 | 3.289 . 0050 . 0120 94.7 
(OSE aie oe eens . 729 . 88 - 5016 .93 . 2488 | 1.7100} 3.409 -0050 | .0119 96.7 
TAU ere ee ee Ais meee ee . 686 . 83 . 4766 . 89 . 2516 1.6250 | 3.410] .0050 . 0120 96.1 
ODS es Se eye . 621 .75 . 4329 . 81 . 2497 1.4840 | 3.428! .0050 . 0119 97.0 
(HGsGueeee see ese Sosa 4 . 593 ~12 . 4124 iid: . 2466 | 1.3400 | 3.249 . 0050 . 0123 92.5 
TMU SeRES Seer patel . 566 . 68 . 3919 .73 . 2434 1.2460 | 3.179 .0050 | .0124 91.1 
[AU feh Sek 2s Re ee ee a - 499 . 60 . 3389 . 63 . 2302 - 9949 2. 936 . 0050 . 0128 86.5 
(UD Se ase ce tee ee . 421 sail . 2749 ol . 2091 <(dl5 | 2.661 - 0050 . 0130 82.0 
7 NCS was 5 ore ae eee eee . 341 41 . 2090 .39 . 1812 - 4887 2.338 | .0050 . 0132 CK ae 
(li ees eco Snneet eee see] 528: | -.235 |> 223 | - 1337 . 2236 1.811 0050 | .0134 70.3 


1 These tests used in deriving formule 26 and 28. 


: THE FLOW OF WATER IN DRAIN TILE. 


TABLE 4.—Elements of experiments for concrete tile—Continued. 


10-INCH TILE—Continued. 


31 


1 1 3 4 5 6 

Depth| gq Area a Hy 
Test No. of D of Tt draulic 

fiow fiow radius 

(d) (a) (R) 

Feet. Sq. ft. Feet. 
i (ila aes set T= poet ae aie i 0. 806 | 0.97 | 0.5338 | 0.99 | 0. 2288 
Aly epee thn ea Ne . 800 97 . 5322 .99 BPAY) 
(QUA i ae ee 779 |- .94]> .5250 | .98] .2392 
TANG i EO eine ees ee . 726 88 - 5000 - 93 . 2491 
TA} ise Se ae er ere Sn .718 287 - 4956 92 . 2498 
(AY ar ta SS eae ae ee . 659 . 80 . 4592 - 8d . 2616 
1 fo ees ag ete Se ga . 627 - 76 - 4371 81 . 2501 
ALO) oe ae aie ame LOB OFn |S OOD05| Aue 2440 
fe eet ae Secreta = . 541 . 65 - 3724 . 69 . 2389 
{PAN a Se atone ame - 487 59 . 3291 . 61 S72N 
[RS RE Se ee ee eee - 408 49 . 2642 49 . 2050 
Ta a acs ea ae Re ae 2S e ae SOs ee O44 ea G le li 40 
(Pr ioe es ee ee a . 224 S20 . 1176 oD, . 1299 
TS Ea pe ere eater . 792 - 96 . 5297 99 . 2349 
(ON Sa sS eae ee ee eee 791 - 96 - 0294 . 99 . 2353 
SOA ae NO ee . 681 - 82 - 4735 - 88 S20 
TPA ee ae ene ene oe ea . 624 3 t5 - 4350 . 81 . 2499 
Rien ca Se ne oc -618 ENO - 4307 - 80 . 2493 
FC ere tee nines es Sn 7 - 595 Bee, . 4139 Tite . 2468 
7S Se lr ne Niger eee SOS ea Oi seo SLO arden oak 
71a) Ba ae on oS oes . 489 . 509 . 3308 - 62 - 2280 
(Oates a eee ae ee - 405 .49 . 2616 49 . 2040 
(Be es ee ee Ont - 40 . L976 OU . 1756 
(Been Soe eee - 207 a4) . 1052 avAl) .1214 
Vial Vocome aR ee EN -810 | .98| .5349] .991 .2267 
(BYERS SSeS Ss eee ees - 809 -98 . 5346 -99 SIVA: 
[Risla tos 5 cee eee eee - 805 -97 . 5336 -99 . 2294 
TAD am eae ieee ee ages -742} .90| .5083} .95] .2470 
(CUS OSS eee eer - 701 85 . 4857 - 90 . 2511 
FEAR ee Sa eee ee ses . 700 - 85 . 4852 - 90 . 2011 
ADs etioe Sse cna . 664 . 80 . 4625 - 86 ASE 
TES Sees See ain a ae . 611 14 ~ 4257 -79 . 2486 
Tf ETS Be ener ae ena - 569 . 69 . 3942 518 . 2438 
(OS Se oa ee ee .543 | .66] .3740] .70] . 2393 
NAGS =n aa eee eee - 463 -56 . 3096 58 SPAN; 
(Ay pea aah a eee 412 ~ 50 . 2674 . 50 . 2063 
PAO oe ee Pose a 314 238 . 1872 fo) . 1704 
(DRESS a ee eee ae . 213 - 26 . 1096 . 20 . 1244 
TED Sneek se ea . 781 .94 . 5257 -98 . 2386 
TAD Sea oe ee ee .624) .75 | .43850} .81} .2499 
(iS en Oe oe eee ee TADS ble |= o2749e1-= . 51) 1. . 20901 
12-INCH TILE. 
AGB. i We Ae es ee io 0.985 | 0.99 | 0.7712 | 0.99 | 0.2587 
Ss a a ee ec ce eee 943 95 7581 9 2836 
7 BS aa ee a ec 889 90 7299 95 2960 
OOS ee oe ee 845 85 7011 91 3006 
Titi wade eee eee ee 782 79 6532 85 3014 
(i eR SS i ee aera 756 76 6317 82 3001 
(SUES See arr ae 691 70 5745 74 2933 
AGG Ns ee ee eee 643 65 5298 69 2854 
TAD Sa Re a a 580 59 4692 61 2717 
(SAE a= Se ee 534 54 4240 55 2594 
MOess= seen — Satna? oll 52 4012 52 2526 
AG es ee ee a tae ee 364 37 2570 33 1991 
OO Ree ee em en 275 28 1747 23 1588 


7 8 9 10 11 
. r Kutter} Chezy 
Dis- Ve- : 
. Slope. | coeffi- | coeffi- 
charge. | locity. Bate | haa 
(Q) Ce (s) (n) (C) 
Cu. ft. | Feet 
per sec. | per sec. 
2.1150 | 3.962 | 0.0075 | 0.0118 95. 7 
2.0900 | 3.927} .0075} ..0120 94, 2 
2.0850 | 3.972} .0075| .0121 93.8 
2.0560 | 4.112] .0075} .0121 95. 2 
2.0440 |] 4.125] .0075) .0120 95. 3 
1.8870 | 4.110] .0075| .0121 94.6 
1.7700 |} 4.050} .0075 | .0122 93.5 
1.5120 | 3.828} .0075 | .0126 89.5 
1.3800 | 3.706 | .0075 | .0128 87.5 
1.1560 | 3.512 0075 | .0129 85. 0 
. 8044] 3.045 | .0075 | .0136 UUeU 
5306 | 2.729 | .0075] .0133 75.5 
2600 | 2.211 | .0075)| .0131 70.9 
2.4060 | 4.542 0100 | .0121 93. 7 
2.4210 | 4.574 0100 | .0120 94.3 
2.2080 | 4.663 0100 | .0123 92.9 
2.0560 | 4.727 0100 | .0122 94.6 
2.0050 | 4.655 0100 | .0123 93. 2 
1.8840 | 4.552 0100 | .0124 91.6 
1.6450 | 4.308 0100 | .0128 87.7 
1.3750 | 4.157 0100 | .0127 87.1 
-9930 | 3.795 0100 | .0128 84.0 
6238 | 3.156 0100 . 0134 75.3 
2318 | 2.203 0100 | .O141 63. 2 
2.7040 | 5.055 0125} .0119 95. 0 
2.7220 | 5.092 01251 .0118 95.5 
2. 6890 5. 040 0125 . 0120 94.1 
2.6800 | 5.272 0125.) .0121 94.9 
2.5920 | 5.336} .0125] .0121 95. 2 
2.5920} 5.343 | .0125] .0121 95.4 
2.4660 | 5.332 OL25 aia OLE 95.1 
2.2410 | 5.265 0125 | .0122 94.5 
2.0000 | 5.073 0125} .0124 91.9 
1.8840 | 5.037 OL253 |= 0123 92.1 
1.4620 | 4.725 0125 | .0123 89. 8 
1.2360 | 4.622 0125 . 0120 91.0 
-7000 | 3.739 0125 | .0126 81.0 
3260 | 2.983 0125 | .0124 75.6 
2.8840 | 5.486 0150 . 0123 91.7 
2. 4540 5. 641 0150 . 0124 92.1 
1.3820 | 5.030 | .0150} .0122 89. 8 
0.9125 | 1.183 | 0.0005 | 0.0110 104.1 
.8938 | 1.179 | .0005 0117 99.0 
-8672 | 1.188} .0005 0119 97.6 
. 8492 } 1.211} .0005 0118 98.8 
. 7540 1.154 - 0005 0123 94.1 
.6986 | 1.106} .0005 0127 90.3 
-6496 |} 1.131} .0005 0123 93.4 
- 6062 | 1.144} .0005 0120 95.8 
-4982 | 1.062] .0005 0124 91.1 
-4485 | 1.058] .0005 0120 92.9 
-4083 | 1.018} .0005 |} ~.0123 90.6 
- 2152 . 837 | .0005 0123 83.9 
- 1120 . 641 0005 0132 72.0 


1 These tests used in deriving formule 26 and 28. 


32 


a 


BULLETIN 854, U. S. DEPARTMENT OF AGRICULTURE. 


