engineer waterways experiment station vicksburg …

53
AO-AL07 735 ARMY ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG-ETC F/6 13/2 LOCK CILVERT VALVE LOSS COEFFICIENTS. NYORAULIC LABORATORY INVE--ETC(U) SEP 8I B A PICKERING LOiCLASSIFIED WESTRIL-61-1O "

Upload: others

Post on 27-Jan-2022

4 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

AO-AL07 735 ARMY ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG-ETC F/6 13/2LOCK CILVERT VALVE LOSS COEFFICIENTS. NYORAULIC LABORATORY INVE--ETC(U)SEP 8I B A PICKERING

LOiCLASSIFIED WESTRIL-61-1O "

Page 2: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

TECHNICAL REPORT H-L-81-10

LOCK CULVERT VALVE L LLOSS COEFFICIENTS

Hydraulic Laboratory Investigation

by

Glenn A. Pickering

Hydraulics LaboratoryU. S. Army Engineer Waterways Experiment Station

P. 0. Box 6.31, Vicksburg, Miss. 39180

September 1981Final Report

Approved For Public Release; Distribution. Unlimited

7i

UNWALU

.j Prepared for Ofie he fEgnes .S ryD T ICOffce Cahiefofgn ees U. S. Army4 ELE T

NOV 2 5 1981

D

Page 3: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

4v

Destroy this report when no longer needed. Do not returnit to the originator.

The findings in this report are not to be construed as an officialDepartment of the Army position unless so designated.

by other authorized documents.

The contents of this report are not to be used foradvertising, publication, or promotional purposes.Citation of trade names does not constitute anofficial endorsement or approval of the use of

such commercial products.

-' d - ,,

Page 4: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

UnclassifiedSECURITY CLASSIFICATION OF THIS PAGE (Wh1en Datl intered)

REPOR DOCMENTTIONPAGEREAD INsTr!UCTIoNsREPORT DOCUMENTATION PAGE BEFORE COMPLETING FORM

I. REPORT NUMBER 2. GOVT ACCESSION NO 3. RECIPIENT'S CATALOG NUMBER

Technical Report HL-81-10 AP-61457 rr-4. TITLE (amd Sbtitl.) S. TYPE OF REPORT & PERIOD COVERED

LOCK CULVERT VALVE LOSS COEFFICIENTS; Hydraulic Final r.portLaboratory Investigation 6. PERFORMING ORG. REPORT NUMBER

7. AUTHOR(.) S. CONTRACT OR GRANT NUMBER(.)

Glenn A. Pickering

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10 PROGRAM ELEMENT. PROJECT. TASK

U. S. Army Engineer Waterways Experiment Station AREA&WORKUNITNUMBERS

Hydraulics LaboratoryP. 0. Box 631, Vicksburg, MiRs. 39180

It. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE

Office, Chief of Engineers September 1981U. S. Army 13. NUMBER OF PAGES

Washington, D. C. 20314 46-14. MONITORING AGENCY NAME & ADORESS(II diferent froe Controliind Office) IS. SECURITY CLASS. (of this report)

UrclassifiedIS. DECL ASSI FIC ATION/DOWNGRADING

SCHEDULE

16. DISTRIBUTION STATEMENT (of this Report)

Approved for public release; distribution unlimited.

17. DISTRIBUTION STATEMENT (of the abetract antered in Block 20. If different frotw Report)

IS. SUPPLEMENTARY NOTES

Available from National Technical Information Service, 5285 Port Royal Road,Springfield, Va. 22151.

19. KEY WORDS (Continue on referee side If neceeary aId Identify by block number)

CulvertsNavigation locksPressure measurementValves

20, AIST'RACT'rCenthas ,e miveril N s neeaeey ad i #dily by block nobmr)

This report presents results of tests that were conducted to determine

valve loss coefficients to use in predicting pressures downstream from navi-gation lock culvert valves. Reliable prediction of these pressures is neededso that a valve can be sited to prevent cavitation either by submergence or

self-aeration with air vents. Tests were conducted with various culvert roofexpansions beginning at several locations downstream from the lock culvert

valve to determine the effect of the expansion on valve loss coefficients.,_

DO FORM M4 EDITION OF INOV 6S IS OBSOLETE Unclassified

SECURITY CLASSIFICATION OF THIS PAGE (tan Data Entered)

Ot]

. . .. .- • ,

Page 5: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

Unclassified

SECURITYv CLASSIFICATION OF T141S PAGUIftk Do& Rue...

SECURITY, CLASSIFICATION OF TIS rAGEAl.nOat. Er .. d)

a

Page 6: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

PREFACE

The study reported herein was conducted under the sponsorship of

the Office, Chief of Engineers (OCE), U. S. Army, as a Civil Works In-

vestigation Work Unit 31479, in the Locks and Dam (Navigation Hydraulics)

Research Program. The study was authorized in FY 77. Tests were con-

ducted in the Hydraulics Laboratory of the U. S. Army Engineer Water-

ways Experiment Station (WES) under the general supervision of

Messrs. H. B. Simmons, Chief of the Hydraulics Laboratory, and J. L.

Grace, Jr., Chief of the Hydraulic Structures Division, and under the

direct supervision of Mr. G. A. Pickering, Chief of the Locks and Con-

duits Branch. Tests were conducted by Messrs. D. B. Murray, J. H.

Ables, Jr., J. F. George, C. L. Dent, T. E. Murphy, Jr., and H. S.

Headley II. This report was prepared by Mr. Pickering.

Technical monitors of the Locks and Dams (Navigation Hydraulics)

Research Program during the course of the investigation and the prepara-

tion and publication of this report were Messrs. S. B. Powell and B.

McCartney (OCE).

Commanders and Directors of WES during the conduct of the study

and the preparation and publication of this report were COL John L.

Cannon, CE, COL Nelson P. Conover, CE, and COL Tilford C. Creel, CE.

Techincal Director was Mr. F. R. Brown.

Accession For

KTIS GRA&IDTAB DTICccnannounced D T I

Justificatio 0ELECTE

By . ... NOV 2 5 1981 IDistribution/

Availability Codes DAvail and/or

Dist special

RL 11

Page 7: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

CONTENTS

Page

PREFACE.................................

CONVERSION FACTORS, U. S. CUSTOMARY TO METRIC (SI)UNITS OF MEASUREMENT........................3

PART 1: INTRODUCTION.........................4

Background...........................4Purpose of Investigation .................... 5

PART II: TEST FACILITY........................6

Description...........................6Appurtenances .......................... 6

PART III: TESTS AND RESULTS.....................8

Test Procedure.........................8Initial Tests .......................... 9Culvert Expansion at Valve...................10Culvert Expansion Downstream from Valve. ........... 10Location of Minimum Pressure ................. 11

PART IV: DISCUSSION AND CONCLUSIONS ................ 13

TABLES 1-9

PLATES 1-10

2

Page 8: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

CONVERSION FACTORS, U. S. CUSTOMARY TO METRIC (SI)UNITS OF MEASUREMENT

U. S. customary units of measurement used in this report can be con-

verted to metric (SI) units as follows:

Multiply By To Obtain

cubic feet per second 0.02831685 cubic metres per second

feet 0.3048 metres

feet per second 0.3048 metres per second

feet per second per second 0.3048 metres per second per second

3

Page 9: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

LOCK CULVERT VALVE LOSS COEFFICIENTS

Hydraulic Laboratory Investigation

PART I: INTRODUCTION

Background

I. Prevention of cavitation downstream from high-lift lock cul-

vert valves has become an increasingly difficult problem for designers

as lifts have increased to values greater than 100 ft.* High velocities

and low pressures are induced as flow accelerates immediately downstream

from the valves during the valve opening period. In some instances, the

local flow acceleration is sufficient to lower the local pressure to the

vapor pressure of water and form cavities within the flow. These cavi-

ties collapse rapidly or implode either in the water or against the

downstream boundaries as they enter the increased pressure that results

from the decreased velocity of flow as it expands and is decelerated in

the culvert downstream of the valve. This has resulted in lock masters

reporting loud pounding noises indicating cavitation implosions within

the flow. In some instances, these booms have been violent enough to

shake the lock walls and break windows. The implosion of the cavities

against solid boundaries results in rapid pitting or damage to valves

and appurtenances and to the concrete culverts.

