DISCHARGE RATINGS FOR TAINTER 

GATES AND ROLLER GATES AT LOCK 

AND DAM NO. 7 ON THE MISSISSIPPI 

RIVER, LA CRESCENT, MINNESOTA

By S.R. Corsi and J.G. Schuler

U.S. GEOLOGICAL SURVEY 

Water-Resources Investigations Report 95-4089

Prepared in cooperation with the

U.S. ARMY CORPS OF ENGINEERS, ST. PAUL DISTRICT

Madison, Wisconsin 

1995
U.S. DEPARTMENT OF THE INTERIOR 

BRUCE BABBITT, Secretary

U.S. GEOLOGICAL SURVEY 

Gordon P. Eaton, Director

For additional information write to:

District Chief 

U.S. Geological Survey 

6417 Normandy Lane 

Madison, Wl 53719

Copies of this report can be purchased from:

U.S. Geological Survey 

Earth Science Information Center 

Open-File Reports Section 

Box25286, MS 517 

Denver Federal Center 

Denver, CO 80225
CONTENTS

Abstract...................................................................................... 1

Introduction................................................................................... 1

Purpose and scope. ..................................................................... .2

Acknowledgments ..................................................................... .2

Theoretical equations for discharge ................................................................2

Tainter and roller gates .................................................................. .5

Measurements of hydraulic-control variables and discharges ............................................5

Equations of discharge ......................................................................... .9

Tainter gates .......................................................................... .9

Roller gates...........................................................................11

Discharge ratings for tainter and roller gates ........................................................ 13

Summary....................................................................................13

References cited ..............................................................................15

ILLUSTRATIONS

Figure 1. Map showing location of Lock and Dam No. 7 on the Mississippi River,

La Crescent, Minnesota. ......................................................... 3

2.-4. Diagrams showing:

2. Location of tainter and roller gates at Lock and Dam No. 7................................ 4

3. Sectional view of tainter gate ....................................................... 7

4. Sectional view of roller gate ........................................................ 8

5.-6. Graphs showing:

5. Relation between submerged-orifice discharge coefficients and orifice-submergence ratios for

tainter gates, Lock and Dam No. 7 on the Mississippi River, La Crescent, Minnesota ........ 12

6. Relation between submerged-orifice discharge coefficients and orifice-submergence ratios for

roller gates, Lock and Dam No. 7 on the Mississippi River, La Crescent, Minnesota ......... 14

TABLES

Table 1. Theoretical equations of discharge for flow controlled by a tainter or roller gate................... 6

2. Summary of hydraulic control variables and current-meter discharge measurements at Lock and

Dam No. 7 on the Mississippi River, La Crescent, Minnesota. ............................. 10

3. Summary of theoretical discharge equations for submerged-orifice flow under a single tainter or

roller gate at Lock and Dam No. 7 on the Mississippi River, La Crescent, Minnesota ........... 15

4. Discharge rating table for a tainter gate with submerged-orifice flow for normal headwater and 

tailwater elevations at Lock and Dam No. 7 on the Mississippi River, 

La Crescent, Minnesota ........................................................... 16

5. Discharge rating table for a roller gate with submerged-orifice flow for normal headwater and 

tailwater elevations at Lock and Dam No. 7 on the Mississippi River, 

La Crescent, Minnesota ........................................................... 17

Mi
CONVERSION FACTORS AND VERTICAL DATUM

Multiply

mile (mi)

pound (Ib)

foot (ft)

square mile (mi2)

cubic foot per second (ft3/s)

By

1.609

453.6

0.3048

2.590

0.02832

To Obtain

kilometer

gram .

meter

square kilometer

cubic meter per second

Sea level: In this report, "sea level" refers to the National Geodetic Vertical Datum of 1912 (NGVD of 1912)-a geodetic datum 

derived from a general adjustment of the first-order level nets of both the United States and Canada, formerly called Sea Level Datum 

of 1912. To obtain elevation in reference to the National Geodetic Vertical Datum of 1929 at Lock and Dam No. 7, subtract 0.49 feet 

from those elevations referenced to NGVD of 1912. NGVD of 1912 is still used throughout the Mississippi River navigation system.

iv
DISCHARGE RATINGS FOR TAINTER GATES

AND ROLLER GATES AT LOCK AND DAM NO. 7

ON THE MISSISSIPPI RIVER,

LA CRESENT, MINNESOTA

By S. R. Corsi and J. G. Schuler

ABSTRACT

The water-surface elevations on the Inland 

Waterway Navigation System of the upper 

Mississippi River are controlled during normal 

operating conditions by various flow controls 

at 29 locks and dams. The headwater (navigation pool) and tailwater elevations at Lock and 

Dam No. 7 are controlled by the regulation of 

11 tainter gates and 5 roller gates. Discharge 

ratings for these tainter and roller gates were 

developed for use in computing discharge 

through Dam No. 7 and to aid in regulating the 

navigation pool within its normal operating 

limits of 639.00 ± 0.20 feet (NGVD 1912). 