TasLe 4.—Elemenis of experiments for concrete tile—Continued. 


Test No. 


ya w 


12-INCH TILE. 


aes 6 

a Ho- 
FI draulic 
tsdius. 

(£) 

Feet. 

9.99 | 0. 2801 
99 - 2812 
.94] .2974 
. 90 - 3013 
. 84 3012 
- 80 . 2989 
75" . 2919 
- 67 - 2828 
-61 | .2720 
555 - 2585 
AT . 2397 
“33 . 1974 
=2t . 1509 
.99 | .2771 
-97 | .2893 
-91 - 3007 
. 84 3011 
aif . 2974 
ath . 2908 
. 68 . 2834 
.60 | .2700 
= - 2514 
-47 . 2393 
32 . 1940 
. 20 1484 
-99| .2757 
.98 . 2872 
741 .2932 
. 64 . 2776 
. 60 . 2700 
By! . 2571 
.46 . 2370 
~o4 . 2020 
. 20 1484 
- 80 . 2988 
. 68 . 2849 
- 65 - 2791 
-59 - 2690 
ay . 2594 
.49 - 2444 
=a: 2102 
- 24 - 1631 
BUY/ - 2822 
see - 2582 
45 - 2335 
<3 - 2036 
- 28 . 1808 
~ 52 - 2556 
53. - 2553 
-48 . 2420 
“35 - 1970 
- 28 - 1817 
ot 2517 
45 - 2339 
“37 . 1949 
-26 - 1716 
48] .2433 
35 - 2133 
- 26 1711 


i 


7 8 
Dic- Ve- 
charge. | locity. 
(Q) (V) 
Cu. ft Feet 
per sec. | per sec. 
1.3180 1.729 
1.2980 | 1.706 
1. 24€0 1.720 
1.1900 | 1.722 
1.0920 | 1.689 
1.0164 1. 642 
- 9312 1. 650 
-8492 | 1.638 

7255 | 1.543 
-6278 | 1.491 
-5114 1.414 
3018 1.192 

1443 . 898 

1.8400 | 2.406 
1.7525 2. 339 
1. 6575 2.367 
1.5350 | 2.377 
1. 41€0 2.331 
1.2520 | 2.244 
1. 1306 2.168 

. 9838 2.128 
. 8364 | 2.006 
. 6804 | 1.887 
. 3820 1.556 

1821 1.165 

2. 2470 2.935 
2. 1660 2. 876 
1.5180 | 2.647 
1.2800 | 2.589 
1.1890 2. 552 
1.0183 2. 448 
-8172 | 2-311 
. 0186 1. 967 
. 2333 | 1.493 
2.2920 | 3.704 
1.9170 | 3.631 
1.7800 3. 552 
1.57€0 | 3.438 
1.3750 3. 243 
1.1880 | 3.165 

-7900 | 2.792 

. 4600 2.518 
1.9700 | 8.821 
1.5900 3. 786 
1.2320 | 3.585 
- 8573 3. 205 
.5954 | 2.739 
1.7150 4.172 
1.7425 4. 249 
1.4960 | 4.060 
. 9040 3. 384 
-6846 | 3.123 
2.0080 | 4.860 
1. 5900 4.613 
1.0420 4.211 
-8010 | 4.026 
1.9780 | 5.310 
1.4080 | 4.843 
- 8510 4.295 


1 These tests used in deriving formule 26 and 28. 


——— ee 


10 11 
Kutter! Chezy 
coeffi- | coeffi- 
cienl. | cient. 

(n) (Cc) 
0.0115 103.3 
-0116 101.7 

0119 99.8 

0120 99.2 

0122 97.3 
. 0124 95.0 
- 9121 96.6 

0120 97.4 

0123 93.6 

0122 92.7 

0122 91.4 

0124 84.8 

0131 73.1 

0116 102.2 

0121 97.3 

0123 96.5 

0123 96.9 

0124 95.6 

0126 93.1 

0128 91.1 

0126 91.6 
. 0129 88. 4 
-0128 86.3 

0132 79.0 

0139 67.6 
. 0116 102.1 

0121 98.0 

0130 89.3 

0128} . 89.7 

0129 89.7 

0128 88.2 

0128 86. 7 

0132 79.9 

0134 70.8 

0124 95.8 
. 0122 96.2 
. 0124 95.1 
. 0124 93.8 
. 0127 99.1 
-0124 90.5 

0125 86.1 
.0117 88. 2 
. 0138 83.1 
-0131 86.0 

0129 << Shek 

0129 82.0 

0136 74 t 

0136 82.5 

0134 84.1 

0134 82.5 

0131 80.7 

0138 aoe 

0130 86. 6 

0130 85.3 
- 0125 85.3 
. 0120 86.9 

0128 87.9 

0127 85.6 

0122 84.8 


& 


Bul, 854, U. S, Dept. of Agriculture, 


Fig.|. Concrete Tile Analytical Method using Selected Tests 
Velocities in Feet per Second 


Fig.2, Concrete Tile Graphical Method using Selected Tests 
Velocities in Feet per Secon 


Fig.3. Concrete Tile Flowing Full 


PLATE X. 


Fig.4. Concrete Tile Flowing.9 Depth 


5 6 7 6 91.0 RSnZ Ob 25 eS ON 40S ad Velocities in Feet per Second Velocities in Feet per Second 
5.0 60 708090 5 6 7.8910 1520 25°30 40 50 60708090 5 6 7 8 910 i520 25 30 40 50 60708090 _5 6 7 8910 5“ “20 25 a0 40 $0 60 100090 
0150 46 SU [62; 
—| 750 
0125 af | soef feral | frac 0150 
hy) 73) 0125 
-0100) Macy hls L 
‘0030 aA, te. 0100 
0080 SE ay f-deel VE) 1 - TT 0030, 
.0070 + i540. 242. 0080 
0060 “ria I i i = pee 
Tl hoy | seme 
0050 IL] 442 EELY 94, (24 | L IL a 
9. 
Ky ek Ll .0050 
0040 it) 
[| o Vy I 0040 
0030 495 f 456f [587 
ie=ai1 4 791. Ny 
: (ss0f” J674 Me q .0030 
0025 ¥ we SVATA 
7 =e AA 
y 57g A 0025 
10020 429, 48, ‘57; 
Q oh F225] fee (4 te + Sg —— so2o! 
9 Wai) I $ bY sf P N 
0015 , 3 M/s 
5 : Yt los imal bois 00159 
(2) OF WA Vv 
S79 ~/n, WA Ps (2) 
oo10 23 | 427 hi Jes9 | ~ SJ 
(009 1520) 766 SSSI 17 0010 
0008 [ a K Ila eee 
5 d 
.0007 t—}+— 0007 
0006 Of 567 — 0006 
Al Sey d 
0005; 7h Sef Shad ky | i “4 |. is 0005 
0004 Lk r h 0004 
0003 ‘ 
09 10 i820 25, 30 09110 15) 20) 25) 30 Gum OneTONoN 0 cA SunTSS ME TETES MSO oes 
Mean Hydraulic Fadil in Feet Mean Hydraulic Fradii in Feet Diameter of Tile in Feet Diameter of Tile in Feet 
Fig.5. Concrete Tile Flowing.8 Depth Fig.6. Concrete Tile Flowing .7 Depth Fig.7. Concrete Tile Flowing 6 Depth Fig.8. Concrete Tile Flowing.5 Depth 
elocities in Feet per Second Velocities in Feet per Second. Velocities in Feet per Second Velocities in Feet per Second 
56 7 8910 Is__-20 25 3040 50 60708090 5 6 7 8910 1520 25 30 40 5060708090 5 6 7 8910 I5__20 25 30 40 50 60 708090 5 6 7.8 910 i520 25 30 40 $0 60708090 
.0)50 ky 0150 
0125 1 +—+t + 0125 
0100) | 5] 0100 
0030 + 7 +14 0090 
0080 0080 
0070 uy, J Lt 5 | 4 0070 
0060 = f a |—+ +4 0060 
.0050 L IL a zt See 0050 
0040 i LI 0040 
ann 7 x 0030 
Ld f = 0025 
0025 J LY = iaeal maT i 
| : ttt +1 9020: 
0020 = + T [; Q 
is RA 4/ /: Wf e/> 2 
© ois S fs spf L-b/- | + Cy 1) SA Sif 0015), 
y aA wi | oe I he ah * g 
Do/ fs SY [S/ | ~ » 
V/s Ay 
4.0010 
oo10 = ima) it 0009 
ane |_| 14 .0008 
g + 0007 
0007 0006 
0006 eae al : 
| =] 0005 
‘005 ee 4) 
.0004 
0004 el a 
S| 0003 
ars 3 Aunts ome eB EOELO) 3 4 5 6 7 8B S10 


3) A) Sone eergi0 
Diameter of Tile in Feet 


a 4b © 7 BOW) 
Diameter of Tile in Feet 


Diameter of Tile in Feet 


Curves USED IN THE DERIVATION OF FORMUL€ FOR CONCRETE TILE. 


Diameter of Tile in Feet 


a a oS a ae 7 AA BEER = 
enema 
te as ay ewes a 


q. 
2 sty 2. 