2. In early designs, pressures low enough to cause cavitation

were avoided by submerging the culvert at the location of the valve so

that thc pressure gradient was maintained above the top of the culvert.

However, as lifts increased, it became increasingly costly to provide

adequate submergence. Through prototype tests at some of the high-lift

locks on the Columbia River it was found that admitting a controlled

amount of air into the culverts at each valve virtually eliminated the

A table of factors for converting U. S. customary units of measure-

ment to metric (SI) units is presented on page 3.

4

L4

Page 10: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

pounding noises. Air was drawn through a vent placed downstream from

the valve into the culvert system during the valve opening period, was

entrained as small bubbles in the highly turbulent flow, and emerged in

the lock chamber so entrained that it merely caused the water to look

milky. It was concluded that the air cushioned the collapse of the

large cavities, eliminated shock pressures, and thus eliminated the

pounding noises. This procedtire allowed the culverts to be placed at

a much higher elevation. Several locks have been constructed by the

Corps using this procedure and no operation difficulties or hazardous

conditions have been reported where pressures on the culvert roof were

low enough to draw air during the valve opening period.

3. Through model tests of various locks it was found that expand-

ing the culvert roof upward downstream from the valve would increase

pressures on the roof of the culvert just downstream from the valve.

Also, in one series of model tests for the Lower Granite Lock* it was

found that the location of the expansion with respect to the valve di-

rectly affected the pressure on the roof of the culvert in the area

immediately downstream from the valve as shown in Plate 1.

Purpose of Investigation

4. The use of expansions downstream from culvert valves is a very

practical means of controlling the pressures and allowing the valves to

be set at a more economical elevation. However, the limited amount of

available test data was not adequate to predict the precise effect of

the degree of expansion and location of the expansion on pressures and

loss coefficients. Thus, systematic tests were needed to determine

these factors. Also, it was expected that the tests would determine the

exact location where minimum pressure occurs during a valve opening

period.

U. S. Army Engineer Division, North Pacific, CE. 1979 (Sep). "Navi-

gation Lock for Lower Granite Dam, Snake River, Washington; HydraulicModel Investigation," Technical Report No. 126-1, Division HydraulicLaboratory, Bonneville, Oreg.

5

Page 11: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

PART 11: TEST FACILITY

Description

5. The test facility (Figure 1) consisted of a headbay, conduit,

valve well, reverse tainter valve, and tailbay. The upstream conduit

was 47 ft long with a straight length of 17 ft upstream from the valve

well and the downstream conduit was 14 ft long. A layout and details

of the facility are shown in Plate 2. The culvert and valve well were

constructed of plastic, and the valve was made from sheet metal.

Appurtenances

6. Water was supplied to the facility through a circulating

system. Discharges were measured by a venturi meter and an orifice

meter installed in the flow lines. Piezometers were used to measure

pressures, and an adjustable tailgate was used to regulate the down-

stream pool elevation (lock chamber elevation).

7. The instrumentation and control system provided for operation

of the culvert tainter valve by means of a programmable d-c motor. The

position of the valve opening was indicated by a linear potentiometer.

The cam and signal plot could be drawn to carefully control the valve

position as a function of time.

6

Page 12: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

=among

~e

Y.

41tie h ~1 t

Page 13: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

PART Ill: TESTS AND RESULTS

8. Pressures downstream from lock filling v, ilvs are a fun(tion

of the valve loss coefficients, K , along with t lher fato rs. 'I licV

valve loss coefficient used in this study refers to the total head ,

at the valve which includes that due to the valve well, the va Ive, ,nid

the culvert expansion. This study was concerned primarily with tht

effect of culvert expansions downstream from the vllve on K I hLtV

valve loss coef f ic ient is def ined by the following equat ion.

SEK -(

v 1 /2g

where

K = valve loss coefficientv

AE = energy loss of the valve, ft

V = average velocity in the culvert upstream from the valve, fps

g = acceleration due to gravity, ft/sec-

9. All of the tests reported herein were conducted with a ver-

tically framed tainter gate as shown in Engineer Manual 1110-2-1610,

"Hydraulic Design of Lock Culvert Valves." Although the valve loss co-

efficients reported herein would probably be slightly different with

the other types of reverse tainter valves shown in the referenced manual,

the conclusions drawn from these tests would be the same regardless of

the type of valve used.

Test Procedure

10. Each test consisted of setting a specific valve opening, dis-

charge, upper pool elevation, and lower pool elevation and then record-

ing pressures as indicated by piezometers installed throughout the test

section. At least three tests were made with each valve position with

either different discharges or different lower pool (lock chamber) ele-

vations. Data were plotted for each test as shown in Plate 3. Slopes

of the pressure grade lines in the culverts upstream and downstream

[ 6

Page 14: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

from the valve section were extended to the valve well to determine the

head loss, AR , at that section. Average velocities in thL sections of

culvert upstream and downstream from the roof expansion, VI and V3

respectively, were determined from the known cross-sectional areas and

discharge. By adding the difference in velocity head in the two sec-

tions, V I2g - V 22g , to the head loss the total energy loss at the

valve section, AE , was determined. The valve loss coefficient was

then computed using Equation I shown in paragraph 8 above. Results for

the various test runs along with pertinent boundary conditions for each

run are shown in Table I.

Initial Tests

11. Initial tests were conducted with a culvert of constant cross

section 0.56 ft by 0.56 ft upstream, through, and downstream of the

valve (type 1 design, Plate 4). Data obtained with this unexpanded

culvert formed the basis for comparison with other designs tested and,

also, for comparison with prototype data since extensive data were avail-

able from McNary Lock which has unexpanded culverts (Plate 5). Pressures

measured with the type 1 design are shown in Table 2.

12. Data obtained were used to compute valve loss coefficients as

indicated in paragraph 10. These coefficients are shown in Table 1 and

are plotted in Plate 5. Points from the curve in Hydraulic Design Chart

534-1 are also shown for comparison. These data are very close and the

agreement between the experimental and prototype values is excellent.

13. The assumption was made that energy loss between the valve

well and the vena contracta is negligible. Thus, the velocity head in

the vena contracta must equal the distance between the energy grade line

in the valve well and the minimum pressure on the roof of the culvert

downstream from the valve. On this assumption, velocities in the vena

contracta and contraction coefficients for the valve were determined.

Contraction coefficients agreed closely with those used in lock filling

and emptying computations in Engineer Manual 1110-2-1610 as shown in

Plate 6 for conditions of no culvert roof expansion. The expansions

-- .

Page 15: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

tested in this study did not influence the contraction coefficient.

