rco
Cr 3
OREGON SlATE UPA?Y
b
ectsn
,;,o.35
c. 3
4.LCTOW
955
Model Studies
of Inlet Designs
for Pipe Culverts
on Steep Grades
By
MALCOLM H. KARR
Instructor in Civil Engineering
and
LESLIE A. CLAYTON
Associate Professor of Civil Engineering
BULLETIN NO. 35
JUNE 1954
In cooperation
WI'?I
Oregon State Highway De
ENGINEERING EXPERIMENT STATION
OREGON STATE COLLEGE
CORVALLJS
THE Oregon State Engineering Experiment Station was established by act of the Board of Regents of Oregon State College
on May 4, 1927. It is the purpose of the Station to serve the state
in a manner broadly outlined by the following policy:
(1)To stimulate and elevate engineering education by developing
the research spirit in faculty and students.
(2) To serve the industries, utilities, professional engineers, public
departments, and engineering teachers by making investigations of
interest to them.
(3) To publish and distribute by bulletins, circulars, and technical
articles in periodicals the results of such studies, surveys, tests, investigations, and research as will be of greatest benefit to the people
of Oregon, and particularly to the state's industries, utilities, and
professional engineers.
To make available the results of the investigations conducted
by the Station three types of publications are issued. These are:
(1) Bulletins covering original investigations.
(2) Circulars giving compilations of useful data.
(3) Reprints giving more general distribution to scientific
papers or reports previously published elsewhere, as for example, in
the proceedings of professional societies.
Single copies of publications are sent free on request to residents
of Oregon, to libraries, and to other experiment stations exchanging
publications. As long as available, additional copies, or copies to others,
are sent at prices covering cost of printing. The price of this publication is 40 cents.
For copies of publications or for other information address
Oregon State Engineering Experiment Station,
Corvallis, Oregon
Model Studies
of Inlet Designs
for Pipe Culverts
on Steep Grades
By
MALc0I.M H. KARR
Instructor in Civil Engineering
and
L1sLIE A. CLAYTON
Associate Professor of Civil Engineering
BULLETIN NO.
35
JUNE 1954
In cooperation with
Oregon State Highway J)epartment
ENGINEERING EXPERIMENT STATION
OREGON STATE COLLEGE
CORVALLIS
Foreword and Acknowledgmenfs
The initial phases of this project were conducted
in part by Russell Avery, a former student at Oregon
State College. Much of the subsequent work, including
compilation of the data, was performed with the aid
of Virgil R. Morton and Ray V. Walter, students in
civil engineering, who first proposed the modification
incorporated in Model 4. Mr. R. H. Shoemaker, Jr.,
instructor in civil engineering, gave much valuable
assistance and advice throughout the project.
The authors thank these people for their capable
assistance.
Table of Contenfs
Page
I. INTRODUCTION --------------------------------------------------------------------------
5
II. FUNDAMENTAL CONCEPTS ------------------------------------------------------
General --------------------------------------------------------------------------
6
8
8
2. Discharge measurements ----------------------------------------------------
8
III. DESIGN, CONSTRUCTION, AND OPERATION ---------------------------1.
3. Head measurements ------------------------------------------------------------ 8
4. Pressure measurements ------------------------------------------------------ 9
5. Photographic data ---------------------------------------------------------6. Accuracy of measurements ----------------------------------------------
7. Experimental procedure
9
9
------------------------------------------------ 11
IV. TESTS AND RESULTS ---------------------------------------------------------------- 11
1. Description of inlets ---------------------------------------------------------- 11
2. Performance of inlets ---------------------------------------------------- 12
3. Entrance loss coefficients -------------------------------------------------- 16
V. CONCLUSIONS AND RECOMMENDATIONS -------------------------------- 18
VI. BIBLIOGRAPHY -------------------------------------------------------------------------- 19
VII.
APPENDIX ---------------------------------------------------------------------------------- 19
Illustrations
Page
Figure
1.
Figure
Figure
Figure
Figure
2.
Inlet Shapes for Models Tested on 4 Per Cent
Slope------------------------------------------------------------------------------
Sketch of Test Setup ------------------------------------------------
Location of Piezometer Tubes for All Models
Typical Data Photograph -----------------------------------------5. Rating Curves for Models 1, 2, and 3 on 4 Per
CentSlope -------------------------------------------------------------------Figure 6. Characteristics of Various Tnlets Installed as
3.
4.
6
8
9
10
12
Orifices------------------------------------------------------------------------ 13
Rating Curves for Models 3, 4, and 6 on 4 Per
CentSlope -------------------------------------------------------------------Rating Curves for Models 3, 4, and 6 on 8 Per
CentSlope -------------------------------------------------------------------Rating Curves for Models 3, 4, and 6 on Flat
Figure
7.
Figure
8.
Figure
9.
Figure
10.
Sketch of System Showing Idealized Energy and
11.
Pressure Grade Lines and Energy Losses -----------Typical Plot of Entrance Loss Coefficients for
Models 4 and 6 with Full Flow on 4 Per Cent
16
Figure
Slope----------------------------------------------------------------------------
17
14
15
Grade---------------------------------------------------------------------------- 16
3
List of Tables
Page
Table
Table
1
2.
Tabulation of Entrance Loss Coefficients for
Models 3, 4, and 6 with Full Flow on All Slopes
.
19
Model 1, Free Flo\v Culvert Slope 4, Pressure
Readings from Piezometer Ttibes ------------------------------ 20
Table
3.
Model 2, Free Flow Culvert Slope 4y, Pressure
Readings from Piezometer Tubes ------------------------------ 21
Table
4.
Model 3, Free Flow Culvert Slopes 04 and 8%,
Pressure Readings from Piezometer Tubes -------------- 22
Table
5.
Model 3, Free Flow Culvert Slope 4, Pressure
Readings from Piezometer Tubes ------------------------------ 23
Table
6.
Table
7.
Table
8.
Table
9.
Model 4, Free Flow Culvert Slopes 0% and 8%,
Pressure Readings from Piezometer Tubes .............. 24
Model 4, Free Flow Culvert Slope 4%. Pressure
Readings from Piezometer Tubes ------------------------------ 25
Table 10.
Table 11.
Model 6, Free Flow Culvert Slopes 0/ and 8%,
Pressure Readings from Piezometer Tubes .............. 26
Model 6, Free Flow Culvert Slope 4%, Pressure
Readings from Piezometer Tubes .............................. 27
Model 3, Full Flow Culvert Slopes 0% and 8%,
Pressure Readings from Piezometer Tubes -------------- 28
Model 3, Full Flow Culvert Slope 4%, Pressure
Readings from Piezometer Tubes .............................. 29
Table 12. Model 4, Full Flow Culvert Slopes 0% and 8%,
Pressure Readings from Piezometer Tubes .............. 30
Table 13. Model 4, Full Flow Culvert Slope 4%, Pressure
Readings from Piezometer Tubes ------------------------------ 31
Tablecontinued ............................................................ 32
Table 14.
Model 6, Full Flow Culvert Slopes 0% and 8%,
Pressure Readings from Piezometer Tubes -------------- 33
Table 15.
Model 6, Full Flow Culvert Slope 4%, Pressure
Readings from Piezometer Tubes .............................. 34
4
Model Studies of Inlet Designs
for Pipe Culverts on Steep Grades
By
MALCOLMH. KARR
Instructor in Civil Engineering
and
LESLIE A. CLAYTON
1ssociatc Professor of Civil Engineering
I.
Infroducfion
Interest in the improvement of culvert operation through the
study of experimental models has increased rapidly in the past few
years. These studies are no longer directed entirely toward the determination of theoretical aspects of culvert operation, but are concerned also with the immediate problems of design to improve the
performance of culverts.
Recently completed tests of inlet designs for box culverts',
conducted at Oregon State College, suggested the need for a similar
series of tests for pipe culvert inlets. As a result, a research project
for undergraduate sttldents in the Civil Engineering Department was
initiated in March 1952 and sponsored by Armco Metal and Drainage
Products, Inc. By June 1953, work on the student project was
thought promising enough to warrant a research study by the Engineering Experiment Station, with cooperation and assistance from
the Oregon State Highway Department.
Need for such experiments was indicated by the fact, observed
in the field, that pipe culverts on steep slopes (normally 1 per cent
or greater) did not flow full when the headwater submerged the
inlet.
Purposes of these experiments were: (1) to observe the behavior of a number of typical culvert installations that did not flow
full, and (2) to evolve a simple and practical means of forcing these
culverts to flow full (prime) under field conditions.
Tests were performed on a 1:12 scale model of a 4-foot diameter
pipe culvert with free overfall on the (loWflstream end. Models 1, 2,
and 3 (Figure 1) were selected as being typical culvert installations
under current design practices. Model 3 is the one most commonly
1Model Studies of Tapered Inlets for Box Culverts, by Roy H. Shoemaker, Jr.,
and Leslie A. Clayton. Research Report 15-B, Highway Research Board, \vash., n. C.,
and Reprint No. 43, Engineering Experiment Station, Oregon State College.
6
ENGINEERING EXPERIMENT STATION BULLETIN 35
used by the Oregon State Highway Department. Models 4 and 6,
modifications of Model 3, were chosen from those tested as the most
economical and practical modifications that permitted the culvert to
prime automatically. The shortest extension lengths that assured
automatic priming of the culvert were chosen as the final dimensions
for the modifications.
II. Fundamental Concepts
Flow through pipe culverts on steep slopes can be controlled in
any one of three ways (as outlined below), depending upon the
elevation of the headwater pool and the location of the control. The
shift in location of control from culvert entrance to culvert exit
can result in a marked increase in flow and may result in unstable
flow conditions.
1. Inlet not submerged. When the inlet is not submerged,
flow through the culvert is controlled by critical depth at the inlet.
Elevation of the water surface drops rapidly to critical depth near
the entrance and open channel flow at supercritical velocities exists
in the remainder of the culvert barrel. Discharge for a given head-
MODEL I
MODEL 3
MODEL 2
MODEL 4
MODEL 6
Figure 1.
Inlet Shapes for Models Tested on 4 Per Cent Slope
INLET DESIGNS FOR PIPE CULVERTS
water pooi elevation can be computed by means of critical depth
relationships, assuming critical depth to occur at the culvert entrance.
Critical depth may occur a short distance downstream from the
culvert entrance, but for design purposes the above assumption is
sufficiently accurate.
