Deg Outfall Spillway Design

DESIGN DATA

Design Discharge (Re‐Modeled) Qd 231 m3/s (Max. discharge of canal)

U/S Full Supply Level HWL 206.857 m asl (Head Water Level)

D/S Full Supply Level TWL 203.433 m asl (Tail Water Level)

U/S Bed Level BLU/S 203.870 m asl

D/S Bed Level BLD/S 200.821 m asl

Canal Bed Slope Sb 0.00015 m/m

Bed Width of Canal Bcanal 68.00 m

Side Slope of Canal z 2.00 1 v: z h

Manning's 'n' for Canal n 0.0260 composite

Manning's Formula

DEG OUTFALL HYDROPOWER PROJECT (DHPP)HYDRAULIC DESIGN OF SPILLWAY

(Metric Units)

1/2 2/31canalv S R

n

A b zy y

22 1P b y z

Flow Velocity in Canal vcanal 1/0.0260*0.00015^(1/2)*(220.96/81.36)^(2/3)

Flow Velocity in Canal vcanal 0.917 m/s

TAILWATER RATING

Q (m3/s) Depth (m)

5.00 0.3

10.00 0.4

20.00 0.7

50.00 1.2

75.00 1.5

100.00 1.8

125.00 2.1

150.00 2.3

175.00 2.5

200.00 2.7

250.00 3.1

300.00 3.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 100 200 300 400

Flow Depth (m)

Discharge (m3/s)

Tailwater Rating Curve

FLUMING RATIO

Head Across / Drop

" " " " HL 206.857‐203.433

Head Across / Drop HL 3.424 m

Bed Width of Canal Bcanal 68.00 m

HL fr

Fluming Ratio 1.25 m 65.0%

1.25 ‐ 3 m 75.0%

Fluming Ratio fr 85.0% Above 3 m 85.0%

Fluming Ratio of 0.85 gives;

Clear Length of Crest Lc 85.0%*68.00

Clear Length of Crest Lc 57.800 m (required)

However, if the height of crest works out to be more than 0.4 times upstream

water depth, the fluming ratio may be increased so as to increase the H and

lower the crest. (S.K. Garg)

S.K. Garg

cr

canal

Lf

B

LH HWL TWL

CREST LEVEL

Broad‐Crested Weir Formula Ref: Garg

Head Over the Crest Hc ( 231/(1.7*57.800))^(2/3)

Head Over the Crest Hc 1.768 m

Upstream Flow Depth

" " " " Yu/s 206.857‐203.870

Upstream Flow Depth Yu/s 2.987 m

Approach Velocity

" " " " va 231/(57.800*2.987)

Approach Velocity va 1.338 m/s

Approach Velocity Head

" " " " hvel 1.338^2/(2*9.8)

Approach Velocity Head hvel 0.091 m

3/21.70 .d c cQ L H

/ /u s U SY HWL BL

/.d

ac u s

Qv

L Y

2

2a

vel

vh

g

Upstream Energy Level

Upstream Energy Level ELu/s 206.949 m asl

Crest / Sill Level

" " " " CLweir 206.949‐1.768

Crest / Sill Level CLweir 205.181 m asl

Say CLweir 205.050 m asl

(Lower the crest height to satisfy the CHECK for stilling basin floor level)

Height of Crest

" " " " Pc 205.050‐203.870

Height of Crest Pc 1.180 m (provided)

Maximum Crest Height Pmax 0.4*2.987

Maximum Crest Height Pmax 1.195 m = 0.4 x Yu/s

Ref: Garg

CHECK: Pc < 0.4 x Yu/s O.K.

/u s velEL HWL h

/weir u s cCL EL H

/c weir U SP CL BL

DISCHARGE COEFFICIENT


Upwnstream Head

" " " " H 206.857‐205.050

Upwnstream Head H 1.807 m

Downstream Head

" " " " h 203.433‐205.050

Downstream Head h ‐1.617 m

weirh TWL CL

weirH HWL CL

Submergence / Modular Ratio h/H ‐0.895h/H C'/C

Use the following Gibson's Curve to get the reduction factor 0.10 0.99

for discharge coefficient of drowned / submerged weirs 0.20 0.980.30 0.970.40 0.960.50 0.940.60 0.910.70 0.880.72 0.860.74 0.840.76 0.820.78 0.800.80 0.780.82 0.750.84 0.730.86 0.700.88 0.660.90 0.620.92 0.580.94 0.520.96 0.400.98 0.201.00 0.00

Check whether the flow is free (modular) or submerged (non‐modular).