Culvert Expansion at Valve

14. After the base data were obtained, tests were conducted with

culvert height expansions from 0.56 to 0.88 ft (type 2 design, Plate 4)

and from 0.56 to 0.72 ft (type 4 design, Plate 4) beginning immediately

downstream from the valve. The roof of the culvert was sloped up IV on

1OH in all designs. Pressures obtained during these tests are shown in

Tables 3 and 4. Valve loss coefficients are shown in Table 1 and are

plotted in Plate 7. As shown in this plot, there is greater energy loss

through the expanded culverts, particularly in the 50 to 70 percent

range of valve openings. With identical valve openings and equal dis-

charge, pressure drops are the same regardless of the roof expansion,

since the expansions did not influence the contraction coefficient. It

is postulated that if the entire system (rather than the valve, as in

these tests) controls flow, the pressure drops would be the same; but

the absolute pressure downstream of the valve would be significantly

higher. The test results indicate that the maximum negative pressure

downstream from the valve is less with an expanded culvert, not because

of flow circulation as had been hypothesized but because the fully ex-

panded flow velocities (thus, discharges) are less in the downstream

culvert, particularly through the range of valve openings that result

in minimum pressure. With relatively small valve openings, the energy

loss is relatively large due to expansion and deceleration of flow.

With the larger valve openings, the change in velocities and energy loss

are minor due to only minor contraction and expansion of flow.

Culvert Expansion Downstream from Valve

15. Tests were conducted to determine the effect of the position

of the beginning of the roof expansion on valve loss coefficients. All

of these tests were conducted with a roof expansion of IV on 10H from a

height of 0.56 to 0.88 ft. Expansion started at distances downstream

10

4'

Page 16: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

from the valve of 0.28 ft (type 3 design), 0.56 ft (type 5 design),

1.b8 ft (type 6 design), 2.24 ft (type 8 design), and 3.64 ft (type 7

design). All of these designs are shown in Plate 4.

16. Pressures measured during these tests are shown in Tables

5-9. Valve loss coefficients computed from these data and the data from

the types I and 2 designs are shown in Table I and are plotted in

Plate 8. These data show valve loss coefficients to be essentially the

same with no roof expansion (type 1) and with roof expansions beginning

4.0 valve heights (type 8) and 6.5 valve heights (type 7) downstream

from the valve. A plot showing the effect of the beginning of the roof

expansion on valve loss coefficients is shown in Plate 9. It appears

from this plot that the effect of the position of the roof expansion on

valve loss coefficients varies slightly with the valve opening. For

each valve opening there is a critical value for the distance to the

beginning of the expansion, beyond which there is no change in the valve

loss coefficient. Expansions that start downstream from these critical

locations would have no influence on valve loss coefficients. This

critical location is about 3.5 to 4.5 valve heights downstream of tile

valve in the range of openings where minimum pressure occurs during a

filling cycle. This is in reasonable agreement with the Lower Granite

results (Plate 1) which show effects within 5 valve heights.

Location of Minimum Pressure

17. Pressures were measured at various elevations and distances

downstream from the valve to determine the location where minimum pres-

sure occurs. These tests were conducted to assist the designer in lo-

cating the air vents downstream from the valve. The culvert expansions

had little effect on the location of the minimum pressure. Isopiestic

lines obtained with valve openings of 40, 50, 60, 70, and 80 percent

are shown in Plate 10. These data are in dimensionless form and are

averages from several tests conducted with the types 1 and 8 dcsigns.

The following was used to convert the data to a dimensionless form.

11

__ _ _ -. ' .

Page 17: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

P - pu

V /2g

where

P = pressure immediately upstream from valve well, ftu

P = pressure at some point downstream from valve, ft

V1 = average velocity in culvert upstream from valve, fps12

g = acceleration due to gravity, ft/sec

2

These data indicate that minimum pressures occur near the top of the

culvert. The distance downstream from the valve where these minimum

pressures occur varies with the valve opening and moves upstream as

the valve is opened. As shown in Plate 10, the location of minimum

pressure at the roof of the culvert with the valve open 60 percent is

between 0.5 and 1.0 valve heights downstream from the valve. Thus, the

common practice of placing the air vents in the roof of the culvert

about 0.5 valve heights downstream from the valve is satisfactory,

although the vents could be placed farther downstream if necessary.

12

4I____. ......__

Page 18: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

PART IV: DISCUSSION AND CONCLUSIONS

18. Accurate valve loss coefficients, particularly in the range

of valve openitigs between 50 and 70 percent, are imperative for close

prediction of minimum pressure downstream from navigation lock culvert

valves. Reliable prediction of these pressures is needed so that a

valve can be sited to prevent cavitation either by submergence or self-

aeration with air vents. The valve loss coefficients determined in

these tests unquestionably are more accurate than can be determined by

picking values from filling curves only. Thus, it is recommended that

in analysis of prototype data and in predictions of performance of

future locks these coefficients be used.

19. The maximum negative pressure downstream from the valve was

found to be less with an expanded culvert. The negative pressure was

reduced because the valve loss coefficients were larger with the ex-

panded culvert, and thus, the discharges were less through ine range of

valve openings that result in maximum negative pressure. The valve

loss coefficients determined in this study can be used to determine

the effect of culvert expansions on pressure downstream from the valve

with expansions up to 57 percent of the valve height. The 57 perctnt

expansion was based on the Lower Granite Lock which is the largest ex-

pansion constructed to date. Also, this was considered to be near the

upper limit from a practical standpoint.

20. The study showed that culvert expansions that begin 4.5 valve

heights or more downstream from the valve have no effect on the valve

loss coefficients for valve openings of 30 percent or greater. Expan-

sions beginning within 4.5 valve heights of the valve increased loss

coefficients linearly as the expansion was placed closer to the valve.

This agrees reasonably well with data obtained from a previous mclel of

Lower Granite Lock which shows minimum pressure decreasing linearly as

the expansion was moved downstream until it reached a distance of 5

valve heights.

21. In design of future locks if it becomes necessary to expand

the culverts to reduce friction losses in the filling system or for

13

Page 19: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

structural reasons, and the expansion is not needed to reduce negative

pressures for optimum location of the valve, then the expansion should

not begin within 4.5 valve neights downstream from the valve. if the

expansion is needed to reduce negative pressures, but the amount of ex-

pansion is greater than that required to obtain optimum pressures with

the expansion beginning immediately downstream from the valve, the ex-

pansion can be moved some distance downstream from the valve to obtain

optimum pressures. The valve loss coefficients shown in this report

can be used to determine this distance.

22. It was concluded that the contraction coefficient is inde-

pendent of culvert roof expansions when the valve is controlling the

discharge as it was in these tests. The pressure drop from the grade

line in the valve well to the minimum pressure downstream from the

valve was dependent upon both the contraction coefficient and the dis-

charge. Thus, expansions influenced this pressure drop only because

they influenced the discharge.

23. Minimum pressure downstream from the valve occurred at or

near the top of the culvert. The location of this pressure varied with

the valve opening and moved upstream as the valve was opened. The mini-

mum pressure was located between 1.0 to 0.5 valve heights downstream

from the valvP with valve openings in the range of 50 to 70 percent open

where minimum pressure usually occurs. Thus, air vents should be located

in the roof of the culvert at a distance of 1.0 to 0.5 culvert heights

downstream from the valve, preferably 0.5 culvert heights, since the

lowest pressure occurs at that location with the valve near a 60 percent

opening.

24. All of the data shown in this report were obtained with a

vertically framed (Holt-type) valve, since it is the most commonly used

type. Valve loss coefficients and contraction likely are different for

other types of valves, such as a double skin-plate valve. Although the

value of the coefficients would be different, the conclusions concerning

the effect of expansion and location of the expansion on loss coeffi-

cients and location of minimum pressure should be the same.

25. The test facility used to obtain data to determine the valve

14

. . .. . . . . . I l ll l ...