} , 7 
; é 5 ot Pe om: ee 
~s : , ae . 4 : 
din 3 By ace 
~ ~ — ta 2 3 ) 4 = 
j s 4 gt 1 re 
et eh & 6 fea? 3 o- : ras 
fico ao. oe — 
z 4) 


ae Oe : 

= a ee Se 8 j 
eae tr bac ! : 

wee fe eee) ae the . 4 

~ 3 aya E os 

+ ees ee 

we : 


4 
7 4 Ae : 
oom ; " PUEDE 
i 
fe hea 
Le Ake +o 
> i 7 
y B 
@ 


a 


ri ANCHE 1 
NS NR 


He 


a 


et A 


Heat 6. 3 ps e. So endl Naa 
cree AVSIM AO Natsonei ‘Dian of Fike ie Bas Sate 


ee ; Giunved Vere fNorHe Dn VATON ee 


THE FLOW OF WATER IN DRAIN TILE. 33 
TABLE 5.—EHlements of experiments for clay tile poorly laid. 
10-INCH TILE. 
1 2 3 1 5 6 7 8 9 10 11 

: Hy- : Kutter | Chezy 

Depth | d Area a a Dis- Ve- 2 

Test No. offlow.| pD | offlow.| 4 gual charge. | locity. Slope. ee ee 

(d) (a) (R) (Q) GV) (s) (n) (C) 

Cu.ft. Feet 
Feet Sq.ft. Feet. | per sec. | per sec. 
ici ARs Hine En atiean 0. 805 | 0.96 | 0.5423 | 0.99 | 0.2355 | 0.5342 | 0.985 | 0.0005 | 0.0120 90.8 
“poSbsawabsomcoudooae 795 | .95} 15389] .98) .2391 . 5679 | 1.054] .0005 | .0116 96. 4 
See ete eee 708 | .85| .4957] .90]| .2537 .5465 | 1.103} .0005 | .0116 97.9 
Mee tere an VE -625 | .75 | .4401} .80 2520 .4934 | 1.121] .0005} .0114 99. 9 
BO OE ee ere ees .524 | .63] .3621 | .66 2368 -3780 | 1.044} .0005} .0116 96. 0 
BEES Ae eee oe eee e429)" 5! 2 52837) 51 2124 .2924 | 1.031 | .0005} .0109 100. 0 
Bae eee SEIS Solas ||) Sail 1876} .34 1704 . 1602 854 | .0005}] .O111 92.5 
Sa Ob ae Cee Orne BEE 214!) .25 1110 | .20 1251 . 0744 671) - 00057) > O11: 84.8 
HORE OURS a OREBeE re . 836 | 1.00 5489 | 1.00 2090 . 5102 .929 | .0005 | .O0117 90. 9 
do SSRGO CARA em eas . 791 -95 |} .5374] .98] .2405 . 5390 | 1.003 | .0005 | .0120 91.5 
Bee racis see ceneie eerie -712 | .85] .4981} .91 2535 .5222 | 1.048 | .0005) .0120 93. 1 
Biers SN eee hate Breccia tee -620 | .74.| .4865] .80] .2514 -4772 | 1.093 | .0005 | .0116 97.5 
So os Sees eae eee OS2H OL) |e SOSo Mle OU Ire 2oG0 -4093 | 1.111] .0005| .O111 101.7 
CBee eriaa cee eco 3 SAS) 6 EO) 2736 | .50 2087 .2737 | 1.000 | .0005| .O111 97.9 
SS SSNS eee Bere .3ll 58 1860 | .34 1696 - 1620 871 | .0005 | .0109 94.6 
Bava a SPIE eatretee me SME || LU L206) 22 1315 . 0780 647 | .0005 | 0117 79.8 
SGA Coe Ee: OS a ae meats .831 | .99 5484} .99 2173 Ole SZ0 | 0010s | SOULS 92.9 
SOS Sane Dee cer 399)" 396 5403 | .98 2378 7964 | 1.474 | .0010 | .0118 95. 6 
Boer Ne lore ieee oot S .697 | .83] .4890] .89 2541 7855 | 1.607 | .0010 | .0115 100. 8 
BBA Sano EES eno ee -628 | .75| .4423) .81 2523 7180 | 1.624] .0010] .0113 102. 2 
SCAR Hae ream .547 | .65] .3806] .69 2415 .6089 | 1.600} .0010] .O111 103. 0 
Jane Hoe Rea nee eee RAD ol: PARTS || eae 2103 4114 | 1.481 | .0010] .0109 102.1 
ISAs ice Sonera 324 | .39 1966 | .36 1749 2656} 1.351 | .0010 |] .0105 102. 2 
Sanpete ee cise ise ORT gas 12o%s |qeees 1349 . 1393 | 1.108} .0010] .0105 95. 4 
Sie ints elas co tere aera - 835 | 1.00 5488 | 1.00 2106 (90 | 1.379" 0010") <s0115 95.0 
SG OSE ARSE see aoe 786} .94 SBN || als || > A PEPAL .7720 | 1.442] .0010} .O121 92.7 
SUSSCAP Bore Na aoaeOne -697 | .83] .4890}] .89 2541 . 7300 | 1.493 | .0010} .0121 93. 7 
SiGoo BE OSuE MO ABORAaee SBI) oie THEI GRAF 7) | SG Pans} -6720 | 1.542} .0010] .0117 7.3 
SoSH COE Sa GE eacne Oat | 64 )-<.3026 | 68 | . 2395 .5465 | 1.467) .0010 |] .0119 94.8 
o6 GA CAR SESSA Ca DHeSaEe . 433 . 52 2870 ~o2 . 2136 . 3720 1.296} .0010} .0122 88. 7 
Epa cra eee ole ey cae .3388 | .40 2080 .38 1805 . 2222 | 1.068} .0010}] .0128 79.5 
Bee se Sint -221| .26| .1161| .21| .1285| .0768| .662| .0010| .0149| 58.4 
12-INCH TILE. 
oS ARCS n eee 0.951 | 0.96 | 0.7546 | 0.99 | 0.2769 | 0.9193 | 1.218 } 0.0005 | 0.0112 103. 5 
Bee eee ees Wt -877 |} .89) .7173 | .94 2954 8396 | 1171} .0005; .0121 96.3 
Cie a epee nn pee eer 731 | .74) .6068| .80 2965 - 6468 | 1.066] .0005] .0130 87.6 
Soe Ree Ge eee Cam eae BOtorIe Oil .0202.| 9100 2844 . 5342 | 1.013} .0005} .0132 85. 0 
Se amie ao Sn Sars eae eS eee -5o9 | .57] .4466 |) .59 1] .2657 - 4335 971 | .0005] .O181 84. 2 
St SUN a ARs a naam -463 | .47 | .3521 |] .46 2365 2814 799} .0005} .O0141 73.5 
© SE Se reg aon ee a 313 | .38| .2646{ .35 | .2025 1512 571 | .0005|] .0166 56.8 
BRR gy aa 2916) 2.93.) .73892 | 97 2882 | 1.2640] 1.710] .0010 | .0117 100.7 
Bene Tee aa ees -789 | .80} .6548] .86| .2999 | 1.0450} 1.596 0010 | .0126 92. 2 
SF Men SOROS eae A ormree [G9 1e |p es oleae on eme zal 8492 | 1.486] .0010 |] .0132 87.0 
Seer ee sei he -594 } .60] .4806] .63 2742 6197 | 1.289) .0010] .G142 77.9 
SRS ae eater -483 | .49 |] .3719] .49 2432 .3760 | 1.011 | .0010] .0159 64. 8 
Sesto as See es -386 | .39|] .2771 | .36 2078 - 2019 .729 | .0010 | .0186 50. 6 
So Wa E ees Se CEE eae 3972) v.99" |— . 7609) |). 99 2654 | 1.7125] 2.251] .0020} .0119 97.7 
ee tee ans te ee ae -926| .94 | .7442 | .98 2856 | 1.6750 | 2.251 .0020 } .0124 94. 2 
Jp OUdaGso sues hee seoe -799 |} .81] .6626| .87 3000 | 1.3940} 2.104} .0020} .0185 85. 9 
Bee ee ea cas -664 | .67] .5469] .72 2882 | 1.0125] 1.851 .0020 | . 0147 77.1 
BS CS Aes Sane eee ee -573 | .58 | .4602} .60 2692 . 7435 | 1.616 | .0020 . 0156 69.7 
BS ce ree ots are ee -470 | .48] .3591 47 2389 - 4634 | 1.291 .0020 ) .0171 59. 1 
Sie sos obosE ean aeeene 368 | .37) .2599| .34 2005 . 2363 - 909 .0020 | .0200 45.4 
ee Caen oe See 2182 | .79 | -.64934 85 2997 | 1.6475 | 2.538] .0030] .0136 84.6 
Cece ase ae en ee 672 | .68| .5542| .73 2896 | 1.2700} 2.293} .00380] .0145 77.8 
Bea eee ies PDD Me ote 64447 | Bel an eooL . 8332 | 1.874) .0080] . 0161 66.5 
Cv ares ee aE sf 457 | .46] .3462] .45 2344 5174 | 1.495] .0030} .0177 56. 4 
See a ee aoe 2360 jeer ou.) webearle ao8 1973 .2737 | 1.085 | .0030 | .0202 44,6 
166597 °—20—Bull. 8543 


PS SS FEI PL EL IO NE I I OY I I ET TO ALES ET I LT EIT LY LILES P LILLE LE LT I OOS Bae REALL S SOR TE 0 EE EEN dN SO SE Ee AEE Te AREER BE ate Se 


34 BULLETIN 854, U. S. DEPARTMENT OF AGRICULTURE. 


TaBLE 5.—Elements of experiments for clay tile poorly laid—Continued. 