Hydraulic-control variables and discharges 

were measured at the tainter and roller gates 

and analyzed for this report.

Fifty-two current-meter measurements of 

discharges that ranged from discharges too low 

to measure to 12,600 cubic feet per second 

were made in the forebays of the tainter and 

roller gates. The measured discharges were 

used to define flow regimes as a function of 

static-headwater depth (hi), static-tailwater 

depth (03), and vertical height of tainter or 

roller gate opening (hg). Submerged-orifice 

flow is the predominant flow regime at Lock 

and Dam No. 7.

Twenty-four discharge measurements were 

used to develop submerged-orifice discharge 

coefficient relations for the 11 tainter gates. 

Twenty discharge measurements were used to 

develop a submerged-orifice discharge coefficient relation for the five roller gates.

Coefficients of discharge (Cgs) ranged fron 

0.126 (hg = 1 foot) to 1.089 (hg = 10 feet) for 

tainter gates and from 0.050 (hg = 1 foot) to 

0.302 (hg = 14 feet) for roller gates. Disch^ge 

was measured at three different tainter gates 

with the gates closed (hg = 0) to evaluate tH 

tainter-gate leakage-discharge relations. No 

measurable leakage was observed. The resulting equations can be used to compute discharge 

at Lock and Dam No. 7 for the tainter and re Her 

gates under normal flow conditions. Discharge 

rating tables for the tainter and roller gates are 

given with a headwater elevation of 639.00 feet 

normal pool elevation for selected tailwate" 

elevations and gate openings.

INTRODUCTION

The Inland Waterway Navigation System presently in use for the upper Mississippi River Ba^in 

was incorporated in 1930 when U.S. Congress 

passed the River and Harbor Act. The funding of 

the River and Harbor Act allowed for the construction of flow-regulating lock and dam structures and 

periodic channel dredging to maintain a 9-ft-deep 

by 400-ft-wide channel between Minneapolis, 

Minn., and St. Louis, Mo., for navigation. The 

St. Paul, Minn., office of the U.S. Army Corps of 

Engineers regulates the control structures on th°. 

Mississippi River from the St. Anthony Falls leeks 

and dam in Minneapolis to Lock and Dam No. 10. 

These lock and dam structures are used for navigation and do not have any flood-control benefits.

Lock and Dam No. 7, the subject of this report, 

is 702.5 river mi. upstream from the mouth of the 

Ohio River and 4.6 river mi. upstream from the city 

of La Crosse, Wis. With reference to other flov-
regulating structures, Lock and Dam No. 7 is 

23.3 river mi. upstream from Lock and Dam No. 8 

and 11.8 river mi. downstream from Lock and Dam 

No. 6 (fig. 1). The Mississippi River upstream from 

Lock and Dam No. 7 has a total drainage area of 

62,340 mi2 (U.S. Army Corps of Engineers, 1971, 

p. 1-3).

The flow control system at Lock and Dam 

No. 7 consists of 5 roller gates, 11 tainter gates, a 

navigation lock, an auxiliary lock, a storage area, 

an earth dike, and a submersible dam. The total 

structure is 10,766 ft long (fig. 2). The total bridge 

length (which includes the tainter and roller gates, 

the locks, and the storage yard) is 1,093 ft; the earth 

dike is 9,003 ft long and the submersible dam is 

670 ft. long. Various combinations of tainter- and 

roller-gate openings at Lock and Dam No. 7 are 

currently (1994) used to maintain the headwater 

(navigation pool) elevation within the normal operating limits of 639.0 ± 0.2 ft (U.S. Army Corps of 

Engineers, 1971, p. 6; all elevations in this report 

are referenced to the NGVD 1912).

Because the water-surface slope between flowregulating structures can approach zero during periods of low flow, the traditional methods that require 

slope to calculate discharge are not satisfactory at 

Lock and Dam No. 7. Previous to this study, discharges determined by using theoretical equations 

for discharge through the gates had not been verified by field measurements. Therefore, a cooperative effort between the U.S. Geological Survey 

(USGS) and the U.S. Army Corps of Engineers, 

St. Paul District, was initiated to develop fieldverified coefficients for the equations of discharge 

for the 11 tainter and 5 roller gates at Lock and Dam 

No. 7.

Purpose and Scope

The purpose of this report is to present discharge ratings for the tainter- and roller-gate flow 

controls under normal operating conditions at Lock 

and Dam No. 7. Coefficients for the theoretical 

equations of discharge were developed from discharge measurements made in the forebays of the 

tainter and roller gates. These discharge measurements were used to develop discharge-coefficient 

relations for hydraulic-control conditions that occur

during normal operating periods. The equations of 

discharge were used to compute discharge racing 

tables for most combinations of headwater ard tailwater elevations and vertical height of tainter- or 

roller-gate openings under normal operating conditions.