Gibson's Curve

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

h / H

C' / C

Gibson's Curve

( ) g ( )

For the flow to be modular, i.e. not affected by submergence, the ratio

h/H, where h and H are the upstream and downstream heads above

the weir crest, is less than 0.75

CHECK: h/H < 0.75 Modular

Reduction Factor C'/C 1.000 (from Gibson's Curve)

If h/H is < 0.1 then C'/C = 1

Discharge Coefficient C 2.10 (SI units‐meters)

Discharge Coefficient C 3.80 (British units‐feet)

Adjusted Discharge Coeff. C' 2.10*1.000

Adjusted Discharge Coeff. C' 2.100

REQUIRED CREST LENGTH

Spillway Formula

or

Minimum Crest Length Lmin 231/(2.100*1.807^(3/2))

Minimum Crest Length Lmin 45.267 m

Say Lmin 46.000 m

' 3/2. .Q C L H

min ' 3/2.dQ

LC H

Assume

Clear Width of Gate / Bay wgate 6.00 m Pier shapes:-

Number of Gates / Bays ngate 8 no. 8 Type kp

Number of Piers npier 7 no. r ≤ 0.1T P1 0.02

Pier Thickness wpier 1.50 m (provided)

P2 0.01

Clear Length of Crest Lclear 48.000 m

Total Length of Crest Ltotal 58.500 m (required) P3 0.0

Effective Length of Crest Abutment shapes

Where: Type ka

Pier Contraction Coefficient kp 0.010 (Type ‐ P2)

Abutment Contraction Coeff. ka 0.100 (Type ‐ A2) A1 0.20

Effective Length of Crest Leff 48.000‐2*(7*0.010+0.100)*1.807

Effective Length of Crest Leff 47.385 m 0.5H0 ≥ r ≥ 0.15H0 A2 0.10

Ref: Small Dams r ≥0.5H0 A3 0.0

DISCHARGE CAPACITY ≤ 450

2 .eff clear p aL L n k k H

' ' 3/2

Actual Possible Flow Q' 2.100*47.385*1.807^(3/2)

Actual Possible Flow Q' 241.8 m3/s

Looseness Factor 4.68%

CHECK: Q' ≥ Qd O.K.

The structure can safely pass the required discharge at given HWL & TWL.

SPACE LIMITATIONS (Use this when limited space is available for spillway)

The above calculations are based on the crest level assumed earlier (in the design data).

However, if the actual space available at site is significantly less than the calculated minimum

length of crest then revised calculation are required to obtain the required crest

level to safely pass the design discharge at given HWL & TWL.

Minimum Stable Width (for alluvial channel)

Minimum Stable Width Bmin 4.75*SQRT( 231)

Minimum Stable Width Bmin 72.194 m

Available Space for Spillway L'total 58.500 m

Available Clear Length of Crest L'clear 48.000 m

' ' 3/2. .effQ C L H

1/2min 4.75 dB Q

Revised Crest / Sill Level CL'weir 205.050 m asl (calculated by hit & trial)

Upstream Head

Upstream Head H' 1.807 m

Available Eff. Length of Crest

" " " " L'eff 48.000‐2*(7*0.010+0.100)*1.807

Available Eff. Length of Crest L'eff 47.385 m Ref: Small Dams

Downstream Head

Downstream Head h' ‐1.617 m

Submergence Ratio h'/H' ‐0.895

Check whether the flow is free (modular) or submerged (non‐modular).

For the flow to be modular, i.e. not affected by submergence, the ratio

h/H, where h and H are the upstream and downstream heads above

the weir crest, is less than 0.75

CHECK: h/H < 0.75 Modular

/

' 'weirH HWL CL

' 'weirh TWL CL

' ' '2 .eff clear p aL L n k k H

Reduction Factor C'/C 1.000 (from Gibson's Curve)

If h/H is < 0.1 then C'/C = 1

Adjusted Discharge Coeff. C' 2.100

Revised Discharge Capacity

Revised Discharge Capacity Qr 2.100*47.385*1.807^(3/2)

Revised Discharge Capacity Qr 241.8 m3/s

Looseness Factor 4.68%

CHECK: Qr ≥ Qd O.K.

For the spillway configuration within the available space the crest level has to be changed to

205.05 m asl. Which is 0 m higher than the previously calculated/assumed crest level.