2. Inlet submerged. After the inlet has been submerged, it
is still possible to have open channel flow in the culvert barrel if the
control remains at the entrance. In this case, flow at the entrance is
analogous to orifice or sluice flow. The stream lines near the bottom
of the culvert remain straight, but the water entering the top portion
of the culvert with a velocity component perpendicular to the axis
of the culvert will not cling to the top of the barrel. The resulting
contraction of the stream leaves an air space at the top of the culvert
near the entrance. At low heads of submergence, open channel flow
exists in the culvert barrel, which permits air to fill the top of the
culvert and prevents full flow. As the head of submergence increases,
channel friction or local disturbance may force the barrel to flow
full near the outlet. The high velocity flow near the entrance carries
away the air which has been trapped at the top of the barrel and full
flow results.
3. Barrel flowing full. With the barrel flowing full, the control
shifts to the outlet, and the additional elevation (due to the slope
of the culvert) is now available to produce additional flow through
the culvert.
In this case, flow through the culvert may be analyzed from the
standpoint of pipe flow theory by assuming that the hydraulic grade
line at exit is at the center of the culvert. The elevation difference
between headwater and hydraulic grade line at exit may be charged
to entrance loss, pipe friction loss, and exit velocity head. For a given
culvert, flow increases as entrance loss decreases.
Culvert operation with the inlet submerged may swing from inlet
to outlet to inlet control if the stream flow is not sufficient to maintain
full flow in the culvert barrel. In many inlets this change in control
is accompanied by a rapid fluctuation in headwater elevation and
severe vortex action when the barrel is flowing full.
With the above concepts in mind, it is possible to define the
ideal culvert entrance as one which will prime automatically and,
in so doing, will prevent an undesirable rise of headwater elevation.
It must be defined further as one which results in a minimum possible
entrance loss.
ENGINEERING EXPERIMENT STATION BULLETIN 35
III. Design, Construction, and Operation
1. General. The model used in these experiments consisted of
an approach channel, culvert inlet section, and culvert barrel, as
shown in Figure 2.
The approach channel was 8 feet long, 4 feet wide, and 4 feet
deep. The channel floor was level throughout the tests. Baffles were
placed in the channel near the 6-inch supply line to redtice turbulence
in the pool to a minimum.
The culvert barrel was fabricated from flat sheets of -inch
plexiglas into a pipe of 4 inches IT) and 82 inches long. The barrel
discharged in a free overfall into a collecting tank leading to the
weighing tanks used in measuring the discharge.
2. Discharge measurements. Weighing tanks mounted on
Toledo scales with a capacity of 12,000 pounds were used in measur-
ing discharge. An average of three or more stopwatch readings
and a predetermined weight increment were converted to cubic feet
per second for each flow. The weight increments were chosen in such
a manner that the time interval for discharge of that weight of water
would be greater than 30 seconds, thus keeping to a minimum the
error due to human reaction time.
8 FT
6-IN SUPPLY
PIPE
FLOW
ROACH CHANNE
4 FT WIDE
BAFFLES
PLEXIGLAS
NLET
MBANKMEWT
CULVERT BARREL
LEVEL
AD.LJSTABLE SLOPE
TO
WE IGHING
TANKS
Figure 2.
Sketch of Test Setup
3. Head measurements. Pool elevation measurements were
taken from three piezometer tubes connected to the bottom of the approach channel at a point 18 inches upstream from the culvert inlet
and spaced evenly at right angles to the culvert and channel axis. The
readings from the three piezometer tubes were averaged for the
pool elevation.
INLET DESIGNS FOR PIpE CULVERTS
4. Pressure measurements. Piezometer tubes mounted on the
bottom of the culvert barrel and spaced along the axis, as shown in
Figure 3, gave pressure readings. Additional tubes, one on top of
the culvert and one on each side (Figure 3), gave pressure readings
at those points.
ACSS
CHANL
®
TOP OF CULVERT
INVERT
I
-I.
4D
ROSS
CHANNEL
TOP OF O.VERT
."
Lr
INVERT
I
D
Figure 3.
Location of Piezometer Tubes for all Models
One-fourth inch ID Tygon tubing was used in the connections
from the piezometer fittings to the i-inch If) glass tubes mounted
on a board rigidly attached to the downstream end of the channel.
The piezometer board was provided with 0.1-inch divisions
ruled with India ink on transparent acetate backed with white drawing
paper, and coated with clear lacquer.
5. Photographic data. Piezometer readings were taken photographically in order to reduce the time necessary to read the tubes
and to eliminate the possibilities for error that would result from
attempts at visual reading and recording in rapid order. Subsequent
printing of the photographic data on 5-in, by 7-in, paper made the
information permanent. Identification of each photograph was accomplished by the use of descriptive legends for each run photographed with the piezometer tubes. A typical data photograph is
illustrated in Figure 4.
6. Accuracy of measurements. The discharge measurements
were the most accurate. A continuous reading of time intervals at
the weighing tank was an accurate means of determining stability
10
ENGINEERING EXPERIMENT STATION BULLETIN 35
Figure 4.
Typical Data Photograph
of flow. It was found that, after a sufficient waiting period, time
interval readings had a variation of less than 1 per cent. For pressure
readings, meniscus of the water column was sufficiently defined to
estimate readings to 0.05 of an inch. Conditions at the inlets for
high heads, however, were such that pressure tube readings for
the inlet regions were constantly fluctuating a small amount. Photo-
graphs taken at the instant water columns were relatively stable
gave an average reading and, at the same time, caught all of the
readings in true relationship to each other. It is estimated these
pressure readings are in error no more than 4 per cent.
Piezometer readings for the elevation of the headwater pool
were very steady for all flows. Approach conditions were such,
however, that the three water columns did not read the same at high
INLET DESIGNS FOR PIPE CULVERTS
11
heads. Because this difference was never more than 0.2 of an inch,
an average of the three readings gave a value of less than per cent
in error.
7. Experimental procedure. Each inlet to be tested was run
through its entire range of discharge for the purpose of visual observation of its operational characteristics. From these observations
it was possible to determine the essential test data to be taken to
describe fully the inlet operation. Subsequently, inlets were again
run through their full discharge range, with photographic data taken
and discharge measured for each run. A rating curve of head versus
discharge was carried along with each test by plotting each point
as it was obtained. In this manner, any obvious errors in calculations
or observations became evident as plotted points that did not follow
the general shape of the curve. Corrections were made immediately.
In the case of inlet Models 4 and 6 (Figure 1), preliminary
testing was necessary to determine the optimum extension length for
the design being tested. The preliminary testing consisted of obtaining
a rating curve for each type of extension at various lengths of
extension.
After determining the optimum extension length, final tests
were made with the extensions of optimum length installed. The
procedure followed for these final tests was the same as that for
the other inlets.
Complete testing of all models was made initially for the culvert
on a 4 per cent grade, with subsequent check-point tests being made
for Models 3, 4, and 6 installed on both 8 per cent and flat grades.
IV. Tests and Results
1. Description of inlets. Inlet shapes tested are shown in
Figure 1. For Model 1 the headwall was vertical, with the inlet set
flush with the headwall and the invert on the channel bottom. For
all other models a 2 :1 embankment slope was used. In Model 2 the
inlet was cut off flush with the embankment slope, with the invert
coinciding with the toe of the slope. Model 3 consisted of a normal,
square-cut end section of pipe extending through the embankment
slope so the invert coincided with the toe of the slope. Inlet 4 con-
sisted of a half-section of pipe mounted as a roof extension on
Inlet 3.
For preliminary tests, extensions were formed of sheet metal
and mounted on the outside of the pipe. The preliminary tests were
macic of extensions varying in length up to one pipe diameter in
12
LNGINEERING LXPERIMENT STATION BuLnTIN 35
increments of D/8. The extension for the final tests was formed from
plexiglas and mounted flush with the end of the pipe.
inlet 6 consisted of a full section of pipe cnt off from a given
extension length at the top to zero at the bottom, and mounted as
a roof extension on Inlet 3. As with Model 4, preliminary tests were
run on extensions formed from sheet metal mounted on the outside
of the pipe. These extensions varied up to one pipe diameter in length
in increments of D/4. The final tests were made on a plexiglas extension mounted flush with the end of the pipe.
2. Performance of inlets. The tests indicated that Models 1,
2, and 3 would not flow full automatically on steep grades. Artificial
priming forced them to flow full until air was admitted to the
entrance, either by vortex action or by drawing down the elevation
of the headwater pool, when they again reverted to free flow. The
typical condition at the entrance in this case was that of an orifice
discharging under head, with a contraction at the top and sides of the
jet and a slight contraction at the bottom.
Rating curves for Models 1, 2, and 3, with the culvert barrel
on a 4 per cent grade (Figure 5), show that variation in flow can
be correlated with relative values of orifice contraction coefficients.
IIIUUUIUUIiUU
..........U.u...........
.UUI!!UU!iIUU!U!Uu
OOCJ-IARGECU FT PER SEC
Figure 5.
Rating Curves for Models 1, 2, and
3 on 4
Per Cent Slope
INLET DESIGNS FOR PIPE CULVERTS
13
Inlet 1, which is on the order of a sharp-edged orifice, would be
expected to yield more flow for a given head than would Inlet 3,
which is similar to a re-entrant tube.
Inlet 2, which shows the poorest performance, is similar to a
sharp-edged orifice lying in an inclined plane which discharges flow
with a velocity component perpendicular to the culvert axis. This
added velocity component in the vertical plane serves to further
contract the area of flow a short distance downstream, and the
result is a lower contraction coefficient.
The modifications of Model 3, as shown by Inlets 4 and 6, gave
an upward component to the velocity, which eliminated the top con-
traction a short distance downstream. This is illustrated in Figure 6,
which shows the shape and characteristics of the jets produced by
Models 3, 4, and 6 installed in a tank as orifices.
A special tank having a vertical headwall was made for this
purpose, and the inlet sections alone (with no culvert barrel) were
mounted in an opening in the side of the tank. The contractions
at the inlets (Figure 6) are as they appeared to the observer while
looking at the inlets from the inside of the tank. The profiles of
the jets are in respect to an observer's position outside of the tank.
The jet cross sections are taken at the plane of the tank wall as
INLET
NO
PROFiLE
ONTRACTIO
AT INLET
PROFiLE CROSS SECTION
OF.T
OF JET
DESCRIPTION OF CI-IARACTERISTICS
ORIFICE
-
..
U,,ifo,,u contr,tjon ]i rom,d thiet.
2. Jt prg fre. fl
I
I
cii
T
UT
ORIFiCE
::
6
2
ORIFICE
Figure 6.
Characteristics of Various Inlets Installed as Orifices
14
uM
LNGINEERING LXPERIMENT STATION BULLETIN 35
uuuuuiiuuuuriu
uuuuauuuui...i
U. UUUUUUU UUU UUIUU.UUU. U
...................U
IUUli!UUflUUBUUUUUIB
Figure 7.
