DISCHARGE RATINGS FOR CONTROL STRUCTURES AT

McHENRY DAM ON THE POX RIVER, ILLINOIS

By Gregory G. Fisk

U.S. GEOLOGICAL SURVEY

Water-Resources Investigations Report 87-4226

Prepared in cooperation with

ILLINOIS DEPARTMENT OF TRANSPORTATION,

DIVISION OF WATER RESOURCES

Urbana, Illinois

1988

DEPARTMENT OF THE INTERIOR

DONALD PAUL HODEL, Secretary

U.S. GEOLOGICAL SURVEY

Dallas L. Peck, Director

For additional information write to:

District ChiefU.S. Geological Survey4th Floor102 E. Main StreetUrbana, IL 61801

Copies of this report can be purchased from:

U.S. Geological SurveyBooks and Open-file Reports SectionFederal center, Bldg. 810Box 25425Denver, CO 80225

CONTENTS

Page

Abstract................................................................ 1Introduction............................................................ 1

Background......................................................... 1Purpose and scope.................................................. 3Approach........................................................... 3Acknowledgments.................................................... 3

Description of McHenry Dam.............................................. 3Discharge ratings....................................................... 5

Spillway........................................................... 9Sluice gates....................................................... 12Evaluation of ratings.............................................. 19Computation of discharge........................................... 20

Summary and conclusions................................................. 23References cited........................................................ 24

ILLUSTRATIONS

Figure 1. Map showing location of McHenry Dam and gaging stationson the Fox River.......................................... 2

2. Diagram showing location of control structures atMcHenry Dam............................................... 4

3. Photograph showing downstream side of sluice gates.......... 6

4. Diagram showing cross section of sluice gate................ 7

5. Photographs showing downstream side of spillway andfish ladder............................................... 8

6-10. Graphs showing:

6. Relation between discharge coefficient for free weir flow and headwater depth for spillway (fish ladder included)............................... 9

7. Relation between discharge coefficient for freeweir flow and headwater depth for sluice gates....... 14

8. Relation between discharge coefficient for freeorifice flow and sluice-gate opening................. 16

9. Relation between discharge coefficient for submergedorifice flow and submergence ratio for sluice gates.. 17

10. Daily discharges for Fox River at McHenry Dam and Fox River at Algonquin for selected days during the data-collection period........................... 21

111

TABLES

Page

Table 1. Equations of flow............................................. 52. Characteristics of discharge at McHenry Dam................... 10

3. Discharge rating table for free weir flow over spillway(fish ladder included)...................................... 13

4. Discharge rating table for free weir flow under fivesluice gates................................................ 15

5. Discharge rating table for free orifice flow under fivesluice gates set to same gate opening....................... 18

6. Summary of hydraulic conditions and discharge equations for different flow regimes at McHenry Dam control structures.................................................. 19

CONVERSION FACTORS AND ABBREVIATIONS

For the convenience of readers who prefer to use metric (International System) units, rather than the inch-pound terms used in this report, the following conversion factors may be used:

Multiply By To obtain

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

square foot (ft2 ) 0.09294 square meter (m2 )9 9square mile (mi^) 2.590 square kilometer (km'2 )

O -3

cubic foot per second (ft°/s) 0.02832 cubic meter per second (irr/s)

Sea level: In this report "sea level" refers to the National Geodetic Vertical Datum of 1929 (NGVD of 1929) a geodetic datum derived from a general adjustment of the first-order level nets of both the United States and Canada, formerly called "Mean Sea Level of 1929."

iv

SYMBOLS AND UNITS

Symbol Definition Unit

B Sluice-gate width, or spillway and fish ladder length ft

C Coefficient of discharge for free orifice flow under sluice gates

Cs Coefficient of discharge for submerged orifice flow under sluice gates

Cw Coefficient of discharge for free weir flow

Cws Coefficient of discharge for submerged weir flow

g Acceleration due to gravity (32.2) ft/s

h-j Headwater depth referenced to sluice-gate sill or spillway ft crest

113 Tailwater depth referenced to sluice-gate sill or spillway ft crest

hq Sluice-gate opening ft

Q Discharge ft3/s

v

DISCHARGE RATINGS FOR CONTROL STRUCTURES AT McHENRY DAM

ON THE FOX RIVER, ILLINOIS

by Gregory G. Fisk

ABSTRACT

Twenty-three measurements of discharge were used to determine discharge ratings for the five adjustable sluice gates, spillway, and fish ladder at McHenry Dam on the Fox River in Illinois. Discharge ratings were determined for free weir, free orifice, and submerged orifice flow regimes.

Hydraulic conditions that identify flow regimes at McHenry Dam are defined by ratios between headwater depth (h 1 ), tailwater depth (h3 ), and gate opening (h_). Flow under the sluice gates is identified as weir flow when the ratio of gate opening to headwater depth is greater than 0.73, and as orifice flow when ha/h« is less than 0.73. Free orifice flow occurs when the ratio of tailwater depth to gate opening is less than 1.3, and submerged orifice flow occurs when h3/h is greater than 1.3. Flow under the sluice gates is identi­ fied as free weir flow when the ratio of tailwater depth to headwater depth is less than 0.75, and as submerged weir flow when h3/h-| is greater than 0.75. Flow over the spillway is identified as free weir flow when the ratio of tail- water depth to headwater depth is less than 0.60, and as submerged weir flow when h3/h 1 is greater than 0.60.

Discharge coefficients to be used in equations to compute discharge for various hydraulic conditions were determined. Four discharge measurements, ranging from 169 to 2,990 cubic feet per second, were used to define discharge coefficients that varied from 2.61 to 3.14 for free weir flow over the spillway,

Nineteen discharge measurements, ranging from 180 to 4,050 cubic feet per second, were used to define discharge coefficients for free weir, free orifice, and submerged orifice flow under the sluice gates. The average value of the discharge coefficient for free weir flow under the sluice gates is 3.17. Discharge coefficients for free orifice flow varied from 0.48 to 0.66 and the discharge coefficients for submerged orifice flow from the two measurements were 0.59 and 0.67.

INTRODUCTION

Background

McHenry Dam is located on the Fox River in northeastern Illinois, 42 miles northwest of Chicago and 2.5 miles south of McHenry (fig. 1). The Illinois Department of Transportation, Division of Water Resources (DWR) operates the

88°l 5' 88°l O 1

42°25' -

42°I5' -

CHAIN O'lLAKES STATE/PARK

234 KILOMETERS

U.S. Geological Surveystream-flow gaging station

U.S. Geological Survey lake station, stage only

Figure 1. Location of McHenry Dam and gaging stations on the Fox River.

dam for recreational and flood-control purposes. Reliable computation of discharge at McHenry Dam is needed in order to effectively operate the dam for those purposes. The U.S. Geological Survey (Survey), in cooperation with DWR, began a study in March 1985 to develop a method for computing discharge at McHenry Dam. The method was to include discharge ratings for the various flow regimes related to hydraulic conditions involving headwater depth, tailwater depth, and sluice-gate openings.

Purpose and Scope

The purpose of this report is to describe the results of a study to develop discharge ratings for the control structures at McHenry Dam. The methods are limited in scope to three types of flow free weir, free orifice, and submerged orifice that occurred during the study period.

Approach

Discharge ratings at McHenry Dam are affected by headwater and tailwater stages, and gate openings. Because it was not feasible to make measurements under all hydraulic conditions, measurements were made to determine discharge coefficients in equations that relate discharge to headwater depth, tailwater depth, and gate openings. Discharge coefficients were then related to depths and gate openings applicable to each measurement.

Standard Survey techniques (Buchanan and Somers, 1969) were used to make discharge measurements. Current-meter measurements of low flows were made by wading across the spillway crest and wading 50 feet (ft) downstream from the sluice gates. Medium and high flows were measured from a boat about 100 ft upstream from the gates and 150 ft upstream from the spillway (fig. 2).

Acknowledgments

The Illinois Department of Transportation and Bill Rice, in particular, provided historical data used in this report. McHenry Dam Lockmaster, Frank Novak, Jr., was very helpful in providing various gate openings to provide the desired flow regime. Their cooperation on this study is gratefully acknowledged.

DESCRIPTION OF McHENRY DAM

McHenry Dam is located at river mile 97.8 on the Fox River in northeastern Illinois (fig. 1). The drainage area at the dam is 1,250 square miles (mi^). The 8,900-acre reservoir created by the dam is part of the Fox Chain O 1 Lakes and is used primarily for recreation and flood control. The control struc­ tures at the dam consist of five sluice gates, a spillway, a fish ladder, and a navigation lock.

Wad

ing

mea

sure

men

t se

ctio

n

D.W

.R.

tail

wa

ter

ga

ge

Fo

x

SL

UIC

E

GA

TE

S

. lad

der

SP

ILL

WA

Y

north

U.S.

G.Sl

gag

e

Bo

at

mea

sure

men

t s

ec

tio

n

/?

iv

e r N

OT

T

O

SC

AL

E

Figu

re 2. Location of control

stru

ctur

es at

McHenry

Dam.

The sluice gates (figs. 2, 3) are operated to regulate discharge when the headwater-pool stage is below the crest of the spillway. Each sluice gate is 13.75 ft wide and can be raised to a maximum opening of 9.0 ft to regulate flow under the gate; flow over the top of the gates does not occur. The sill on which a closed gate rests (fig. 4) is at an elevation of 731.15 ft above sea level. All gates are set to similar openings, ranging from 0 to 9 ft, to maintain the headwater-pool stage at 4.00 ft during the recreational season, April through October. Headwater-pool stages are referenced to a datum of 733.00 ft above sea level. In November of each year, the sluice gates are gradually adjusted to lower the headwater pool to a stage between 1.5 and 2.0 ft to provide storage for flood control during spring runoff. The tailwater- pool stage, which is referenced to a datum of 730.15 ft above sea level, can be partially regulated during floods by adjustment of the sluice-gate openings.

The spillway is a broad-crested, concrete and stone-faced weir that is arced upstream and measures 282 ft along the arc. Water begins to flow over the spillway (figs. 2, 5) when the headwater pool rises above the weir-crest elevation of 736.68 ft. A 6-foot-long fish ladder, also having a crest eleva­ tion of 736.68 ft, is adjacent to and in the same approach section as the spillway (figs. 2, 5). The discharge rating for flow over the spillway includes flow over the 6-foot-long fish ladder.

DISCHARGE RATINGS

The four flow regimes that may occur at dams are discussed by Collins (1977). The flow regimes and hydraulic conditions defining each regime, along with equations for computing discharge, are listed in table 1. Collins states that the hydraulic conditions (table 1) are general criteria for defining the flow regimes.

Table 1. Equations of flow

[Equations from Collins, 1977. Q, Discharge, in cubic feet per second; C, Free orifice discharge coefficient; Cs , Submerged orifice discharge coefficient; C^, Free weir discharge coefficient; C^g, Submerged weir

discharge coefficient; hg , Gate opening; h 1 , Headwater depth; ho, Tailwater depth; B, Sluice gate width or spillway length;

g, Acceleration due to gravity; Ah equals h-j-h^]

Flow regime

Free orifice

Submerged orifice

Free weir

Submerged weir

Hydraulic condition

h <0.67h1 and h3 <h

hg<0.67h 1 and h3 >h

h^>0.67hi and h-s/h 1 <0.6 g_ i -j iha>0.67h<| and h3/h 12.0.6j

Equations

Q=C[hgB(2gh 1 )°- 5 ]

Q=Cs [h3B(2gAh)°' 5 ]

Q=Cw [Bh 1 1-5 ]

Q=CWCWS [fih^-5]

Equation number

(1)

(2)

(3)

(4)

~f

Figure 3. Downstream side of sluice gates

Concrete walkway Motor.for adjusting gates

Concrete pier

Datum 733.00 ft

h1 Headwater depth

hg Gate opening

h3 Tailwater depth

Sluice gateHeadwater pool stage

Tailwater pool stage

Concrete sill Elev. 731.15 ft

NOT TO SCALE

_ Datum 730. I 5 ft

Figure 4. Cross section of sluice gate.

Figure 5. Downstream side of spillway and fish ladder.

Spillway

Discharge measurements 5, 13, 15, and 20 (table 2) were made during free weir flow over the spillway. Free weir flow over a spillway, as defined by Collins (table 1), occurs when the ratio of tailwater depth (h3 ) to headwater depth (h-j) is less than 0.6. Both depths are referenced to the spillway crest, The greatest submergence ratio (h3/h 1 ) measured for the spillway was only 0.20, Submerged weir flow, which occurs when the submergence ratio (h3/h^) is equal to or greater than 0.6, did not occur during the study period; thus, the general submergence ratio suggested by Collins (0.6) is assumed to be appli­ cable for the spillway.

Upstream pool stage for the discharge measurements ranged from 4.05 to 5.90 ft, and discharge ranged from 169 to 2,990 cubic feet per second (ft3/s). The discharge coefficients for free weir flow defined by the measurements ranged from 2.61 to 3.14 (table 2). The relation between headwater depth (h-j) and free weir discharge coefficient for the spillway is shown in figure 6. The resulting equation relating the discharge coefficient for free weir flow to headwater depth is

Cw = 2.94 h-,0.087 . (5)

10.0 T I I I I I I T

15, Discharge measurement and number (table 2)

Cw=2.94h1 °-087

o

zUJo

UJo occUJ5 I

UJ UJ

J315

1.0 i i i i i I I iO.I i.o 10.0

HEADWATER DEPTH (h,), IN FEET

Figure 6. Relation between discharge coefficient for free weir flow and headwater depth for spillway (fish ladder included).

Table 2. Characteristics of discharge

at Mc

Henr

y Dam

Measure­

ment

Stru

ctur

e *

numb

er

Date

Sluice

1 03

-22-

85gates

Do.

2 03-22-85

Do.

3 03-26-85

Do.

4 03-26-85

Spillway

5 05

-16-

85

Sluice

gates

6 05

-16-

85

Do.

7 1 1-

04-8

5

Do.

8 1 1-

04-8

5

Do.

9 03

-17-

86

Do.

10

04-2

2-86

Do.

11

04-2

2-86

Do.

12

05-2

3-86

Spillway

13

08-2

8-86

Sluice

14

08-2

8-86

gates

Gate

opening

(hg

> (ft)

out of

water

73.

00

out

ofwater

73.30

7.60

83.15

82.50

out

ofwater

71.2

94@2

iei " 2 7.2

[ft,

feet;

ft3/

s,

Head

wate

r-

pool

Flow

stage3

regime2

(ft)

FW

3.51

FO

3.68

FW

2.64

FO

2.71

FW

4.05

FO

4.03

FO

3.98

FO

4.05

FW

4.31

FO

3.23

FO

3.13

FO

4.16

FW

4.23

FO

4.22

cubic feet per second]

Head

wate

r depth

(h,)

1*

(ft)

5.36

5.53

4.49

4.56 .37

5.88

5.83

5.90

6.16

5.08

4.98

6.01 .55

6.07

Tailwater-

pool

stage5

(ft)

3.90

3.70

3.45

3.42

1.35

1.35

2.82

2.75

5.03

1.71

1.85

2.25

1.05

1.05

Tailwater

dept

h (h

3)6

(ft)

2.90

2.70

2.45

2.42 ~ .35

1.82

1.75

4.03 .71

.85

1.25

.05

Measured

disc

harg

e (ft3/

s)

2,790

1,99

0

2,100

1,85

0

169

448

1,83

0

1,46

0

3,230

833

1,18

0

967

342

180

Computed

coef

fi­

cient

3.27 .51

3.21 .48

2.61 .56

.54

.54

3.07 .56

.53

.60

2.91 .66

Deviation

from

rati

ng

(per

cent

)

3.0

-1.5 1.4

-7.5

-2.9

-6.1 5.7

3.5

-3.0 -.3

-1.9

6.2

4.6

1.7

Tabl

e 2. Characteristics of discharge

at Mc

Henr

y Dam Continued

Structure

1

Spillway

Slui

cega

tes

Do*

Do.

Measure­

ment

number

15 16 17 18

Gate

open

ing

<vDa

te

(ft)

09-2

7-86

09-27-86

74.0

09-27-86

out of

water

09-27-86

74.9

Flow

regime ̂

FW FO FW FO

Head

wate

r-pool

stag

e3

(ft)

5.34

5.35

5.20

5.22

Headwater

depth

(h,)"

(ft)

1.66

7.20

7.05

7.07

Tailwater-

pool

stag

e5

(ft)

6.12

6.15

6.25

6.25

Tailwater

dept

h (h

3)6

(ft) « 5.15

5.25

5.25

Measured

discharge

(ft3/

s)

1,880

3,040

4,050

3,60

0

Computed

coeffi­

cient

3.05 .51

3.15 .50

Devi

atio

nfrom

rati

ng

(percent)

-1.1 1.3

-1.8 1.1

Do.

1909-27-86

74.5

FO5.26

7.11

6.30

5.30

3,320

.50

Spillway

20

09-30-86

FW

5.90

2.22

6.98

.45

2,990

3.14

-.7

Sluice

gates

Do.

21

09-30-86

74.0

SO

5.90

7.75

6.98

5.

98

2,600

22

09-30-86

74.5

SO

5.86

7.71

6.98

5.98

2,920

.59

.67

-.4 .3

Do.

23

10-15-86

out

of

FW

water

4.25

6.10

5.10

4.10

3,270

3.16

-.3

1Dat

um of spillway cr

est

and

sluice gates

are

736.68 an

d 731.15 ft

ab

ove

sea

leve

l, re

spectively.

2FW

designates fr

ee weir fl

ow,

FO designates free or

ific

e flow,

and

SO designates submerged

orif

ice

flow.

^Ref

eren

ced

to Su

rvey

ga

ge da

tum

of 733.00 ft above

sea

level.

**He

adwa

ter

dept

hs ar

e computed by applying an

adjustment factor (-

3.68

ft

for

spil

lway

; 1.

85 ft for

sluice ga

tes)

to the

headwater-pool st

ages

.

^Ref

erenced

to Survey ga

ge da

tum

of 730.15 ft

ab

ove

sea

level.

6Tailwater de

pths

are

computed by applying an

adjustment factor (-6.53 ft for

spil

lway

; -1.00

ft for

sluice gates) to

the

tailwater-pool st

ages

.

7Five gates

set

to same opening.

8Fou

r gates

in operation

set

to sa

me op

enin

g, on

e gate cl

osed

.9Fou

r ga

tes

were

set

to 2.0

ft an

d on

e gate at

1.0

ft;

the

coefficient

from

fi

gure

8

was

used to

su

btra

ct fl

ow for

a 1.0-ft

open

ing;

a

coef

fici

ent

for

a 2.0-ft op

enin

g wa

s determined from the

meas

urem

ent.

Discharge for free weir flow over the spillway is computed by combining equation 3 in table 1 with equation 5 for the free weir coefficient (Cw ). The resulting equation of discharge is

Q = 847 (h^ 1 ' 59 (6)

where h-j is the headwater depth above the spillway crest. Discharges for free weir flow over the spillway are given in table 3 and are extrapolated to include the historical peak stage of 6.36 ft.

Sluice gates

Nineteen discharge measurements, ranging from 180 to 4,050 ft3/s, were made to describe flow under the sluice gates. Characteristics of flow and the discharge coefficient associated with each measurement are listed in table 2. Discharge coefficients, required for the equations of flow (table 1), were determined for free weir, free orifice, and submerged orifice flow. Submerged weir flow did not occur during the study period.

Nineteen measurements of discharge, stage, and gate opening provided data for identifying the flow regimes for the sluice gates at McHenry Dam. The criteria for identifying free weir flow are that the ratio of gate opening (hg) to headwater depth (h-j) is greater than 0.73, and the ratio of tailwater depth (113) to the headwater depth is less than 0.75 (fig. 4). Submerged weir flow occurs when hq/h-j is greater than 0.73, and h3/h 1 is greater than 0.75. Orifice flow occurs when hq/h-| is less than 0.73 (the bottom of the gate must be touching the water surface) and is free orifice flow when the submergence ratio (ho/hg) is less than 1.3. Submerged orifice flow occurs when the sub­ mergence ratio is equal to or greater than 1.3.

Free weir flow under the sluice gates occurred during measurements 1, 3, 9, 17, and 23 (table 2). The headwater-pool stage ranged from 2.64 to 5.20 ft, and the discharge ranged from 2,100 to 4,050 ft /s. A discharge coef­ ficient for free weir flow of 3.17 was defined by. the measurements (fig. 7). Discharge for free weir flow under five sluice gates is computed by using using equation 3 in table 1 and a coefficient of 3.17. The resulting equation of discharge is

Q = 218 (h^ 1 ' 5 (7)

where h-j is headwater depth above the sluice-gate sill. Discharges for free weir flow are given in table 4.

Measurements 2, 4, 6-8, 10-12, 14, 16, 18, and 19 were used to calculate discharge coefficients for free orifice flow. Discharge coefficients varied from 0.48 to 0.66 for free orifice flow for a range of gate openings (fig. 8) The resulting equation relating the discharge coefficient for free orifice flow to gate opening (hg ) is

C = 0.57 (hg )"°- 084 . (8)

12

Table 3. Discharge rating table for free weir flow over spillway (f

ish

ladder included)

Headwater

pool stage,

in feet

1

3.60

3.70

3.80

3.90

4.00

4.10

4.20

4.30

4.40

4.50

4.60

4.70

4.80

4.90

5.00

5.10

5.20

5.30

5.40

5.50

5.60

5.70

5.80

5.90

6.00

6.10

6.20

6.30

Headwater pool st

age,

in hundredths of

feet

.00

1.7

29 76

138

213

299

396

502

618

742

874

1,010

1,160

1,32

01,480

1,650

1,82

02,010

2,190

2,390

2,590

2,800

3,010

3,230

3,450

3,680

3,920

.01

3.2

33 82 145

221

309

406

514

630

755

888

1,030

1,180

1,330

1,500

1,670

1,840

2,020

2,210

2,410

2,610

2,820

3,030

3,250

3,480

3,710

3,940

.02

5.1

37 88 152

230

318

417

525

642

768

898

1,04

01,190

1,350

1,510

1,680

1,860

2,040

2,230

2,430

2,630

2,840

3,050

3,270

3,500

3,730

3,960

.03

Di scharge

7.2

41 93 160

238

327

427

536

654

781

915

1,060

1,210

1,360

1,530

1,700

1,880

2,060

2,250

2,450

2,650

2,860

3,080

3,300

3,520

3,750

3,990

.04

, in cubic

9.7

46 99 167

246

334

437

547

666

794

929

1,070

1,220

1,380

1,550

1,720

1,90

02,080

2,270

2,470

2,670

2,880

3,100

3,320

3,540

3,780

4,010

.05

feet per

12 51 106

174

254

347

448

559

679

807

943

1,090

1,240

1,400

1,560

1,740

1,910

2,100

2,290

2,490

2,690

2,900

3,120

3,340

3,570

3,800

4,040

.06

second 15 55 112

182

264

356

459

571

691

820

957

1,10

01,

250

1,410

1,58

01,

750

1,930

2,120

2,310

2,510

2,710

2,920

3,140

3,360

3,590

3,820

4,060

.07

18 60 118

190

272

366

470

582

704

836

971

1, 120

1,270

1,43

01,

600

1,77

01,950

2,140

2,330

2,530

2,730

2,950

3,160

3,380

3,610

3,850

.08 0.

022 66

125

197

281

376

480

594

716

847

986

1,130

1,290

1,450

1,610

1,790

1,97

02,160

2,350

2,550

2,760

2,970

3,180

3,410

3,640

3,870

.09 0.

625 71 132

205

290

386

491

606

729

861

1,000

1,15

01,

300

1,460

1,630

1,81

01,990

2,180

2,370

2,570

2,780

2,990

3,210

3,430

3,660

3,890

1Referenced to Survey gage datum of 733.00 ft

above se

a level.

10.0

O

UJ

gLL LL LLJ O O

ocLLI

LLI LLI

1.0

Discharge measurement and number (table 2)

23

917

HEADWATER DEPTH (h,), IN FEET

Figure 7. Relation between discharge coefficient for free weir flow and headwater depth for sluice gates.

14

Table 4. -Discharge rating table for free weir flow under five sluice gates

Headwater pool stage, in feet 1

0.20.30.40.50.6

0.70.80.91.01.1

1.21.31.41.51.6

1.71.81.92.02.1

2.22.32.42.52.6

2.72.82.93.03.1

3.23.33.43.53.6

3.73.83.94.04.1

4.24.34.44.54.6

4.74.84.95.05.1

Headwater pool stage,

.00

640687736785836

888940994

1,0501,100

1,1601,2201,2801,3401,400

1,4601,5201,5801,6501,710

1,7801,8401,9101,9802,050

2,1202,1902,2602,3302,400

2,4702,5502,6202,7002,770

2,8502,9303,0103,0803,160

3,2403,3203,4103,4903,570

3,6503,7403,8203,9103,990

.01

645692741790841

893946

1,0001,0501,110

1,1701,2201,2801,3401,400

1,4601,5301,5901,6501,720

1,7801,8501,9201,9802,050

2,1202,1902,2602,3402,410

2,4802,5602,6302,7102,780

2,8602,9403,1013,0903,170

3,2503,3303,4103,5003,580

3,6603,7503,8303,9204,000

.02

649697746795846

898951

1,0001,0601,120

1,1701,2301,2901,3501,410

1,4701,5301,6001,6601,720

1,7901,8601,9201,9902,060

2,1302,2002,2702,3402,420

2,4902,5602,6402,7102,790

2,8702,9403,0203,1003,180

3,2603,3403,4203,5003,590

3,6703,7603,8403,9304,010

.03

Discharge

654702751800851

903956

1,0101,0701,120

1,1801,2401,2901,3501,420

1,4801,5401,6001,6701,730

1,8001,8601,9302,0002,070

2,1402,2102,2802,3502,420

2,5002,5702,6402,7202,800

2,8702,9503,0303,1103,190

3,2703,3503,4303,5103,600

3,6803,7603,8503,9304,020

.04

in hundredths of feet

.05

, in cubic feet

659707755805857

909962

1,0201,0701,130

1,1801,2401,3001,3601,420

1,4801,5501,6101,6701,740

1,8001,8701,9402,0102,070

2,1402,2102,2902,3602,430

2,5002,5802,6502,7302,800

2,8802,9603,0403,1203,200

3,2803,3603,4403,5203,600

3,6903,7703,8603,9404,030

663711760811862

914967

1,0201,0801,130

1,1901,2501,3101,3701,430

1,4901,5501,6201,6801,740

1,8101,8801,9402,0102,080

2,1502,2202,2902,3602,440

2,5102,5902,6602,7402,810

2,8902,9703,0403,1203,200

3,2803,3703,4503,5303,610

3,7003,7803,8703,9504,040

.06

per second

668716765816867

919973

1,0301,0801,140

1,2001,2501,3101,3701,430

1,5001,5601,6201,6901,750

1,8201,8801,9502,0202,090

2,1602,2302,3002,3702,440

2,5202,5902,6702,7402,820

2,9002,9703,0503,1303,210

3,2903,3703,4603,5403,620

3,7003,7903,8703,9604,050

.07

673721770821872

924978

1,0301,0901,140

1,2001,2601,3201,3801,440

1,5001,5601,6301,6901,760

1,8201,8901,9602,0302,090

2,1602,2402,3102,3802,450

2,5302,6002,6802,7502,830

2,9002,9803,0603,1403,220

3,3003,3803,4603,5503,630

3,7103,8003,8803,9704,050

.08

678726775826877

930983

1,0401,0901,150

1,2101,2701,3201,3801,450

1,5101,5701,6301,7001,760

1,8301,9001,9602,0302,100

2,1702,2402,3102,3902,460

2,5302,6102,6802,7602,830

2,9102,9903,0703,1503,230

3,3103,3903,4703,5503,640

3,7203,8103,8903,9804,060

.09

682731780831882

936989

1,0401,1001,160

1,2101,2701,3301,3901,450

1,5101,5801,6401,7001,770

1,8401,9001,9702,0402,110

2,1802,2502,3202,3902,470

2,5402,6102,6902,7702,840

2,9203,0003,0803,1603,240

3,3203,4003,4803,5603,650

3,7303,8103,9003,9904,070

15

Table 4. Discharge rating table for free weir flow under five sluice gates Continued

Headwaterpool stage,in feet1hi .00

Headwater pool stage, in hundredths of feet

.01 .02 .03 .04 .05 .06 .07 .08 .09

Discharge, in cubic feet per second

5.25.35.45.55.6

5.75.85.96.06.1

6.26.3

4,0804,1704,2604,3404,430

4,5204,6104,7004,7904,890

4,9805,070

4,0904,1804,2604,3504,440

4,5304,6204,7104,8004,900

4,9905,080

4,1004,1904,2704,3604,450

4,5404,6304,7204,8104,910

5,0005,090

4,1104,1904,2804,3704,460

4,5504,6404,7304,8204,910

5,0105,100

4,1204,2004,2904,3804,470

4,5604,6504,7404,8304,920

5,0205,110

4,1204,2104,3004,3904,480

4,5704,6604,7504,8404,930

5,0305,120

4,1304,2204,3104,4004,490

4,5804,6704,7604,8504,940

5,0305,130

4,1404,2304,3204,4104,500

4,5904,6804,7704,8604,950

5,040

4,1504,2404,3304,4204,500

4,5904,6904,7804,8704,960

5,050

4,1604,2504,3404,4204,510

4,6004,6904,7904,8804,970

5,060

^Referenced to Survey gage datum of 733.00 ft above sea level.

1.0

O

zUJ O U. U. UJOoUJ O U. QC O

UJ UJocU.

1412

19

-0.084C= 0.57 h0

e Discharge measurement and number (table 2)

O.I i i i i I I0.1 1.0 10.0

GATE OPENING (hfl ). IN FEET

Figure 8. Relation between discharge coefficient for free orifice flow and sluice-gate opening.

16

Discharge for free orifice flow under the five sluice gates is computed by combining equation 1 in table 1 with equation 8. The resulting equation of discharge is

Q = 314 (h)°- 916 (9)

where hg is sluice-gate opening and h1 is headwater depth above the sluice­ gate sill. The relation between upstream-pool stage, gate opening, and discharge is presented in table 5.

Measurements 21 and 22 were made during submerged orifice flow. The sub­ mergence ratio (h3/hg ) for measurement 21 was 1.50 with a coefficient of 0.59. Measurement 22 had a submergence ratio of 1.33 and a coefficient of 0.67. The relation between the discharge coefficient for submerged orifice flow and sub­ mergence ratio is illustrated in figure 9. The resulting equation relating the discharge coefficient for submerged orifice flow to the submergence ratio (h 3/hg ) is

Cs = 0.89 (h3/hg ) -1.00 (10)

I.O

O

UJ I-o z

O ULI UL

O UJuj OO O

CO

O.I

21

22

Discharge measurement and number (table 2)

Gate opening

Tailwater depth

Cs = 0.89 (h 3 /hg)-1.00

1.0 10.0 ORIFICE SUBMERGENCE RATIO (h3 /li9 )

Figure 9. Relation between discharge coefficient for submerged orifice flow and sub­ mergence ratio for sluice gates.

17

00

Table 5. Discharge rating table for free orifice flow under five sluice gates set to same gate opening

[Fre

e orifice flow does not occur in

the areas marked by dashed li

nes]

Upstream

pool stage,

in feet

1

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

4.6

4.8

5.0

5.2

5.4

5.6

5.8

6.0

6.2

Gate openings, in feet

0.1 64 67 69

71 73 75 77 79

8082

84

86 87 89

91 9294

95

9798

100

0.2 121

126

130

134

137

141

145

148

152

155

158

162

165

168

171

174

177

180

183

185

188

-

0.4 229

237

244

252

259

266

273

280

286

292

299

305

311

317

322

328

334

339

344

350

355

0.6 332

343

355

365

376

386

396

406

415

424

433

442

451

459

468

476

484

492

500

507

515

_

_

0.8

432

447

462

475

489

502

515

528

540

552

564

575

586

598

609

619

630

640

650

660

670

1.0

Discharge,

530

548

566

583

600

616

632

647

663

677

691

706

719

733

746

760

772

785

798

810

822

-

1.5

in cubic

768

795

821

845

869

893

916

939

960

981

1,000

1,020

1,040

1,060

1,080

1,100

1,120

1,140

1,160

1,170

1,190

-

2.0

feet per

1,000

1,030

1,070

1,100

1,130

1,160

1,190

1,220

1,250

1,280

1,300

1,330

1,360

1,380

1,410

1,430

1,460

1,480

1,500

1,530

1,550

2.5

second

1,340

1,370

1,410

1,450

1,480

1,520

1,550

1,580

1,620

1,650

1,680

1,710

1,740

1,770

1,800

1,830

1,850

1,880

-

3.0

1,77

01,810

1,850

1,890

1,930

1,970

2,010

2,040

2,080

2,110

2,150

2,180

2,220

2,250

3.5

2,180

2,220

2,270

2,310

2,350

2,390

2,430

2,470

2,510

2,550

2,590

2,630

2,660

2,700

2,740

2,770

2,810

4.0

2,660

2,700

2,750

2,800

2,840

2,880

2,930

2,970

3,010

3,050

3,090

3,130

3,170

4.5

3,110

3,160

3,210

3,260

3,310

3,350

3,400

3,440

3,490

3,530

5.0

3,590

3,640

3,690

3,740

3,790

3,840

3,890

1Referenced

to Survey ga

ge datum

of 733.00 ft ab

ove

sea

level.