APPROACH VELOCITY

Height of Crest

" " " " Pc 205.050‐203.870

Height of Crest Pc 1.180 m (provided)

Velocity in U/S Floor Ref: Small Dams

' ' '3/2. .r effQ C L H

/c weir U SP CL BL

/ . .d

u s floortotal c

Qv

L P H

" " " " vu/s.floor 231/(58.500*(1.180+1.807))

Velocity in U/S Floor vu/s.floor 1.322 m/s

Approach Velocity va 1.322 m/s

Approach Velocity Head v2a/2g 0.089 m

Velocity at Crest

" " " " vc 231/(47.385*1.807)

Velocity at Crest vc 2.697 m/s

Crest Velocity Head v2c/2g 2.697^2/(2*9.8)

Crest Velocity Head v2c/2g 0.371 m

CREST WIDTH

Width of Crest;

Broad Crest

Ref: Garg

Narrow Crest

.d

ceff

Qv

L H

2.5crestw H

2

3crestw H

While a broad crest ensures a constant discharge coefficient for varying heads.

If the fall/weir is to be used as a meter then broad crest is recommended otherwise

a narrow crest provides a higher coefficient of discharge than that for a broad crest and

therefore recommended.

Crest Width wcrest 1.807*2/3

Crest Width wcrest 1.205 m

Say wcrest 1.300 m

An upstream straight glacis (bed approach) with 1v : 2h slope and a downstream

straight glacis with 1v : 3h slope is recommended.

Ref: Garg

Horizontal Length of U/S Glacis lu/sglacis 2.359 m 1v : 2h

Horizontal Length of D/S Glacis ld/s

glacis 12.687 m 1v : 3h

Length of Upstream Glacis Lu/s

glacis 2.638 m 1v : 2h

Length of Downstream Glacis Ld/s

glacis 13.374 m 1v : 3h

CRITICAL DEPTH

Discharge Intensity

3

dc

clear

Qq

L

Discharge Intensity at Crest qc 4.813 cumecs/m

Critical Depth

" " " " yc (4.813^2/9.8)^(1/3)

Critical Depth yc 1.332 m

GATED DISCHARGE

Height of Gate hgate 1.900 m hgate > H

Clear Width of Gate / Bay wgate 6.000 m

Number of Gates / Bays ngate 8 no.


Upstream Head H 1.807 m

Downstream Head h ‐1.617 m

Head Across / Drop HL 3.424 m

1/32

c

qy

g

dc

clear

Qq

L

/ p L

The free flow below a gate occurs as long as the roller of the hydraulic jump does

not submerge the section of minimum depth of jet which is located downstream

of the gate.

Free Flow Discharge Ref: Davis

& HEC‐RAS Manual

When a gate discharges with the jet submerged, Hcenter is replacedwith HL ;

Submerged Flow Discharge Ref: Davis

& HEC‐RAS Manual

Where: Cd = Coefficient of Discharge (Typically 0.6 to 0.7)

Cd 0.670

ngate = Number of Gates

wgate = Width of Gate

a = Gate Opening

Hcenter = Head to Center of Gate Opening

HL = Head Across / Drop

. . . 2 .gates d gate gate centerQ C n w a g H

. . . 2 .gates d gate gate LQ C n w a g H

Qgates HWL TWL Hcenter HL opening

20 206.857 201.507 1.777 5.351 0.061

50 206.857 202.022 1.728 4.835 0.160

75 206.857 202.350 1.683 4.508 0.248

100 206.857 202.637 1.637 4.221 0.342

125 206.857 202.895 1.587 3.962 0.441

150 206.857 203.131 1.535 3.727 0.546

175 206.857 203.352 1.479 3.506 0.656

200 206.857 203.562 1.421 3.295 0.774

Gate Opening for Various Discharges with Constant Upstream Water Level

200 206.857 203.562 1.421 3.295 0.774

250 206.857 203.950 1.293 2.908 1.030

300 206.857 204.305 1.148 2.552 1.319

Qgates HWL TWL Hcenter HL opening

20 206.857 203.433 1.770 3.424 0.076

50 206.857 203.433 1.713 3.424 0.190

75 206.857 203.433 1.665 3.424 0.285

100 206.857 203.433 1.618 3.424 0.380

125 206.857 203.433 1.570 3.424 0.474

150 206.857 203.433 1.523 3.424 0.569

175 206.857 203.433 1.475 3.424 0.664

200 206.857 203.433 1.428 3.424 0.759

250 206.857 203.433 1.333 3.424 0.949

300 206.857 203.433 1.238 3.424 1.139

These tables are indicative only. The gated operation of spillway will be further

refined using the outputs from HEC‐RAS model studies.