Rating Curves for Models 3, 4, and 6 on 4 Per Cent Slope
observed from outside the tank and show that Models 4 and 6
eliminated the top contraction. By eliminating the top contraction,
water was allowed to cling to the top of the culvert, forcing the air
out and resulting in full flow.
The performance of Models 4 and 6 for free flow (inlet not
submerged), with the culvert on a 4 per cent slope, corresponded
closely to the performance of Model 3 for the same conditions
(Figure 7). Immediately upon submergence of the inlet, both Models
4 and 6 caused the culvert to prime and the discharge was increased
90 per cent, while the corresponding increase in headwater elevation
was the equivalent of only of a pipe diameter.
This same rise in head produced less than 15 per cent increase
in flow for Model 3. To obtain 90 per cent more flow upon submergence of the inlet of Model 3, a head increase equivalent to 1pipe diameters was required. When Model 3 was artificially primed,
however, the flow was greater than the flow in Models 4 and 6
at the same heads, which indicated a higher entrance loss for the
modifications as compared with Model 3.
Vortex action was present in Models 4 and 6 up to
1
diameters of submergence. While these vortices admitted air to the
inlets, causing the flow to fluctuate a small amount (less than 2 per
cent), they did not cause the culvert to lose its prime. The culvert
INLET DESIGNS FOR PIPE CULVERTS
15
remained full until the discharge increased sufficiently to drop the
head below the top of the inlet. At this point the culvert could no
longer maintain its prime and the head would again increase until,
shortly after submergence, the modifications again would cause the
culvert barrel to fill. This cycle of priming, dropping head, losing
prime, and rising head would continue until the stream discharge had
been increased the previously mentioned 90 per cent, at which point
a stable full-flow condition was reached.
Verification of the above results was made by testing Models 3,
4, and 6 with the culvert on an 8 per cent grade. The results are
similar to those with the culvert on a 4 per cent grade, as shown
by the rating curves of Figure 8. In this latter case, the increase in
NORMAL OPtRATON
.$XEL 3
o
0
CL 4
OL 6
OISCHA.F ru rr pen crc
Figure 8.
Rating Curves for Models 3, 4, and 6 on 8 Per Cent Slope
flow given by the modifications, which caused the culvert to flow full
upon submergence of the inlet, was more than 100 per cent of the
normal flow of Model 3. Artificial priming of Model 3, however,
once again confirmed the fact that Models 4 and 6 caused an appreciable increase in entrance loss.
Additional tests of Models 3, 4, and 6 were made with the
culvert on a flat grade. Reference to the rating curves of Figure
9 shows that Model 3 produced the greatest discharge under all
head conditions. These culverts on flat grades primed of their own
accord, and for this reason the increased energy loss at the entrance
given by the modifications was a detriment to the flow.
ENGINEERING EXPERIMENT STATION BULLETIN 35
16
uuuuuuuuuuurnauu
U UU....UUV
U.U.UUUUUUUUUUUUdUUUU
UUUUUUUUUUUdUUUUUU
uuuuiuuuuuu
UUUUUUlUn:'aiUU
.....UU.................
-'
.
.UU!UUIU!UUUU!!UUl!11
UISCtAMbt,UJ
I
EtH 5tt
Figure 9.
Rating Curves for Models 3, 4, and 6 on Flat Grade
Ke
JRADL
TUM
-
T4-J
Figure 10.
Sketch of System Showing Idealized Energy and
Pressure Grade Lines and Energy Losses
3. Entrance loss coefficients. Referring to Figure 10, the
energy equation for steady flow may be written
H=+Ke++ +Z
W
where
H
V
V2
V2
fL
V2
2q
2g
D
2g
P
energy at the upstream pond above a common datum
taken as the culvert invert at the outfall
velocity in the pipe
INLET DESIGNS FOR
Ke
friction factor for Darcy-Weisbach equation
distance from the culvert inlet
pipe diameter
f
W
If
potential head at the point as measured by the
+Z
h
17
CILVERTS
entrance loss coefficient
L
D
P
Pipi:
piezometer reading for that point
equals the difference between the upstream water level and
P/W + Z at any point, then
fL
zh= 1+Kc+
D
which can be rewritten
_
=1+Kc+
V2/2g
A plot of
fL
B
versus L may be assumed as a straight line for
V2/29
those values of L sufficiently removed from the inlet that the corQ =0606 FS
P.e (moM PLOT) = 0615
-----------=
(0
IJ
I
I..---
---------------------I.c - -
010
- - - - - - - - - 20
30
40
0
60
L, INCHES FROM CULVERT INLET
70
A0
Figure 11.
Typical Plot of Entrance Loss Coefficients for Models 4 and 6 with
Full Flow on 4 Per Cent Slope
ENGINEERINC EXPERIMENT STATION BuIJTIN 35
18
responding piezorneter readings no longer are affected by the curvi-
linear path of the water upon entering the inlet. Protracting this
straight line back to the entrance gives the value of 1 + Ke, and
the slope of the line is f/D. Since &i and V both vary with the discharge, it seems reasonable to expect the value for Ke to vary with
the discharge. Figure 11 is a typical plot of the data for Model 6
and a 4 per cent slope, as described above.
The tabulations in Table 1 (appendix) show the range of en-
trance loss coefficients found for Models 3, 4, and 6 for full flow
on all slopes tested. The average coefficients for Models 3, 4, and 6
are 0.50, 0.67, and 0.57, respectively. These verify the indications
noted earlier that Models 4 and 6 caused greater energy loss at the
entrance than Model 3.
No further analysis of the data was made other than that
described herein. All the data taken, however, are included in
tabular form in the appendix for the convenience of those who may
desire to go further into an analysis of the results.
V. Conclusions and Recommendafions
Models 1, 2, and 3, which are typical pipe culvert installations
on steep grades in use today, are not efficient because they do not
allow full flow upon submergence of the inlet.
Modifications as proposed with Models 4 and 6 insure full
flow of the culvert when the inlet is submerged. This means the
capacity of existing installations on steep slopes can be increased
materially with a minimum of added cost, and the size of future
installations can be reduced if the modifications recommended are
made.
The proposed modifications can be installed easily and rapidly.
They are simple to fabricate, low in cost, and will give more efficient utilization of the pipe material.
Further experimentation to produce an inlet (lesign resulting
in smaller entrance losses is desirable. This must be a simple design,
however, or the increased cost of fabrication and installation will
not be offset by the gain in efficiency.
INLET DESIGNS FOR PIPE CULVERTS
19
VI. Bbliography
1.
Allen, J. Scale models in hydraulic engineering. New York: Longmans,
2.
Culvert hydraulics. Highway Research Board, research report 15-B, 1953.
King, Horace W., Wisler, Chester 0., and Woodburn, James G. Hydraulics,
5th ed. New York: John Wiley and Sons, 1948.
Mavis, F. T. Hydraulics of culverts. Bulletin 56, Engineering Experiment
Station, Pennsylvania State College, 1942.
Green and Co., 1952.
3.
4.
5.
Straub, Lorenz G., Anderson, A. G., and Bowers, C. E. Effect of inlet
design on capacity of culverts on steep slopes. University of Minnesota,
St. Anthony Falls Hydraulic Laboratory project, report no. 37, August 1953.
6. Vennard, John K. Fluid mechanics, 2d ed. New York: John Wiley and Sons,
1947.
VII. Appendix
Tables 2-16 contain tabulations of all data taken for the project.
The column headed "Tube No." refers to the piezometer tubes
located as shown in Figure 3 of the text. "L" is the distance in inches
from the culvert invert at the inlet to the respective piezometer tube.
Table 1. TABULATION OF ENTRANCE Loss COEFFICIENTS FOR MODELS
3, 4, AND 6, WITH FULL FLOW ON ALL SLOPES TESTED
Model 4
Model. 3
Slope
Q,
cfs
I
Ke
Q,
cfs
Ke
Model 6
Q,
cfs
Ke
Flat grade
0.405
0.506
0.500
0.550
0.352
0.413
0.477
0.530
0.565
0.460
0.465
0.420
0.445
0.496
0.519
0.559
0.515
0.525
0.435
0.515
4 per cent
grade
0.285
0.445
0.535
0.655
0.715
0.820
0.334
0.360
0.395
0.418
0.451
0.481
0.509
0.540
0.550
0.575
0.608
0.590
0.575
0.645
0.610
0.660
0.640
0.630
0.590
0.645
0.600
0.595
0.429
0.490
0.537
0.605
0.550
0.640
0.372
0.478
0.545
0.610
0.625
0.720
0.338
0.381
0.439
0.505
0.545
0.606
0.550
0.570
0.650
0.600
0.540
0.615
0.469
0.505
0.565
0.570
0.590
0.560
8 per cent
grade
Table 2.
MODEL
1,
FREE FLOW CULVERT SLOPE
4%
PREssuRl READING FROM PIEZOMETER TUBES
Tube
L
No.
(in.)
....
1,
4
1
5
6
3
................................................
7
8
9
10
7
..............................................
12
13
15
9
11
11
14
5
..............................................................
..............................................................
13
15
17
19
21
23
16
17
18
19
27
20
51
21
59
63
22
23
31
35
43
67
24
71
25
73
75
77
79
81
...............................................................
................................................................
26
27
28
29
0046
0.099
0.159
0.272
0346
0.398
0221
0.449
4.80
4.25
5.90
4.95
4.65
4.30
4.25
4.20
4.05
3.85
3.85
3.80
3.70
3.50
3.50
3.40
3.25
3.05
2.75
2.40
2.10
2.00
1.90
1.70
1.70
1.60
1.50
1.30
0.90
7.15
9.90
6.00
6.15
5.60
5.20
5.10
4.98
4.90
4.85
4.80
4.70
4.65
4.60
4.40
4.35
4.15
3.90
3.55
3.25
3.10
3.00
2.85
2.80
2.70
2.65
2.30
1.60
12.50
5.90
6.40
5.90
5.40
14.75
3.40
6.40
6.15
5.80
5.45
4.90
4.70
4.75
4.85
4.90
8.40
5.80
17.60
2.60
6.70
6.30
3.85
3.70
3.65
3.55
3.40
3.35
3.30
3.20
3.10
3.05
3.00
2.80
2.70
2.50
2.25
2.00
1.70
1.50
1.40
1.20
1.15
1.05
1.05
0.95
0.80
Readings are in inches above culvert invert at outfall. Q is flow in cfs.