Page 20: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

loss coefficients did not include the culvert intake or distribution

culverts and ports of the filling and emptying system. Also, the tests

were conducted with constant upper and lower pool elevations and valve

openings. Thus, the effective inertia of a prototype filling and empty-

ing system was not reproduced. However, by using the valve loss coeffi-

cients determined in this study, along with other loss coefficients for

the culvert intakes, friction, and exit manifold in the CORPS* H5320

computer program, accurate hydraulic data such as pressures and lock

filling and emptying times can be obtained.

26. Future studies with a model of an entire bottom longitudinal

filling and emptying system would be very beneficial in determining

other loss coefficients such as the intakes to the culverts, in the

distribution system and at the outlet manifolds.

* Conversationally Oriented Real-Time Program Generating System (CORPS)

Computer Program H5320, "Lock Filling and Emptying Symmetrical Sys-tems." Available from: WES Library, U. S. Army Engineer WaterwaysExperiment Station, CE, P. 0. Box 631, Vicksburg, Miss. 39180, andfrom several CE computer systems.

15

K.

Page 21: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

- -- - - - - - - - - - - -CC

00 000 0. . . 0 00 .0.. .00. 00

1*1

- - - - - - - 4- - - - .L..-..I..-..

- -

. 0 0.. I . . 0 0 .0 0 ... . . . . .0 -. .0 0

- - -C---C - ----- -- ------Q-I -- --4 -LI- -1. --.44 O O I4 C - 0 I. C - - C-0 - -I 4--4-00--

-~~~ -c -44 .. ~ - - -. -000 .- ~ -4 4

- I - -- - - -t -- ~......... ..............................

14C C 000..0 0 00 4 4 4 - 00 0 0 0 0 0 0 0-=--

" C C o 4-CCL4000-1- 4I-C C-0000I;t - 0

II.I OO0 0O00 04

0 CCC I00O 000 0000 C00 000 000t -bX--i

Page 22: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

4.4. ~ ~ ~ ~ . .. .t..0 . . . . . . . . . . . . . . . . . 40. . 0

'd - - -4 - - ---. -44 4 . - - .- - -.4 - -4 -- .4 00

"2:7,.99 oo o g o o o- -c

.............................

,,20,. 2 .... 2 0

- 24

. . . . . .. . .. . . . ..

- - - - - - 0.4 -044 -"C 0 71..4

S. .. 00000.000.00. .0.I. 00.

, 0 0 0 0 00 0 0 0 00 -.. 44

"I >4 .4. 4 , i , ,., , , ,4 . ,. . . . .

o04..o o o o oo o oo o oo mo o o o

K 1 0

Page 23: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

- - - ----.

~4.'c4 0 00 0 - . 4 c, 00 -

4.-J 0.14- 04,J O O O Z 7CC'- -C o' D' 00 T1 01 3 1

m m ,4,.4. cln m - - - - - -

-4 ' 4 1440 oO 0 T'D00 00 DI 01 104 1 0 00. 1 - 0 '..-m09i C 1 1 9 1 1 1 1 91 7 l c i1 C 1

,I 0'T 4.T0 0 .)0 000000 0 0 0 0 )0 0--------

-n 0 0 ON OD 0.~'.~0 In 000 0 D0 000 000.00 D 4- 1 .40 0O U

'T - CT 0T 'T ' .4 0 - . 4~-7~- 0' 7044--0' -7 0N C 7 CN CN C4. C4.

'o C), n 0cy70 I00 000'D 000000 00 0 o00 C 000 c 0

0 o. 0 00 zO ' 0 m (400w '0r m 0"4. '7 wT. .13, 74.C?4! C? '4 C

.0 0 D CII 4 000 4 C4 0 0 T 0 CO -. 700' 0 07-7-0J ON0 0 -~0 -JS ' 0 J 4 -0 N A C4""I 10 - 0 C4C4C NC

, '

4O' .- 00 0 -'D' n ' - T je n0 D o1 ' 1

aj 0 a 0 00 'D00 'D0D0000T'I 0') ON000n00 0 0 CIO ID 0 0 0 00 -

I z t TI '0-0 'T -r 00000 00 0 0 -.CD-0-.7-7 .w

't 1'~ 00 1 nI lc 0a-m1 04) 1 n 0(10 0 0 0a

4~ ~ 0 '.-77-.-7- 0 0 00 000000 .- C) 0 0 cc '00-C4444.C4-44-' 4'J . .

ml ~ ' " 0 NCSCN0 N0 0a 00 0 40 DCOma Nc,0 0l

In. In-'7.7.77 1- 00 00 0 .t.- .444444'4-4 N N NCC

00

0'

w 0

0

-1 '.0 0O o 0 N01 1 ' 1C,0 m T ' 7-4' ____,___C_____ __ (N__C_4 __C _ __M__ '--

Page 24: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

0~0 0D00 000 m' ?00

c) I C)C CoC )o0--

co ~O 0- 0 C, "0I 11 0

0 n M41. .m C 'C0 0 0C

I..' 'I '? 'D 0 Io 'D oo 0.0 .r 40.-'T I04C)404co 01Go0 - 03 4o

0 - - 1 "1

1 ~ ~ ~ I I 1 I I 1) I 1

I I I I I I I I

04 'C.--00 0 0000 00C)C; 0 4---- - - -

c; I 40l0400 1 0 000000CC)0 o -40 -4 - -- -- -- --

-c I 1 -IZT- 0 -

.00

M0 .00 0 1 C00 0r00 D00 oo0O r4 0 TOD004 00 D0/D -

r4I C0040 411 0 1 000c 0000D.o.0 c o0 0 04.6c 40 - -I ---- 4

c) Ij In

-,? .- l "1' -1 04l-1 "' 1

o

04 ' 0CInf101..0.0C 4 I0000?tDrI00 000''-l400 D T0IDI C D0 0 00 0nC

04 00 T00 C000 0 0 0 0 V0 04CD 40 0 4 4 r II a,4.1

.0

04

'10 0000In0404M 0 InTI 000CD00000M000004 - 0 0- - - - I -- ----

Page 25: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

o N NN4 !04N r04, Or! C"! NNNNC]r]NNCI N . . . NN 4 r44 r4 41

M0, MM OM M- OM ('0 C- NC 'CO N C- C0 N4 rq N4 . . . N N C- N 4 . . .N . .N.

N 0 N1 N N N N N N N N N CN N 1 . - 4O ! li'o NM N " N N N m -4 . .4 N N NNNNNNN - -~ -

N N .- -4-4- 0-4-4 -4 -4 4 1.4 - 4 -4 1--4 4 -4 1-4 -4 - -4 -4 4.- -4 -4 . - - .4

-, .- r.4~ .. tM 1 WM - O0401 I

N L",M f4 0 -4l 4NN 2 NC4 .- 4 " 4 . -4 C4. . . .~

N NN N N4 0 0 0 0 0 0 . . -4 .4 - -- 44 -4 - .-4 - -4. -~ - - -

0

NO 0 - 4 0cy0 0as17,N Ni N N 0 N , 1 1 ll.0.0' 0 . 1 r .01 4 (

MM 'M Mo n,4!'4L "o 4C 4CJ" 1

IN "c ' ' 00 04 N 0'0 'nM4] 004 -4 A-14 -40 0 4 4 - -

N4C4C C4 N4 . N0 0 0 0 - -4 14- 4- 4 -4 - 4 4 -4.-4 1-4 4

04 y ' DC C4~t 10 ZrC0OC400. N -4%0 4C n .e - C T ,

,- r4NN(4 NC4 0 00 0 00 0 00 0 4A- 4- 4 - 4-

0 >I

,-4 N tN - 0 0 4 f - T.W. . . . . . . . .