12-INCH TILE—Continued. 


2 2 3 4 5 6 i 8 9 10 11 
Depth} g Area Hy- . roe Kutter] Chez 
Test No. of D of t draulic 7 ISS 1 > Slope. | coeffi- coeiie 
flow flow radius. | ©218e- aye cieno. | cient. 
(d) | (a) (£) (Q) CV) (s) (n) (Cc) 
Cu. ft. Feet 
Neet. Sq. fe. Feet. | per sec. | per sec. 
SSo Re nie oe Se ea 0.756 | 0.77 | 0.6280 | 0.82 | 0.2987 1.8025 | 2.870 | 0.0050 | 0.0152 74.3 
(tS) See Seer iia Sn ae . 636 - 65 - 9207 - 68 . 2830 1.2980 | 2.493 - 0050 . 0164 66,3 
Geese ne ee Ce Ret - 49 . 56 . 4368 Say . 2630 -9820 | 2.248 - 0050 . 0170 62.0 
toto) ees Sas Ee eee . 450 46 . 3394 -45 . 2320 . 5887 1.735 - 0050 -O019T=2=55029 
SROr hes oe Se ee - 396 .36 - 2485 .33 . 1955 Seyi! 1.300 « 0050.) 2s seeeee 41.6 
COSY cea ga re te ie a ee 929 | .94| .7455 | .98] .2847] 2.8640} 3.842] .0075| .0137 83.1 
baton) 55x ae ice ee sutin Ss Se . 849 . 86 - 6991 - 92 - 2982 2.5800 | 3.691 . 0075 . 0146 78.0 
SS eter tesa Ree ame - 709 shine - 5877 Stitt - 2941 2.1360 | 3.635 - 0075 . 0147 77.4 
SOUR eee ee ee =100°\> 2 7 | 57965 =< 76) | 29316 |= 220380) Sa5l6) |= 0075: |— -OrSED 75.0 
SOTO Pry ete ae ere - 638 -65 - 5225 . 69 . 2834 1. 7350 3.321 . 0075 . 0154 72.0 
SO 2 2 as ao ae | .d519) .53 - 4073 503 . 2544 1.0260 | 2.519 - 0075 . 0178 57.7 
SORES oa eee et ancoe | .428 | - 43 | .3178 | .42 | .2240 .6265 | 1.972 | .0075 | .0198 48.1 
| |. | 


Note: Nos. 825 to 832, inclusive, 841 to 848, inclusive, and 857 to 893, inclusive; grade of flume uniform. 
Nos. 833 to 840, inclusive, and 849 to 856, inclusive; grade of flume undulating. 


DISCUSSION OF COMPUTATIONS. 


All of the formule derived herein are of the exponential type 
since this seems to be the only form capable of representing the data. 
It seemed most natural to determine first the relation of velocity to 
slope, other elements being unchanged. In using for this purpose 
the same line of tile without disturbing the joints, the most uncertain 
element in tile observations was removed. The chief remaining diffi- 
culty lay in the observations of depth of flow, to secure a constant 
value for comparison at different slopes. When, for a given size of 
tile and constant depth of flow, slopes are plotted logarithmically as 
ordinates against their corresponding velocities as abscisse, the 
resulting points are approximately on a straight line. The equation 
of such a line is of the form, 

s=mV2 (14) 


which in logarithmic terms may be written, 
log s—log m +z log V | (15) 


where m is the intercept on the unity vertical axis, and zis the slope 
of the line, i. e., the tangent of the angle which it makes with the 
axis of V. 
For several different sizes of tile of the same material, the values 
of m follow the equation, 
m=eD* (16) 


, 


THE FLOW OF WATER IN DRAIN TILE. 30 
Substituting in formula 14, 
| s=eD*Ve ake 
This expressed in Peoria terms is 


log s=log e+a log D+z2 log V (18) 
FORMUL4 FOR TILE FLOWING FULL. 


In deriving the various formule, both analytical and graphical 
methods were used in order to insure accuracy. Figure 1 of Plate X 
shows the results obtained by the analytical method for the concrete 
tile. This diagram was obtained by plotting the velocities of all the 
selected experiments in Table 4 against their respective slopes. The 
centers of gravity of the various points for each size of tile were 
plotted, after being calculated as outlined below. Straight lines 
were drawn through these centers of gravity for each size. Thusa 
series of approximately parallel lines was obtained. It should be 
noted that in using the analytical method, equal weight is given to 
the least velocity and the greatest velocity. The slopes and intercepts 
of each of the lines on this diagram were determined analytically. 

The following description gives the methods of derivation. Taking 
the experiments in which the tile were approximately full, shown in 
Table 4,1 the center of gravity of all the points belonging to any one 
size of tile was determined as follows: The antilogarithm of the 
mean value of the logarithms of the various velocities gave the 
velocity coordinate of the center of gravity; the slope coordinate of 
the center of gravity was found in a similar manner. This point, C, 
shown by a solid circle (Pl. X, fig. 1), divides the plotted points into 
two groups. The center of gravity of the two groups separated by 
the principal center of gravity must also be found. These points, 
A and B, are shown by open circles. Having these two points, the 
equation of the line for that particular size of tile and depth of flow 
can be readily determined, as shown by the following sample calcula- 
tion for 4-inch concrete tile: 


Let C=center of gravity of the 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. 


1The serial numbers of these selected experiments are indicated in Tables 3 and 4. 


SS A RE I TE RE NE Sm 


36 BULLETIN 854, U. S. DEPARTMENT OF AGRICULTURE. 


Let C,, A,, By, and C,, A,, B,, be the V and s coordinates, respec- 
tively, of the above centers of gravity. The calculations for these 
coordinates are as follows: 


No. ¥. | — Log V. | Log s. 
| 
= ios} : =were = 
ae ees ta meh ere een ene ye (os 9/0| Sum=28.477121 
amy gaa | One | 9.90das ea SIRE Be 7 af ee ee 
435 1.204 | “0030 | 10.080590 Antilog By=0.8283 |747719] | ABUlog Bs—0.0013181 
9 7 5 9 {7 R07) 
Tate cat are “Ooe5 | Ap eseorg| Sum—41 493438 (F832) | sum—s1.847032 
461 | 2.711 0125 | woaaena( A ea OSS AP hs 0ugn et 
467 30558 "0150 | 10.485125 Antilog A »=2.3624 8.176091 Antilog A s=0.0091571 
Sum=81.165182 Sum=60.324153 
Mean=10.1457727= Cp Mean=7.540519= Cs 
Antilog Cp=1.39885 Antilog Cs=0.0034715 


A» — Cyp=10.373359 —10.1457727= 0.227586 
Cy —By=10.1457727— 9.918186 = .227587 
A s— Cs= 7.961758 — 7.540519 = .421239 
Cg—Bs= 7.540519 — 7.119280 = .421239 


Since 
A,—C, A,—G, 
C,-—B, GB; 


the three points, A, @, and B are in a straight line, which checks the 
accuracy of the work (see American Civil Engineers’ Pocketbook, | 
second edition, p. 848). 

The exponent, z, of V in formula 14, is the inclination of the line 
ACB, and is equal to the tangent of the angle formed by the line and 
the unity axis of V. 


A,—B, 0.842478 
SSS s SSS 
Ao BS 04a 

The intercept, m, is determined as follows from equation 15, using 
the coordinates of the center of gravity, C: 


Log m=log s—z log V (19) 
= (C.—z2 CG, 
= 7.540519 — 1.8509 X10.1457727 =7.270709 
and m=0.0018651. 


The exponent of V and the value of m are found in the same man- 
ner for the other sizes of both concrete and clay tile, running nearly 
full. These values are shown in column 7 of Table 6. This table 
gives the formula derived as explained above for each size of tile as 


well as the range of velocities used in the derivation. 
j 


Bul, 654, U. S, Dept. of Agriculture, 


Fig! Clay Tile Analytical Method using Selected Tests 


Ve/ocit(es.in Feet per Second 
20) 25 30 40 50°60 708090 


§ 6 7-8 910 


15 


$2 [22 


Fig.2. ClayTile Graphical Method using Selected Tests 


Velocities in Feet per-Second. 