This study was limited to the analysis of submerged-orifice flow under the tainter and roller 

gates. No attempts were made to define or develop 

discharge ratings for flow through the navigation 

lock, possible flow over the earth dike, or openriver flow when all gates are out of the water.

Acknowledgments

A special thanks is extended to Lockmas*er 

Terry Jessessky and the crew at Lock and Dam 

No. 7, who were helpful in providing desired gate 

openings and gage-height information. A special 

thanks is also extended to Terry Alexander, whose 

information and report on Lock and Dam No. 25 

(Alexander, 1992) were instrumental in the design 

of this project and the format of this report.

THEORETICAL EQUATIONS FOR 

DISCHARGE

Under normal flow conditions, the tainter gates 

and the roller gates pass most of the flow through 

Lock and Dam No. 7, and the Lock passes a small 

but measurable amount of water; no flow passes 

over the earth dike or the submersible dam. For this 

reason, equations of discharge have been developed 

only for the tainter and roller gates in this study. The 

theory behind the equations was described by Alexander (1992, pp. 4-5) as follows:

Collins (1977, p. 2-3) and Stuthmanr 

and Sanders (1982, p. A-36 through A-40) 

summarize the hydraulic-control condition* 

that define flow regimes possible at some 

flow- regulating structures and present 

their corresponding theoretical equations 

of discharge. The hydraulic theory used to 

develop these equations assumes steady, 

uniform flow. This theory requires that 

energy and mass are conserved between 

an approach section and a section just 

downstream from the control structure. 

Possible flow regimes, necessary 

hydraulic-control conditions, and the
43

Base from U.S. Geological Survey digital data

25 MILES 

J

I 

25 KILOMETERS

Figure 1. Location of Lock and Dam No. 7 on the Mississippi River, La Crescent, Minnesota
CENTRAL CONTROL 

STATION

0 200 400 _ 600 FEET

50 100 METERS

Figure 2. Location of tainter and roller gates at Lock and Dam No. 7
theoretical equations of discharge for flow 

controlled by a tainter or roller gate are 

summarized in [table 1, in this report].

The bracketed parts of these four 

equations represent theoretical expressions of discharge for a tainter or roller 

gate B units in width. The independent 

hydraulic-control variables are static-headwater depth (h-|), static-tail water depth (h3), 

and vertical height of tainter or roller gate 

opening (hg). The static depths (h-, and h3) 

are the vertical distances between the 

headwater and tailwater elevations and the 

sill [fig. 3 and 4, in this report]. The coefficients of discharge (C, Cgs , Cw, and Cws) 

are unknown, but can be determined 

through a calibration process. These coefficients are defined by the ratio of measured discharge to theoretical discharge; 

therefore, a coefficient of discharge can be 

calculated from each current-meter 

measurement of discharge if all other 

hydraulic-control variables are known or 

fixed.

Tainter and Roller Gates

The independent hydraulic-control variables hg,

D

hj, and 113 are used to determine the tainter- and 

roller-gate flow regimes. The hydraulic-control 

conditions that separate orifice and weir flow 

regimes is based on a critical-depth analysis of flow 

in a rectangular section. In this analysis, one 

assumes that flow over the downstream edge of the 

sill is critical unless the gate or the tailwater prevent 

critical flow. If he is less than the critical depth

o

(0.67hj), then orifice flow occurs under the gate. If 

the gate opening equals or exceeds the critical depth 

and the tailwater depth is less than the gate opening, 

the gate opening has no effect on the discharge. In 

this case, weir flow results, and the concrete gate sill 

functions as a broad-crested weir (Collins, 1977, 

p. 4; Stuthmann and Sanders, 1982, p. A-37). The 

hydraulic-control conditions used to determine the 

pertinent equations of discharge for this study are 

listed in table 1.

Under normal flow conditions, the tainter and 

roller gates at Lock and Dam No. 7 operate within 

the submerged-orifice flow regime. During highflow, the gates are periodically raised completely

out of the water. In this case, free-weir or submerged-weir conditions would apply. Only oire 

discharge measurement at each type of gate was 

made while the gates were raised completely out of 

the water solely for informational purposes. The 

free-weir and submerged-weir flow regimes were 

not studied for this report. During winter and 

spring, the roller gates are submerged periodically 

so that ice or other debris can be flushed over the 

top of the gates (Terry Jessessky, U.S. Army Corps 

of Engineers, oral commun., 1993). Three measurements were made for reference purposes wher the 

gates were submerged; the measurements are not 

sufficient for complete analysis of this flow condition. The predominant tainter and roller gate f ow 

regime is submerged-orifice flow; therefore, it is 

the only type of flow described in this report.

MEASUREMENTS OF HYDRAULICCONTROL VARIABLES AND 

DISCHARGES

The five roller gates operate between pier vails 

with 80-ft openings and are 20 ft high. The 11 

tainter gates operate between pier walls with 35-ft 

openings and are 15 ft high. The roller and tainter 

gates are built under a service deck that allowsaccess to the individual forebays; thus, discharge 

could be measured using standard USGS currentmeter measuring equipment.

Stage-discharge relations for all flow regimes 

can be developed from measurements of hydraulic-control variables and discharges at a single roller 

or tainter gate if all gates are of the same design 

(Collins, 1977, p. 4); however, in an attempt to 

average variations in roller- and tainter-gate 

entrance and exit losses, 44 current-meter discharge 

measurements were made in the forebays of 5 roller 

gates and 11 tainter gates during submerged-orifice 

flow conditions. Also, three current-meter discharge measurements were made with the gates 

completely closed, two current-meter measurements were made with the gates completely out of 

the water, and three measurements were made at 

roller gates with the gate completely submerged. 

These measurements of hydraulic-control variables 

and discharges were used to develop stage-discharge relations for submerged-orifice flow 

(table 1).
Table 1 . Theoretical equations of discharge for flow controlled by a tainter or roller gate

Abbreviations:

hg, vertical height of tainter or roller gate opening

hj, static-headwater depth

h3, static-tailwater depth

Q, discharge

C, free-orifice flow coefficient of discharge

B, tainter or roller gate width

g, acceleration due to gravity

Cgs, submerged-orifice flow coefficient of discharge

Ah, static head differential (h1 -h3)

C^,, free weir flow coefficient of discharge

Cws, submerged-weir flow coefficient of discharge

<, less than; >, greater than; >, greater than or equal to 

Table modified from Collins (1977)

Flow regime Hydraulic-control conditions Equation of discharge Equation no.

Free-orifice

Submerged-orifice

Free- weir

Submerged-weir

hg<0.67h! and h3 < hg

hg < 0.67hj and h3 hg, 

or ahg > 0.67hj and h3 > hg

hg 0.67h! and hyhj < 0.6

hg 0.6711!, hyhj 0.6, 

and ah3<hg

Q = C[hgB(2gh1 )°-5]

Q = Cgs[h3B(2gAh)°-5]

Q = Cw [Bh1 15]

Q = CwCws[Bhi ]

1

2

3

4

 Stuthmann and Sanders (1982, p. A-37).

Discharge measurements for the roller- and 

tainter-gate openings were made between the pier 

walls along the upstream handrail of the service 

deck approximately 32 ft upstream from the roller 

gates and 12 ft upstream from the tainter gates. During these discharge measurements, velocity 

observations were made by use of a Price type AA 

current meter suspended with a Columbus sounding 

weight (100 or 150 Ib) from a collapsible bridge 

boom. The four-point method for discharge measurement was used instead of the traditional 

two-point method because of the influence of tainter 

and roller gates on the vertical velocity profile. In 

the traditional two-point method, 2 velocity observations are made at depths of 0.2 and 0.8 of the 

static-headwater depth at approximately 20 locations across the width of the section being measured 

(Rantz and others, 1982, p. 134). The four-point 

method used for this study consists of velocity 

observations at depths of 0.2,0.4,0.6, and 0.9 of the 

static-headwater depth at approximately 15 locations across the width of the section being

measured. The four-point method was used because 

comparison of the two-point method with the vertical-velocity curve method (0.1-depth increments 

between 0.1 and 0.9 of the static-headwater depth; 

Rantz and others, 1982, p. 132) showed differences 

of as much as 12 percent. Several three-point and 

four-point methods where the velocities were measured at different combinations of depths wer?. 

tested. The four-point method described above was 

the only method that resulted in differences from 

the vertical-velocity curve method of 5 percent or 

less over a selected range of gate settings.

To minimize the effects of differential ga*e 

openings on the flow field in the measurement sections (the effects of differential gate openings on the 

flow field were not analyzed in this study), field 

personnel ensured that the gates on both sides were 

set at the same opening. All gate openings we-e set 

by U.S. Army Corps of Engineers personnel. The 

roller gates were set by use of a position-indicator 

gage inside the roller-gate pier house, and the
Tainter gate in 

raised position

Tainter gate

Top of service 

bridge deck

Headwater 

elevation

Tail water 

elevation

4:0

Row

h,

Upstream sill 

, elevation 624 feet

10 20 30 FEET

1 0 METERS

Figure 3. Sectional view of tainter gate
Pier house

Roller gate in 

raised position

10 20 30 FEET

Top of service 

bridge deck

10 METERS

Upstream r«l 

elevation 

, r 619 feet

Figure 4. Sectional view of roller gate
tainter gate openings were set from the service deck 

by referencing the gate-indicator gages on the 

downstream pier walls. The 16 gates at Lock and 

Dam No.7 are of the submersible type, and accurate 

calculation of a true roller- or tainter-gate opening is 

impossible. Therefore, the gate and position-indicator gages were assumed to be correct within ± 0.1 ft. 