0 W.14

Ir J .0 wm r 1 oa . n1 na 0 10 C4e TL 0 C,0-z' 4_4_________ C_4_ -4_C4____ 4e4_C4__ fnfM___ M_ (n_____-

Page 26: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

I I I I I I I I I

C) 0 7 T 0 m0 0 0 0n0 00 00 T0 0 D ,a

- - ' - -~ I 'q 0'9 ,

- - -- - --

'N t07~ 000 0 (2:! 0 000 00

C D "0 0 -1N ' ' CN N N D N ' ' ' ' D (, - a' * 0' 0 0- ' -i

'N 0, N00 o00 1000o D00a,00 CD N'~ . . . m w

'N''N'0 c 00000o C00000Z0000 00 0 -10 )0

- 'N~~ - -'N -'N -N 'N -N' 'N' N' -tS 4 flC' 'N NZ N'N N'NN

'N . .oooco o co o0 6 0

-tt-n'tt 00 0 0 0 00 0 0 0 0 C) ' oI O )'r oo 7 w

0000 000 00 0r 0T 0 0000 D'

o ' i C C n (::, w -'ow ow- a,-D" "1,c

4 -14 t.4 - -N 'N ,- .- - - -.- - - - -N - - 'N 'N 'N 'N 'N 'N 'N 'N 'N'

o4

'N'NC0 CCC~r CC~r-.~~O'0' ''NC0 ' 'c 'N-,

a 0 0 ''

. . . . . . . . . . . . .4 1'- - - - -NDN' - - -

r* 'N' a 's c00"0000 00 00 00 00 - -

'N 0'4' .4 . .N .~ .' 4 C14 -n () M n 'N 'N T 4

Page 27: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

l~Cfl~Cfl0~Jz fl Cfl r' 14C fl O Cl 3-,- C -l -1>J

04 04 0

A O OS ~'4 0404 000 s0

S~ ~. ~ 0 0004 ON I 0 4~C *. C'C' 0 - - -N -N -N -C -0 -' -4' ~ -~ -

04 CN1 4 4- 1 411

-S.OSOJ' -- - O--N-ON o9O O ~ O O ON S S 0 N

c. oo mc o' TmI D o z D mc c

o~ 0 D ot 3 oC 'o c>w D x >:rc-1 005. IsO wI 040 wN 'D ,I - D o~ CN o1 0 -? xz-7

CC1(D IC 30 c ) c ;c

sOsOOs 0 1u0 0( s . s 0 ( - ( . -

0 ' ~ 4 ..- 0-I~0z cOm' D, N 1 D a

o cf 7-154N04 0000 000 000o0

-0 10 <-D -) 0 -(0 sC -60-o. 6 (0-4. 0(-71 N'. 5 0 0- 0c.1iD -o'(

-TC. , w ro o0- D- X040.?0 0 C> 1(000 s O'' ON NO ' 0.t NO 0 05l0

'4 T M -1 Z 00 Z C

0 04030 a) 0003 0 0cc c 0 o 0 o000-6~c(0o ON

0.5.

o4 m nO ,a m1 .1 Tml

CD40 -( 1 :c

'-44

Page 28: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

0 -0.. 4 ' - - 0 - -~ -0 -' - - -4 - : - - -0 -~ -7 -4 -'" . ~'0~( 0~

'T -T'T T T C C o S cz 00 0CD0 00 - - -7 - - -4- -0 -' -'0 0'

.40 (0 V) - c ~'D .0D .D '0 0 0 44) 0 N ~00 -7- 00 (00 00 0 0 0~

mj mN - ) 4 - 0 CD 4'4 cs o 0 04 c) C; c7 CD o0 0 o, 0 o7 o o0 oo 0 o .- 0 -0. 0.

1~4 ~ 00000000 0 0 S 0 0 0 0 0 00 0 0 0 0 0

'n co I n m "I

Q , 'aCC44.4.4,444.44(4400000-- 00(0 '04N-. ~-..

MI I-4a,

,T In -I I I , T 00 1 ' " '0 - >C

m m m )0 0000000C

qD 1 , O.ON( 1 mITL O T 0 D00 ' 0 N N L

Oco

NIC O C O O 0' '0444'47.. N444'(0-(4'0N-7'0"00'.70.-4.-4000 W

"T,0!"O "T )00 0'0 '0000 00 0 00 00 00 -4444.04.4-0.-4.-

r

.1 * 0

0

Q) CC0 0

44 '0 l 10 0 1 , 00 01 0 4 44 TI 0 00N401 0 -1 4 M L) 0 00M -0 - C44 -4 4(44In'M In0'M''0'0M I) M 0(0( (0 _ _ t_ _ -__ T

Page 29: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

. . .. . 0D'Tm 14 Ln as k 0 o V

Cl 10 n0 ' ~ l~~~ en11o 1 !1 1 o: 1 14 0 )c )00000

I I I I 1 I

enele le n0 0 0 0 0 0 0- 0l oo o o(o o l Cl - l Cl - i - - - Cl --

CA e -t 0 A C) o3 c0. oe Ce 0 0 - c- 0C C C . nene 0i I- -0 -l C- -Cl 0 -

.0 I 0

114"CC-I 4C en e0 0 00 060 o00c06666000000----0 --

I I I I

lI I I l I I

0oo 0 CC f N14NI o 1

14 0 -~ Cl Cl -4 1-. 0 0 0 01 0 D- VA Cl Cl R~- . 0 l m C" lo a'0 -4C n- lo 4' ~ 0. l

'A0 C)0 'nel - .3 o' -30 1 0' -e a' 0 0o -. 2i C en' -~ -1 - C-. oo a' 0' 0 0 0A 0 0: 0o

.41 4A IA 4A A 0 1 !5 C'! 5550000000-Ic - 1 -I-- -I .-- I.I--'- Cl o: C C-i Cl Cl7 7

4 n n n 0 en 0 '0 c- 0na 0 'cD cl '0 en 006 a' 00 6 oo -- -3 -~ -ee -- -n -l0e'te

0 a) l0 e n -C a 0 a' C- Cl ell en CC .1 -D a'' -0 C- c n 4 0 en ce Cl-400

0

o

0 )

Ln o o y o ,c o(, D r o214C q- ,'

Page 30: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

01 ~ ~ '' -o a-, 4 ! .- 4o0004-4 0004400

aN c4 ' a, f) o 0 n 0 m 0 , '

-4C . . 0 4 4 1

-, 1 -, 1 00 - 0 '-40 1 1 0 4 0 ,M 0,01 , - O O

a04 T1 - m I4T mmoL o-. op ioc o )

10 JOC C4 N N 4JJ'CC CJJ N 4'001 00 094041 1 1 l L 1 1 91 r 9 o l ol 1 c

0 C>--------------

W1 T D D n nMMI 1 TW0 a D WW10 0 1 1 C . 0 00 00 =- ( - : r 1 :C

- ----

00

C 40 0 c )0 00 0 4c) 04 0 4 0 4

.0 .4 . -

I1I1I1I I

o

0 -4

W.