Ss 


6 7-89 10 


1S 


20 


25 3) 


Fig.3. ClayTile Flowing Full 


Velocities in Feet per Second 
_=40 *50 60°70 8090 5 6 7 8 310 1S. 20 25 30 40 50 60 708090 


Sf 123 aa 
ual 2/8 
1S 19. 
( 
I96f 23,4 304, of 


Je /- 


sci 


PLATE XI, 


Fig.4. ClayTile Flowing .9 Depth 


Velocities in Feet per Second 


SAT) 


— 


15 


25 30 


— 


40 


50 60 70 80.9.0 


— 


xg". 
Se 


o> 


4” 


Ea 


be 
6° 
/00 


oe 


| [ I> 


lo ” 
135 


176 


5 


09 10 


15 


| 


20 


x sical Gaal 


25 30 


Mean Hydraulic Fadii 1a Feet 


Fig.5. ClayTile Flowing .8 Depth 


Velocities in Feet per Second 


67 8 9 10 


1S 


2.0 


25 30 _40 50 60 708090 


5 


.08 10 


AS 


20 


25 30 


Mean Hydraulic Fradii in Feet 


Fig.6. ClayTile Flowing .7 Depth 


Velocities in Feet per Second 


67 8 910 


15 


20 


WS 4° «5 6 78,9 10 
Diameter of Tile in Feet 


Fig.7. ClayTile Flowing .6 Depth 
Velocities in Feet per Second 


25 30 40 50 60 70 8090 § 6 7 8 910 15 20 25 30 40 50 60 706090 


d5 


8 7 8 910 


3 


4 


* 


0150 


0125 


0100 
.0090 
0080 
.0070 


,0060 
0050 


0040 


0030 
0025 


= 


0020," 


P 


0015 


sZzo 


0010 
0009 
0008 
0007 
0006 
0005 


0004 


0003 


‘ 5 6 78 910 
Olameter of Tile in Feet 


Fig.8. ClayTile Flowing .5 Depth 


Velocities i Feet per Second 
15 20 25 30 


40 50 60 708090 


iV 


e 


ie 


0150 
0125 


gq” 


Lge 


Se 


& 
Uo 


Uo 


ce 
10" 


Sims UO NTRBNSIIO 
Diameter of Tile in Feet 


ast 
3 4 5 6 7 8910 
Olameter of Tile in Feet 


Curves USED IN THE DERIVATION OF FORMUL€ FOR CLAY TILE. 


3 4 5 6) 7 8.9 10 
Diameter of Tile in Feet 


+ 


56.7 8.910) 


of Tile in Feet 


0100 
.0090 


0080 
0070 


0060 
0050 


0040 


0030 
0025 


0020 


0015 


LOPE 


Ss 


0010 
0009 
0008 


0007 
0006 
.0005 


0004 


0003 


ACE 0 ; 


SPN Sy 
AS Shes = | 


ea he Sh BGS Bei . 


apne ieee ete 


pe: P r. +7 , | B 

= ; SF bud AP at, 

z 4 58 eg AsIge/ SS 

: a 2 OF Of. Ore Oc 70B—> OP oe 
‘.  espeenetn aw ‘ - = 2 ; pee oo e 
¥ a 


i » . ; t } ’ a : - d . 
2S jae ” Set : ' 5 tr agp oaie el “5 Gi ho 
EN OE PR, ROUGE? ce REED me A A BETS age ae ay ee, ee ee ee 

+h. i Pras Ve Ne ee ee ae ie lt a) eae _ Pe a ao 


tee, Bh, A aes Hy ci | 


sel 


noe 


ps 
ae 


sir ; rea! 


eae 


me 


Pr 


rae 
? s 
A 


Ce a 


TA IES 
: NAMA ge e. 
NES 5 


WR ee. Se 


vr aa Pi 
6: ‘BSW 
er: or dite if? Pest 


a 


Oe 5 ea ee 
Mets TAN ‘6 nstone 


de Ee es 


Qurnves Uska ih THE Denvahioke 


THE FLOW OF WATER IN DRAIN TILE. 3 


TABLE 6.—Jndividual tile formule and revised intercept values. 


| 
Tile 
Num- f 
ber of | Formul derived sep- Hevised, 
Nom-| Actual Velocity. ob- arately for each tile aah cep 
Kind. inal f é an 
size, | diame-| bore tions 
ter. 


Inches.| Feet. | Sq.feet. | Feet per second. 
ard busned clay - 4} 0.3398 | 0.0907 | 0.607 to 3.328... 14 | s=0.0014797 V2-0326_____ 0. 0015185 


ANS te 5 - 4193 .1381 | .634 to 4.030... 17 | s= .0010494 V1-9729____.| .0010524 

Soft burned clay.. 6 -5184 -2111 | .765 t0 3.368... 6 | s= .000819 V1-8321_____ - 000761 
Hard-burned clay . 8 - 685 -3685 | .893 to 4.423... 15 | s= .000617 V1-9914____. - 0006297 
Watrified sss. 2s 10 - 836 - 5489 | 1.168 t0 5.717... 18 | s= .000384 V1-9918_____ . 0003927 
ID Yo See eee 12 - 9857 - 7631 | 1.176 to 4.002... 6 | s= .0003185 V1-9907_____ . 0003241 
Concrete. .........- 4 - 3280 -0845 | .504t0 3.056... 8 | s= .0018651 V1-8509____. . 0017954 
MOS eek: 5 -4127 -1338 | .640t0 3.891... 9 | s= .001077 V1-9183_____ . 0010444 
DOs eee 6 - 4970 -1940 | .705t03.274... 7} s= .000856 Y2-0104_____ . 0008791 
DO mest Bees 8 - 6585 -3406 | .914 t0 4.959... 18 | s= .0005674 V2-0373_____ . 0006079 
WOM se eos 10 . 8274 -5377 | .898t0 5.486... 26 | s= .0005003 V1-9682_____ . 0004997 


DON ease 12 - 9915 - 7721 | 1.183 to 2.935... 4 | s= .0003449 V2-0059.____ | - 0003546 


Since for the same kind of tile the exponents V vary for the differ- 
ent sizes, the mean of the exponents has been taken as correct; thus, 
For clay tile, z=1.96859. 
For concrete tile, z=1.96433. 
Using these mean values of z instead of the values derived for each 
separate size of tile, new values, m’, were computed for the inter- 
cepts on the unity vertical axis, as follows: 


For clay tile, log m’ =log s—1.96859 log V (20) 
For concrete tile, log m’ =log s— 1.96433 log V (21) 


These values of m’ are given in column 8 of Table 6. 

To introduce the mean hydraulic radius into the formule, the rela- 
tion of the values of m’ to the hydraulic radii for the different sizes 
of concrete tile is represented by the formula, 


i = 2 (22) 


in which e and x are determined analytically, by a method similar to 
that previously explained, as follows: 


Mean 
3 - | Intercept 
aus bydtaulie values log R. log m’. 
: R Mm’. 
Inches.| Feet. 
4 0.0915 0. 0017954 8.96142) Sum=27.16319_........--- 7.254171) Sum= 21.217044 
5 - 1154 .0010444 | 9.06221$Mean—9.05439= D,;...-...-- 7.018853$Mean= 7.072348= Dm’ 
6 - 1379 -0008791 | 9.13956} Antilog Dr=0.1133...-...- 6.944020} Antilog Dm’=0.0011813 
8 - 1840 .0006079 | 9.26482) Sum=28.0655_..........-- 6.783850) Sum= 20.032332 
10 . 2316 -0004997 | 9.36474$Mean=9.35519= Hy...-..-- 6.698711$Mean=6.677444= Em’ 
12 - 2729 -0003546 | 9.43600) Antilog H;=0.2265........ 6.549771} Antilog #m’= .00047582 
Sum=55.22875 Sum= 41.249376 
Mean= 9.20479= F, Mean= 6.874896= Fin’ 


Antilog Fr= 0.1602 Antilog Fin’= 0.00074971 


38 BULLETIN 854, U. S. DEPARTMENT OF AGRICULTURE. 


The line representing equation 22 is shown in figure 1 of Plate X. 
The mean hydraulic radii in the above computations were obtained 
by averaging the hydraulic radii for the selected tests in Table 4 for 


each size of tile, and not by using = because these radii are for 


tests varying from 95 per cent full to full. The mean hydraulic radii 
have been plotted as abscisse with their respective revised intercept 
values as ordinates. These pomts are designated in the figure by 
stars. The centers of gravity as computed above have also been 
plotted, and a line drawn through them. Substituting in equation 22, 
transposing, and using the center of gravity just computed, 


Log e=log m’— (— 1.3128) log R (23) 
= 6.874896 + 1.3128 «9.20479 
and e=0.00006775 
Thus 
m’ = 0.00006775 R-1-3128 (24) 


where 0.00006775 is the intercept on the line R =1, and — 1.3128 is the 
inclination of the line to the horizontal axis. The logarithmic 
diagram showing the development of the line for equation 24 is shown 
in figure 1 of Plate X. A similar line for clay tile is shown im figure 1 - 
of Plate XI. | 
Substituting equation 24 and the mean value of 2 (p. 40) in the 
general formula 17, this general equation is now obtained for concrete 
tile: 
$= 0.00006775 P-1-3128 [1 -96433 
_0.00006775 V-2%88 


P21:3128 (25) 
From this, solving for V, we get 
V = 132.5 R088 50-509 (26) 


which is the formula derived analytically, using the mean hydraulic 
radii for the selected experiments for each size of concrete tile in 
Table 4. 
In a like manner, the formula as derived analytically for clay tile 
was found to be 
Vi TAR cee ae 2 (27) 


The data used in deriving equation 27 for clay tile are shown on figure 
1 of Plate XI. This diagram has been prepared similarly to the 
diagram in figure 1 of Plate X, except that the values used are from 
the selected tests in Table 3, for clay tile. 
Formule 26 and 27 were derived by the analytical method, using 
only experiments with the tile flowing from 95 per cent full to full, 


THE FLOW OF WATER IN DRAIN TILE. 39 


but not under pressure. In order to derive a formula graphically, 
using the same data as those from which equation 26 was derived 
analytically, a separate diagram was necessary. This diagram 


(Pl. X, fig. 2) was obtained by plotting the velocities used in figure 1 _ 


of Plate X as abscissx, against their respective slopes as ordinates, 
just as in figure 1. Straight lines were drawn through each set of 
symbols, averaging the points by eye. Although these lines were not 
intentionally drawn parallel, it will be seen that they are practically 
so. The slopes of these lines were determined by scale, and the 
intercepts of the various lines with the unity vertical axis were read 
from the diagram. The inclination and location of the line involving 
the mean hydraulic radii and the intercepts were determined analyti- 
cally. The formula as derived graphically for concrete tile is 


V=138.5 Ro-080 0-510 (28) 


It should be noted that the exponents of s are the same in equations 


_ 26 and 28, while the exponents of Ff and the coefficients preceding R 


vary slightly. 