ENERGY DISSIPATION

Conjugate Depths

Discharge Intensity q 4.813 cumecs/m

Gate Opening for Various Discharges with Constant U/S & D/S Water Levels


Entrance Loss Ref: Davis

Entrance Loss Coefficient Ke 0.160

Entrance Loss he 0.160*2.697^2/(2*9.8)

Entrance Loss he 0.059 m

Flow Depth Entering the Jump D1 0.435 m (calculated by hit & trial)

Flow Velocity Entering Jump v1 4.813/0.435

Flow Velocity Entering Jump v1 11.062 m/s = q/D1

Friction Loss Ref: King

Mean Velocity

Mean Velocity v 6 880 m/s

2

2c

e e

vh K

g

2 24/3

1( )f m crest glacish n v L L

R

1

2c

m

v vv

Mean Velocity vm 6.880 m/s

Hydraulic Radius R (1.807*((48.000+0.435)/2))/(2*1.807+((48.000+0.435)/

Hydraulic Radius R 1.573 m = A / P

Manning's Coefficient n 0.015 (for concrete)

Friction Loss hf 0.015^2*6.880^2*(1.300+12.687)/1.573^(4/3)

Friction Loss hf 0.081 m

Assume

Bed Level of Stilling Basin BLsb 200.038 m asl (calculated by hit & trial)

Energy Equation Ref: King

RHS LHS

206.857 = 206.857 O.K.

Incoming Froude Number

Incoming Froude Number F1 11.062/SQRT(9.8*0.435)

Incoming Froude Number F1 5.357

Jump Type Ref: PaterkaSteady

21

1 2sb e f

vHWL BL D h h

g

11

1

vF

gD

(Recommended Froude Number 4.5 ≤ FR1 ≤ 9, for stable & steady hydraulic jump)

Conjugate Depths Ratio Ref: Paterka

Flow Depth After the Jump D2 0.435*0.5*(SQRT(1+8*5.357^2)‐1)

Flow Depth After the Jump D2 3.086 m

Increase the flow depth after jump by 10% as recommended by USBR, therefore

Flow Depth After the Jump D'2 3.086*1.1

Flow Depth After the Jump D'2 3.394 m = D2 x 1.1

Water Level in Stilling Basin

Water Level in Stilling Basin TWLsb 203.433 m asl

D/S Full Supply Level TWL 203.433 m asl

TWL and TWLsb should be as close as possible.

CHECK: TWL ‐ TWL b < 0 01xD2 O K Ref: Davis

221

1

0.5 1 8 1D

FD

'2sb sbTWL D BL

CHECK: TWL TWLsb < 0.01xD2 O.K. Ref: Davis

Basin Type Ref: Paterka

Recommended Stilling Basins Types

(According to USBR Standard)

Floor Lining Only. No Special Energy Dissipating Devices Type 0

Upstream Chute Blocks and Optional End Sill Type I

Upstream Chute Blocks, Interm. Baffle Blocks and End Sill Type II

Upstream Chute Blocks and Terminal Dentated Sill Type III

Based on

Design Flow

Not to be Used

Not to be Used

Recommended

Recommended

Length of Basin Ref: Paterka

F1 Ljump/D2 F1 Ljump/D2 F1 Ljump/D2 F1 LJ/D2

1.70 4.00 1.70 4.00 4.50 2.22 4.00 3.60

2.50 4.88 2.50 4.82 5.50 2.40 5.00 3.86

3.50 5.58 3.00 5.26 6.00 2.46 6.00 4.03

4.00 5.80 3.50 5.58 7.50 2.60 7.60 4.20

The stilling basin floor should be joined with the downstream bed in a minimum slope

Natural Jump Length Length of Basin Type I Length of Basin Type II Basin Type III

of 1 v : 5 h.