w, 'n 04 0D '? -j 00 o, co o , o 4 04 m' en 'o 04 m 4~4~ 4 0 0 -40'4

.504 -~ ~ ~ C .-,4 .5. .04~' 04 4 = 0 " ,' '00 04 M M'0 0'00' M

Page 31: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

a,'i a',- a '4 o~ C -r. n ~a C w~ c e- V) m 0a, wc z a)~ m

c C w

0 'T Cren m 71 -,7 lC M 000C C 'D 4.- C 00-- Y ) 1

cc ,-T a'Ccc(N(NmN'I C-4D JCD00 O,-,e-. cr.cca'...4c1- c ccJC100 en(a:c 119 (N(N c 00C00C000l!O0OOO -L 1

cc c n'nr9 -' -

'ao (N7' 7 '-C 'N "4NCl -7 NIC

-T -0771 -7- - - Ca 'a-0 C.-.1en1SC- -0 j-.a'a a r

'Do I c~c C- -. C CC, -. S Cc 0c , .'

m l o I I I I III I

C: c (Nc c . ... . . . . . . . . . . . . . .Cc CC c c7- -- - - - - - - - -(C cI I-CIcN

0'....... .5-7nC~CINrNNr.7N.'7r-0 'CSc.f .,.7 e

0 c o Ic(N 0'a''a'aa'aa'a''a''aa0a'aa'O0-.C(N~7 7CN-.cccccc Ic

r-..c o 57--.-4e nn c c c-CI ( C ICe nn-t.S CW -.. Ni-CC. zC

> I . . . . . . . . . . . . . . .< Enenene!nenenc oC' c oz)o z00c0c c00000CzC- --- -- - ---

00nccccccccccc'- C'C-.n77Cccc c -t-C

> I 5 0 0 0 C 0 - - - - - - -

-~1 .C 7-7rC5-.7n~r-7-.57S C~C SNC-.-.7 r.en 70' 00X

i C *- - - - - - - --a, a o-cl Cro.-TC..'CIN -C -cr D' 1o 1cc tx c'f o

c~ ~~~~ 'I~o~~ 00 0 0 0 0 0c 00 00

Page 32: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

01 0ONO N r10000 ON00m 00aOD00 0404

1N.4 1 4 - .4 - -4,4 - 4 -. 4 -.4 .- 4'4 - N 4 " (N 1N ( N 4 (N A ' (N (N 4 .4 . 4 .4 '4 14

0o 0 In m

0104 .11! oO, -- -' -o'o-"

(N N4 0- 4 "4 4 -- -- -- -4 '4 '(N ,4 C14.

m4 0Dc n00 C0 0400(-0 0000 m0 044m 0

C4~ " CN (4-t.0 0 ~- 0 0 0 (D ( ~ 0 C() 0 -0 0 - -4 -~ - -4 0-

I c I I In

C)1 4 4 ! C'0 004 " 00CO 0'C)0 Ln20 4') 0!.4 N- ( IL" ! !o !'