Gate leakage is common to submersible roller or 

tainter gates because of clearance between the gate 

and the sill or piers and from normal wear and tear 

on the gates. In this study, the magnitude of the 

leakage discharge per gate was not measurable; 

therefore, leakage was not separated from the current-meter discharge measurements. The headwater 

and tailwater elevations were monitored from U.S. 

Army Corps of Engineers continuous-recording 

gages in the control house. The static headwater and 

static tailwater depths, hj and 113, are referenced to 

the tainter-gate sill elevation of 624.00 ft and the 

roller-gate sill elevation of 619.00 ft.

EQUATIONS OF DISCHARGE

The gates at Lock and Dam No. 7 operate 

within the submerged-orifice flow regime during 

normal flow conditions. Submerged-orifice flow 

equations of discharge (eq. 2, table 1) were developed for the tainter and roller gates at Lock and 

Dam No. 7. Field measurements were used as input 

to equation 2 to develop the coefficients of discharge, Cgs. Relations between Cgs and the 

orifice-submergence ratio (h3/hg) were developed 

by use of ordinary-least-squares regression.

Tainter Gates

Twenty-four coefficients of discharge, Cgs, 

were computed (eq. 2, table 1) by use of the results 

of the current-meter discharge measurements made 

at hydraulic-control conditions that satisfy 

submerged-orifice flow criteria. The computed 

coefficients ranged from 0.126 (hg = 1 ft) to 1.089 

(hg = 10 ft) and are listed in table 2. The relation 

between the coefficient of discharge (Cgs) and orifice-submergence ratio (h3/hg) was determined by 

ordinary-least-squares regression of the natural logarithms of each variable. As can be seen in figure 5, 

the relation can be represented by two straight lines 

in log-log space. The breakpoint between the two 

lines is at an orifice-submergence ratio of about 1.5.

The discharge-coefficient equation for orifice-submergence ratios from 1.5 to 8.5 is

(5)

For orifice-submergence ratios of 1.4 to 1.5 the 

equation is

-5.03

(6)

Three current-meter discharge measurements 

made at hg = 0 (gates 9-11) indicate that leakage 

through the tainter gates is negligible. Very low 

magnitude, multidirectional water velocities made 

it impossible to determine the amount of leakage. 

For this reason, the measurements made at hg = 0 

are not included in the data tables in this repeat.

The relations for Cgs in equations 5 and 6 can be 

substituted into the theoretical submerged-orifice 

equation of discharge (eq. 2, table 1) to determine 

the final equations of discharge for the tainter gates 

on Lock and Dam No. 7. For orifice-submergence 

ratios of 1.5 to 8.5, the equation of discharge is

-0.975

(2g(h-h)) 0.5

(7)

For orifice-submergence ratios of 1 .4 to 1 .5, the 

equation of discharge is

h -5.03 

Q = 5.05h3BM (2g(h 1 -h3 )) C5 (§)

where Q is the discharge,

113 is the static-tailwater depth, 

h3/hg is the orifice-submergence ratio, 

B is the width of the gate, 

g is acceleration due to gravity, and 

(hi-h3) is the static-head differential.
Table 2. Summary of hydraulic-control variables and current-meter discharge measurements at

Lock and Dam No. 7 on the Mississippi River, La Crescent, Minnesota

[Measurements are listed in order of increasing vertical height of gate opening; static depth, headwater and tailwate 

elevations minus sill elevation; hj, static-headwater depth; h3 , static-tailwater depth; hg, vertical height of tairter o 

roller gate opening; h3/hg, orifice-submergence ratio; Q, discharge; Cgs, submerged-orifice flow coefficient of 

discharge; ft, feet; ft3/s, cubic feet per second;--, not definable]

Tainter or roller Date of 

gate number measurement

1 10/5/92

9/16/93

4/2/93

2 10/6/92

8/18/92

9/16/92

9/16/93

3/30/93

3/31/93

4/1/93

4/2/93

4/8/93

4/8/93

3 9/15/92

4/14/93

4 10/6/92

10/6/92

10/6/92

10/6/92

8/18/92

9/16/92

3/31/93

4/1/93

Static depth

"1 

(ft)

19.99

20.16

20.40

19.97

19.87

20.36

20.16

20.10

20.27

20.34

20.40

20.16

20.15

20.10

21.21

19.95

19.96

19.88

19.94

19.83

20.26

20.29

20.35

"3 

(ft)

Roller gates

12.40

15.05

18.01

12.38

12.32

13.56

15.09

15.86

16.87

17.70

18.25

18.69

18.69

13.00

20.64

12.33

12.47

12.52

12.33

12.28

13.32

16.79

17.62

(ft)

2

5

12

1

2

3

5

7

9

10

12

14

14

2

OPEN

-1

-2

-3

1

2

3

9

10

MS

6.2

3

1.5

12.4

6.2

4.5

3

2.3

1.9

1.8

1.5

1.3

1.3

6.5

--

--

--

12.3

6.1

4.4

1.9

1.8

Q

(tf/s)