4.00 5.80 3.50 5.58 7.50 2.60 7.60 4.20

4.50 5.92 4.00 5.79 9.00 2.70 9.00 4.28

5.00 6.01 4.50 5.93 10.50 2.76 11.00 4.33

6.00 6.10 5.00 6.00 15.00 2.76 12.50 4.33

7.00 6.14 16.50 2.72 13.50 4.31

8.00 6.15 14.50 4.28

9.00 6.14

10.00 6.12

12.00 6.05

13.50 5.99

15.00 5.91

17.00 5.78

19.00 5.59

20.00 5.45

Length of Jump Ljump 8.059 m (from above table)

Length of Basin Lbasin 9.000 m (Basin Type ‐ I)

Alternatively;

Length of Basin Lbasin α (D'2 ‐ D1) α = 5.00

" " " " Lbasin 14.80 m

Alternatively;

Ref: Mays

Length of Basin

" " " " Lbasin 4.5*3.394/5.357^0.38

Paterka, USBR

'2

sin 0.381

4.5ba

DL

F

" " " " Lbasin 8.07 m

Alternatively;

Length of Basin

" " " " Lbasin 2*0.435*5.357^1.5

" " " " Lbasin 10.79 m

Stilling Basin Type “K”

1.4

1.7

2

Select the larger value of Lbasin

Length of Basin Lbasin MAX(10.79,8.07,14.80,9.000)

Length of Basin Lbasin 14.800 m

The length of basin may increase during sub‐surface flow analysis. For final dimensions

refer to the summary page.

Stilling basin with a vertical or sloping end sill and one or two rows of baffle

blocks.

Stilling basin with a vertical or sloping end sill

Stilling basin with a sloping end sill and one or two rows of baffle blocks

1.5sin 1 1baL KD F

Velocity After Jump

Conjugate Depths Ratio

Outgoing Froude Number Ref: Mays

Outgoing Froude Number F2 ((((0.435/3.086)*2+1)^2‐1)/8)^(1/2)

Outgoing Froude Number F2 0.284

Flow Velocity After the Jump

Flow Velocity After the Jump v2 0.284*SQRT(9.8*3.086)

Flow Velocity After the Jump v2 1.560 m/s

Alternatively;

Flow Velocity After the Jump v'2 4.813/3.086

Flow Velocity After the Jump v'2 1.560 m/s = q/D2

CHECK: v2 ≈ v'2 O.K.

212

2

0.5 1 8 1D

FD

2 2 2. .v F g D

2

12

2

2 1 1 / 8D

FD

Efficiency of Jump

Efficiency of Jump (%) Ref: Mays

Where E1 & E2 are the energy heads before and after the hydraulic jump.

Efficiency of Jump E2 / E1 ((8*5.357^2+1)^(3/2)‐4*5.357^2+1)/(8*5.357^2*(2+5.3

Efficiency of Jump E2 / E1 48.06%

Energy Dissipation (%)

Energy Dissipation (1‐48.06%)

Energy Dissipation 51.94%

Enery Loss in the Jump Ref: Mays

Enery Loss in the Jump EL (3.086‐0.435)^3/(4*3.086*0.435)

Enery Loss in the Jump EL 3.468 m

Height of Basin Walls

Height of Basin Walls Ref: Davis

32 22

1 122 2

1 1 1

8 1 4 1

8 2

F FE

E F F

2

1

1 .100E

E

2 1 10.1wallh D D v

3

2 1

2 14L

D DE

D D

Height of Basin Walls hwall 3.394+0.1*(0.435+11.062)

Height of Basin Walls hwall 4.544 m

Say hwall 4.600 m

Elevation of Wall Top TLbasin 4.600+200.038

Elevation of Wall Top TLbasin 204.638 m asl

Blocks and Sill

Type ‐ II Basin

Height of Chute Block hB‐chute 0.400 m = D1

Width of Chute Block wB‐chute 0.300 m = 0.75 D1

Spacing of Chute Block SB‐chute 0.400 m = D1

Spacing along Each Side of Wall SB‐wall 0.200 m = D1 / 2

Ref: Paterka

The minimum height of chute/deflector blocks is 20 cm as recommended by USBR.

The horizontal top length of the deflector blocks should be at least 2D1. The upper

surface of each block is sloped at 5º in a downstream direction for better operation

especially at lower discharges.

Height of Solid Sill hS‐solid 0.700 m = 0.2 D2

Top Length of Solid Sill tlS‐solid 0.140 m = 0.2 hS‐solid

Height of Dentated Sill hS‐dent. 0.700 m = 0.2 D2

Width of Dentated Sill wS‐dent. 0.500 m = 0.15 D2

Max. Spacing of Dentated Sill SS‐dent. 0.500 m = 0.15 D2

Ref: Paterka

For solid end sill the slope is 2:1 upward in the direction of flow.