5.68
5.55
5.10
4.85
4.70
4.50
4.50
4.40
4.35
4.20
4.15
4.10
3.90
3.85
3.60
3.45
3.00
2.70
2.50
2.40
2.30
2.20
2.10
2.00
1.90
1.40
5.15
4.90
4.90
5.00
4.95
4.80
4.80
4.75
4.50
4.50
4.30
4.10
3.80
3.45
3.30
3.25
3.05
3.00
2.90
2.85
2.50
1.60
4.90
4.80
4.55
4.60
4.40
4.10
3.80
3.05
3.40
3.30
3.20
3.15
3.00
2.95
2.55
1.65
5.75
5.30
4.95
4.90
4.70
4.65
4.60
4.55
4.40
4.35
4.30
4.15
4.05
3.85
3.60
3.20
2.95
2.80
2.65
2.50
2.40
2.30
2.25
2.00
1.40
5.65
5.30
4.75
4.60
4.70
4.70
4.70
4.75
4.70
4.40
4.50
4.25
4.05
3.60
3.40
3.30
3.20
3.05
3.05
2.90
2.90
2.40
1.40
MODEL 2, FREE FLOW CULVERT SLOPE 4%
PRESSURE READING FROM PIEZOMETER TUBES
Table 3.
Tube
No.
1,
2,
3
0.037
0.082
Q=
0.118
0.163
Q=
0.219
0.354
4.90
5.50
6.00
6.60
7.45
9.40
15.35
4.75
4.30
4.00
5.30
4.85
4.50
4.30
4.10
4.00
3.80
3.75
3.60
3.55
3.50
3.40
3.10
2.90
2.60
2.30
1.90
1.80
1.65
1.50
5.85
5.55
5.00
4.35
7.40
7.20
6.90
9.30
9.05
8.40
6.93
15.05
14.45
12.70
1.45
1.60
1.50
1.55
1.45
1.00
6.50
6.30
5.90
5.25
4.80
4.65
4.50
4.35
4.20
4.15
4.10
3.90
3.65
3.50
3.20
2.80
2.40
2.40
2.20
2.00
1.90
1.80
....
4
3
6
5
.............................................................................
7
7
8
9
9
10
................................................................................
................................................................................11
11
15
12
13
14
17
19
21
15
23
................................................................................
................................................................................
........................................................................................
16
17
18
19
...............................................................................
13
27
31
20
33
43
51
21
59
63
67
...............................................................................
................................................................................
................................................................................
...............................................................................
........................................................................................
22 ...............................................................................
23
24
25
26
27
28
29
Q=
1
5
t'a
0=
0.033
I.
(in.)
71
73
75
77
...............................................................................
................................................................................
79
81
................................................................................
..............................................................................
...............................................................................
Readings are in inches above culvert invert at outfall. Q is flow in cfs.
4.00
3.90
3.65
3.60
3.55
3.40
3.20
3.20
3.15
2.90
2.70
2.45
2.00
1.70
1.60
1.50
1.20
1.20
1.15
1.30
1.05
1.25
1.10
0.90
0.80
0.90
4.40
4.30
4.15
4.00
3.90
3.85
3.80
3.55
3.40
3.15
2.83
2.50
2.10
2.10
1.90
1.65
6.20
5.40
5.10
4.90
4.80
4.60
4.50
4.45
4.25
4.00
3.75
3.50
3.10
2.70
2.70
1.85
2.58
2.25
2.20
2.00
2.10
1.70
1.30
1.90
1.40
5.35
4.95
9.30
6.05
2.90
2.95
2.80
2.50
2.45
2.30
2.35
2.15
4.60
4.20
4.00
4.70
5.00
5.00
4.55
4.30
4.15
4.00
3.50
3.20
3.40
3.20
2.90
2.80
2.60
2.70
2.40
1.45
1.50
4.95
4.80
4.70
4.70
4.55
4.40
4.10
3.90
3.70
3.25
MODEL
Table 4.
3,
FREE FLOW CULVERT SLOPES
0%
AND
8%
PRESSURE READING FROM PIEZOMETER TUBES
Tube
L
No.
(in.)
1,2,3
4
5
6
7
1
8
9
10
3
5
7
11
9
12
13
11
13
15
17
19
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
21
25
29
33
41
49
57
61
65
69
71
73
75
Culvert slope 0%
Q
Q
Culvert slope 8%
I
Q=
0.087
Q=
0.238
Q=
0.320
Q=
0.406
6.10
4.40
9.40
12.30
1.90
1.90
1.80
1.70
8.65
8.05
2.20
1.90
2.00
2.10
2.15
2.20
2.20
2.20
2.20
2.20
2.20
2.15
2.10
2.00
2.00
2.00
2.90
2.70
2.30
2.10
8.40
8.10
8.20
8.10
9.20
9.20
8.60
8.20
7.90
7.70
7.50
7.30
7.10
6.90
6.80
15.30
10.50
8.00
8.10
19.90
10.30
7.90
8.00
6.40
0.070
0.236
2.80
4.50
1.90
1.80
1.80
1.75
1.70
1.70
1.60
7.55
7.30
7.10
6.85
6.65
6.45
6.25
6.10
1.90
1.90
1.90
1.90
1.90
1.90
1.90
1.90
1.95
6.00
5.50
5.30
4.90
4.20
3.50
2.80
2.50
2.20
2.00
2.10
2.20
3.00
3.10
3.10
3.10
1.90
1.70
1.40
1.30
3.05
3.00
3.00
6.35
6.10
5.70
5.05
4.30
3.60
3.20
3.00
2.50
2.40
2.20
220
9.60
9.60
9.00
8.50
8.00
7.70
7.70
7.60
7.40
7.30
7.10
6.60
6.40
6.10
5.40
4.60
3.90
3.60
3.30
3.00
2.80
2.60
2.50
Readings are in inches above culvert invert at outfall. Q is flow in cfs.
7,
9.60
9.00
8.30
7.80
7.60
7.40
7.30
7.30
7.35
6.70
6.50
6.20
5.60
4.75
4.10
3.80
3.60
3.10
3.10
2.80
2.80
MODEL 3, FREE FLOW CULVERT SLOPE 4%
PRESSURE READING FROM PIEZOMETER TUBES
Table 5.
Tube
L
No.
(in.)
0.064
0.098
0.175
0.212
0.260
0.342
0.411
8.50
7.30
5.00
5.00
6.10
5.90
5.35
4.90
4.75
4.70
4.65
4.60
4.40
4.35
4.30
4.10
3.80
3.60
3.30
2.80
2.60
2.40
2.20
2.00
10.10
7.20
4.80
4.80
6.40
6.10
5.60
5.10
4.80
4.85
4.90
4.80
4.60
4.60
4.40
4.25
4.10
3.80
3.60
3.10
2.80
2.60
2.40
2.30
2.20
2.20
2.20
13.10
7.20
4.50
4.70
6.90
6.40
5.90
5.30
4.85
4.60
4.70
4.90
4.80
4.70
4.60
4.40
4.25
4.10
3.80
3.30
3.00
2.80
2.70
2.60
2.30
2.30
2.30
16.20
7.10
4.40
4.60
7.10
6.60
6.20
5.50
5.00
4.80
4.90
4.90
4.60
4.90
4.70
4.60
4.40
4.10
4.00
3.40
3.10
3.00
2.80
2.70
2.50
2.50
2.50
-
1,
4
5
2, 3
..................................................................................
6
7
1
8
9
10
3
11
12
13
14
15
16
5
7
.................................................................................
9
................................................................................11
................................................................................
13
15
17
19
17
18
19
................................................................................21
................................................................................
20
22
23
33
41
49
57
24
61
25
65
69
21
26
27
28
29
5.40
7.40
4.50
4.70
4.80
4.30
4.00
3.90
3.80
3.70
3.60
3.50
3.40
3.30
3.20
3.10
2.90
2.70
2.20
1.90
1.70
1.50
1.30
1.20
1.00
0.80
0.80
...............................................................................
25
29
71
73
75
................................................................................
................................................................................
...............................................................................
...............................................................................
Readings are in inches above culvert invert at outfall. Q is flow in cfs.
6.10
7.30
4.80
4.80
5.20
4.90
4.40
4.20
4.10
4.00
3.90
3.80
3.70
3.60
3.55
3.40
3.20
2.90
2.70
2.20
1.80
1.70
1.60
1.40
1.30
1.20
1.20
7.60
7.40
5.10
5.20
5.80
5.60
5.10
4.80
4.60
4.50
4.50
4.40
4.20
4.15
4.15
3.90
3.70
3.50
3.10
2.70
2.30
2.20
2.00
1.80
1.70
1.70
1.70
1.90
1.90
1.80
Table 6.
FREE FLOW CULVERT SLOPES 0% AND 8%
PRESSURE READING FROM PIEZOMETER TUBES
MODEL
4,
Culvert slope 0%
Tube
No
L
(in.)
0.160
11060
0.160
2.80
4.80
4.70
4.80
10.50
1.60
1.30
1.60
1.30
3.15
3.30
3.55
3.55
3.55
3.55
3.55
3.55
3.55
3.55
8.70
10.30
8.20
8.10
8.00
7.60
7.20
7.00
6.80
6.50
6.30
6.10
6.00
5.80
355
5.61)
3.40
3.10
3.20
3.10
3.00
2.90
2.80
2.85
2.75
2.70
2.60
2.50
5.20
5.00
4.60
4.00
3.20
2.50
2.30
1.90
1.60
2.20
2.10
2.10
2.15
2.15
2.15
2.15
2.15
2.15
2.15
2.15
2.10
2.05
2.00
1
3
5
7
9
12
13
11
13
15
17
19
21
14
15
16
17
18
19
25
29
20
33
41
21
22
23
1.90
1.85
1.80
1.80
1.75
1.70
1.65
1.60
1.60
49
24
25
26
27
28 .............................................
29 .............................................
Q=
0.067
5
11
Q=
Q
1,2, 3
4
6
7
8
9
10
Culvert slope 8%
Q
57
61
65
69
71
73
75
Readings are in inches above culvert invert at outfall.
24
1.40
1.20
1.10
Q is flow in cfs.
8.90
8.50
8.80
9.00
8.60
8.20
7.80
7.60
7.30
7.10
6.90
6.70
6.50
6.15
6.80
6.40
4.80
4.00
320
2.90
2.60
2.30
2.10
1.80
1.80
Table 7. MODEL 4, FREE FLOW CULVERT SLOPE 4%
PRESSURE READING FROM PIEzOrfETER TUBES
Tube
No.
L
(in.)
0.041
4.80
...............................................................................
4
7.60
5
4.40
6
4.60
7
1
4.40
8
3
3.90
9
3.80
5
10 .................................................................................
7
3.70
..................................................................................
.................................................................................
11
3.60
9
................................................................................
................................................................................
12
11
3.50
13
13
3.40
14
15
3.30
15
17
3.20
16 ................................................................................19
3.10
17
21
3.00
2.90
18
25
29
2.70
19
20
33
2.60
21
2.30
41
22
49
2.00
................................................................................
................................................................................
................................................................................
...............................................................................
23 ...............................................................................
57
1.50
24
61
1.40
65
1.20
25
26
69
1.10
1.00
27
71
28
73
0.90
75
0.90
29 ...............................................................................
...............................................................................
...............................................................................
1, 2, 3
to
Readings are in inches above culvert invert at outfall. Q is flow in cfs.
0.063
0.066
0.100
0.102
0.132
0.174
5.50
7.50
4.55
4.70
4.75
5.50
7.60
4.70
4.80
4.90
4.50
4.10
4.00
3.90
3.80
3.70
3.60
3.50
3.40
3.30
3.20
3.00
2.80
2.50
6.10
6.10
7.50
4.70
4.50
5.30
5.00
4.70
4.60
4.40
4.20
4.10
4.00
3.90
3.80
3.70
3.60
3.50
3.20
2.90
2.40
2.10
6.70
7.00
5.00
4.80
5.55
5.40
5.00
4.80
4.60
4.50
4.30
4.20
4.05
4.00
3.90
3.70
3.55
3.45
3.00
2.60
2.20
2.10
7.40
7.00
4.40
4.10
4.00
3.90
3.70
3.60
3.50
3.40
3.30
3.20
3.10
2.90
2.70
2.40
2.00
1.65
1.50
1.35
1.20
1.10
1.00
0.95
7.40
4.65
4.60
5.30
5.00
4.65
4.40
4.30
4.20
4.05
3.85
3.70
3.70
3.60
3.45
3.30
3.00
2.00
2.70
2.30
1.80
1.60
1.40
1.30
1.20
1.10
1.00
1.90
1.80
1.60
1.40
1.30
1.20
1.20
1.90
1.80
1.70
1.60
1.50
1.40
5.10
4.90
5.80
5.90
5.65
5.30
1.60
5.00
4.90
4.70
4.55
4.40
4.35
4.30
4.10
3.90
3.70
3.30
2.85
2.55
2.40
2.20
2.10
2.00
1.50
1.90
1.50
1.90
1.90
1.75
Table 8. MODEL 6, FREE FLOW CULVERT SLOPES 0% AND 8%
PREssuI1 READING FROM PIEZOM ETER TUBES
Culvert slope 0%
Q
Tube
L
No.
(in.)
Q
Q
Q
0.100
0.191
0.064
0.157
5.35
4.45
3.45
3.10
3.30
3.45
3.65
3.70
3.75
8.90
0.60
8.40
8.20
7.90
7.70
7.30
7.10
6.90
6.70
6.40
1.70
1.50
10.70
10.40
9.60
8.30
8.20
8.80
8.60
8.00
7.70
7.40
7.20
7.00
6.80
6.60
6.50
6.10
5.70
5.40
4.70
3.90
3.20
2.80
2.60
2.20
2.10
1.30
1.30
1.80
1.80
7..
1
8
3
9
10
5
3.50
4.40
2.85
2.10
2.10
2.30
2.05
7
1.90
11
9
1.90
12
13
11
2.10
2.35
2.50
2.50
2.50
1,2,3........................
....
4....................
5 .............,.............................
6
.
13
14
15
15 ..............................................17
16
19
20 ............................................
21
25
29
33
21 .............................................
41
22
49
57
17 ............................................
18 ............................................
19 ............................................
23 .............................................
25 .............................................
61
65
26 .............................................
69
27
71
28 .............................................
73
75
24 .............................................
29 .............................................
Culvert slope 8%
2.55
2.45
2.45
2.40
2.35
2.30
2.20
2.20
2.20
2.10
2.00
2.00
1.90
3.75
3.80
3.75
3.70
3.75
3.75
3.70
3.65
3.60
3.60
3.50
3.50
3.45
3.40
3.40
3.35
3.30
3.20
6.25
6.10
6.00
5.70
5.30
5.10
4.70
4.10
3.40
2.70
2.30
2.00
Readings are In inches above culvert invert at outfall. Q is flow in c/s.
26
Table 9.
MODEL
FREE FLOW CULVERT SLOPE 4%
6,
PRESSURE READING FROM PIEZOMETER TUBES
Tube
L
No.
(in.)
1,2,3
4
1
5
1
6
7
1
8
3
9
5
10
7
9
11
13
15
17
19
11
12
13
14
15
16
17
18
19
21
25
29
20
33
41
21
22
23
24
25 .........................
26
27
28 .........................
29 .........................
49
57
61
65
Q
Q
Qr
0.O,7
0096
0.127
5.25
7.05
6.00
7.10
4.80
4.65
4.45
4.20
4.05
3.90
3.75
3.60
3.60
3.40
3.30
3.20
3.10
5.55
5.30
3.05
3.40
3.20
2.90
2.60
2.10
6.60
7.10
5.90
5.40
5.10
5.20
4.95
4.70
4.45
4.30
4.20
4.00
3.95
3.90
3.80
3.60
3.50
3.25
2.90
2.40
2.10
2.00
1.80
1.60
1.50
1.40
1.40
4.90
4.80
4.60
4.40
4.20
4.00
3.90
3.75
3.70
3.65
3.45
2.80
2.70
2.30
1.90
1.60
1.40
69
1.20
1.10
71
73
75
0.90
0.80
0.80
1.90
1.70
1.50
1.30
1.20
1.20
1.20
Q=
0.147
Q=
6.90
7.00
6.10
5.40
5.30
5.30
7.30
6.80
5.90
5.25
4.90
4.70
4.50
4.40
4.20
4.10
4.10
4.00
3.80
3.60
3.40
3.00
2.50
2.20
2.10
1.90
1.70
1.60
1.50
1.50
Readings are in inches above culvert invert at outfall. Q is flow in cfs.
27
0.172
5.30
5.40
5.60
5.50
5.10
4.90
4.70
4.60
4.40
4.35
4.30
4.10
4.00
3.80
3.60
3.20
2.70
2.40
2.30
2.10
1.90
1.80
1.70
1.70
Table 10.
MODEL 3, FULL FLOW CULVERT SLOPES 0% AND 8%
PRESSURE READING FROM PIEZOMETER TUBES
Culvert slope 0%
Tube
No.
1,2,3
I.
(in.)
....
4
5
6
7
1
8
9
10
3
11
12
13
9
11
13
15
17
19
14
15
16
17
18
19
20
21
22
23
5
7
21
25
29
33
41
49
57
24
61
25
65
69
26
27
28
29
71
73
75
=
Q
0.405
Culvert slope 8%
Q
0.506
Q
=
0.445
Q =
0.496
=
Q
0.519
=
Q
0.559
10.00
14.30
11.50
13.90
14.00
16.50
-0.40
-1.50
-1.30
-3.30
-4.20
-4.20
2.40
2.70
3.20
3.60
3.60
3.70
-1.60
-2.10
-2.10
-1.50
-4.10
-3.50
-4.40
-1.60
-4.00
-4.70
-4.10
-2.60
-5.10
-5.80
-6.10
-2.80
2.10
3.10
3.70
1.80
3.10
3.50
3.60
3.70
3.75
3.80
3.80
3.75
3.70
3.50
3.50
3.35
3.20
2.90
2.70
2.65
2.60
2.50
2.50
2.40
2.20
3.30
3.80
3.90
4.10
4.20
4.20
4.15
4.15
4.10
3.90
3.80
3.70
3.40
3.00
2.80
2.70
2.60
2.50
2.50
2.40
2.40
2.00
3.10
3.70
3.80
4.00
4.10
4.10
4.00
4.00
3.90
3.60
3.65
3.55
3.30
2.90
2.65
2.60
2.50
2.30
2.30
2.20
2.20
1.90
3.75
3.70
3.70
3.70
3.70
3.55
3.50
3.40
3.20
2.90
2.75
2.70
2.70
2.55
2.55
2.50
2.50
1.10
3.75
4.00
4.10
4.10
4.00
4.00
4.00
3.70
3.70
3.60
3.30
2.90
2.70
2.60
2.55
2.40
2.40
2.20
2.20
2.40
Readiiigs are in inches above culvert invert at outfall. Q is flow in cfs.
28
3.20
3.90
4.00
4.10
4.30
4.30
4.25
4.25
4.20
3.90
3.90
3.70
3.50
3.00
2.70
2.60
2.50
2.30
2.30
2.20
2.20
Table 11.
MODEL 3, FULL FLOW CULVERT SLOPE 4%
PRESSURE READING FROM PIEZOMETER TUBES
Tube
L
No.
Q-
(in.)
0.352
1,2,
8.20
..
6
0.477
-0.70
-0.40
9.70
0.20
-2.10
-2.10
12.30
-3.20
-3.60
-3.70
'-1.40
5
Q__
Q
0.413
Q
0.530
14.20
-4.20
-4.80
-4.90
7
1
1.60
1.30
1.10
1.00
8
3
2.20
2.80
3.00
3.10
3.20
1.80
1.90
2.90
3.20
2.20
3.20
5
10 .............................................
7
11 .............................................
9
12 .............................................
11
13
14 ............................................
15
15 ............................................
17
16 ..............................................19
17 .............................................
21
18 .............................................
25
19 .............................................
29
3.20
3.30
3.20
3.20
3.10
3.10
3.05
23 .............................................
33
41
49
57
3.00
2.80
2.60
2.60
24 ............................................
61
25 ............................................
65
69
2.50
2.40
2.40
2.30
2.30
2.30
13 ............................................
20 ............................................
21
22 .............................................
26 .............................................
27 .............................................
71
28 .............................................
73
75
29 ---------------------------------------------
Readings are in inches above culvert invert at outfall.
29
2.50
2.90
3.00
3.10
3.20
3.30
3.20
3.20
3.20
3.10
3.10
3.00
2.90
2.50
2.50
2.40
2.30
2.30
2.20
2.30
2.30
3.40
3.60
3.70
3.80
3.60
3.60
3.50
3.50
3.40
3.25
3.10
2.60
2.50
3.40
3.50
3.65
3.80
4.00
3.70
3.70
3.60
3.65
3,55
3.40
3.10
2.60
2.50
2.40
2.30
2.20
2.10
2.20
2.20
2.40
2.20
2.15
2,00
2.00
2.00
is flow in
cf's.
Table 12.
MODEL 4, FULL FLOW CULVERT SLOPES 0% AND 8%
PRESSURE READING FROM PIEZOMETER TUBES
Culvert slope 0%
Tube
L
No.
(in.)
1,2, 3
4
5
6
7
1
8
9
10
3
11
9
11
12
13
14
15
16
17
18
19
20
21
22
5
7
13
15
17
19
21
25
29
33
41
49
23 ..........c7
24
61
25
65
69
26
27
28
29
71
73
75
Q
Q
0.285
0.445
7.10
4.85
0.40
1.20
12.60
5.20
2.60
3.20
3.50
-3.30
-3.30
1.15
3.00
3.00
2.95
2.85
2.85
2.80
3.70
3.90
4.00
3.90
4.00
4.00
3.90
3.85
3.80
3.80
3.60
3.60
3.50
3.25
2.90
2.70
2.60
2.55
2.45
2.40
2.30
2.80
2.30
3.55
3.60
3.60
3.65
3.60
3.60
3.55
3.55
3.50
3.45
3.40
3.25
3.10
Culvert slope 8%
Q=
0.535
Q
Q
0.429
0.490
0.537
17.60
6.60
-5.60
11.40
5.70
-4.30
13.80
-0.50
-3.20
-0.70
2.70
-1.40
-0.50
2.00
-6.30
-1.00
2.80
16.40
-0.80
-7.50
-3.30
-1.60
2.10
3.30
3.80
3.90
4.10
4.20
4.30
4.20
4.20
4.20
4.10
4.30
4.35
4.35
4.30
4.25
4.20
3.90
3.85
3.70
3.50
3.00
2.70
2.60
2.50
2.40
2.40
2.20
3.30
3.60
3.65
3.70
3.75
3.75
3.75
3.75
3.75
3.50
3.55
3.40
3.20
2.90
2.70
2.70
2.65
2.55
2.50
2.40
2.20
2.40
3.55
3.95
360
3.75
3.90
4.10
4.15
4.15
4.10
4.10
4.00
3.80
3.80
2.80
2.70
2.60
2.50
2.50
2.40
3.90
3.90
3.70
3.40
3.00
2.70
2.60
2.50
2.40
2.30
2.20
2.40
2.20
3.65
3.40
3.00
Readings are in inches above culvert invert at outfall. Q is flow in cfs.
30
Table 13. MODEL 4, FULL FLOW CULVERT SLOPE 4%
PRESSURE READING FROM PIEZOMETER TUBES
Tube
L
Q
Q
No.
Q=
0.334
Q=
0.360
0.395
Q=
0.418
Q=
(in.)
0.451
0.481
8.50
4.35
10.00
4.60
10.70
4.50
1
6
1
-1.00
-2.00
-1.00
-2.40
-1.80
-3.00
-2.10
0.70
2.80
3.10
3.15
3.25
3.30
3.40
3.30
3.30
3.30
3.30
3.25
3.20
3.15
3.05
2.70
2.60
2.60
2.50
2.40
2.30
2.30
0.90
2.65
3.10
3.25
3.30
3.40
12.30
4.80
-3.70
-3.50
0.80
3.00
3.20
3.30
3.40
3.50
3.60
3.50
13.40
5.10
5
7.80
3.90
-0.50
1,2,3
4
7
1
1.50
1.40
8
9
10
3
2.70
2.90
11
9
2.50
2.90
3.10
3.20
3.20
3.30
3.20
3.20
3.20
3.20
3.10
3.10
3.10
2.90
2.70
2.60
2.55
2.50
2.45
2.40
2.40
2.40
12
13
14
15
16
17
18
19
5
7
11
13
15
17
19
21
21
22
23
25
29
33
41
49
57
24
61
25
26
65
69
27
71
28
29
73
75
20
3.10
3.20
3.25
3.30
3.25
3.20
3.20
3.20
3.10
3.10
3.05
2.95
2.80
2.70
2.60
2.65
2.50
2.50
2.50
2.50
2.30
3.50
3.35
3.30
3.40
3.40
3.35
3.30
3.20
3.00
2.65
2.60
2.55
2.50
2.40
2.30
2.30
2.30
3.43
3.50
3.55
3.40
3.40
3.30
3.05
2.70
2.60
2.50
2.40
2.35
2.30
2.30
2.30
Readings are in inches above culvert invert at outfall. Q is flow in cfs.
31
-4.70
-4.40
-050
2.90
3.40
3.40
3.60
3.65
3.75
3.60
3.50
3.60
3.60
3.50
3.45
3.30
3.05
2.60
2.50
2.45
2.35
2.30
2.15
2.15
2.15
Table 13.
MoD1i. 4, FULL FLOW CULVERT SIoPE 4% (C0NT'D)
PRESSURE READING FROM PIEzoIrETER TUBES
Tube
L
No.
(in.)
1,2,3 ...................
4
5
6
7
1
8 .........................
3
9 .........................
10 .........................
5
7
9
11
12
13 .........................
14
15
16
17
18.........................
19 .........................
11
13
15
17
19
21
23
25
29
33
41
49
57
24 .........................
61
25 .........................
65
69
20 .........................
21
22 .........................
26
27
28 .........................
29 .........................
71
73
75
Q
Q
Q
Q
0.509
0.540
0.558
0.575
0.608
14.50
5.40
-4.80
15.80
6.00
17.30
-6.00
-7.20
0.20
2.30
-6.90
-7.10
-1.00
3.60
17.80
6.20
-6.50
19.80
6.70
-7.70
-0.20
2.60
-0.20
3.40
3.60
3.60
3.75
4.00
3.75
3.70
3.75
3.90
3.60
3.65
3.50
3.20
2.60
3.90
3.90
3.90
3.95
4.10
3.75
3.75
3.80
3.90
3.75
3.70
3.60
3.25
2.60
2.50
2.50
2.20
2.20
2.00
2.00
2.00
-5.60
0.50
3.10
3.50
3.55
3.55
3.60
3.80
3.60
3.55
3.60
3.65
3.50
3.50
3.40
3.10
2.60
2.50
2.50
2.30
2.30
2.10
2.10
2.10
2.60
2.50
2.40
2.30
2.20
2.20
2.20
6.35
3.60
3.80
3.90
4.10
4.25
3.90
3.90
4.00
4.10
3.90
3.80
3.70
3.30
2.70
2.60
2.50
2.30
2.30
2.10
2.05
2.05
Readings are in inches above culvert invert at outfall. Q is flow in cfs.
32
3.30
3.80
3.90
3.80
4.10
4.40
4.00
4.00
4.10
4.20
4.00
4.00
3.80
3.40
2.70
2.60
2.50
2.30
2.20
2.10
2.00
2.00
Table 14.
FULL FLOW CULVERT SLOPES 0% AND
PRESSURE READING FROM PIEZOMETER TUBES
MODEL
6,
Culvert Slope 0%
Tube
No.
L
(in.)
1,2,3
Q0.372
9.40
4.45
0,25
0.15
4
5
6
7
1
1.40
8
3
9
10
11
12
13
5
7
2.20
2.90
3.30
3.50
3.60
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
9
11
13
15
17
19
21
25
29
33
41
49
.57
61
65
69
71
73
75
3.65
3.60
3.60
3.60
3.55
3.45
3.40
3.30
3.10
2.90
2.70
2.70
2.65
2.60
2.55
2.45
2.45
Culvert slope 8%
Q=
Q=
4.60
17.30
5.20
-1.50
-2.20
-3.20
-3.70
12.70
5.00
3.55
1.20
1.70
0.40
1.10
1.00
1.00
2.40
3.10
3.50
3.75
3.85
3.90
3.90
3.90
3.85
3.65
3.65
3.55
3.30
2.90
2.70
2.60
2.55
2.45
2.45
2.20
2.20
2.30
3.10
2.30
3.20
3.50
3.70
3.80
3.80
3.80
3.80
2.10
.3.10
3.70
4.00
4.10
4.20
4.20
4.20
4.20
3.90
3.90
3.70
3.40
3.00
2.80
2.70
2.60
2.50
2.50
2.30
2.30
Q
0545
0.478
13.50
3.55
3.90
4.10
4.10
4.15
4.15
4.10
3.90
3.90
3.70
3.50
3.00
2.70
2.60
2.50
2.40
2.40
2.20
2.20
0.469
-2.60
-0.10
3.7.5
3.60
3.60
3.40
3.20
2.90
2.70
2.60
2.60
2.40
2.40
2.30
2.30
Q
0.505
14.60
-0.60
-2.80
-1.80
-0.30
Readings are in inches above culvert invert at outfall. Q is flow in cfs.
33
8%
0.565
17.20
6.40
-0.90
-4.20
-0.90
0.60
2.60
3.60
4.20
4.40
4.50
4.40
4.40
4.30
4.30
4.10
4.00
3.80
3.50
3.00
2.70
2.60
2.50
2.30
2.30
2.20
2.20
Table 15.
MODEL 6, FULL FLOW CULVERT SLOPE 4%
PRESSURE READING FROM PIEZOMETER TUBES
Tube
L
Q=
No.
(in.)
0.338
1,2,3
1
7.85
3.60
6
1
2.10
-0.30
7
1
8
3
9
10
5
4
.
5
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
7
9
11
13
15
17
19
21
25
29
33
41
49
57
61
65
69
71
73
75
1.10
1.60
2.10
2.50
2.70
2.90
3.05
3.10
3.10
3.10
3.10
3.10
3.10
3.00
2.90
2.60
2.60
2.60
2.50
2.40
2.35
2.40
2.40
Q0.381
Q=
0.439
Q=
0.505
9.10
3.70
0.70
-1.10
0.60
1.40
2.10
2.60
2.80
3.00
3.15
11.70
2.50
14.30
2.40
-1.30
-2.40
0.40
-2.20
-3.60
1.10
1.90
2.60
2.90
3.10
3.30
3.40
3.40
3.40
3.30
3.30
3.30
320
3.15
3.20
3.15
3.10
3.10
3.05
2.90
2.50
2.60
2.60
2.45
2.40
2.30
2.30
2.30
3.15
3.00
2.60
2.50
2.50
2.30
2.30
2.10
2.20
2.20
0.10
1.20
2.20
2.90
3.30
3.60
3.85
3.90
3.70
3.70
3.60
3.60
3.55
3.30
3.10
2.60
2.40
2.40
2.30
2.20
2.00
2.00
2.00
Q
0.545
0.606
15.70
4.40
-2.70
-3.10
0.10
0.90
2.10
3.00
3.50
3.60
3.90
4.00
3.95
3.90
3.65
3.70
3.65
3.50
3.20
2.60
2.50
2.45
2.20
2.20
2.50
2.50
2.50
19.40
4.20
-6.00
Readings are in inches above culvert invert at outfall. Q is flow in cis.
34
-5.90
-1.40
0.20
1.60
2.70
3.40
3.80
4.10
4.20
4.10
4.10
4.00
3.90
3.90
3.70
3.40
2.70
2.60
2.50
2.20
2.20
2.00
2.00
2.00
OREGON STATE COLLEGE
ENGINEERING EXPERIMENT STATION
CORVALLIS, OREGON
LIST OF PUBLICATIONS
BulletinsPreliminary Report on the Control of Stream Pollution in Oregon, by C. V.
No.
1.
No.
2.
No.
3.
No.
4.
Interpretation of Exhaust Gas Analyses, by S. H. Graf, G. W. Gleeson, and
W. H. Paul. 1934.
No.
5.
Boiler.Water Troubles and Treatments with Special Reference to Problems in
Western Oregon, by R. E. Summers. 1935.
No.
6.
A Sanitary Survey of the Willamette River from
No.
7.
Industrial and Domestic Waste of the Willamette Valley, by G. W. Gleeson
No.
8.
An Investigation of Some Oregon Sands with a Statistical Study of the Predictive Values of Tests, by C. E. Thomas and S. H. Graf. 1937.
Langton and H. S. Rogers.
Fifteen Cents.
1929.
A Sanitary Survey of the Willamette Valley, by H. S. Rogers, C. A. Mock.
more, and C. D. Adams. 1930.
Forty Cents.
The Properties of Cement-Sawdust Mortars, Plain and with Various Admix.
tures, by S. H. Graf and R. H. Johnson. 1930.
Twenty Cents.
Twenty-five Cents.
None available.
Columbia, by G. W. Gleeson.
Twenty-five Cents.
and F. Merryfield.
Fifty cents.
Seliwood
Bridge to the
1936.
1936.
Fifty cents.
Preservative Treatments of Fence Posts.
1938 Progress Report on the Post Farm, by T. J. Starker, 1938.
Twenty-five cents.
Yearly progress reports, 9-A, 9-B, 9.C, 9-D, 9-E, 9-F, 9-G.
Fifteen cents each.
No. 10. Precipitation-Static Radio Interference Phenomena Originating on Aircraft, by
E. C. Starr, 1939.
No.
9.
No. 11.
Seventy-five cents.
Electric Fence Controllers with Special Reference
No. 13.
Oil-Tar Creosote for Wood Preservation, by Glenn Voorhies. 1940.
No. 14.
Optimum Power and Economy Air-Fuel Ratios for Liquefied Petroleum Gases,
y W. H. Paul and M. N. Popovich. 1941.
to Equipment
Developed
for Measuring Their Characteristics, by F. A. Everest. 1939.
Forty cents.
No. 12. Mathematics of Alignment Chart Construction without the Use of Determinants,
by J. R. Griffith. 1940.
Twenty-five cents.
Twenty-live cents.
twenty-five cents.
Rating and Care of Domestic Sawdust Burners, by E. C. Willey.
Twenty-five cents.
No. 16. The Improvement of Reversible Dry Kiln Fans, by A. D. Hughes.
No. 15.
1941.
1941.
Twenty.five cents.
No. 17.
An Inventory of Sawmill Waste in Oregon,
No. 18.
The Use of the Fourier Series in the Solution of Beam Problems, by B. F. Ruff.
Twenty-five cents.
ncr.
1944.
by
Glenn Voorhies.
1942.
Fifty cents.
1945 Progress Report on Pollution of Oregon Streams, by Fred Merryfield and
W. G. Wilmot. 1945.
Forty cents.
No. 20. The Fishes of the Willamette River System in Relation to Pollution, by R. E.
Dimick and Fred Merryfield. 1945.
Forty cents.
No. 21. The Use of the Fourier Series in the Solution of Beam-Column Problems, by
B. F. Ruffner. 1945.
No. 19.
Twenty-five cents.
35
No. 22.
No. 23.
Industrial and City Waste, by Fred Merryfleid, \V. B. Bolten, and F. C.
Kachelhoffer. 1947.
Forty rents.
Ten-Year Mortar Strength Tests of Some Oregon Sands, by C. E. Thomas and
S. H. Graf. 1948.
Twenty-five cents.
No. 24.
Space Heating by Electric Radiant Panels and by Reversr.Cvcle, by Louis Siegel.
1948.
Fifty cents.
Banki Water Turbine, by
No. 25.
C.
A. Mockmore and Fred Merryfield. Feb
1949.
Forty cents.
No. 26.
Ignition Temperatures of Various Papers, \Voods, and Fabrics, by S. H. Graf.
No. 27.
Cylinder Head Temperatures in Four Airplanes with Continental A-65 Engines, by S. H. Lowy. July 1949.
Forty cents.
Dielectric Properties of Douglas Fir at High Frequencies, by J. J. Wittkopf
and M. D. Macdonald. July 1949.
Forty cents.
No. 28.
Mar 1949.
Sixty cents.
No. 29.
Dielectric Properties of Ponderosa Pine at High Frequencies, by J. J. Wittkopf anti M. D. Macdonald, September 1949.
Forty cents,
No. 30.
Expanded Shale Aggregate in Structural Concrete, by P. P. Ritchie and S. H.
No. 31.
Graf. Aug 1951.
Sixty cents.
Improvements in the Field Distillation of Peppermint Oil, by A.
Aug 1952.
Sixty cents.
No. 32.
A Gage for the Measurement of Transient Hydraulic Pressures, by E. F. Rice.
No. 33.
The Effect of Fuel Sulfur and Jacket Temperature on Piston Ring Wear as
Determined by Radioactive Tracer, by M. Popovich and R. \V. Peterson.
1).
Hughes.
Oct 1952.
Forty cents.
July 1953.
Forty Cents.
No. 34.
Pozzolanic Properties of Several Oregon Pumicites, by C. 0. Heath, Jr. and
N. R. Brandenburg, 1953.
No. 35.
Model Studies of Inlet Designs for l'ipe Culverts on Steep Grades, by Malcolm
H. Karr and Leslie A. Clayton. June 1954.
Forty cents.
Fifty Cents.
CircularsNo.
1.
A Discussion of the Properties and Economics of Fuels Used in Oregon, by
No.
2.
Adjustment of Automotive Carburetors for Economy, by S. H. Graf and G. \V.
No.
3.
Elements of Refrigeration for Small Commercial Plants,
C. E. Thomas and G. D, Keerins.
Twenty-five cents.
Gleeson.
1929.
1930.
None available.
by \V. H.
Martin.
1935.
None available.
Some Engineering Aspects of Locker and Home Cold-Storage Plants, by W. H.
No.
4.
No.
5.
Martin. 1938.
Twenty cents.
Refrigeration Applications to Certain Oregon Industries, by \V. H, Martin.
No.
6.
The Use of a Technical Library, by W. E. Jorgensen.
No.
7.
Saving Fuel in Oregon Homes, by E. C. Willey.
No.
8.
Technical Approach to the Utilization of Wartime Motor Fuels, by W. H. Paul.
No.
9.
Electric and Other Types of House Heating Systems, by Louis SIegel.
1940.
Twenty-five cents.
1942.
Twenty-five Cents.
Twenty-five cents.
1942.
1944,
Twenty-five cents.
1946.
Twenty-five cents.
No. 10.
Economics of Personal Airplane Operation, by W. J. Skinner.
No. 11.
Digest of Oregon Land Surveying Laws, by C. A. Mockmore, M. P. Coopey,
B. B. Irving, and E. A, Buckhorn. 1948.
Twenty-five cents.
Twenty-five cents.
36
1947.
No. 12.
The Aluminum Industry of the Northwest, by J. Granville Jensen.
1950.
No. 13.
None available.
Fuel Oil Requirements of Oregon and Southern Washington, by Chester K.
Sterrett. 1950.
Twenty-five cents.
No. 14.
Market for Glass Containers in Oregon and Southern Washington, by Chester
K. Sterrett. 1951.
No. 15.
Twenty-five cents.
Proceedings of the 1951
April 1951.
Sixty Cents.
No. 16.
Water Works Operators' Manual, by %Varren
No. 17.
Proceedings of the 1953 Northwest Conference on Road Building. July 1953.
Oregon State
Conference on Roads and
Seventy-five cents.
C.
Streets.
Westgarth. March 1953.
Sixty cents.
Reprints.
No.
1.
Methods of Live Line Insulator Testing and Results of Tests with Different
Instruments, by F. 0. McMillan. Reprinted from 1927 Proc NW Elec
No.
2.
No.
3.
Some Anomalies of Siliceous Matter in Boiler Water Chemistry, by R. E.
Summers. Reprinted from Jan 1935, Combustion.
Ten cents.
Asphalt Emulsion Treatment Prevents Radio Interference, by F. 0. McMillan.
Reprinted from Jan 1935, Electrical West.
No.
4.
Some Characteristics of A-C Conductor Corona, by F. 0. McMillan. Reprinted
No.
5.
A Radio Interference Measuring Instrument, by F. 0. McMillan and H. G.
No.
6.
Water-Gas Reaction Apparently Controls Engine Exhaust Gas Composition, by
G. W. Gleeson and W. H. Paul. Reprinted from Feb 1936, National
Lt and Power Assoc.
Twenty cents.
None available.
from Mar 1953, Electrical Engineering.
None available.
Barnett. Reprinted from Aug 1935, Electrical Engineering.
Ten Cents.
Petroleum News.
None available.
No.
7.
Steam Generation by Burning Wood, by
No.
8.
The Piezo Electric Engine Indicator, by W. H. Paul and K. R. Eldredge.
No.
9.
Humidity and Low Temperature, by W. H. Martin and E.
Apr 1936, Heating and Ventilating.
Ten cents.
R. E.
Summers.
Reprinted from
Reprinted from Nov 1935, Oregon State Technical Record.
Ten cents.
printed from Feb 1937, Power Plant Engineering.
C. Willey.
Re-
None available.
No. 10.
Heat Transfer Efficiency of Range Units, by W. J. Walsh.
No. 11.
Design of Concrete Mixtures, by I. F. Waterman. Reprinted from Nov 1937,
No. 12.
Water-wise Refrigeration, by W. H. Martin and R. E. Summers.
Aug 1937, Electrical Engineering.
None available.
Reprinted from
Concrete.
None available.
from July 1938, Power.
Reprinted
Ten Cents.
No. 13.
Polarity Limits of the Sphere Gap, by F. 0. McMillan.
No. 14.
Influence
Short.
Reprinted from
No. 15.
Corrosion and Self-Protection of Metals, by R. E. Summers.
Sept and Oct 1938, Industrial Power.
Reprinted from
58, AIEE Transactions, Mar 1939,
Ten cents.
of Utensils on Heat Transfer, by W. G.
Nov 1938, Electrical Engineering.
Ten cents.
Reprinted from Vol.
No. 16.
Ten cents.
Monocoque Fuselage Circular Ring Analysis, by B. F.
from Jan 1939, Journal of the Aeronautical Sciences.
Ten cents.
No. 17.
The Photoelastic Method as an Aid in Stress Analysis and Structural Design,
by B. F. Ruffner. Reprinted from Apr 1939, Aero Digest.
No. 18.
Fuel Value of Old-Growth vs.
Ruffner.
Reprinted
Ten cents.
Second-Growth
Reprinted from June 1939, The Timberman.
Ten cents.
37
Douglas-Fir, by
Lee Gabie.
No. 19.
Stoichiometric Calculations of Exhaust Gas, by G. W. Gleeson and F. W.
Woodfield, Jr. Reprinted from Nov 1, 1939, National Petroleum News.
Ten cents.
The Application of Feedback to Wide-Band Output Amplifiers, by F. A.
Everest and H. R. Johnston. Reprinted from Feb 1940, Proc of the
Institute of Radio Engineers.
Ten cents.
No. 21. Stresses Due to Secondary Bending, by B. F. Ruffner. Reprinted from Proc
of First Northwest Photoelasticity Conference, University of Washington,
Mar 30, 1940.
Ten cents.
No. 22. Wall Heat Loss Back of Radiators, by E. C. Willey. Reprinted from Nov
1940, Heating and Ventilating.
Ten cents.
No. 23. Stress Concentration Factors in Main Members Due to Welded Stiffeners, b
W. R. Cherry. Reprinted from Dec 1941 The Welding Journal, Researc
Supplement.
Ten cents.
No. 24. Horizontal-Polar.Pattern Tracer for Directional Broadcast Antennas, by F. A.
Everest and \V. S. Pritchett. Reprinted from May 1942, Proc of The
Institute of Radio Engineers.
Ten cents.
No. 25. Modern Methods of Mine Sampling, by R. K. Meade. Reprinted from Jan
1942, The Compass of Sigma Gamma Epsilon.
Ten cents.
No. 26. Broadcast Antennas and Arrays. Calculation of Radiation Patterns; Impedance Relationships, by Wilson Pritchett. Reprinted from Aug and Sept
No. 20.
1944, Communications.
None available.
No. 27.
Heat Losses Through Wetted Walls, by E. C. Willey. Reprinted from June
1946, ASHVE Journal Section of Heating, Piping, & Air Conditioning.
No. 28.
Electric Power in China, by F. 0. McMillan.
Electrical Engineering.
Ten cents.
No. 29.
The Transient Energy Method of Calculating Stability, by P. C. Magnusson.
Ten cents.
No. 30.
No. 31.
No. 32.
No. 33.
Reprinted from Jan
1947,
Reprinted from Vol 66, AIEE Transactions, 1947.
Ten cents.
Observations on Arc Discharges at Low Pressures, by M. J. Kofoid. Reprinted
from Apr 1948, Journal of Applied Physics.
Ten cents.
Long-Range Planning for Power Supply, by F. 0. McMillan. Reprinted from
Dec 1948, Electrical Engineering.
Ten cents.
Heat Transfer Coefficients in Beds of Moving Solids, by 0. Levenspiel and
J. S. Walton. Reprinted from 1949 Proc of the Heat Transfer and Fluid
Mechanics Institute.
Ten cents.
Catalytic Dehydrogenation of Ethane by Selective Oxidation, by J. P. McCul.
tough and J. S. Walton. Reprinted from July 1949, Industrial and Engineering Chemistry.
No. 34.
Ten Cents.
Diffusion Coefficients
No. 35.
Ten cents.
Transients in Coupled Inductance-Capacitance Circuits Analyzed in Terms of
No. 37.
EnergyChoose It \Visely Today for Safety Tomorrow, by G. W. Gleeson.
of Organic Liquids in Solution from Surface Tension
Measurements, by R. L. Olson and J. S. Walton. Reprinted from Mar
1951, Industrial and Engineering Chemistry.
a Rolling-Ball Analogue, P. C. Magnusson. Reprinted from Vol 69, AIEE
Transactions, 1950.
Ten cents.
No. 36 Geometric Mean Distance of Angle-Shaped Conductors, by P. C. Magnusson.
Reprinted from Vol 70, AIEE Transactions, 1951.
Ten cents.
Reprinted from August 1951, ASHVE Journal Section of Heating, Piping,
and Air Conditioning.
Ten cents.
No. 38. An Analysis of Conductor Vibration Field Data, by R. F. Steidel, Jr and
M. B. Elton. AIEE Conference Paper presented at Pacific General Meeting,
Portland, Oregon, August 23, 1951.
Ten cents.
No. 39. The Humphreys Constant-Compression Engine, by W. H. Paul and I. B.
Humphreys.
Ten cents.
Reprinted from SAE Quarterly Transactions April
38
1952.
Gas.Solid Film Coefficients of Heat Transfer in Fluidized Coal Beds, by J. S.
Walton, R. L. Olson and Octave Levenspiel. Reprinted from Industrial
and Engineering Chemistry June 1952.
Ten cents.
No. 41 Restaurant Ventilation, by \V. H. Martin. Reprinted from The Sanitarian, Vol
14, No. 6.
May.June, 1952.
Ten cents.
No. 42. Electrochemistry in the Pacific Northwest, by Joseph Schulein. Reprinted from
No. 40.
the Journal of the Electrochemical Society, June 1953.
Twenty cents.
No. 43.
No. 44.
Model Studies of Tapered Inlets for Box Culverts, by Roy H. Shoemaker and
Leslie A. Clayton. Reprinted from Research Report 15.B, Highway Research
Board, Washington, 13. C. 1953.
Twenty cents.
Bed.Wall Heat Transfer in Fluidized Systems, by 0. Levenspiel and J. S. Walton.
Reprinted from Heat TransferResearch Studies, 1954.
Ten cents.
No. 45.
Shunt Capacitors in Large Transmission Networks, by E. C. Starr and E. J.
Harrington. Reprinted from Power Apparatus & Systems, December 1953.
Ten cents.
The Design and Effectiveness of an Underwater Diffusion Line for the Disposal
of Spent Sulphite Liquor, by H. R. Amberg and A. G. Strang. Reprinted
from TAPPI, July 1954.
Ten cents.
No. 47. Compare Your Methods with This Survey, by Arthur L. Roberts and Lyle E.
Weatherbee. Reprinted from Western Industry, December 1953.
Ten cents.
No. 46.
3.
THE ENGINEERING EXPERIMENT STATION
Administrative Officers
R. E. KLEINSORGE, President, Oregon State Board of Higher Education.
CHARLES D. BYRNE, Chancellor, Oregon State System of Higher Education.
A. L. STRAND, President, Oregon State College.
G. W. GLEESON, Dean and Director.
D. M. GOODE, Director of Publications.
M. PopovIcH, Assistant Dean of Engineering.
Station Staff
A. L. ALBERT, Communication Engineering.
H. D. CHRISTENSEN, Aeronautical Engineering.
L. A. CLAYTON, Hydraulic Engineering.
M. P. COOPEY, Highway Engineering.
W. F. ENGESSER, Industrial Engineering.
G. S. FEIKERT, Radio Engineering.
J. B. GRANTHAM, Wood Products.
C. 0. HEATH, Engineering Materials.
G. W. HOLCOMB, Civil and Structural Engineering.
A. D. HUGHES, Heat Power and Air Conditioning.
J. G. JENSEN, Industrial Resources.
F. 0. McMILLAN, Electrical Engineering.
FRED MERRYFIELD, Sanitary Engineering.
0. G. PAASCHE, Metallurgical Engineering.
W. H. PAUL, Automotive Engineering.
M. C. SHEELY, Manufacturing Processes.
Louis SLEGEL, Mechanical Engineering
E. C. STARR, Electrical Engineering.
C. E. THOMAS, Engineering Materials.
J. S. WALTON, Chemical Engineering.
Technical Counselors
R. H. BALDOCK, State Highway Engineer, Salem.
R. R. CLARK, Designing Engineer, Corps of Engineers, Portland District,
Portland.
R. W. COwLIN, Director, Pacific Northwest Forest and Range Experiment
Station, U. S. Dcpartment of Agriculture, Forest Service, Portland.
DAVID DON, Chief Engineer, Public Utilities Commissioner, Salem.
C. M. EVERTS, JR, State Sanitary Engineer, Portland.
F. W. LIBBEY, Director, State Department of Geology and Mineral Industries,
Portland.
PAUL B. MCKEE, President, Pacific Power and Light Company, Portland
B. S. MORROW, Engineer and General Manager, Department of Public Utilities
and Bureau of Water Works, Portland.
J. H. POLHEMUS, President, Portland General Electric Company, Portland.
S. C. SCHWARZ, Chemical Engineer, Portland Gas and Coke Company, Portland.
C. K. STERRET-T, Manager, Industries Department, Portland Chamber of
Commerce.
J. C. STEVENS, Consulting Civil and Hydraulic Engineer, Portland.
Oregon State College
Corvallis
RESIDENT INSTRUCTION
Liberal Arts and Sciences
LOWER DIvisioN (Junior Certificate)
SCHOOL OF SCIENCE (BA., B.S., M.A., M.S., Ph.D. degrees)
Professional Schools
SCHOOL OF AGRICULTURE (B.S., B.Agr., MS., M.Agr., Ph.D.
degrees)
SCHOOL OF BusINEss AND TECHNOLOGY (B.A., B.S., degrees)
SCHOOL OF EDUCATION (BA., B.S., Ed.B., MA., M.S., ECI.M.,
Ed.D. degrees)
SCHOOL OF
ENGINEERING AND INDUSTRIAL ARTS (B.A., B.S.,
MA., M.S., A.E., Ch.E., CE., E.E., I.E., M.E., Min.E.,
Ph.D. degrees)
FORESTRY (B.S., B.F., M.S., M.F., F.E. degrees)
SCHOOL OF
SCHOOL OF
HOME ECONOMICS (B.A., B.S., M.A., M.S., M.H.Ec.,
Ph.D. degrees)
SCHOOL OF PHARMACY (B.A., B.S., MA., MS., Ph.D. degrees)
Graduate School (M.A., M.S., Ed.M., M.F., M.Agr., M.H.Ec., A.E.,
OLE., CE., E.E., FE., I.E., M.E., Min.E., Ed.D., Ph.D.
Degrees)
Summer Sessions
Short Courses
RESEARCH AND EXPERIMENTATION
General Research
Science Research Institute
Agricultural Experiment Station
Central Station, Corvallis
Union, Moro, Hermiston, Talent, Astoria, Hood River, Pendleton, Medford, and Squaw Butte Branch Stations
Klamath, Maiheur, Red Soils, The Dalles, Central Oregon, and
Milton-Freewater Experimental Areas
Engineering Experiment Station
Oregon Forest Products Laboratory
EXTENSION
Federal Cooperative Extension (Agriculture and Home Economics)
General Extension Division