2,890

5,790

8,670

1,250

2,580

3,820

5,500

6,730

8,180

7,730

8,380

9,980

9,460

2,630

12,600

650

1,260

1,770

1,080

2,740

3,910

8,590

8,010

cw

0.132

.265

.48*

.057

.119

.168

.252

.321

.410

.419

.488

.686

.652

.118

--

--

~

-

.049

.126

.173

.426

.429

8/18/92 19.85 12.28 6.1 2,960 0.136

10
Table 2. Summary of hydraulic-control variables and current-meter discharge measurements at

Lock and Dam No. 7 on the Mississippi River,

Tainter or roller Date of 

gate number measurement

La Crescent, Minnesota-Continued

Static depth

hi 

(ft) (ft) (ft) M, Q

(tf/s) c*

Tainter gates

6 10/19/93

4/8/93

7 4/1/93

4/8/93

8 10/19/93

9 10/9/92

4/2/93

10 10/8/92

9/17/93

5/27/93

5/26/93

4/2/93

11 10/8/92

3/31/93

4/1/93

4/14/93

12 10/7/92

13 10/7/92

14 10/7/92

3/31/93

15 10/8/92

4/7/93

16 10/8/92

5/27/93

4/7/93

15.12

15.13

15.39

15.13

15.12

15.18

15.42

15.01

15.22

14.9

14.98

15.42

15.03

15.24

15.38

16.21

14.87

14.91

14.91

15.28

15.04

15.03

15.04

14.88

15.03

8.50

13.68

12.39

13.67

8.52

7.86

13.36

7.55

10.18

12.09

12.34

13.34

7.40

11.48

12.50

15.64

7.39

7.37

7.34

11.64

7.41

13.62

7.41

12.13

13.60

1

10

5

10

1

1

9

1

4.5

5

7

9

1

4

7

OPEN

1

1

1

4

1

9

1

7

9

8.5

1.4

2.5

1.4

8.5

7.9

1.5

7.5

2.3

2.4

1.8

1.5

7.4

2.9

1.8

--

7.4

7.4

7.3

2.9

7.4

1.5

7.4

1.7

1.5

889

5,040

2,300

4,680

825

784

3,660

729

2,920

2,150

3,390

3,690

771

2,000

3,650

4,510

752

751

778

1,970

783

2,900

817

3,330

2,930

.145

1.089

.382

1.009

.134

.131

.68C

.126

.455

.378

.602

.683

.134

.320

.613

--

.132

.132

.137

.316

.136

.638

.142

.589

.641

11
1.5

O

LLJ 

O 

DC 

<

O 

CO

Q

UJ 

O

UJ 

O 

O 

UJ 

O 

y_ 

DC 

O

Q 

UJ

O 

CC 

LU

2 

CD

ID 

CO

0.1

-5.03

-0-975

C = 0.975 ( gs a v iihg

2 . Data point-Number indicates number in cluster

ha Static-tailwater depth

hg Vertical height of tainter gate opening

10

ORIFICE-SUBMERGENCE RATIO (h3/hg)

Figure 5. Relation between submerged-orifice discharge coefficients and orifice-submerged ratios for tainter gates, 

Lock and Dam No. 7 on the Mississippi River, La Crescent, Minnesota

12
Roller Gates

Twenty coefficients of discharge, Cgs, were 

computed (eq. 2, table 1) by use of the results of 

the current-meter discharge measurements made 

at hydraulic-control conditions that satisfy submerged-orifice flow criteria. The computed 

coefficients ranged from 0.050 (hg = 1 ft) to 0.302 

(hg = 14 ft) and are listed in table 2. The coefficient 

of discharge (Cgs) and orifice-submergence ratio 

(h3/hg) relation was determined by ordinary-leastsquares regression of the natural logarithms of each 

variable. As can be seen in figure 6, the relation can 

be represented by two straight lines in log-log 

space. The breakpoint between the two lines is at 

an orifice-submergence ratio of about 1.5. The discharge coefficient equation for orifice-submergence 

ratios from 1.5 to 12.4 is

(9)

For orifice-submergence ratios of 1.3 to 1.5, the 

equation is

(10)

The relations for Cgs in equations 9 and 10 can 

be substituted into the theoretical submerged-orifice 

equation of discharge (eq. 2, table 1) to determine 

the final equations of discharge for the roller gates 

on Lock and Dam No. 7. For orifice-submergence 

ratios of 1.5 to 12.4, the equation of discharge is

3 0*5 Q = 0.78h 3 B Up (2g(h 1 -h3 )) U- 5 (ll)

For orifice-submergence ratios of 1 .3 to 1 .5, the 

equation of discharge is

where Q is the discharge,

h3 is the static-tailwater depth, 

h3/hg is the orifice-submergence ratio, 

B is the width of the gate, 

g is acceleration due to gravity, and 

(hph3 ) is the static-head differential.