It is not necessary to stagger the chute blocks with respect to the sill dentates.

It is recommended that the sharp intersection between chute and basin apron be

replace with a curve of reasonable radius of at least 4D1 when the chute slope is 1:1

or greater.

If baffle piers are foreseen then the upstream face of the baffle piers should be

set at a distance of 0.8D2 from the downstream face of the chute blocks.

Height of Baffle Pier hbaffle 0.400 m = D1

Width of Baffle Pier wbaffle 0.300 m = 0.7 D1

Top Length of Baffle Pier tlbaffle 0.090 m = 0.2 D1

Ref: Paterka

Baffle blocks are prone to cavitation damage and should not be used for approach

velocities above 20 m/s. For velocities between 20 and 30 m/s, a chamfer on the

block edges should be provided to reduce the cavitation potential.

PIER SHAPE & SIZEPIER SHAPE & SIZE

Square Pier with Corners Rounded

Min. Width of Pier wpier‐min 0.500 m = 0.267 Hd

Rounding Radius for Corners rcorners 0.100 m = 0.033 Hd

Upstream Length from Crest lu/s 0.600 m = 0.282 Hd

Pier Thickness wpier 1.500 m (provided)

Rounded Nose Pier

Min. Width of Pier wpier 0.500 m = 0.267 Hd

Rounding Radius rround 0.300 m = 0.133 Hd


CHECK: wpier ≥ wpier‐min O.K.

90o Cut Water Nose Pier

Min. Width of Pier wpier 0.500 m = 0.267 Hd

Rounding Radius rround 0.500 m = 0.267 Hd


WATER SURFACE PROFILE

Position of Jump

Energy Level at start of Jump

" " " " E1 0.435+11.062^2/(2*9.8)

Energy Level at start of Jump E1 6.678 m

Energy Level at end of Jump

21

1 1 2

vE D

g

22

2 2 2

vE D

g

" " " " E2 3.086+1.560^2/(2*9.8)

Energy Level at end of Jump E2 3.210 m

Elevation at start of Jump Py 203.433‐3.210

Elevation at start of Jump Py 200.223 m asl

Bed Level of Stilling Basin BLsb 200.038 m asl (calculated above)

CHECK: Py ≥ BLsb O.K. Ref: Garg

Distance of start of jump from toe of D/S Glacis is given by;

Where:

Slope of D/S Glacis zGd/s 3.00 1 v : z h

Distance Px 3.00*(200.223‐200.038)

Distance Px 0.554 m

Therefore the jump will occur at a distance of about 0.554 m u/s from the toe of d/s glacis

and at a heihgt of about 0.185 m from the stilling basin floor, i.e. on the d/s glacis.

/ .Gx d s y sbP z P BL

Pre‐Jump Profile

The parabolic upstream water surface profile is estimated using Montague curves.

The Montague profile is given by the following equation;

Where:

X = The horizontal ordinate of any point of profile measured from the d/s edge of crest

X = The vertical ordinate measured from crest level



Water Level at end of Crest WLc 206.382 m asl

Water Level at start of Jump WLJ1 200.658 m asl = Py + D1

Upstream Profile Table

Xup 0.00 2.12 3.79 5.09 6.01 7.03 8.61

Yup 0.00 0.69 1.61 2.41 3.02 3.71 4.83

0.00 ‐0.80 ‐1.61 ‐2.41 ‐3.02 ‐3.71 ‐4.83

Post‐Jump Profile

4.crest

YX v Y

g

Incoming Froude Number F1 5.357 F12 = 28.701

Flow Depth Entering the Jump D1 0.435 m

For any value of x‐ordinate along the post jump profile calculate X/D1 and then using the

following table obtain the value of Y/D1 for the given Froude number. Hence different

values of X & Y may be estimated.