Z 0 0 O( n0 1 4L 4M 1 .1?11 M 0

~~~~~ C:) o~. ~( ( ( 0 o4 6 - (N (0 .0 64 C00. -'- -'- -0 -4 -4 -4 -4 -40 40

rn 1 144 N 0 0 0 0C0 0 0 0 0 00 0 -- 0 4 -4

0 C

',' *0'44 .400 00C -4- c-,. ]o 'fN( -M N- ] t40(N"(0 .0"4 L"',40((

CY (N0 0 00000 0 000 00 0 0

C4~ ~ ~ -4 4 I4 - - - -I -

T (1 , 1 n D10 01 'I4U 0 I 0 I

00

m0 04.0 0.0 0 00(0(.-~-(

04~ .00 0 .00. . .- m. (N( 04000N ('()--4-4-4-4--- -- -- -- 4 --- 4- 4 - - - --4 -- 4-- -T-4t

Page 33: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

UN .4 0 10 00. 0 01 00 T .- CIJ 0% Lr .- 0 ON 00 ( 0 C4 1- ~" 0 -1* -1 -4~ C -

I" C"Cl " 0 0 00000D u( M ,I'mNOD(*,1(N GA r 0 Lr 1L rV)m m,. 00 00 0 00 00 00CD000000000r 00 4H-4HH-(

A 0t - 1. O 1-4 C-4- 0. -4 4 -4 -4 04 -4* 0 -4 C- -4 -A, (N o r 4 r4 004 -J CH C-40005C

C11 ~ Az; e n nC 0 0 000 0 00 a 0 00 0 00(DCD0 H H H H 14 1 H

0 :3

WG z

T4n r. DMIC4Z lA- 1- 4C4ML 0 - nC DC 03 n0000a

10 Do D0 r, 10Ind 0O C- M 0 r - 0 O H 4cn V)r, OD~ 0( sO 0 Ar, ON 0 OD0 OD C4 (N4 " N GA C

0

w 0 oONa .4 0 0 ~ 5 0 H4O 0 .A, A, Ct 0C-J H

EG m( C(ACA( I m m Mo 0000 000000 00 00c000 00HHHHHHH40

I 1 - 1 0An T TTs D O 7h0C D0 naL)T- rI1GA O O O l~ l

co nr10ooc oo0ooooooc ooA. A1- 4-

MI 4- )(10 -O Nr4MTL Dr ONN( ~0 0 0 40 0-f 1 -N t 0 0 DODOGA C-i I---- 1 1 1 iC C!C!C " 1 I L 1 t O O O

.0

0 0

CU 0

wU

Az 0

80 ITH 0r D(1 L 0r 0C%0 4CIM It 0 O % tL 0 O 4C4M TUz 4H - 4Cjc 414(4C nm m m MI T' T4

Page 34: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

I 1 11 1 0

MC 0 M- a'r- 0 C'4 - C-) 0- 0 N 1 -0a - '' . . C C( C' ~ ~(4

f N 'C4 C 'C 0000 C) 0" 4 t 0 C 0 0 -( - - "4 - ( - C 'C -4 N C'C' C

'n N 0 00 00'I 0. m0 000 n4ON000 00 .- 40% , 4

I ~I I I (I II I

-Q Nn 0 C C N00Y" 4 'C T 0 N"~' 0 0 T 4In N D VC 10' 00 'C C4 D r- 'C M'

m 4 m 4 m (") In -4 . 0- 00 00 00 00 00 00 000 .- 0-4 1- ~.'-

("4~~ ~ 0"a 'C 'C 0'(4 f4C4 0 0I' 0 0 0 'C 41' 0!' 0 0t' C)' C 41' 'C 0C -144 44 -4 0A

I I I I I I I I I I I

oI-I nm0" I.n 000'1.00 0000000N"CONO 'C'44( MO"400 N 00"Cn

C-) M4 M 00 00 0 00 0 0 0 0 0 0 -4--'4'-4 -4 -1 -4 N

0 'DO~' N.' 0 a' a, en 0) 'C 00 ' 4 CC 44 0 ' 0 C 41'4 0 4t 0 f 000 'C 4r LN N r - T 0 en,I o04 44 4r4N N( 4 '0 4 a: 0''0c ' c c

en ." ."~" ." ("4 (4 0 0 00 00 0 0C0 000 '-'- 0- ,-0-~ -4 .' -4 14 -4 11 '-4 .-4 -4

--4 C*0 I 0 1 r 4000 0- ) w 0 ML 0"w r 0

m. m'4)C )0C 000000C 00014- - 4-

o l 4C CN0. " 0 0 0 0 C) C) 0000 0 00Nf' 00 4'00004'~'N'I47"

(" -4NNN ZNOOOO0 OOOOOO-OO-1O1O .O. O. 4 4

-4 00o

0. >

-4C> 4~CY' (4C7 0 4(00 T00" 0 0 T00 0000T 00 0 C400MD-4 %D T- V)

A % ' C O r . 'C C"4C 9 C 'C N 19 0. (4c 4 0 44' 94' Nl N Nl CI4 0 0 N N 'C I4' 414

0 C V 00 a' - 0 0 0 0 0 0 0 -4 N 4 -4 14 "' 'C N 'C M' a'MM-1ID0 ,-

I Lf %D 0 0 00000 00000 (' C tL C 00 001-4 -I'Ir'-N4 'C4 -

.N .O . .C .' .C . .C .C N .C N N -' -~ 00 -O -C N 4 0 400

Page 35: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

N a C C4 14 N0 In C' C4 N1 10 C 0 O N OD~ N 4 D 0 O 0% ON 00 Lr -7

0 ~ ~ ~ ~ . C),~00 ' a a a

-c-t

0 0 In 00 -T 0CN 0 CO M~ N0 C1 0N Lf 00 Ln 00 ) aS en ) 0n l N N 0 0

c' 000 0,1 ,-T0 1 n oNN1 - li nNNN nNN 0. -

m - 4 -4 C) C 0 N -4 N4 1- _-q O ~N ~ ~ N ~ ~ N

D 0 V) ON Cf4 -I 0 0 ' -1 ) .. ? cn 00 0 0 m ~ .d) a'00

m0 0 m N o I n' n r 7 ' , 00 NNN 0 c)'D0 - 0,

M NN N NN4 -4 N 1 - -4 -4 C-4N N N NN NN " N4C4 C4 C4C4C4

cu.

'T- 0- 4 V n0 0C4 L )0 m0 01'qL n 9- lr 0

~I I

M 0 14(31 0 00 14 C1 00 0 0 0 00 N TNNTDNNNN a,

041 (5 C' IS 8~ 'Q C '4 0 -4 -1 N N 0- A 'I 0 4 f o N -N n a 'D 0% 20 0 N 5 0 a' Z

N N, N 0 0 L00014 00 %0 00On 0401 r)0T00N N 0N 0

m ' Iq N a' 0 CD 0 C ) 0 0 0 I0 N 0 0 0 a' N4 -4 N 0a -Na N

I I i I I1

1

'0 4 0C 0 DC =

0

W-nJ M0 0m'

ON NN NN ON C3mim f In a' n0cmC 0NI.' cm C'N. N 0 1=3 r Im im n0 0 .

O 00 1 0 14 -4 N4 4 04 0 0 0 0 0 N 1~ 0 W a'l -N

NI Nl I N . a (,'

z -- I

Page 36: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

. .- - -0 - - - - -

0in4~~0.~4.Si..'~ - --id%.C -i.% -',n o - - - -- - - -- - - -- - -

-~~~~~~~~~~~~~~~~ -400 -...,..- -0-.4 0 3 -.%jiil -1. - - - - - - - - -0% %0% % 0 %

. . . . . .0. . .

0% 0%0%%0%----------.

-, ~-------------------------

0%in.-.O0%04i'0.fl~in...0- -0n~ n~ii -'Oin. -.. 0 .- - - - - - -

0%.0*inninniniini 14- - - - - - - - - - - - - - - -

.0%... . .ini--- -- -- --- -- -- - -- -- - --00

- - - - - - - - - - - - - - -

F 1 c

- O0%%00 ----01N---------------------u----liinC0 inir'.'.

- - - - - - - - - - - - - - -

inin~in--------------------0

0 .0ininc'i.-i0%i'.0111i04~~~~~~~ 0- -r4nf..c 0 -iirir.n- -.t0 %i.' 0 .1 ii- - - -

.2 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 1 0l 19.i,.i'.iC ri1e.i., 0.,cjn i .0.Or-.0%%0%0%0in04iN~i~j04'J 00 0-------------0 0--

. . . . . . . . .I

v% - ii.-.0 00 %i iCi %0,o 0 0 4i i 0 0 i 100n j

0%~~~ ~~~~ -%','.-..-0 --.,~r -f.in% % -n1ii -0 -Cn 0 - - - - - - - - - -

Page 37: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

-------- l ~- 4-?-------.. ---------- 0

:c~H ~ ------------00 -------- - - - - -

-cc- OC C O --

................ ...........

- - - - - - - - - - - - - - -O- - - - -S I

Il ,,

-' - - - - - - - - - - -C - -O C- -C C- -C --

- --- - - - - - - - - - - - - - - - -.. . . . . . - -

-~~~~~~~~~~~ -C -~-~ -C -C t- ~ c 0. i C a C ~ -o c cr, t - - c c - - - .--rc--

- - - - - -O - - - -C- - - - - - - --

-,Z C C 0 0 0 --

rz

o - - <-'C it c- - - - - - - -- - ----r

0C 00 C

i ' t 000 00000000

- - --- C- -: -~ .- 2 C O- .<! ,C". CfZ J'- C ~ -. i

4 .- .1

Page 38: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

m 4C . 0 I -0CC -C0 C D CD go 0 40 N -04 C 0C O 0 aN C0441N Co

---044400 0000000000000000 -- -- I-,-- - - -I I I I I I I

00 .0 C C 4 0-0 -C0 440 1 e 0. ' en OD 0-c - - 004.1-en413. 0.1 C040 -1,- CC' 111 Oen4-7-7aC:NN0-CCCCCCC 09

I I I t

4 Clennenen - - - -00 00000 0eeeee eeeee

a- -C' - 044 N C en C' en C' en C 'e Ne 0 OD4 011 a, 0 C en0 n 0 C

en CN -CC- - -0000-------C' -1 4 en --- a~~a

4) mnenen0 en 000000ON 00o 000 00- - - - - - --- - - -veI

C 4C'T 4 0 C: C 04 C C 44 C C 1 n4e 'CC-e 0 1C nCC 4e 09 C' C

.fl1 47-04404400000000000-l -- ------ -

0-I

a > ~ ~ ~ ' C . ms wfl 0 n c ~ ' . a , . n

C

P. m o -I N aC~-70C, .0 'DNN-o71 00m DeNa,- OO -000

-7 neenneenOOOOOOOOOOO-r-------- - - -

000 00000 'T00 z00~ 1---