In a similar manner, the formula for the flow of water in clay tile 
was derived graphically from the selected experiments in Table 8, 
this diagram being shown in figure 2 of Plate XI. In this case the 
inclination and location of the lne involving the mean hydraulic 
radii and the intercepts were also determined analytically. The 
formula as derived for clay tileis ~~ 


V= 121.4 Ro 50-8 (29) 


Comparing this formula with equation 27, it will be noted that the 
exponents of s are practically the same, while the exponents of F as 
well as the coefficients preceding 2? vary somewhat. This difference 
is probably due to the fact that the observations on the 6-inch tile 
are slightly inconsistent with those on the other sizes, and this dis- 
crepancy is treated somewhat differently in the analytical and graphi- 
cal methods. In the latter method, greater weight was given to the 
higher velocities than to the lower ones. The diagrams (Pl. XI, 
figs. 1 and 2) show the variation in the inclination of the lines for the 
6-inch tile. 

It will be noted that the formula for flow in clay tile, equation 27, 
was derived analytically. In order to determine the variation in the 
coefficient, the velocities for the selected experiments (column 8, 
Table 3), together with their respective hydraulic radii and slopes, 
were substituted in equation 27 and new coefficients computed. 
The mean of the coefficients obtained for clay tile was 137.6. Thus 
the formula for clay tile, using the same exponents for # and s as 
in equation 27, was found to be 


= 137.6, YO 5050 (30) 


| 
sense enenenienrepavenenenetemenenimabenmemnneereaamin 


40 BULLETIN 854, U. S. DEPARTMENT OF AGRICULTURE. 


In a like manner, the data for the experimental velocities for the 
selected experiments (Table 4) were substituted in equation 26, and 
the formula for concrete tile became 


= Bees 2 (31) 


Noting how close the exponents of R and s were to 2 and i, it was 
deemed advisable to determine what the coefficient would be when 
using these latter values. For the clay tile, using all the various sizes 
and lengths of tile, the formula became, 


V =136 R? s3 oe. (32) 


In the case of concrete tile, the data for the 4-inch size show that 
greater resistance to flow is offered in this size than in the larger 
sizes. ‘This is clearly shown in the diagram in Plate X as well as in 
column 10 of Table 4. Therefore, it was decided to eliminate the 
4-inch size and use the remainder of the sizes in the derivation of the 
formula. The formula for concrete tile, then, is 

V=138.2 F's? (33) 


None of the previous formule were derived from the combined data 
for both clay and concrete tile. Therefore, it was decided to derive 
a formula by using the velocities for both clay and concrete tile flow- 
ing full as obtained from Plate IX. These velocities were plotted as 
abscisse against their respective slopes as ordinates (Pl. XII). 
The formula derived graphically for both clay and concrete tile is 


V2= 137 06g seo (34) 


This formula is practically the same as that derived for concrete 
tile as given in equation 33. Since it was derived from the data for 
both clay and concrete tile, equation 34 is recommended as the general 
formula for computing the capacity of tile, merely eliminating the 
decimal in the coefficient and making the exponents 2 and 3, respec- 
tively, thus, | 

V =138 R? s? (13) 
FORMUL FOR TILE FLOWING PARTLY FULL 


A great many experiments were made at other depths of flow as 
shown in Tables 3 and 4. These have been plotted and mean curves 
drawn through the points (see Pl. TX, figs. 1 to 12). The velocities 
at 0.5, 0.6, 0.7, 0.8, and 0.9 depths and for the tile flowing full were 
read from these curves and plotted on logarithmic charts as abscissa, 
against their respective slopes as ordinates, to determine the equa- 
tions for flow at these different depths. 

Figures 3 to 8, Plate XI, show the studies made of clay tile at 
various depths of flow. With the exception of the 0.5 and 0.6 depths 
of flow (figs. 7 and 8), the lines were drawn through the various points 
by eye, the centers of gravity not being determined analytically. 


Bul. 854, U. S. Dept. of Agriculture. PLATE XII. 


pee in Feet per Second 
5 9 10 i520 25 30 40 50 60 708090 


FE eh 
25 a ar 


.0100 

ies (ihe SAG lcs 
ee — eee 
Gba6 Sa aera cc ne 
Pace See ee 


encase oie od mee 
oe SAGES 


aes 
CH AMAA TT 
Coe TT 


WA ‘a 
Boo a a0 aa a ee eas 
0005 Thi ed.  Saaaeaaar 
bd 


fA) 30 
Mean Tee Radi In Feet 


CuRVES USED IN THE DERIVATION OF A FORMULA APPLYING TO BOTH CLAY 
AND CONCRETE TILE. 


aa fy gee eh 


COPS 


Dal yee 


THE FLOW OF WATER IN DRAIN TILE. : 4l 


However, for the 0.5 and 0.6 depths of flow the exponents of s were 
found to be rather high; so for these two depths the centers of gravity 
of the various sizes of tile were computed analytically, and the 
exponents of s were found to be the same as the values determined 
graphically. It should be noted that the diameter of the tile and 
not the mean hydraulic radius was used in the formule derived for 
various depths of flow. In determining the equation of the line 
showing the relation of m and the diameter D (equation 16), the 
centers of gravity were computed lest appreciable error should be 
introduced in attempting to draw these lines by eye. However, after 
the lines were drawn through the computed centers of gravity, the 
slopes of these lines were determined by scale and the intercept was 
read direct from the diagram. 


d 
Depth of flow D 


Va/ues.of K 


Equation of Line K=55.5. 7(Z) 
Fig. 1.—Reiation of coefficient K to depth of flow in formulae 35-40. 


The formule for clay tile as derived from figures 3 to 8, Plate XI, 
are as follows: 


Tor tile flowing full, VERN AS IDE hee (35) 


For tile flowing 0.9 depth, V=57.5 D°-®78 50.502 (36) 
For tile flowing 0.8 depth, V=57.1 D°-®? 50-498 (37) 
For tile flowing 0.7 depth, V=60.5 D®-7°6 59-507 (38) 
For tile flowing 0.6 depth, V=63.4 D°-5S! 50.518 (39) 
For tile flowing 0.5 depth, V=72.2 D!.°! 59.541 (40) 


These equations furnish sufficient basis for determining next a 
general formula to cover every depth of flow. Since in this group cf 
formule the exponent of s is about 0.5, each equation is of the form 


ees (41) 
Plotting the values of the coefficient A in formule 35 to 40 as 
ordinates, against their respective depths of flow as abscisse, an 


equation involving K and $ is determined (see text-fig. 1). This 
equation is found to be 


d \—0-3087 
K= 55.57( 5) (42) 


42 BULLETIN 854, U. S. DEPARTMENT OF AGRICULTURE. 


In a like manner, plotting values of ‘the exponent of D as ordinates 
against their respective depths of flow as abscissz, the equation for 
the exponent of D for any depth of flow was found to be (see text: 
fig. 2) 


d —0.639 
= 0.6284( 5) (43) 


Then writing the equation to cover every depth of flow in clay tile, 
we have 


0.6284 


pe Sorat lor i 


Cm 3067 5° . 


Depth of Flow £ 
7 


oy 


ae of Exponent of D 
ron 


a 


L£guation Of Line a=. ae: 


Fig. 2.—Relation of exponent of D to depth of flow in formule 35-40. 
d ; aes 
When D equals 1—in other words when the tile is flowing full— 


and assuming the exponent of s to be 0.5 for all depths of flow, 
Ve 55 e (45) 


A study of figures 3 to 8, Plate X, shows that the 4-inch concrete 
tile appears to have a greater coefficient of roughness than do the 
larger sizes. This is also indicated in Table 4. Therefore it was 
decided to eliminate the 4-inch tile and consider only the remaining 
sizes in deriving a new formula. The formule for the concrete tile 
for the 5, 6, 8, 10, and 12 inch sizes for all depths of flow then become: 


For tile flowing full, V=51.15 D9-590 50-496 (46) 
for tile flowing 0.9 depth, V=50.80 D°589 50-491 (47) 
for tile flowing 0.8 depth, V=51.49 D582 50-496 (48) 
for tile flowing 0.7 depth, V=51.93 D®-625 50-501 (49) 
for tile flowing 0.6 depth, V=51.37 D728 39-504 (50) 


for tile flowing 0.5 depth, V=49.22 D789 59-510 (51) 


THE FLOW OF WATER IN DRAIN TILE. 43 


Depth of Flow # 
els 8 


Values of K 


Fig. 3.—Relation of coefficient K to depth of flow in formule 46-51. 


| qd 
Depth of Flow e 


Values of Exponent of D 


=460/ 


s e OW 
Eguation of Line a = 558I(p 
Fic. 4.—Relation of exponent of D to depth of flow in formule 46-51, 


The exponent of s in all cases is very nearly 0.5, while the constant 
K also varies but little. Following the same method as before (see 
text-figs. 3 and 4) to obtain the formula for any depth of flow, 


s d 0-01653 5 
eae » es 
K=51.26( 77) (52) 


qd. \—0-4601 


and 


Thus, the equation for any depth of flow in concrete tile is 


0.5581 


Ve 51.2655) | D|o) as (54) 


44 BULLETIN 854, U. S. DEPARTMENT OF AGRICULTURE. 
d cae 
When D. equals 1 (when the tile is flowing full) and assuming the 


exponent of s to be 0.5 for all depths of fiow, 
V- 5126 De (55) 


The similarlity of this formula to Prony’s formula in equation 7 
should be noted. 