DISCHARGE RATINGS FOR TAINT1R 

AND ROLLER GATES

The discharge equations applicable to 

submerged-orifice flow at each tainter and roller 

gate at Lock and Dam No. 7 are summarized1 in 

table 3. The constant terms (gate width, gravitational constant, and regression constant) are 

combined into a single term in each equation in 

the table.

Discharge rating tables for a headwater elevation of 639.00 ft and normal tailwater elevations 

and gate openings were developed from the equations for submerged-orifice flow under a single 

tainter gate (table 4) and a single roller gate 

(table 5). The discharge through Dam No. 7 for any 

combination of headwater-tailwater elevations and 

gate openings, during normal submerged-orifice 

operating conditions, can be computed by use of the 

equations of discharge given in table 3.

SUMMARY

Lock and Dam No. 7 includes 11 tainter gates 

and 5 roller gates that are regulated to control the 

water-surface elevation of the navigation pool and 

discharge of the Mississippi River, La Crescent, 

Minn. Discharge relations for these tainter and 

roller gates during normal operating conditic ns 

have been developed and are presented in this 

report. These relations can be used by the U.S. 

Army Corps of Engineers (St. Paul District) in their 

water-control management of the upper Mississippi 

River Basin. During high flow, all gates are raised 

out of the water to allow open-river flow. This 

unregulated condition was not evaluated in this 

study.

-2.55

(2g(h,-h3 )) 0.5

Fifty-two current-meter measurements of 

discharges that ranged from discharge too low to 

(12) measure to 12,600 ft3/s were made in the for?.bays

13
0.8

O,

HI 

O

cc 

<

o

CO 

Q

UJ 

O

UJ

O 

O

UJ

o

LL 

QC

O

Q 

UJ 

O 

CC 

UJ

CO

ID 

CO

0.1

0.04

-i r

-2-55

h -1.03

h3 Static-tailwater depth-Depth above gate sill 

hg Vertical height of roller gate opening

10 14

ORIFICE-SUBMERGENCE RATIO (h3/hg)

Figure 6. Relation between submerged-orifice discharge coefficients and orifice-submerged ratios for tainter gates, 

Lock and Dam No. 7 on the Mississippi River, La Crescent, Minnesota

14
Table 3. Summary of theoretical discharge equations for submerged-orifice flow under a single tainter or 

roller gate at Lock and Dam No. 7 on the Mississippi River, La Crescent, Minnesota

[<, less than or equal to; h3 , static-tailwater depth, in feet; hg , vertical height of tainter or roller gate opening, ir feet; 

Q, discharge, in cubic feet per second; h^ static-headwater depth, in feet; g, acceleration due to gravity, in fee* per 

second squared]

Flow control Hydraulic-control 

conditions Equation of discharge Equation 

numb r

Tainter 

gate

-0-975

1.5 < r^ < 8.5 Q = 274h3 (;-) 0.5

Tainter 

gate

*3

1.4 < -5-03

Q = 1420h3 (T-) 0.5

Roller 

gate 1.5 < r^ < 12.4 hg

Q = 500h3 (:-) 0.5

11

Roller 

gate 1.3 < < 1.5 h -2.55 120.5

of selected tainter and roller gates. A total of 24 

coefficients of discharge (Cgs) ranging from 0.126 

to 1.089 were used to define the submerged-orifice 

discharge-coefficient relation for the 11 tainter 

gates. Twenty coefficients of discharge (Cgs) ranging from 0.050 to 0.302 were used to define the 

submerged-orifice discharge-coefficient relation 

for the five roller gates. Submerged-orifice flow 

was the predominant flow regime at Lock and Dam 

No. 7. Discharge was measured at three different 

tainter gates with the gates closed (hg = 0) to evaluate the tainter-gate leakage-discharge relations. No 

measurable leakage was observed.

From these relations, the equations of discharge 

(two for tainter gates and two for roller gates) were 

developed that express discharge per gate (Q) as a 

function of the discrete hydraulic-control variables 

of static-headwater depth (hj), static-tailwater depth 

(h3), and vertical height of gate opening (hg). The 

four equations of discharge are presented so that a 

tainter or roller gate elevation-discharge rating can

be computed for any discrete combination of 1~adwater-tail water elevations and gate opening. 

Discharge rating tables for submerged-orifice flow 

under a single tainter gate and a single roller gate 

are given for normal navigation pool (headwater) 

elevations of 639.00 ft and selected tailwater elevations.

REFERENCES CITED

Alexander, T.W., 1992, Discharge ratings for tainter 

and roller gates at Lock and Dam No. 25 on the 

Mississippi River near Winfield, Missouri: U.S. 

Geological Survey Water-Resources Investig"- 

tions Report 92-4118, 20 p.