Cen0 .- r~04o~-.-C -.-en-1 - -c.,0 n- .C r~-r.r.r. - 7

-4 0010004OnmaaC C CC '1.-0e- r1000 00000000

-7D -4-- 0000000 0 -- - -1,-I-n.-m co

00

0

0 8 as a% aC C -N C C C oo Do ?oo co iw N c.NP

4I 0 000000000000 ---- ....... a

0 a,0 m 10 . O

Page 39: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

I -t.0 'T 0.( e 0 a% 0 00 I - - - - - -000

0 0 co- --- -0m 0 0

'O 'D D - 0 1 1 1 I

2 7 . . 0c 0 10 z ?I . -9 111 I m w .4 -- (e-

- -- - t -----4..4 -4-- -- - --- ------ ICN(

'D zrn 0a..0 .r-rr-r. r-r-r-.r-00.0 o z Nnneee

o -- -- - -- - I -- - - -- -

a, a co m0. e.0--.0.0.0.D I .0 C, 0 0, .- 4d-0O O mr

0 0 0 0 0 0 0 ----- ~~-4- ----4 --

II II

00I0 4 4 -4 - - CI- - -

m-t D CJN J N J-0000-.I-..e.-.10 00 C) 0 10 1 O

I I I

m.0 0-c -c 0 C, " 'D0. 0T0a, m m m - -( 0- 00.0-ll0 7en(N7.0 : -Ienenenen.0.0.0.0..0.0 o.0.0I I (I Ic-4(Nen e

0 a 0 0CD 00 0 a .tennC-a 0(- -O-- -

'D a'.0' 0a 'D' m (N 0'0-D o co -T 00 00 ID C4 a, -T I I I I I

.0 0 .1 1 .i

0

.0

en, m %w 0 wN1 y

-7 000 000 0 9 14HI4...44.....4.4(N 1N(N90 ODCT" O COO O -- Wa

10 w a 10 .000 0wa0 e-. -- MI en 100-(N - -'.0.I-.4 - I-------

Page 40: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

+ + -+ d o o o c o o ~ o '5 o + -J :- - --- - - - - - - - ---- -- -" - " - - - - "

[:'+' ~ C ., 0,- + - o 0 o o o - -2gd g - - - - - -: -: -:+ ;. :22. :_

. .- ... oooooooo OOCooo . . . . . .. . . ..01~~ ~ .40 ,n ~ . . . .S. . . . . C..

" r+' I II.II IrI,.rI

-. .. .. .. . . .. . . . . . . . .. . .

1 , il i i 1 i i1 ii

S .....4 . o, o, 0,. ... ..............

-.; 1,. C; 0 C; C; ; o 0 c o - - - - - -

I .4 . . . . . . . . . .O . . . . . . . .

-t~~ -+ -t -- - -1 - - -

. ., .. ... . . . .,.,.

O1:~ 0 1i0J.00C0 0 o0i 0 Q 0 0 000

---- ----

C; ~~ o 0 o C; C; o ;o C

i n . . . . . . . ..40 C~f . . . . . . . . . . . ....I- C C N fl0 . r n C l i 11 7 .0'l . . . . . . ..cc ccc01. .4tt.. C O OC C C O C2~

Page 41: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

44-,..-. . . 4 .. . . . l .. t t~ .. 0.0 .0 .. C~ - ,~ r 2

*~~~~~~~~~~~~ .~ .'~ ~ ..13 0. ,- . . . . j,. 4C. 4 C.,.. ',,

.. .. .1- - 0 0 . . . . . . ...... ... .

.r4>1.04O40.40.44&l14-4- - - - -,- - - -40...- 4 -'... -. S, -4

>1444 ~ ~ ~ ~ -- - - -44 -.. 04 0 4 1 4 4 . . l 4 - ,- .4- 44- 44-

-414 > - - - - - -- - - - -

...... 44 . 0 -.- .. i 1 1. 7 1 , . ......

>7 - 0 0 0 0 0 0 0 0 0 0 0 .. .0. . 0. 0. . 0.0. . 0.

10 -W o C; 141> 0 o0.. Th 1 40 4 4 1- . o .' . . . m - c o 4 ..

414>1>114.4444.4.71>000-4- -0 -1'' .C 1 t- 44 $4-04-.r-4 -

Page 42: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

0D Z

LD 0

0 ~

L) 0->

LL <-U O f

0 w y

<Z 4

z A l z a 1. Cc.J - c~

0 c

r~ 3 tL < z

CLL IL <i 0 wu

(z

0 0 >~-

L-J

a: LLI L

00 LL

(I CL a If 7

I

EG'G+6L is0 U->

0

0 -

zK 01K z4

p

o

v0

Page 43: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

43V Cl V arSE

-4I I

LUa

0-

0;

z LU

j4 0aC.

a.

io[~ u ,u

0 noo~ 2Vis In

3NIfl H-4.LVr4 x 3N11I HDIVV

00

a

neL 0.

AVUOV3H <1 0

00

~0N ~ Pofl/xfr' '009 flSL 9tp

4 ~ viSui 4 -

Ad 3rJ<

PLATE 2

Page 44: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

a-

9V w

co U

_n NNC

_ _ _ 0-u

IX

<N- L

CC

"N

q N - 0

U3±VM JO .L3i3&iflSS3Wid

PLATE 3

Page 45: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

o s~' 10 W6

-~1'TYPE I

TYPE 2

-', 056' 088,

TYPE 3

0O,56'/007

TYPE 4

0.5to/ 0 88'

TYPE 5

68, to088

0o56' <1 68 --- /08'

TYPE 6

__T)_ zz-

1

058' J 64' -08

TYPE 7

TYPE 8

CULVERT EXPANSIONS

PLATE 4

Page 46: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

1000

ow

20 -- A-

g o 0

o 10 - T

40

06

03 a ;T ANTHONY i ALLS LoWt H LOCK -

02 9 SI ANTHONY t AL LS LOWER LOCK

V ST1 ANTHONY f AL LS LOW[F R10CK

01 0 OALLFS LOCK MODEL

006 * MNAHY LOCK PRIOTOTYPEF RUN '

004 X VALVE LOSS COEFFICIENT :-

002 003 004 006 000 01 0 30 6 0 02

AREA Or VALVE OPENING 1A.1AREA OF CULVERT %AC/

FROM HYDRAULIC DESIGN CHART 531 VALVE LOSS COEFFICIENTSUNEXPANDED CULVERTS

PLATE 5

Page 47: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

w Z

LLar-w

N~ 0a

0 z

W-

0n

6~ Wz0 0r

00

cn- w0

w 0

0

0 0

0.L 0 -

zu

-w w

W

< >-

0~ 'U

0~)-

0

2 0

PLT 6

Page 48: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

LEGEND

80TYPE I8 0> TYPE 2

flTYPE 4

, >7

36

0

4

3

030 40 so 60 70 80 90 100

PERCENT VALVE OPENING

EFFECT OF CULVERT EXPANSIONS ONVALVE LOSS COEFFICIENTS

PLATE 7

Page 49: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

0

4

0

TYWE 6

0

o TYPEES

TYE2

x TYPE s4, TYPE 3

TYPE 70o TYPES 8

04L PERCENT VALVE OPENING 708

EFFECT OF CULVERTEXPANSION LOCATION ON

VALVE LOSS COEFFICIENTS

PLATE 8

Page 50: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

23 -T I -

1i? 000 0

20 JO 0,V V P N

19 41l.

10-

ID

w 40%

o 9E-

35

60%

BEGINING OF ROOF EXPANSION 0VALVE HEIGHTS DOWNSTREAM FROM VALVE

EFFECT OF ROOF EXPANSION BEGINNINGON VALVE LOSS COEFFICIENTS

PLATE 9

Page 51: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

z-J

U

C,,

- 0

oo It~

z z

2 2 5

N 0 4 c <I

m .I a >x (L z

0 w .D (L U

I I

0 0

M - I a.IU

PLT 10

Page 52: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …

In accordance with letter from l';,d.-RDC, AEN-ASI dated22 July 1977, Subject: Facsimile Catalog Cards forLaboratory Technical Publications, a facsimile catalogcard in Library of Congress MARC format is reproducedbelow.

Pickering, Glenn A.Lock culvert valve, locs so int hydraulic

laboratory investirati-,n ' by A. Pickering(Hydrauli*cs Laboratcrv, Army .Enineer WaterwaysExperiment Station). - Vicksburr, 'i ss : The StationSpringfield, V'. labe :'ror NTIs, 199i.

15, [2!] p., 10 . , 1te : 1. ; 27 cm. --(TecIhnical report / :'. ,rmy !nvuer WatervaysExperiment Statin * HE--ICover title."September 1981Final report."Prepared for S)ffic, Chie" of Engineers, U.S. Army."1. Culverts. '. Locks (Hydraulic engineering).

3. Pressure--Measurement. 4. Valves. I. United States.

Army. Corps of Engineers. ffice of the Chief of Engineers.

II. U.S. Army Engineer Waterways Experiment Station.Hydraulics Laboratory. III. Title V. Series: Technicalreport (U.S. Army Engineer Waterways Experiment Station)HL-81-10.

TA7.W3 no.HL-,ql-1

i I

Page 53: ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG …