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HYDRAULIC DESIGN CRITERIA

1. Hydraulic Designing the computation effortvarious side slopes from 1supercritical flow. It is

SHEETS 610-1 to 610-7TRAPEZOIDAL CHANNELS

Charts 61o-1 to 610-7 are design aids for reduc-in the design of trapezoidal channels havingto 1 to 3 to 1 with uniform subcritical orexpected that the charts will be of value in

preliminary design work where different channel sizes, roughness values,and slopes are to be investigated. Certain features of the charts werebased on graphs prepared by the Los Angeles District, CE. Charts 61o-1 to610-7 can be used to interpolate values for intermediate side slopes.

2* Basic Equations. Mannings formula for1.486A S112 R2139.=

ncan be separated into a factor, involving slope

open channel flow,

and friction

Cn = 1.486 S1/2nand a geometric factor involving area and hydraulic radius

Ck = AR213 .

Chart 61o-1 and -1/1 show values of the factor, C , for slopes of 0.0001to 1.0 and n values of 0.010 to 0.035. ~harts 10-2 to -4/1-1 showvalues of the geometric factor, Ck , for base widths of O to 600 ft anddepths of 2 to 30 ft. Charts 610-5 to -7 show values of critical depthdivided by the base width for discharges of 1,000 to 200,000 cfs and basewidths of 4 to 600 ft.

3* Application. Preliminary design of trapezoidal channels forsubcritical or supercritical flow is readily determined by use of thecharts in thea.p.

following manner:With given values of n and S , C. can be obtained fromcharts 61o-1 and -1/1.. 11Since Q = CnCk the required value of Ck canby dividing the design Q by Cn .

be obtained

610-1 to 61.o-7Revised 5-59

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c. With the required c~ value, suitable channel dimensionscan be selected from charts 610-2 to -4/1-1.

d. Charts 610-5 to 610-7 can be used to determine the relation of design depth to critical depth.

610-1 to 610-7Revised 5-59

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-.

-

wa0-1(n

0.4 0.6 0.8 I.0 2 4VALUES OF Cn

FORMULA:1.486 S +C= ~

WHERE:S = SLOPEn= MANNINGS< n

OPEN

6 8 10

CHANNEL FLOWSLOPE COEFFICIENTS0.0001 < s < 0.010HYDRAULIC DESIGN CHART 610-1

20

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-

4 6 8 10 20 40VALUES OF Cn

FORMULA:1.486 S+c~= ~

WHERE:S=SLOPEn= MANNINGs n

OPEN

60 80 100 200

CHANNEL FLOWSLOPE COEFFICIENTS

0.01 < s < 1.00HYDRAULIC DESIGN CHART 610-1/1

REVISED 8-5S WES 2-54

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0 20 40 60 60 100b= BASE WIDTH IN FEET

120 140 160 180 200

CK = AR23WHERE:

A= AREAR = HYDRAULIC RADIUS

S T TRAPEZOc~ Vs DAL CHANNELSBASE WIDTH)=5 SIDE SLOPE I TO IHYDRAULIC DESIGN CHART 610-2WES 2-54

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200 250 300 350 400 450 500 550 600BASE WIDTH IN FEETCK=AR 2/3

WHERE:A=ARE+R=HYDRAULIC RADIUS

TRAPEZOIDAL CHANNELSC~ VS BASE WIDTH

SIDE SLOPE I TO IHYDRAULIC DESIGN CHART 610-2 /1

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..

L

13

12

II

10

9

8

7

6

5

4

3

2

I

0 0 5 10 15 20CK = AR23

WHERE:A = AREAR = HYDRAULIC RADIUS

25b= BASE WIDTH IN FT

30 35 40 45

TRAPEZOIDAL CHANNELSCK VS BASE WIDTH

SIDE SLOPE I TO IBASE WIDTH O TO 50 FEETHYDRAULIC DESIGN CHART 610-2/1-1

PREPARED BY U. s, ARMY ENGlt4EER WATERWAYS EXPERIMENT STATION. VICKSBURG MLSSESIPPI WES 5- 5S

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L0

BASE WIDTH IN FEET

C~=AR 2/3WHERE:

A= AREAR= HYDRAULIC RADIUS TRAPEZOIDAL CHANNELS

10

T .%l---b------l

C~ VS BASE WIDTHSIDE SLOPE I-$TO I

HYDRAULIC DESIGN CHART 6102/2--

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----/

mU.13-1s

200 250 300 350 400 450 500 550 600BASE WIDTH IN FEET

CK =A~ 2/3WHERE:

A=AREAR= HYDRAULIC RADIUS

II t


SIDE SLOPE I +TO IHYDRAULIC DESIGN CHART 610-2/3

WI= a. u

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L.

--

CK = AR2/3WHERE: TRAPEZOIDAL CHANNELSA= AREA

R= HYDRAULIC RADIUS CK VS BASE WIDTH~

SIDE SLOPE l+ TO IBASE WIDTH O TO 50 FEET

+~+ HYDRAULIC DESIGN CHART 610-2/3-1PREPARED BY . S. ARMY ENGINEER WATERWAYS EXPERIMENT STATION. VICKSBURG, MISSISSIPPI WES 5- 59

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----

L0

70

65

60

55

50

45

40

35

3C

25

2C

15

10

5

o 20 40 60 80 100 120 140 160 180 2BASE WIDTH IN FEET

CK. AR 2/3WHERE:

A = AREAR = HYDRAULIC RADIUS

l-b--l


SIDE SLOPE 2 TO IHYDRAULIC DESIGN CHART 610-3

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.-

200 250 300 350 400 450 500 550 600BASE WIDTH IN FEETCK=AR 2/3

WHERE:A= AREAR=HYDRAULIC RADIUS

~


SIDE SLOPE 2T0 IHYDRAULIC DESIGN CHART 610-3/1

WES 9 5

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- I

I

I

I

4

3

2

II

10

9

8

7

6

5

4

3

2

I

0 0 5 10 15 20 25 30 35 40 45 50b= BASE WIDTH IN FT

CK = AR2/3WHERE:

A =AREAR = HYDRAULIC RADIUS. 1= b

2t---~+

TRAPEZOIDAL CHANNELSCM VS BASE WIDTH

;DE SLOPE 2 TO IBASE WIDTH O TO 50 FEET

HYDRAULIC DESIGN CHART 610-3/1-1... PREPARED Y u .s ARMY ENGINEER WATERWAYS EXPERIMENT STATION, vlc KsOuRG, MISSISSIPPI WES 5-59

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,.,

65

60

55

50

45

zaz 40

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L

200 250 300 350 400 450 500 550 600BASE WIDTH IN FEETCKZAR 2/3

WHERE.A AREAR HYDRAULIC RADIUS


SIDE SLOPE 2*TO IHYDRAULIC DESIGN CHART 6 0-3/3

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---

L

-

0 5 10 15 20 25 30 35 40 45b=BASE WIDTH IN FT

50

CH=AR23WHERE : TRAPEZOIDAL CHANNELS

A= AREAR= Hydraulic RADlus CKVS BASE WIDTH

SIDE SLOPE 24 TO IBASE WIDTH O TO 50 FEET*$HYDRAULIC DESIGN CHART 610-3/3-1

PREFAREO dY u. s ARMY ENGINEER WATERWAYS EXPERIMENT STATION, VICKSBURG, MISSISSIPPI WES 5-59

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BASE WIDTH IN FEET

cK+R2/3WHERE:

A= AREAR =HYDRAULIC RADIUS TRAPEZOIDAL CHANNELS

CK VS BASE WIDTHSIDE SLOPE 2~T0 I

HYDRAULIC DESIGN CHART 610-3/4-._

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-.

200 250 300 350 400 450 500 550 600BASE WIDTH IN FEETCK= ~ ~ 2/3

WHERE:A=AREAR= HYDRAULIC RAOIUS.


SIDE SLOPE 2+T0 IHYDRAULIC DESIGN CHART 610-3/5

WES 9-54

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. .

gz

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-____

.-

-.

70

65

60

55

50

45

40

35

30

25

2C

15

10

5

0BASE WIDTH IN FEET

2/3CK =ARWHERE:

A= AREAR = HYDRAULIC RADIUS TRAPEZOIDAL CHANNELS

---h+

CK VS BASE WIDTHSIDE SLOPE 3T0 I

HYDRAULIC DESIGN CHART 610-4

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%..

200 250 300 350 400 450 500 550 600BASE WIDTH IN FEETC~=AR2/3

WHERE:A=AREAR= HYDRAULIC RADIUS


SIDE SLOPE 3 TO IHYDRAULIC DESIGN CHART 610-4/1

WES 9-54. ..

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. 14

13

12

II

10

9

8

7

6

5

4

3

2

I

o 0 5 10 Is 20 25 30 35 40 45 50b= BASE WIDTH IN FT

CK = AR23WHERE:

A = AREAR = HYDRAULIC RADIUS


~ SIDE SLOPE 3 TO I3 BASE WIDTH O TO 50 FEET

HYDRAULIC DESIGN CHART 610-4/1-1PREPARED Y U, S, ARMY ENGINEER WATERWAYS EXPERIMENT STATION, VICKSBURG, MISSISSIPPI WES 5-59

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L

0.

DISCHARGE IN 1000 CFS

BASIC FORMULA:

TRAPEZOIDAL CHANNELSCRITICAL DEPTH CURVES

SIDE SLOPE I+TO 1HYDRAULIC DESIGN CHART 610-5 /1

wES 9-54

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----

L

I 2 345 10 20 30 40 50 100 ---duoDISCHARGE IN 1000 CFS

BASIC FORMULA:

(-J . & 1b+ ZDc)3 ~ ~b+2ZDc TRAPEZOIDAL CHANNELSCRITICAL DEPTH CURVES

SIDE SLOPE I TO IHYDRAULIC DESIGN CHAR-r 610-5

WES 2-54

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\

---- I 2 345 10 20 30 40 50 100DISCHARGE IN 1000 CFS

BASIC FORMULA:

= D2-

200

.s~ 1 TRAPEZOIDAL CHANh ELCRITICAL DEPTH CURVES=b~e-1 SIDE SLOPE 2 TO IHYDRAULIC DESIGN CHART 610-6

wES 2-54

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--

L

---

3.0

1.0

0.5

0.3

0.1

0.0

0.0

0.0

0.0

0.0DISCHARGE IN 1000 CFS

BASIC FORMULA:

(-J . &2 1b+ ZDc)s ~ ~b+2ZDc~ I

TRAPEZOIDAL CHANNELSCRITICAL DEPTH CURVES

SIDE SLOPE 2*TO IHYDRAULIC DESIGN CHART 610-6/1

WES 9-54

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-

L.

BASIC FORMULA:

(-J = & db+ ZDc)3 , ~b+2ZDcDISCHARGE IN 1000 CFS

TRAPEZOIDAL CHANNE .sCRITICAL DEPTH CURVES

SIDE SLOPE 2+T0 IHYDRAULIC DESIGN CHART 610-6 /2

wES 9-54

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I 2 3456 10 20 30 40 50 100DISCHARGE IN 1000 CFS

BASIC FORMULA:

200

Q.@ 4b+ ZDc)3 ~ ~b+2ZDc TRAPEZOIDAL CHANNE .sCRITICAL DEPTH CURVES

SIDE SLOPE 3 TO IHYDRAULIC DESIGN CHART 610-7

WES 2-54

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\

smms 610-8 m 610-911-1OPENCmumm mu

RECTAIKWLAR SECTIONS

10 Hydraulic Desi~ Charts 61o-8 to 610-9/1-1 are aids for reducingthe computation effort in the design of rectangular channels. These chartsare usefhl also in the backwater computations presemted on Chart 010-2.20 Basic Equations. Chart 610-8 shovs plots ofnonnal depth (yo)vith respect to discharge per foot of width (q) for tide rectangular sec-tions where the side wall effect may be neglected. No-l depth curvesare shown for Mannings n of O.011 and 0.013 and for slopes of 0.01 to0.50. h e r ou gh n ess and slope6 values are those commonly used in the de-sign of spillway chutes. The c-es are computed fmm a variation of the

Manning formula for open channel flow.. CY 5/3~.

wherec =

Critical depth (y@) with respect

1.486 sl/2n

to q is lso plotted on this chart.Critical depth in-rectangularchannels is a

J

0 20 40 60 I 00b = &sE wlDTH

BASIC EQUATIONCK=AR24

WHERE:A= AREAR= HYDRAULIC RADIUS

1

120IN FEET

O PENCK

40 160 80 200

CHANNEL FLOWVS BASE WIDTH

RECTANGULAR SECTIONSBASE WIDTHS OF O TO 200 FT

HYDRAULIC DESIGN CHART 610-9

.

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-----

----

200

I 80

160

140

120

100

80

60

40

20

02

BASIC EQUATIONCK= AR2/3

WHERE:A= AREAR = HYDRAULIC RADIUS

OPEN CHANNEL FLOWCK VS BASE WIDTH

RECTANGULAR SECTIONSBASE WIDTHS OF 200 TO 600 FT

HYDRAULIC DESIGN CHART 610-9/1

WES 3-S6

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5 10b

-10 20 30 40 50b= BASE WIDTH IN FT

60

CK=AR23WHERE:

A= AREAR= HYDRAULIC RADIUS OPEN CHANNEL FLOW

rdI

CK VS BASE WIDTHRECTANGULAR SECTIONSBASE WIDTH O TO 60 FEET~~~ HYDRAULIC DESIGN CHART 610-9/l-l

PREPARED BY . S. ARMY ENGINEER WATERWAYS EXPERIMENT STATION, VICKSBURG, MISSISSIPPI WES 5-59

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HYDRAULIC DESIGN CRITERIA. SHEETS 623 TO 624-I

SUBCRITICAL OPEN CHANNEL FLOWDROP STRUCTURES

1. Purpose. A channel invert slope can vary from a maximum de-fined by a line connecting the crests of two drop structures to a mini-mum fixed by the elevation of the end sill of the upstream structure,the elevation of the crest of the downstream structure, and the distancebetween the two structures. The minimum slope should be that which re-sults in stable channel conditions.

2. ~draulic Design Charts (HDCS) 623 to 624-1 present designcriteria for drop structures in subcritical flow used to prevent channeldegradation. The criteria shown in HDC 623 are recommended for dropswhere the unit discharge is large relative to the drop height. The de-sign criteria shown in HDC 624 and 624/1 are recommended for drop struc-tures where both the unit discharge and drop height are large and whereoptimum energy dissipation is required to reduce downstream erosion.In most cases economy of construction is the deciding factor.

3* Background. The accepted relation between the height of droph (difference in elevation between the crest and the end sill of thedrop structure), critical depth dc at the drop, and the requiredstilling basin length LB is attributed to Etcheverr~ and defined bythe equation

B = CL ~hdc (1)where is an empirical apron length coefficient.and ~o;gonp Studies by Morrisresulted in design of the CIT (California Institute ofTechnology) structure restricted to h/de ratios greater than 1.0.Subsequent studies by Vanoni and Pollak3 included ratios as low as 0.3.While initial research efforts were directed toward erosion control ingullies, subsequent application has been mostly in alluvial streams.

44. Donnelly and Blaisdell investigated drop structures havingh/de ratios from 1 to 15 and developed the SAF drop structure for pri-mary use in the control of erosion in gullies. The major differencein CIT and SAF structures is the difference in tailwater depths, i.e.shallow and deep, respectively.

5. CIT-Type Drop Structures. Extensive WES tests5 on the CIT-type structure resulted in the design criteria given in HDC 623. TheVanoni and Pollak results appear to correlate well with the WES tests.

-.

WES tests showed that optimum structure performance is obtained if the

623 to 624-1

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structure is designed to have a tailwater-critical depth ratio between1.25 and 1.67. This results in a strong ground roller, a confined,strong and stable surface roller, and a depressed secondary roller down-stream. Curved, upstream abutment walls are recommended for narrowchannels to help prevent concentration of the flow. For wide channelswith flow width >20 times the depth, rectangular abutments are satisfac-tory. Stilling basin training walls should be sufficiently high to pre-vent the tailwater returning over the walls into the stilling basin.Wing walls at the end of the basin are not recommended. The channeledge should be recessed as indicated in HDC 623.

6. SAF-Type Drop Structures.(HDCS 624 and

The SAF-type drop structure 4,6624-1) is recommended for designs having large unit dis-

charges and drop heights. The basic layout is shown in HDC 624. Theprimary controlling parameter in this design is the location at whichthe upper nappe of the falling jet impinges on the stilling basin floor.This is a function of the total fall of the jet and the depth of thetailwater. Dimensionless curves for determining the impact location ofthe upper

7*following

where LB

na-ppe on the basin floor are shown in HDC 624-1.The dimensions of the stilling basin are computed from theequations.

LB=Xa \ Xc (2)

equals basin length. HDC 624 graphically defines the distanceXa , Xb , and Xc . Numerical values of Xb and Xc are obtainedfrom the following equations:

Substituting equations 3 andL.

\ = ().8dc (3)

Xc = 1.75dc (4)4 into equation 1 results in

B = Xa + P.sstic (5)with dc as defined in paragraph 3 and as shown in HDCS 623 and 624.Laboratory tests4 have resulted in the following recommendations forbaffle pier and end sill heights.

Baffle pier height = 0.8dc (6)

End sill height h = 0.4da (7)

These tests also showed that optimumbaffle pier width and spacing effectflow width and the minimum tailwater

623 to 624-1

L

basin performance occurs when thea 50 to 60 percent reduction indepth is not less than 2.15d .c

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8should be--

whereQ=c=L=H=

((

(

Design Discharge.computed using the

Design discharge for the drop structureequation

Q= ~jH3/2

iesign discharge, cfsiischarge coefficient = 3.0*Length of the drop structure crest, ftmergy head on the crest, ft

(8)

The length L of the weir should effect optimum use of channel crosssection upstream. A trial-and-error procedure should be used to balancethe crest height and width with the channel cross section.

9 Riprap Protection. Riprap protection should be providedimmediately upstream and downstream of each structure. It is recommendedthat design criteria given in HDC 712-1 be used to meet stilling require-ments and that given in EM 1110-2-1601 (reference 7) for upstream pro-tection.

10. References.(1)(2)

(3)

(4)

(5)

(6)

Etcheverry, B. A., Irrigation Practice and Engineering. 1st cd.,Chapter VII, McGraw-Hill Book Company, New York, N. Y., 1916.Morris, B. T. and Johnson, D. C., Hydraulic design of drop struc-tures for gully control. Transactions, American Society 6f CivilEngineers, VO1 108 (1943), pp 887-940.Vanoni, V. A. and Pollak, R. E., Experimental Design of LowRectangular Drops for Alluvial Flood Channels. Report No. E-82,California Institute of Technology, Pasadena, Calif., September1959.Donnelly, C. A. and Blaisdell, F. W., Straight Drop SnillwavStilling Basin. Technical Paper No.15, Se~ies B, St: AnthonyFalls Hydraulic Laboratory, University of Minnesota, Minneapolis,Minn. , November 1954.U. S. Army Engineer Waterways Experiment Station, CE, Drop Structurefor Gering Valley Project, Scottsbluff County, Nebraska, HydraulicModel Investigation, by T. E. Murphy. Technical Report No. 2-760,Vicksburg, Miss., February 1967.U. S. Department of Agriculture, Soil Conservation Service, Engi,neer-Handbook, Drop Spillways. Section 11, Type C, Washington, D. C.,p 5-11.

* Reduced for submergence effects when applicable.

623 to 624-1

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(7) LJ. S. ~y, Office, Chief of Engineers, Engineering and Design;Hydraulic Design of Flood Control Channels. Engineer ManualEM 1110-2-1601, Washington, D. C., 1 July 1970.

623 to 624-1

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B

VE

cuww

C

LN

SO

Nd

TC

D

O

C

h=HG

OD

h=G

OESL

HH

OWR

d

hV

T

H

L

OBN

L=

OWRC

E

PO

OTC

A

NR

FL

S

7 6 5

\

4~

\\

\\

3

-.

-_

2

I

2

3

4

5

6

7

8

LHOBN

06 05

r/

4

04

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h

/

x

/

0

r

0

f

oo

I

2

3

4

5

6

7

8

9

ESLHG

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TC

OC

FOW

CTT

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SRU

H

CDGC

6W77

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L

FLOCY? BLOCKS U

-LONGITUDINAL SILL

[ 1

1

- END S/L L

c

1

H

(p.::4:

j:.

i..:. :: HEIGHT d= ~2. /5 de.. .4.:.

h= ;dc . . .

. .:4::i:.. . U-zb: ;.:4 ,= Le . .

~OTE:H =HEAD ON WEIR= ~(dc) CENTER-LINE SECTION

hd =VELOCITY HEADd2 =TAILWATER DEPTHd= =CRITICAL DEPTH OVER CRESTh =HEIGHT OF DROPh =HEIGHT OF END SILL

LB =LENGTH OF STILLING BASIN=Xa + xb+)(cXa =HORIZONTAL DISTANCE FROM CREST TOINTERSECTION OF UPPER NAPPE ANDSTILLING BASIN FLOORXb=HORIZONTAL DISTANCE FROM INTERSECTION OFUPPER ~APPE AND STILLING BASIN FLOOR TOUPSTREAM TACE OF FLOOR BLOCKSxc =HORIZONTAL DISTANCE FROM UPSTREAM FACEOF FLOOR BLOCKS TO END OF STILLING BASIN

REDRAWN FROM FIG. 10, REFERENCE 4.

TFREEBOARD

SUBCRITICALOPEN CHANNEL FLOWSAF-TYPE DROP STRUCTURE

BASIC GEOMETRYHYDRAULIC DESIGN CHART 624

WES 7-73

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-----

.=.

I

-1

-2

-3

-4h+hd=

5

-6

-7

-8

-9

_lol

x_ad=I 2 3 4 5 6 7 8 9

I

NOTE:dc=CRITICAL DEPTH OVER CRESTh = HEIGHT OF DROPh =HEIGHT OF END SILLXa=HORIZONTAL DISTANCE FROM CRESTTO INTERSECTION OF UPPER NAPPEAND STILLING BASIN FLOORYt=VERTICAL DISTANCE FROM CREST TOTAlLWATER SURFACE (Yt IS POSITIVE

WHEN TAl LWATER SURFACE IS ABOVETHE CREST NEGATIVE WHEN TAlLWATERSURFACE 1~ BELOW CREST)

SUBCRITICALOPEN CHANNEL FLOW

SAF- TYPE DROP STRUCTUREREDRAWN FROM FIG. 2, REFERENCE 4. JET IMPACT LOCATION

HYDRAULIC DESIGN CHART 624- IWES 7-73

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HYDRAULIC DESIGN CRITERIASHEETS 625-1 TO 625-1/2DROP INTAKE STRUCTURES

\-

1. Purpose. The purpose of these Charts is to present designcriteria for rectangular drop structures upstream from steep chute chan-nels. These criteria were developed from tests conducted at the U. S.Army Engineer Waterways Experiment Station, Vicksburg, Mississippi.Discharge calibration curves for various drop configurationsarepresented.

2. The general design of the structure with parameter definitionsis presented on Chart 625-1. The calibration data obtained for variouslengths and drops are presented on Chart 625-1/1. Drop length to chutewidth ratios B/W ranged from 1 to 4 and drop depth to chute widthratios D/W ranged from O to 1. Design Criteria. The dimensions of the structure can be de-termined from a known discharge and allowable head or width of chute us-ing Chart 625-1/1. All of the calibration data were obtained using anabutment radius equal to three times the width of the chute. If it be-comes necessary to increase the radius of the abutments because of up-stream embankments or other reasons, as probably will be the case forsmaller chutes, the curve on Chart 625-1/1 labeled D = O should beused for design. This design without drop will provide a conservativeestimate of the discharge rating curve, and the change in the radius ofabutments will have little effect on the discharge.4. An alternate method of design has been developed by the Nash-

ville District for design of drop intake structures on the Tennessee-Tombigbee Waterway.* The curves on Chart 625-1/2 illustrate this proce-dure. This form allows the direct determination of chute width for aknown discharge and head.5. These criteria apply to drop structures upstream from steepchute channels. The slope of the chute will have little effect on thedrop structure discharge capacity as long as critical flow occurs withinthe chute. However, the length of horizontal channel shown on Chart

625-1 could cause a backwater to affect the head on the drop structurefor high discharges. It is recommended that the drop structure be de-signed to operate with weir control or that backwater curves be computedto determine what effect this backwater will have on the head.

U. S. Army Engineer Waterways Experiment Station, CE, Divide Cut Drain-age Structures, Tennessee-TombigbeeWaterway, Mississippi and Alabama;Hydraulic Model Investigation,by Jackson H. Ables. Technical ReportH-76-18, Vicksburg, Miss., October 1976.

625-1 to 625-1/2

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6. HDC Chart 625-1/2b presents a typical drop intake structureused on the Tennessee-TombigbeeWaterway. All drop intake designs forthe Tennessee-TombigbeeWaterway used a D/W ratio of 0.6 and a B/Wratio of 3.0. Drops were designed to pass an approximate 10-year dis-charge at a head of about 3 ft. Sidewalls were designed to pass a25-year storm without overtopping. To date severalhave experienced events involving a 100-year returnwithout difficulty.of these structuresperiod rainfall

625-1 to 625-1/2

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..

----

CHUTE CHANNEL\

\- BQ

APPROACH INVERT // -// //~//SECTION A-A

LEGEND:B = LENGTH OF DROP, FTD = DEPTH OF DROP, FTW = CHUTE WIDTH, FTH = UPSTREAM HEADWATER DEPTH, FTQ = DISCHARGE, CFS

DROP INTAKESTRUCTURESHDC CHART 625-1

PREPARED BY U S ARMY ENGINEER WATERWAYs EXPERIMENT STATION, VICKSBuRG, MISSISSIPPI WES 11-07

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=----

\

10

m 100

5

,0-1

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5

In

5

,()-1

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1 I 1 1 , 11 1 I 1 , , , 1,0-1 5 ,00 5 ,01H/W

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,01 r , 1 I r r 11 , 1 r T 1 , ,BIW=l5

10 0 --

1 1 1 I , , , i 1 $ , L L

,01

5

5

,()-1

,0-1 5 ,00 5 0 1H/W

, , , 1 I I 1I T 1 1 , I f 1BIVV=3

4

1 1 1 1 i 1 , , I , , t ,,0-1 5 ,00H/W

LEGEND~ D=OA D/W= 0.20 D/W= 0.4 D/W= 0.60 D/W=l.O

5 ,01

DROP INTAKE STRUCTURESCALIBRATION CURVES

HDC CHART 625-1/1PREPARED BY U.S. ARMY ENGINEER WATERWAYS EXPERIMENT STATION, VICKSBURG, MISSISSIPPI WES 11-87

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403G

20

THE DISCHARGE RATINGCURVE IS A TRANSFORMATIONOF THE CURVE PRESENTEDON CHART 625-1/l FORSPECIFIED RATIOS OF B/WAND D/W.

1-LAxLz

I 11 tDESIGN EXAMPLE I I1GIVEN: Q = 600 CFS

H = 2.5 FTFOR : DIW = 0.6

BIW = 3.0THEN: W=15FT

B=45FTD = 9.0 FT

1 1 1I r 1

l I I 1 I4t=i=tt3 f E 1

t U vv U. u

11 I I I 1 B/Mj = 3. 02 * I

10 20 304050 100 200 300 500 1000 20C0 4000DISCHARGE, CFS

a, DISCHARGE RATING CURVE a

1 2 ml -- -

ROAD>c,t% . ..- .-~ ORIGINAL GiOUND

SECTION A-A LB (&

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HYDRAULIC DESIGN CRITERIASHEETS 631 TO 631-2

-

OPEN CHANNEL FLOWRESISTANCE COEFFICIENTS

1. General. Because of its simplicity, the Manning equation hasbeen used extensively in the United States in the evaluation of resist-ance losses in open channel flow. A comprehensive summary of the use ofthis equation in channel design is given in reference 1. Flow data andlknnings ns for 50 natural streams, together with color photographs ofthe channels, have also been published.2 The Chezy equationl includesa resistance coefficient term that is applicable to all flow conditions.~draulic Design Chart 631 presents a general resistance diagram relat-ing Chezys C , Reynolds number, and relative roughness. The chart isuseful in open channel flow problems.

2. Laboratory and field investigations have shown that the resist-ance coefficient varies with Reynolds numbers as well as with boundarysurface roughness. Keulegan3 has demonstrated that the Von Karman-Prandtlsmooth and rough pipe resistance equations based on the Nikuradse testdata can be applied to open channel flow with only minor adjustments inthe equation constants. A recent ASCE progress report4 recommends aMoody-type diagram for use in open channel flow, especially for flows inwhich the viscous effects are important.

3. Chezy Equation. The Chezy equation is

V=C4Rwhere

V = mean channel velocity, ft per secC = Chezy resistance coefficient which is a function of Reynolds

number and relative roughness of channelR = hydraulic radius of channel, ftS = slope of energy gradient

4. Resistance Coefficient Relations. The Darcy resistance coeffi-cient f see Hydraulic Design Chart 224-1) is defined as

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f

where g = acceleration of gravity.The relation between C and f is

Similarly, the relation of C and n can be shown to be

~ = 1.486R1/6n

59 Effects of Reynolds Number. The Chezy resistance coefficient Cis plotted as a function of Reynolds number in Chart 631. An auxiliaryscale of Darcy resistance coefficient f is also shown for alternativeuse by the designer. 5e method of plotting is a form of the Moody dia-gram (Sheet 224-1). The resistance equations for smooth and rough flowbased on Keulegans results and recommended by Cho are given andplotted i~ Chart 631. The rough flow limit based on Rouses pipe flowcriterion is also shown. The Keulegan constants were used in theColebrook-White equation (Chart 224-1) for the transition flow zone. TheReynolds number used for plotting is

4VRRe= vwhere v = the kinematic viscosity.

The use of this form of the Reynolds number is recommended in the ASCEtask force report.q

6. Basic Data. The plotted data in Chart 631 are for concrete-lined channels. Both tranquil- and rapid-flow data are presented. Thetranquil-flow data were computed from U. S. Army Engineer Waterways Ex-periment Station (WES) laboratory tests in brush d-concrete flumesG>Tand from field tests results compiled by Scobey. k,9 More recently ob-tained U. S. Bureau of Reclamation (USBR)10 and Italianll field data havealso been included. These data were selected on the basis of accuracy offlow measurements and conditions of concrete channel lining. Tests at theUniversity of Iowa12 indicate that the energy loss in flows having Froudenumbers greater than 1.6 becomes a function of the Froude number and den-sity and size of roughness elements. Additional energy loss is caused byinstability of the flow. The plotted data points based on prototype testsat the Fort Randallls and Fort Peck14 spillway chutes are for rapid flowwith Froude numbers exceeding the stability criterion. These data repre-sent the only known available measurements at Re numbers approaching 108.631 to 631-2Revised 1-68

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7. Suggested Design Criteria.L- a. Resistance coefficients. The data plotted in Chart 631 can be used for guidance in the design of concrete-lined channels

with subcritical velocities. Resistance coefficients forthese channels generally are in the transition zone shown inthe chart. The flow regime is seldom hydraulically smooth orfully rough and the resistance coefficient is usually a func-tion of both the Reynolds number and the relative roughness.Chart 631-1 is a plot relating Chezy C, Mannings n, theequivalent roughness ks , and the hydraulic radius. Theo-retically it is only applicable to rough flow conditions.This chart should be useful for relating C and n for thedesign of channels with riprapped banks (Charts 631-4 and631-4/1). The equation for n on Chart 631-1 was developedby solving the rough flow equation given in Chart 631 interms of Mannings n.

-.

b. Equivalent roughness ks . In the use of Chart 631, a valueof ks (equivalent sand grain diameter) has to be specifiedfor the prediction of resistance. The hydraulic roughnessks in pipe flow is dependent only on the type of construc-tion or the surface finish specified. However, in openchannel flow it includes the effects of secondary flow re-sulting from boundary geometry and to a lesser extent thefree water surface. Experimental data for correlation ofsurface texture, channel geometry, and the resulting hydrau-lic equivalent roughness ks are very limited. However,considerable variation in the selected ks value resultsin only small changes in the flow energy loss.(1) The following tabulation presents average ks values

resulting from different types of concrete formingand surface finishing. It is based on computationsmade from the open channel resistance data plotted inChart 631.AveragekS>ft Concrete Surface Finish0.0006 18-year-old, 10-ft-wide rectangular aqueduct.

Troweled sides and float-finished bottom(ref 9)

0.002 Laboratory rectangular and trapezoidal chan-nels, brushed concrete finish (refs 6 and 7).Field channels, smooth, troweled cementfinish (refs 8, 9, and 11)

(Continued)

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Averageks,ft Concrete Surface Finish0.003 10- to 20-year-old, 8- to 50-ft-wide trape-

zoidal channels constructed with modern rail-mounted slip traveling forms (ref 10)

0.005 Screed-finished spillway chute blocks withtransverse joints at 20- to 25-ft intervals(refs 13 and 14)

(2) The tabulation above canbe used for selecting designks values if the concrete forming and surface finish-ing can be obtained with good assurance. For generaldesign computations the following ks values for con-crete are suggested:

Design Problem Suggested ks Value, ftDischarge capacity 0.007Maximum velocity 0.002Proximity to critical depth*

Subcritical flow 0.002Supercritical flow 0.007

* To prevent undesirable undulating waves, flow-depth-to-critical depth ratios between 0.9 and 1.1 shouldbe avoided.

(3) The determination of the equivalent surface roughnessfor riprap channels, rubble masonry, or other largeroughness protrusions should be based on some estimateof the mean protrusion, riprap, or rock size. Use ofthe D50 (mean) size as ks , based on equivalent sphereweight, is a good approximation for stone riprap.

8. Application. Chart 631-2 is a sample computation sheet illus-trating the use of Charts 631 and 631-1.

9= References.(1) Chow, V. T., Open-Channel Hydraulics. McGraw-Hill Book Co., Inc.,

New York, N. Y., 1959, PP 109-123.(2) U. S. Geological Survey, Roughness Characteristics of Natural

Channelsl by H. H. Barnes, Jr. Water-Supply Paper 1849, Washington,D. C., 1967.

(3) I@ulegan, G. H., Laws of turbulent flow in open channels. Journalof Research, National Bureau of Standards, vol 21, Research PaperNo. 1151 (December 1938) > -PP 707-741.

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----(4)

(5)

(6)

(7)

(8)

(9)

(lo)

(11)

(12)

(13)

(14)

Progress Report of the Task Force on Friction Factors in Open Channels,Friction factors in open channels. ASCE, Hydraulics Division,Journal, vol 89, HY 2, paper 3464 (March 1963), pp 97-143.Rouse, H., Engineering Hydraulics; Proceedings of the Fourth Con-ference, Iowa Institute of Hydraulic Research, June 12-15, 1949.John Wiley Sons, Inc., New York, N. Y., 1950, p 404.U. S. Army Engineer Waterways Experiment Station, CE, RoughnessStandards for Hydraulic Models; Study of Finite Boundary Roughnessin Rectangular Flumes, by Irene E. Miller and Margaret S. Peterson.Technical Memorandum No. 2-364, Report 1, Vicksburg, Miss., June 1953.

Hydraulic Capacity of Meandering Channels in StraightFloodways; Hydraulic Model Investigation, by E. B. Lipscomb.Technical Memorandum No. 2-429, Vicksburg, Miss., March 1956.U. S. Department of Agriculture, The Flow of Water in Flumes, byF. C. Scobey. Technical Bulletin No. 393, Washington, D. C.,December 1933.

, The Flow of Water in Irrigation and Similar Canals, byF. C. Scobey. Technical Bulletin No. 652, Washington, D. C.,February 1939.U. S. Bureau of Reclamation, Analyses and Descriptions of CapacityTests in Large Concrete-Lined Canals, by P. J. Tilp and M. W.Scrivnero Technical Memorandum 661, Denver, Colo., April 1964.Grassino, R., Determination of roughness coefficients for CimenaCanal. LEnergia Elettrica, vol XL, No. 6 (June 1963), pp 429-436.Translation by Jan C. Van Tienhoven for U. S. Army Engineer Water-ways Experiment Station, CE, Translation No. 65-3, Vicksburg, Miss.,May 1965.Rouse, H., Koloseus, H. J., and Davidian, J., The role of the Froudenumber in open-channel resistance. Hydraulic Research, Journal ofthe International Association for Hydraulic Research, vol 1, No. 1(1963), pp 14-19.U. S. Army Engineer Waterways Experiment Station, CE, Flow in ChuteSpillway at Fort Randall Dam; Hydraulic Prototype Tests, by C. J.Huval. Technical Re_port No. 2-716,vicksburg,Miss.,A-pri~1966,U. S. Army Engineer District, Omaha, Nebraska. (Unpublished memo-randum on Fort Peck Smillwav tests. 1951 .). J /, . ,

631 -tO631-2Revised 1-68-.

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o x > R + a c

I

I

L

1

I R, +R ITR R T R AT 1AT XTDS

W

T23

W

T24

S

U

T

S

U

T

F

R

C

F

P

C

U

C

CM

C

,3

2

4

681

2

4

681

2

4

681

2

N

4

81

2

4

681

RH

C

RUF

4

i1 01 01 00 ~0 -0 ;0 0 00 00I6

0

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0

z F v

gA

O

OGT

FS

Rv

VKNMCvsT

Fs

IG

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------

II II II IIucaxm

t I I , I , 1 t

UjIdzz ft

0.00.0010.0060.0200.0470.0900.1550.2450.3650.5190.7110.9451.2261.5581.9452.3912.9013.4794.1294.8555.6616.5537.5328.6059 ~776

11.04712.42413.91115.51117.22919.06821.03423.129

0.0O.OQ10.0080.0250.0590.1130.1950.3080.4590.6520.8931.1881.5411.9582.4453.0063.6474.3735.1906.1027.1168.2369.46710.81512.285

13.88115.61017.47719.48521.64123.94826.41329. 04c

CURVED CHANNELSSPIRAL CURVE TABLESHYDRAULIC DESIGN CHART 660-2/2

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--- n

01234

2:9

10111213141516lj181920212223242526272829303132

012?2:9

10111213141516171819202122232425262728293031

L

0.012.525.037.550.062.575.087.5100.0112.5

125.0137.5150.0162.5175.0187.5200.0212.5225.0237.5250.0262.5275.0287.5300.0312.532Z.O337.5350.0362.5375.0387.5400.0

0.012.525.037.550.062.575.087.5100.0112.5

125.0137.5150.o162.5175.0187.5200.0212.5225.0237.5250.0262.5275.0287.5300.0312.5325.033-7.5350.0362.5375.0387.5

Dr, ft o 1.

No. 56 Curve

11,5107,6745>7554,6043,8373,2892,8782,5582,3022,0931,9181,7711,6441,5351,4391,3541>2791,2121,1511,0961,0461,0019599218 5853822794

767743719

9,0796,0524,5393,6313,0262,5942,2702,0171,8161,6511,5131,3971,297l,z?lo1,1351,0681,009956

9088658257897577266982626605586

00 00 0000 00 560003 4400 08 2400 14 56cm 2 3 2000 33 360045 4400 59 44ol 15 3601 33 2001 52 5602 14 2402 374403 02 5603 30 0003 58 5604 294405 02 2405 36 5606 13 2006 51 3607 31 4408 13 4408 57 3609 43 2010 30 56u 20 2412 11 4413 04 5614 00 m14 56 5615 55 44

No. 71 Curve

00 00 0000 ol u00 04 440010 3900 18 5600 29 350042 3600 57 5901 15 44ol 35 51ol 58 2002 23 u02 50 2403 19 5903 5~ 5604261505 02 5605 41 590623 2407 07 1107 53 2008 41 5109324410 25 59u a 36I-2 19 3513 19 5614 22 3915 274416 35 u17 45 0018 57 H

x, f-t

12.50025.00037.50050.00062.50074.99987.49899.997112.495

124.991137.485149.977162.466174.950187.430199.932L2.369224.826237.272249.705262.124271.525286.907299.267311.601323.906336.179348.417360.614372.766384.869396.918

12.5CQ25.OGC37.50050.CQO62.50074.99987.49899.995112.491

124.985137.476149.963162.445174.920187.387199.844212.289224.720237.133249.526261.895274.237286.547298.82231J.056323.243335.38o347.458359.472371.415383.279

Y, ft

0.00.0020.0100.0320.0750.1440.2480.3920.5840.8301.1371.5121.9612.4923.1113.8254.6415.5656.6047.7659.05410.47712.04313.756

15.62417.65319.84922.21924.76827.50330.43033.55436.882

0.00.0020.0130.0410.0950.1830.3140.4970.740I .0521.4411.9172.k873.1603.9444.8495.8837.0548.3709.84a

11.47313.27615.25717.42619.78922.35425.12928.12331.34134.79238.48142.417

PREPARED BY U. S. ARMY ENGINEER WATERWAYS EXPERIMENT STATION. VICKSBURG, MISSISSIPPI

n

o12:

1?78910111213141516171819202122232425262728

0123456ii9

10111213141516171819202122232425

LA

0.012.525.037.550.062.575.087.5100.0112.5125.0137.5150.0162.5175.0187.5200.0212.5225.0237.5250.0262.5275.0287.5300.0312.5325.0337.5350.0

0.012.525.037.550.062.575.087.5100.0112.5125.0137.5150.0162.5175.0187.5200.0212.5225.0237.5250.0262.5275.0287.5300.0312.5

Aer, ft ~-

No. 90 Curve

7,1624,7753,5812,8652,3872,o461,7901,592l,h321,3021,1941,1021,023

95589584379675471668265162359i573551531512

00 00 0000 o l 300006 000013 300024 000037 300054 0001 13 30ol 360002 o l 300230 0003 ol 300336 000413 3004 54000537 300624000713 300806000901 3010 00001101 301206 001313 301424 001537 3016 54m18 13 301936 00

No. 113 Curve

5,7043,&132,8522,2821,9011,6301,4261,2681,1411,037951878815

761713671634600570543519496475456

0000 000001 5300 07 3200 16 5700 30 0800 47 0501 07 48ol 32 1702 00 3202 32 3303 08 2003 47 5304 31 1205 ~8 1706 09 080703 4508 02 0809 04 1710 10 1211 19 5312 33 20~3 5Q 3 315 u 3216 36 1718 04 4819 37 05

x, f

12.50025.00037.50050.OQO62.49974.99887.49699.992112.486

124.976137.462149.941162.41I.174.872187.319199.7502L2.16222h.550236.911249.239261.529273.775285.971298.WI310.182322.182334.099345.924

12.50025.cx3037.50050.00062.49974.99787.49499.988112.478

124.962137.439149.906162.360174.798187.215l%. 606211.967224.291236.571248.801260.970273.071285.092297.024308.853

Y, t-t

0.00.0030.0160.0520.1200.2320.3980.6300.9381.3331.8272.4293.1524.0054.9996.1457.4558.93710.60412.465

14.53116.81219.31722.05725.04128.27931.78035.55139. 6U3

0.00.0030.0210.0650.1510.2910.5000.7911.1781.6742.29h3.0503.9565.0276.2747.7J-39.35511.21413.30315.635

18.22221.07624.20927.63331.35935.397


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\

-

n

o1:42789

10111213141516171819202122

012;i?T89

10n12131415161-(181920

u

0.012.525.037.550.062.575.087.5100.0112.5

125.0137.5150.0162.5175.0187.5200.0212.5225.0237.5250.0262.5275.0

0.012.525.037.550.062.575.08T.5100.0112.5

125.0137.5150.0162.5175.0187.5200.02.12.5225.0237.5250.0

Air, ft O r x, ft

No. 139 Curve

4,6373,0922,3191,8551,5461,3251,1591,03192784377371366261858o54651548846L442422

00 00 0000 02 190009 ~600 20 5100 370400 57 55ol 23 24ol 53 3102 28 1603 07 3903 51 400440 1905 33 3606 31 310734 0408 41 ~509 53 0411 09 3112 30 3613 56 1915 26 401701 3918 41 16

No. 168 Curve

3,8372,5581,9181,5351,2791,096959853

767698639590548E451426404384

CKl00 0000 02 4800 11 1200 25 1200 44 4801 10 0001 40 4802 1-( 1202 59 1203 46 4804 40 0005 38 4806 43 ~207 53 1209084810 30 00~~ 564813 29 1215 07 12~6 50 48184000

12.50025.00037.50049.99962.49874.99687.49099.981112.466

124.943137.408149.858162.289174.694187.068199.40421I. .694223.928236.096248.187260.188272.086

12.50025.00037.50049.99962.49774.99387.48699.973112.451

124.917137.366149.793162.191174.553186.870199.130211.323223.436235.45224j.356

Y, t

0.00.0040.0250.0800.1850.3580.6150.9731.4492.0592.8213.7514.8666.1817.7159.4.8211.49913.78216.345

19.20522.37525.86929.702

0.00.0050.0310.0970.2240.4330.7431.1761.7512.4893.4094.5335.8797.4689.319

11.45213.88516.63619.72423.16626.978

n

o1;42;910111213141516171819

01;4z:91011121314151617

L=

0.012.525.037.550.062.575.087.5100.0112.5

125.0137.5150.0162.5175.0187.5200.02u2.5225.0237.5

0.012.525.037.550.062.575.087.5103.0112.5

125.0137.5150.0162.5175.0187.5200.0212.5

r, ft o I

No. 200 Curve

3,2232,1491,6111,2891,074921806716

6455865374964&1430403379358339

00 00 0000 03 20cm 13 2000 30 0000 53 20OL 23 2002 00 0002 43 2003 33 2004 30 0005 33 2006 43 2008 00 0009 23 2010 53 2012 30 0014 13 20~6 03 20~8 00 0020 03 20

No. 237 Curve

2,7201,8131,3601,088

907777680604544494453418389363340320

0000000003 5700 15 4800 35 33ol 03 1201 38 4502 22 1203 13 3304 12 4805 19 5706 35 0007 57 5709284811073312 54 1214 48 4516 51 1219 01 33

x, f%

12.50025.00037.50049.99962.49674.99187.48099.961

112.430124.882137.310149.707162.063174.367186.607198.769210.834222.786234. 6Q2

12. 5(XI25.00037.50049.99862.49574.98787.47299.946112.402

124.834137.233149.588161.886174.112186.248198.273210.164

Y, ft

0.00.0060.0360.1150.2670.5150.8851.4CKI2.0842.9624.0585.3946.9968.88511.086

13.61916.50819.77223.43227.507

0.00.0070.0430.1360.3160.6101.0481.6592.4693.5104.8076.3908.28510.52113.123

16.11719.52723.3~

PREPARED B Y u. s. ARMY ENGINEER WA7ERWAY5 EXPERIMENT STATION, VICKSBURG. MISSISSIPPI


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012

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2

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10111213

Lfi

0.012.525.037.550.062.575.087.5100.0112.5125.0137.5150.0162.5175.0187.5200.0

0.012.525.037.550.062.575.087.5100.0112.5125.0137.5150.0162.5175.0

0.012.525.037.550.062.575.087.5100.0112.5125.0137.5150.0162.5

Asr, ft m 1 x, fi

No. 280 Curve

2,3021,5351,151

921767658576512460419384354329307288

00 00 000004 4000 18 40WI 42 0001 14 4001 56 4002 48 0003 48 4004 58 4006 18 0007464009 24 4011 12 0013 08 h15 14 4017 30 0019 54 40

12.50025 coo37.49949.99862.49374.98287.46199.924112.363

124.769137.128149.426161.644173.762185.754197.593

No. 340 Curve

12.5000000000005 401,896 002240

1,264 00 51 00948 01 30 40758 02 21 40632 03 24 co542 04 37 40474 060240421 073900379 092640345 u 25 40316 13 3600292 15 57 40271 ~8 30 40

No. 420 Curve

OQcooo00 07 001,535 00 28 001,023 01 03 00767 01 52 00

614 02 55 00512 04 12 00438 05 43 00384 072800341 0927m3307 11 4000279 14 0700256 164800236 19 43 co

25 .bo:;.4&.62.48974.97387.44299.888112.298

124.659136.952149.154161.239173.177

12.50025.00037.49949.99562.48374.95987.41299.829112.192

124.480136.664148.711160.580

Y, ft

0.00.0080.0510.1610.3730.7211.2381.9592.9174.1455.6777.5459.78112.41715.482

19.00523.013

0.00.0100.0620.1960.4530.8761.5042.3793.5415.0316.8899.153u. 86215.05018.754

0.00.0130.0760.2420.5601.0821.8572.9384.3736.2n8.50111.29014.62118.537

L

0.012.525.037-550.062.575.087.5100.0112.5

125 . o137.5

0.012.525.037.550.062.575.087.5

100.0112.5125.0

0.012.525.037.550.062.575.087.5100.0

Asr, ft Ot

No. 520 Curve

1,240826620496413354310275248225

00 00 co00084000 344001 18 0002184003 36 4005 12 0007 04 4009 14 4011 42 0014 26 401728 40

No. 720 Curve

00 00 00oo 1200895 004800597 01 48 cm448 03 12 00358 05 00 00298 07 12 00256 094800224 12 48 00199 161200179 20 00 00

x, f-t

12.50025 .OQO37.49849.99262.47574.93787.36599.738112.029

124.204136.220

12.50024.99937.49649.98462.45174.88087.24199.498

111.598123.477

No. 1080 Curve

00000000 18 00 12.500597 01 12 00 24.999398 02 42 00 37.491298 044800 49.96423 ) 07 30 00199 10 48 001~ 14 42 00149 19 12 m

62.39174.73086.91998.873

Y, ft

0.00.0160.0950.2990.6931.3392.2993.6365.4107.682

10. 5C913.946

0.00.0220.1310.4140.9601.8533.1825.0297.478

10.60714.49

0.00.0330.1960.6221.4392.7784.7667.524

11.167

PREPARED BY u. s. ARMY ENGINEER WATERWAYS EXPERIMENT STATION. VICKSBURG, MISSISSIPPI


(SHEET 5 OF 5)W ES 9 7

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GIVEN:Design Q = 15,000 cfsChannel width W = 50 ftInvert slope S = 0.005Curve deflection angle l=45degChannel shape - rectangularDesign controls - Sheets 631 to 631-2, par 7b(2)

Capacity Curve geometryEquivalent roughness k~ 0.007 ft 0.002 ftDepth y 11.26ft 10.33ftVelocity V 26.65 fps 29.05 fpsCritical depth dc 14.0 ft 14.0 ftFroude No. 1.40 1.59

REQUIRED:Spiral (minimum length) and simple curve (minimum radius) geometries with invert banking

COMPUTE:a. Simple curve radius (rein)

4V2W 4(29.05)2(50)r =mi n = (32.2) (10.33) = 507.42 ft (Eq 2, Sheet 660-1)9Yb. Approximate banking (Chart 660-1) = 2 AY

r 507.42 - 10.14w= 50 -For V = 29.05 fps and ~ = 10.14 ; $ = 2.6w

Ay = 2.6(0.5) = 1.3 ftc. Spiral length (rein) L

L =30 Ay=30(l.3) =39 ft (Eq 3)d. Spiral curve geometry

For rmin = 507 and L =39 use spiral curve No. 520 (Chart 660-2/2, Sheet 5 of 5)As = 021840

n ZL r an(ft) (ft) 0

1 12.5 00 08 402 25.0 1 ~40 00 26 003 37.5 826 00 43 204 50.0 620 01 00 40

x(ft)

12.50025.00037.49849.992

Y(ft)

0.0160.0950.2990.693

02 18 40* an = (2n - 1)8, (Chart 660-2)

CHANNEL CURVEEXAMPLE COMPUTATION

PREPARED BY u. s. ARMY ENGINEER WATERWAYS EXperiment STATION, VICKSBURG, M5SSISSIPP[

HYDRAULIC DESIGN CHART 660-2/3(SHEET i oF 2)

WES 9-70

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e. Simple curve geometry (use r = 620 ft)(1) Central angle O (Chart 660-2)

6=1 - 2A~= 45- 2(02018401)= 45- (043720) = 402240

(2) Curve length L, (Chart 660-2)L = ( I - zAJr _ (dozzl@II)(bzO)

c 57.2958 - 57.2958_ 40.38 (620) = 43695 f+ 57.2958

f. Total curve length LcL~ =2 L+LC= 2(50) + 436.95 = 536.95 ft

g. Corrected invert banking = 2 Ay= ~= 12.40w 50For V = 29.05 fps and ~ = 12.40w = 2.2 (Chart 660-1)cAy = 2.2C= 2.2(0.5) = 1.10 ft

2Ay = 2.20 fth. Maximum allowable Aymx

2Aym = 0.18W = 0.18(50) = 9.O ft (Eq 3, Sheet 660-1Ayw =4.5 ft > Ay= 1.10 ft item g OK

i. Curve tangent distance Ts

Ts=X-rsin As+ Y+rcos As tan+49.992-620 sin(021840) + (0.693 + 620 cos 021840) tan 22300049.992- 620(0.04033) + [0.693 + 620(0.99919)] 0.4142149.992-25.005 + (0.693 + 619.498)0.4142124.987 + (620.191)0.41421 = 281.87 ft

CHANNEL CURVEEXAMPLE COMPUTATION

PREPARED By u. s ARMY Et+G t t tEERATERWAYSXPERIMENTTATION,ICKSBURG,15S1551PPIHYDRAULIC DESIGN CHART 660-2/3

(SHEET 2 oF 2wES 9-7o

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/----- TOP OF LEFT WALLf TOP OF RIGHT WAILL-_ - -

L _ -

G WATER SURFACE -- _FLOW

LEFT WALL INVERTRIGHT WALL INVERT

~ INVERT @=O.005-_ /t -~.-50- f~ h

ENTRANCE 436.95SPIRAL CIRCU.L AR CUR VE - 50 _

PROFILE EXIT SPIRAL

(EXISTING WALL

SPIRAL CURVENO. 520L~=50FTT~ 281.87FT

PLAN

t 1= 50 eCURVE SECTION

HYDRAULIC ELEMENTS - K= O.007 FTSTA TO STA ] SECTION I SLOPE I Yc, FT I V, FPS I Y,FTI F

[ I\ Q ,CFS

Io+oo 18+oo 50 RECT 0.005 14.0 26.65 ] 11.26 ] .4 I 15,000

CURVED CHANNELSEXAMPLE PLAN AND PROFILE

HYDRAULIC DESIGN CHART 660-2/4PREPARED BY U, S. ARMY ENGINEER WATERWAYS EXPERIMENT STATION, VICKSBURG, M,ss, SS, PP, wES 9-7o

Channel 1

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