Discharge for submerged orifice flow under five sluice gates set to the same opening is computed by combining equation 2 in table 1 with equation 10 The resulting equation of discharge is

Q = 491(Ah) 0 ' 5 (1D

where h is the gate opening and Ah equals the difference between the head­ water depth and tailwater depth.

Submerged orifice coefficients and the submergence ratio (h3/hg ) general­ ly plot on logarithmic paper as a straight line when submergence ratios are greater than 2.0 (Collins, 1977). For ratios less than 2.0, coefficients may be greater than those extrapolated from the straight line relation. The dis­ charge coefficients for submergence ratios greater than 2.0 may be greater than those illustrated in figure 9 because the submergence ratios for discharge measurements 21 and 22 were less than 2.0. Additional discharge measurements are needed to determine if the discharge coefficients for submerged orifice flow are applicable when submergence ratios (h3/hg ) are greater than 2.0.

Evaluation of ratings

The discharge of the Fox River over the spillway and fish ladder and through the sluice gates at McHenry Dam can be calculated from records of headwater- and tailwater-pool stages and gate openings using equations of dis­ charge for free weir, free orifice, and submerged orifice flow regimes which are summarized in table 6. Hydraulic conditions used to identify flow regimes are also summarized in table 6. Discharge for free weir and free orifice flow can also be obtained from tables 3, 4, and 5.

Table 6.--Summary of hydraulic conditions and discharge equations for different flow regimes at McHenry Dam control structures

[Q, Discharge, in cubic feet per second; h-|, headwater depths are computed by applyingan adjustment factor (-3.68 ft for spillway and 1.85 ft for sluice gates) to the

headwater-pool stage; h3/ tailwater depths are computed by applying anadjustment factor (-6.53 ft for spillway and -1.00 ft for sluice gates)to the tailwater-pool stage; hg, sluice-gate opening; Ah equals h1 -h3 ]

Structure

Spillway

Sluice gates

Sluice gates

Sluice gates

Flow regime

Free weir

Free weir

Free orifice

Submerged orifice

Hydraulic conditions

h3/h., <0.6

hg.^0.73 h 1 and h3/h 1 <0.75

hg<0.73 h 1 and h3 <1.3 h

hg<0.73 h1 and hjXI.3 h

Equation of discharge

Q = 847 (h.,) 1 ' 59

Q * 218 (h,) 1 - 5

Q = 3.14 (hg)°- 916 ( hl )°- !

Q = 491 h (Ah) 0 ' 5

Equation number

(6)

(7)

' (9)

(11)

19

Submerged weir flow did not occur during the study; therefore, discharge coefficients were not determined. Based on observations of flow during the near-record flood of September-October 1986, it is probable that the occurrence of submerged weir flow is rare. On occasions when it could have occurred, the operating procedure of the dam prevented it.

Figure 10 compares daily discharge for the Fox River at McHenry Dam to discharge at the gaging station on the Fox River at Algonquin for selected days in the 1986 and 1987 water years. Daily discharge at McHenry Dam was computed from hourly records of headwater-pool stage, twice-daily readings of the tailwater-pool stage and gate opening, and equations 6, 7, 9, and 11. The gaging station at Algonquin is 16 miles downstream from McHenry Dam and has a drainage area of 1,403 mi2 , 12 percent larger than at McHenry Dam. The solid line in figure 10 represents a 1:1 ratio of discharges at McHenry Dam and Algonquin. Daily discharge at Algonquin is 10 to 12 percent larger than McHenry Dam, except during periods of rapidly increasing discharge at McHenry Dam. During these periods, the daily discharge at Algonquin is only 1 to 2 percent larger than at McHenry Dam, but, after the initial rise, the relation returns to the 10 to 12 percent range.

Computation of discharge

The following are examples of how discharge may be calculated using equa­ tions in table 6 and discharge from the rating tables for free orifice and free weir flow.

Example 1: The following conditions exist:

Headwater-pool stage is 5.20 ft, tailwater pool stage is 3.0 ft, and all gates are out of the water.

Flow through the sluice gates is determined by first converting the stages to depths above the sluice-gate sill. This is done by adding the difference between headwater gage datum and the elevation of the sill (1.85) to the head­ water stage and then subtracting the difference between the tailwater gage datum and the elevation of the sill (1.00) from the tailwater stage.

h-, = 5.20 + 1.85 = 7.05 ft

h3 = 3.00 - 1.00 = 2.00 ft

Because the gates are out of the water and h3/h^ (0.28) is less than 0.75 (table 6), free weir flow exists.

Using equation 7 from table 6, discharge is

Q = 218 (h-,) 1 * 5

= 218 (7.05) 1 * 5

= 4,080 ft3/s.

20

7,000

< 6,000 Q

oczQJ

O 5,000

QZg 4,000QJ COOC QJ 0.