A formula for the clay tile using only the data on the 5, 6, and 8 inch 
sizes (1-foot lengths) was derived, as well as a formula for the 10 and 
12 inch clay tile (2-foot lengths). These, however, were not deemed 
of great importance as indicating the effect of joints in the tile line, 
since an insufficient number of tile sizes were available for considera- 
tion. | 

From a study of the data on the flow in tile running partly full, it 
will be seen that the velocity does not vary in accordance with the 
variation of the hydraulic radius. This fact suggested an attempt to 
derive a formula that does not involve the hydraulic radius, but is of 
the type, 


That is, instead of the hydraulic radius, or the area divided by the 
wetted perimeter, it was recognized that the area might have one 
exponent and the perimeter a different exponent. A careful study of 
this type of formula revealed the fact that it would be impracticable. 
Another type of formula which was considered was of the form 


5 Dae eae 
V=K ps7) ® (57) 


where k, z, and ( are unknown constants. This type was also con- 
sidered inadvisable. 
Still another formula considered was of the type 


th A a 0-5 
V -(prp) s (58) 


where F'and £ are constants and B is the breadth of the water surface 


in the tile exposed to the air. This type was investigated quite care- 
fully with the data relating to the concrete tile, but was not consid- 
ered applicable to the conditions. 

From a study of the velocity-depth of flow curves it will be seen 
that the greatest velocity 1x a pipe is approximately at 0.8 depth. 
Theoretically it would be at 0.81 depth. Below this the velocity 
decreases rapidly with the depth of flow. Observations on the flow in 


c 


THE FLOW OF WATER IN DRAIN TILE. 45 


the tile during the experiments indicated that there is additional 
resistance to the flow caused by the action of the air on the water sur- 
face in tile flowing partly full, to which may be due the decided decrease 
in the velocity at the partial depths. ‘Therefore it was decided to vary 
the formula for concrete tile, 


V=51 D™* 90-5 (59) 


by substituting = for D, thus, 


V= (sp) (60) 


and to determine the proper values of ffor the various depths of flow. 
In the formula 60, the values of V, s, A, and P from the experiments 
(V from Plate IX, the others from Table 4) were used, and the values 
of f were found to be as follows: ; 


diilestlowguae tiie eee ck See ee cerns See Ph on os sees 1. 00 
lero wines(): Sede pthse = oh oe ee ee oe ee Me Sa e 1,15 
dhileptlowmne: 0S iets ya. ie ee See ts ee ee 1. 20 
siilesttowame: Ove pte san nets a Ses ie. en ns 1. 25 
bike ntlowaimesO: Orde ptlice esse e se epee She te ee Naira 1. 35 
fintepiowaneO25: de ptlt 2 aise ee ee Sees eee aes eee 1.50 


The above discussion is given merely as a method of making allow- 
ance for air resistance to flow. Further experiments are considered 
necessary to establish the necessity of making such allowance. 

A comparison of the various formule which have here been derived 
may be made from Table 7. The formule have been arranged sys- 
tematically, so that variations may be noted at a glance. They have 
been so classified that all involving the hydraulic radius are in one 
column, while those involving the diameter are in another column. 
The number opposite each formula refers to the corresponding equa- 
tion in the text. 


BULLETIN 854, U. S. DEPARTMENT OF AGRICULTURE, 


46 


~ & 
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: “pariwap eynuLof fo hinmung—) ATAV J, 


THE FLOW OF WATER IN DRAIN TILE. 47 


COMPARISON OF VARIOUS FORMUL&. 


Since from a practical standpoint we are interested only in the 
tile flowing full, velocities as computed by formula 34 are compared 
with velocities as taken from figures 1 to 12, Plate EX, for the tile 
flowing full. These results are shown in Tables 8 and 9. The differ- 
ence is shown, rather than the ratio, between each two determina- 
tions of velocity, in order that the variations in the low velocities shall 
be given only equal weight with equal variations in the high veloci- 
ties. To get the average differences given in Tables 8 and 9, the arith- 
metical sum of the differences is divided by the number of items. 


Slope in Feet per /00 feet 
2 6 7 8 9 1.0 


5505 


er Second 


2 so | 
Chega eer TT 
pee | 
ee 
Ze 
Pee ee Exper/mental Velocities 
fas 


Pornce/er.... N= 48V¥7+54D 
Willigms-Hazen. V= CyRs%0,0017 °° 
ee L =/000 ft. a Chezy-Hutter. N=CVRs_ 
Ke 3s Eliott .......P48Vizerb 
223 Cw= /20 * Derived......N=\38 R? 5? 
0 


Fie. 5.—Comparison of velocities computed by various formule. 


Both the Poncelet and the Beardmore formule gave greater dif- 

ferences when applied to the experimental data than does the ten- 
tative formula, No. 13. The velocities from the curves in Plate IX 
were substituted in the Williams-Hazen formula, and the average 
value of C,, was found to be approximately 120. Using this value 
in the Williams-Hazen formula, recomputing the velocities, and 
comparing them with the velocities from the curves in Plate IX, it 
was found that the average differences were practically the same as 
the average differences stated at the bottom of Tables 8 and 9. 
_ A comparison of the velocities computed by the various formule 
for one size of tile may be obtained from text-figure 5. This figure 
shows the velocities for 8-inch tile as computed by the Poncelet,. the 
Williams-Hazen, the Chezy-Kutter (with the coefficient of roughness, 
n, taken equal to 0.013), the Elliott, and formula 13 herein derived 
from the experimental data. The observed experimental velocities 
are also shown. 


VK 


Feer 
La id p 
| ‘ee 


Ve/ocss 
: N 


x 


in 
ie 
ce) 


48 


BULLETIN 854, U. S. DEPARTMENT OF AGRICULTURE. 


TABLE 8.—Comparison of velocities for ciay tile flowing full. 


if 2 3 4 5 1 2 3 i § - 
Velocity Difference Velocity Difference]. 
Size from. Velocity | between || Size from Velocity | between 
of Grade. | curvesin | byfor- | column 3 of Grade. | curvesin| byfor- | column3 
tile Plate mula 34. and tile. Plate mula 34. and 
: IX. column 4. IX. column 4. 
Inches.| Per cent. | Ft. per sec.| Ft. per sec.| Ft. per sec. || Inches.| Per cent. | Ft. per sec.| Ft. per sec.| Ft. per sec. 
4 0.05 0. 60 0. 59 —0.01 6 0. 75 3.33 3. 04 —0. 29 
-10 -77 - &4 + .07 1.00 3.78 3.51 —*).27 
- 20 1.08 1.18 + .10 
.30 1.36 1.45 + .09 8 -05 . 87 - 95 + .08 
50 1.76 1. 87 + .11 .10 1. 23 1.34 + .11 
5 U8 22 2. 29 + .17 . 20 1. 82 1.89 + .07 
1.00 2.44 2. 64 + .20 - 30 2.13 2.32 ae ol) 
525 2. 93 2. 96 + .03 - 50 2. 92 2. 99 + AT 
1.50 3.27 3. 24 — .03 aD 3. 53 3. 66 + .13 
5 -05 . 60 - 68 + .08 10 05 1.06 1.08 ae oY 
-10 1.02 . 96 — .06 -10 1.57 2 — .05 
- 20 1.35 1. 36 + .01 . 20 PPA 2.16 — .ll 
- 30 1.70 1. 67 — .03 30 2. 74 2. 65 — .09 
- 50 MUI 2.15 + .04 - 00 3.50 3.42 — .08 
5D 2. 52 2. 64 + .12 50h 4. 23 4.19 — .04 
1.00 2. 83 3. 04 + .21 1.00 4. 98 4. 84 — .14 
1.25 3.39 3.40 + .01 1.25 5. 63 5. 40 — .23 
1. 50 3.90 3.73 = Gili 
12 -05 Wsil7/ a2 + .04 
6 -05 77 .79 + .02 -10 1. 86 Ue 7Al — .15 
- 10 1. 04 Hei + .07 . 20 2.35 2.41 + .06 
- 20 1. 63 1.56 — .07 -30 2.95 2. 96 + .O0L 
. 30 2.03 1. 92 — ll - 00 3. 94 3. 82 — .12 
- 50 2.59 2. 48 — .li 
Motalplus ditlerencec.52 0. Hie he aes ee re eee ce ee rere ee eee +2. 11 
Totaliminusdiulerencess - 2 es hes Saws Ss eieew te see oe oe eee So Eee —2.16 
ING ETTND OTOL TE TING Se aia aie Se ap iia esa aie rs SIS ee 44 
Average difference’. 22. so eons © ome ep isioe aston Sine eaters foot per second. - 097 
TABLE 9.—Comparison of velocities for concrete tile flowing full. 
1 2 3 4 5 1 2 3 4 5 
Velocity Difference Velocity Difference 
Size from Velocity | between || Size from Velocity | between 
of Grade. | curvesin| byfor- | column3 of Grade. | curvesin | by for-. | column 3 
tile. Plate mula 34. and tile Plate mula 34. and 
IDS column 4. TEXS: column 4. 


Inches.| Per cent. 


4 


Ft. per sec.| Ft. per sec. | Ft. per sec. 
0. 0. 