Collins, D.L., 1977, Computation of records of streamflow at control structures: U.S. Geological Survey 

Water-Resources Investigations 77-8, p. 2-3.

Rantz, S.E., and others, 1982, Measurement and computation of streamflow-vol. 1. Measurement of 

stage and discharge: U.S. Geological Survey 

Water-Supply Paper 2175, 284 p.

15
Table 4. Discharge rating table for a tainter gate with submerged-orifice flow for normal headwater and tailwa^r 

elevations at Lock and Dam No. 7 on the Mississippi River, La Crescent, Minnesota

o

[ft, feet; ft /s, cubic feet per second; , outside normal control conditions for Lock and Dam No. 7]

Gate opening 

(ft)

0.5 

1.0 

2.0

Discharge, in ftVs, for a headwater elevation of 639.00 ft and indicated tailwater elevations, in f*

630.50 631.00

426 414 

837 813 

1,640 1,600

631.50

401 

789 

1,550

632.00

388 

763 

1,500

632.50

737 

1,450

63" 00

709 

1,390

Discharge, in ftVs, for a headwater elevation of 639.00 ft and indicated tailwater elevations, in r

3.0 

4.0

632.50 633.00

2,150 2,070 

2,850 2,740

633.50

1,980 

2,630

634.00

1,890 

2,510

634.50

1,800 

2,380

63£ 00

1,700 

2,250

Discharge, in ftVs, for a headwater elevation of 639.00 ft and indicated tailwater elevations, in f

5.0 

6.0 

7.0

634.50 635.00

2,960 2,790 

3,530 3,340 

4,110 3,880

635.50

2,620 

3,120 

3,630

636.00

2,420 

2,900 

3,370

636.50

2,220 

2,650 

3,080

637.00

1,980 

2,370 

2,750

Discharge, in ftVs, for a headwater elevation of 639.00 ft and indicated tailwater elevations, in fi

8.0 

9.0 

10

635.5 636.00

4,920 3,840 

6,940

636.50

3,500 

5,370

637.00

3,140 

4,100 

6,970

637.50

2,720 

3,050 

5,180

63800

2,220 

2,490 

3,660

Stuthmann, N.G., and Sanders, C.L., Jr., 1982, Instructions for processing digital streamflow data collected at dams (program E466), in WATSTORE 

user's guide: U.S. Geological Survey Open-File 

Report 77-729, v. 5, chap. 2, 45 p.

U.S. Army Corps of Engineers, 1971, Mississippi River 

nine foot channel navigation project: La Crescent, 

Minn., Reservoir regulations manual, Lock and 

Dam No. 7, appendix 7.

16
Table 5. Discharge rating table for a roller gate with submerged-orifice flow for normal headwater and tailwater 

elevations at Lock and Dam No. 7 on the Mississippi River, La Crescent, Minnesota

[fr/s, cubic feet per second; ft, feet; --, outside normal control conditions for Lock and Dam No. 7]

Gate opening 

(ft)

1.0 

2.0

Discharge, in ft3/*, for a headwater elevation of 639.00 ft and indicated tailwater elevations, In ft

630.50 631.00

1,360 1,310 

2,770 2,680

631.50

1,270 

2,600

632.00

1,230 

2,510

632.50

1,180 

2,410

633.C*)

1,131 

2,310

Discharge, in ft3/*, for a headwater elevation of 639.00 ft and indicated tailwater elevations, in ft

3.0 

4.0

631.50 632.00

3,940 3,800 

5,300 5,120

632.50

3,660 

4,920

633.00

3,510 

4,730

633.50

3,360 

4,520

634.D

3,20^ 

4,301

Discharge, in ftVs, for a headwater elevation of 639.00 ft and indicated tailwater elevations, in ft

5.0 

6.0 

7.0

633.00 633.50

5,950 5,690 

7,170 6,860 

8,410 8,040

634.00

5,420 

6,540 

7,660

634.50

5,130 

6,190 

7,260

635.00

4,840 

5,830 

6,840

635.fn

4,520 

5,450 

6,390

Discharge, in ftVs, for a headwater elevation of 639.00 ft and indicated tailwater elevations, in ft

8.0 

9.0 

10

634.50 635.00

8,330 7,850 

9,410 8,860 

10,500 9,870

635.50

7,330 

8,280 

9,230

636.00

6,780 

7,660 

8,540

636.50

6,190 

6,990 

7,790

637.0^

5,530 

6,240 

6,960

Discharge, in ft3/*, for a headwater elevation of 639.00 ft and indicated tailwater elevations, In ft

11 

12 

13 

14

635.50 636.00

10,200 9,420 

12,300 10,900 

15,100 13,400 

18,200 16,100

636.50

8,590 

9,500 

11,700 

14,100

637.00

7,680 

8,400 

9,980 

12,100

637.50

6,640 

7,260 

8,280 

10,000

638.C*

5,420 

5,930 

6,490 

7,840

17