UJ 3,000

LL

gmoZ 2,000Qj"

O OC<

OCO | fOOOa

0

9 Discharge measurement at McHenry Dam

Steady flow

S Rapidly rising flow

1,000 2,000 3,000 4,000 5,000 6,000

DISCHARGE, IN CUBIC FEET PER SECOND, AT ALGONQUIN

7,000

Figure 10. Daily discharges for Fox River at McHenry Dam and Fox River at Algonquin for selected days during the data-collection period.

21

Flow over the spillway and through the fish ladder is determined by first con­ verting the headwater stage to depth above the spillway crest. This is done by subtracting the difference between headwater gage datum and the elevation of the spillway crest (3.68) from the headwater stage reading,

h-, = 5.20 - 3.68 = 1.52 ft,

and using equation 6 from table 6. The discharge is

Q = 847 (h-,) 1 * 59

= 847 (1.52) 1 ' 59

= 1,650 ft3/s.

Total discharge = 4,080 + 1,650 = 5,730 ft3/s.

Alternately, the discharge may be computed from tables 3 and 4 for a headwater-pool stage of 5.20 ft.

Free weir flow over the spillway = 1,650

Free weir flow under the sluice gates = 4,080

Total discharge = 5,730 ft3/s.

Example 2: The following conditions exist:

Headwater-pool stage is 3.68 ft, tailwater-pool stage is 3.70 ft, and five gates are set to 3.0 ft each.

First, pool stages must be converted to depths above the sluice-gate sill.

h<| = 3.68 + 1.85 = 5.55 ft

h3 = 3.70 - 1.00 = 2.70 ft

Because hg/h<| (0.54) is less than 0.73 and h3/h (0.90) is less 1.30 (table 6), free orifice flow exists.

Using equation 9 in table 6, the discharge is

Q = 314 (hg )°- 916 (h,) Q ' S

Q = 314 (3.0)°* 916 (5.55) 0 * 5

Q = 2,020 ft3/s.

Alternately, the discharge may be computed from table 6 for an upstream- pool stage of 3.68 ft.

Free orifice flow under five sluice gates = 2,020 ft3/s.

22

Example 3: The following conditions exist:

Headwater-pool stage is 5.90 ft, tailwater-pool stage is 6.98 ft, and five gates are set to 4.0 ft each.

First, the pool stages must be converted to depths above the sluice-gate sill.

h 1 = 5.90 + 1.85 = 7.75 ft

h3 = 6.98 - 1.00 = 5.98 ft

Ah = 1.77 ft

Because hg/h 1 (0.52) is less than 0.73 and h3/hg (1.50) is greater than 1.30 (table 6), submerged orifice flow exists.

Using equation 11 from table 6, the discharge is

Q = 491 hg (Ah) 0 - 5

= (491)(4.00)(1.77) 0 ' 5

= 2,610 ft3/s.

Flow over the spillway and fish ladder is determined by converting the headwater-pool elevation to depth above the spillway crest,

h-, = 5.90 - 3.68 = 2.22 ft,

and using equation 6 from table 6, the discharge is

Q = 847 (h-,) 1 * 59

Q = 847 (2.22) 1 ' 59

Q = 3,010 ft3/s.

Total discharge = 2,610 + 3,010 = 5,620 ft3/s.

SUMMARY AND CONCLUSIONS

Twenty-three discharge measurements were used to develop discharge ratings for the control structures at McHenry Dam on the Fox River. Discharge ratings were developed for free weir flow over the spillway and fish ladder; and free weir, free orifice, and submerged orifice flow under the sluice gates. Hydraulic conditions that identify flow regimes at McHenry Dam were defined by ratios between headwater depth (h-j), tailwater depth (h3 ), and gate opening (hg ). Flow under the sluice gates was identified as weir flow when the ratio of gate opening (hg) to headwater depth (h^) is greater than 0.73 and as orifice flow when hg/h-j is less than 0.73. Free orifice flow occurs when the ratio of tailwater depth (h 3 ) to gate opening (hg ) is less than 1.3,

23

and submerged orifice flow occurs when hg/hj is greater than 1.3. Flow under the sluice gates was identified as free weir flow when the ratio of tailwater depth (113) to headwater depth (h-j) is less than 0.75 and as submerged weir flow when h3/h^ is greater than 0.75. Flow over the spillway was identified as free weir flow when the ratio of tailwater depth (h3 ) to headwater depth (h-|) is less than 0.60 and as submerged weir flow when h3/h^ is greater than 0.60.

Discharge coefficients used in equations to compute discharge were deter­ mined for free weir, free orifice, and submerged orifice flow. Equations that relate discharge coefficients to headwater depth, tailwater depth, gate open­ ing, or a combination of these, were developed. These equations were combined with equations of flow to form discharge equations for the control structures at McHenry Dam.

Additional discharge measurements are needed to determine discharge coef­ ficients for submerged weir flow. Additional discharge measurements are also needed to determine if the discharge coefficients for submerged orifice flow are applicable when submergence ratios (h3/hg) are greater than 2.0. Hydraulic conditions for submerged weir and submerged orifice flow occur only at very high streamflows and did not occur during the data-collection period of this project.

All of the measured flow regimes were used in a comparison of daily discharge with the Fox River at Algonquin. Computed daily discharges for Fox River at McHenry Dam are reasonable and consistent when compared with the com­ puted daily discharge for Fox River at Algonquin.

REFERENCES CITED

Buchanan, T. J., and Somers, W. P., 1969, Discharge measurements at gaging stations: U.S. Geological Survey Techniques of Water-Resources Investigations Book 3, Chapter A8, 65 p.

Collins, D. L., 1977, Computation of records of streamflow at controlstructures: U.S. Geological Survey Water-Resources Investigations 77-78, 57 p.

24

GOVERNMENT PRINTING OFFICE 1988-543-271/62103