Inches. Per cent. | Ft. persec.| Ft. per sec.| Ft. per sec. 
0 0 


0.05 52 58 +0. 06 8 05 : . 90 —0. 02 
- 10 78 . 82 + .04 -10 1.31 1.30 — .01 
- 20 99 1.16 + .17 . 20 1.89 1. 84 — .05 
-30 1.18 1.41 + .23 30 - 2.30 2. 26 — .04 
. 50 1.69 1. 83 + .14 50 2.99 2.91 — .08 
Ahi) 2.15 2. 24 + .09 75 3. 53 3. 57 + .04 
1.00 2.39 2. 58 + .19 1.00 3. 98 4.11 + .18 
1. 25 2. 82 2. 89 + .07 1. 25 4.42 4.61 + .19 

1.50 3.06 3.16 + .10 1.50 4. 83 5. 04 + .21 
05 61 . 67 + .06 10 -05 . 90 1.07 + .17 
-10 97 .95 — .02 -10 1.38 1. 52 + .14 
. 20 1.36 1.32 — .04 - 20 2. 06 2.15 + .09 
30 sei 1.65 — .06 30 2.47 2. 63 + .16 
- 50 2. 30 2.13 5 17/ . 50 3. 23 3.39 + .16 
5 0B 2. 69 2.61 — .08 5s 3. 87 4.16 + .29 
1.00 3.19 3.01 — .18 1.00 4.49 4. 80 + .31 
1.25 3. 53 3.37 — .16 1.25 4.99 5.37 + .38 

1.50 5.37 5. 88 + .51 
05 67 . 76 + .09 
-10 1.13 1.08 — .05 12 -05 1.20 1.21 + .01 
. 20 1.58 1. 53 — .05 -10 a2 ie — .0l 
30 1.97 1. 87 — .10 . 20 2. 37 2. 42 + .05 
50 2.30 2.41 + .11 30 2. 93 2. 97 + .04 
5 Os 2.95 2.95 + .00 

1.00 3. 26 3.41 + .15 
15745) 3.77 3. 81 +, .04 
1.50 4. 28 4.18 — .10 

Total plusidifierence wpe) oie A aise aches sea a eee eo 


Total minus difference. oo. orc <M wee «tec atone Maia eee nie otic otek eae eee 
Number of items: « =<) She. Mccaiteic cic) pa care hacen yates eR Oe on ame 48 
Average difference: 3. 5 .k entids wienlassawet tists alte ayes oRNeRee foot per second, . 


50 
45 
40], 
35 
30 


25 


25 


20 


CORKECTION 


ment of Agriculture, entitled "The Plow of Waters! 
Drain Tile," the formula given in the beg end seem | 


bottom of Plate XIII (facing page 48) should read; 


V= “98 APF S# 


c=) un eo 
[ay mon oe 


0 
iS 
i6 


Lx-9 7 


10; 
§ 


10 
REPRE RA RATT 


a 


Bul. 854, U. S. Dept. of Agriculture. 


N= 


00.0 


Ne 


SLOPE IN INCHES PER 100 FEET. 


2 3 4 5 6 7 8 9WNI2 18 24 


30 


20.0 


s 
Ss 


a 


S 


3000 
8000 


U-7000| 
6000-- 


4500- 
4000) 
3500 


3000- 
2500 


2000 


e 


1000 
900/- 


800) 


o 
=] 


V/\4 \ 


> 
S 


‘= 
i=) 


v 


5 


“ONOOSS H3d 1554 018ND NI SeuvHoSIG 


700 


450- 


A 


SNe 
a 


w 
i= 
T 


2 3 4. 5 10 2.0 


SLOPE IN FEET PER 190 FEET. 


DISCHARGE CURVES FoR DRAIN-TILE BASED ON FORMULA V~=138 S.! R.4. 


10 


6000} 


+5000; 


4500 
4000) 


S000] $90! 


3000 


2500) 


2000} 


1500 


+1200 


1500-1000 
fF 900. 


1200- 800 


700 
600 


500, 
450 


600+ 400 
- 350 


300 


250 


4500) 
4000 


3500 
3000 


2500 


2000 


1500 


1200 


1000 
900 


800 
700 
600 


500 
450 
400 
350 


3007 250 
a 200 


3500 
3000) 


2500 


2000 


1500} 


yyt2es 


P1000 
900 
800 
700 


600 


180 
200- 160 
180 140 
160 120 
140 

F 100 
\20, 90 
100- 80 
90, 79 
co i 
70 

- 50 
60 

i 45 
50 40 
45 35 
40], 

35 2 
jor 25 
25- 20 
0 
a 15 
15 

10 
10 

5 


5 


PLATE XIII. 


ACRES DRAINED 


3000 


asoo} “00? 


2000} 1500) 


120 
1500 ag 


1000) 
1200+ 300) 


1000 ay 
g00;- 700) 
B00} 600) 
700 500 
600+ 450 


4 
500) +2? 
450) 350 
400 300 
350 


300 
250 180 


3{R=4 [Ree] R=#"|R-8"| R=2 | R=1" 


aw! hk. & : 
ivNA Se 


4 


ZVOV I 


ae Ga a: | 


SSE Be 
SUMMA SE aia 
TINE Joh Peel kg 


PrRaeeres=s3 vi sa0ue 


| Mian Qon6? aayaUD,RDRAHOVIG) 6) 52 2, 


THE FLOW OF WATER IN DRAIN TILE. 49 


Equation 13 is tentatively offered for use in computing the capacity 
of tile drains, though with full recognition of the fact that further 
experiments are necessary to determine its applicability to tile of 
sizes larger than those used in these experiments. Additional data 
also are desirable to determine whether the variation in length of the 
» individual tiles is an important item to consider in the derivation | 
of a formula. — : 
For convenience in quickly determining the number of acres ; 
drained, for each size of tile and for various rates of run-off, Plate : 
XIII has been prepared from formula 13. Several velocity curves | 
are also shown for use in determining approximately the velocity | 
of flow. 


LOSS OF HEAD IN CATCH-BASINS. 


To actually determine the loss of head resulting from the installa- 

tion of a surface inlet or catch-basin in a tile line, experiments were 

* made on 8-inch clay tile at three different grades, 0.2, 0.75, and 1.50 

feet in 100 feet, with differences of 0.1, 0.2, and 0.3 foot between the 
elevations of the inlet and the outlet tiles. 

The catch-basin was made by inserting in the flume two wooden 

bulkheads 4 feet apart. The space between the bulkheads was | 

cleared of tile and earth and thus formed a basin 2 feet wide by 4 | 


ee me = 


feet long. The inlet and outlet tiles extended through the respective 
bulkheads. A piezometer was installed at the outlet of the catch- 
basin, another at a point 2 feet below the outlet, and a third at a 
point 2 feet below the second. Tests were made with and without 
the use of a 12 to 8 inch reducer at the outlet of the catch-basin. 
This reducer actually consisted of two sewer-pipe reducers (12 to 10 
inch and 10 to 8 inch), each 2 feet long. When the reducer was 
* used the middle piezometer was omitted. 


TABLE 10.—£Effect of reducers on the loss of head at outlets of catch-basins. 


Elevation of water surface without | Elevation of water surface 
reducers. with reducers. 
Drop ee Head: 
in rade saved by 
; 2 feet 4 feet 4 feet / 
Se of tile. [tn catch-| below below | Loss of} , ane below | Loss of | ,. ase Ont 
basin. catch- catch- head. asin catch- head. mel 
basin. basin. basin 
Foot. | Per cent. Foot. Foot. Foot. Foot. Foot. Foot. Foot. Foot. 
0.3 0. 20 0. 46 0. 44 0. 41 0. 05 0. 45 0. 41 0. 04 0. 01 
. 84 79 SHE .07 . 14 alo O01 . 06 
B15) . 08 Slay 45 ali . 56 ti . 04 . 09 
97 83 83 .14 . 81 80 O1 13 
1.50 65 53 49 zall6 . 64 53 ast! 05 
78 66 64 .14 . 16 76 00 14 
2 20 46 46 45 .O1 .44 43 01 00 
83 79 78 . 05 sD 74 O1 04 
75 53 53 52 .O1 .53 52 01 00 
76 74 74 . 02 .74 74 00 02 
1.50 67 65 53 .14 . 60 56 04 10 
Tega) 1.02 80 . 3d . 82 77 05 30 
1 20 44 43 . 43 . 01 . 45 43 O2n ew eae 
79 73 73 . 06 . 76 73 03 03 
75 56 48 43 aa[8} . 54 45 09 04 
89 68 66 .23 80 70 10 13 
1.50 68 60 56 Eel? 65 56 09 03 
1.11 80 | 78 OS 88 76 12 21 


166597 °—20—Bull, 8544 


50 BULLETIN 854, U. S. DEPARTMENT OF AGRICULTURE. 


The results of these observations are shown in Table 10. The 
data indicate that the use of reducers with tile flowing approximately 
full reduces the loss of head to practically nothing, while with tile 
flowing half full some loss of head occurs. Without reducers, the 
loss of head decreases with the decrease in slope. The variation in 
drop in the catch-basin did not materially affect the loss of head, 
which seems to be about equal to the grade through 15 feet length 
of drain. 


ADDITIONAL COPIES 


OF THIS PUBLICATION MAY BE PROCURED FROM 
THE SUPERINTENDENT OF DOCUMENTS 
GOVERNMENT PRINTING OFFICE 
WASHINGTON, D. C. 

AT 


25 CENTS PER COPY 
WV
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