0 5 10 15 20 25 X/D1

1 1.5 1.6 1.5 1.55 1.6 Y/D1

0 5 10 15 20 25 X/D1

1 2.1 2.5 2.5 2.5 2.5 Y/D1

0 5 10 15 20 25 X/D1

1 2.7 3.1 3.5 3.7 3.8 Y/D1

0 5 10 15 25 30 X/D1

1 2.7 3.65 4.4 5 5.1 Y/D1

0 5 10 15 25 30 X/D1

1 2.7 3.65 4.6 6.2 6.8 Y/D1

0 5 10 15 25 30 X/D1

1 2.7 3.65 4.7 6.75 7.5 Y/D1

Downstream Profile Table

Xdown 0.00 1.33 2.67 4.00 5.00 6.15 8.0

X/D1 0.00 3.06 6.13 9.19 11.49 14.1 18.4

Y/D1 1.00 2.04 2.91 3.50 3.93 4.44 5.1

Ydown 0.44 0.89 1.27 1.52 1.71 1.93 2.24

F12 = 60

F12 < 2

F12 = 4

F12 = 8

F12 = 15

F12 = 30

down 0.44 0.89 1.27 1.52 1.71 1.93 2.24

Profile Plot Ref: Garg

Based on above calculations the tentative water surface profile is shown below;

PROTECTION WORKS

U/S and D/S Sheet Piples

Discharge Intensity in Canal qcanal 3.397 cumecs/m = Qd / Bcanal

203.870

205.050

200.038200.821

206.857

206.382

203.433

199.0

200.0

201.0

202.0

203.0

204.0

205.0

206.0

207.0

208.0Water Surface Profile

Intensity on U/S Floor qu/s Floor 3.949 cumecs/m = Qd / Ltotal

Intensity at Crest qu/s Floor 4.813 cumecs/m = Qd / Lclear

Intensity on D/S Floor qd/s Floor 3.949 cumecs/m = Qd / Ltotal

Avg. Particle Size in Bed dmm 0.10 mm

Lacey's Silt Factor

Lacey's Silt Factor f 0.557

Scour Depth Below WL

Scour Depth Below WL R 4.100 m 3.506 m

(Use maximum value of scour depth)

Upstream Flow Depth Yu/s 2.987 m = HWL ‐ BLu/s

Downstream Flow Depth Yd/s 2.612 m = TWL ‐ BLd/s

For the design of sheet piles, it is just enough to take them down to the level obtained by

measuring the normal depth of scour R, below the water level. However, a value of

1/32

1.35q

Rf

1/3

0.47Q

Rf

1.76 mmf d

measuring the normal depth of scour R, below the water level. However, a value of

1.25 R on the U/S side and 1.5 R on the D/S is widely accepted.

Ref: Garg

Bottom Level of U/S Sheet Pile

" " " " SPu/s 203.870‐4.00

Bottom Level of U/S Sheet Pile SPu/s 201.732 m asl

Depth of U/S Sheet Pile dpu/s 2.138 m = BLu/s ‐ SPu/s (minimum)

Bottom of Intermediate Pile SPint 201.732 m asl

Depth of Intermediate Pile dpint 2.138 m (minimum)

Bottom Level of D/S Sheet Pile

" " " " SPd/s 200.821‐5.00

Bottom Level of D/S Sheet Pile SPd/s 197.283 m asl

Depth of D/S Sheet Pile dpd/s 3.538 m = BLd/s ‐ SPd/s (minimum)

Provide

Depth of U/S Sheet Pile dpu/s 4.00 m

Depth of Intermediate Pile dpint 5.00 m

Depth of D/S Sheet Pile dpd/s 5.00 m

/ 1.25u sSP HWL R

/ 1.5d sSP TWL R

Bottom Level of U/S Sheet Pile SPu/s 199.870 m asl

Bottom of Intermediate Pile SPint 198.870 m asl

Bottom Level of D/S Sheet Pile SPd/s 195.821 m asl

Filter and Aprons

An inverted filter is recommended at the end of D/S concrete floor to reduce the

possibility of piping . T filter consists of layers of materials of increasing permeability

from bottom to top with selected gradation to allow free flow of seepage water

without the danger of clogging.

The depth of inverted filter is kept equal to the depth of D/S launching apron.

Scour Depth Below Bed

" " " " Dd/s 1.25*4.100‐2.612

Scour Depth Below Bed Dd/s 2.513 m

Length of Inverted Filter Lfilter 4.398 m = 1.5 to 2 D

Say Lfilter 4.300 m Ref: Garg

Length of Stone Apron Lapron 4.300 m

Thickness of Stone Pitching1/30.06t Q

/ /1.25d s d sD R Y

" " " " t 0.06* 231^(1/3)

Thickness of Stone Pitching t 0.368 m

Say t 0.400 m

Ref: Garg

Thickness of Apron Tapron 0.700 m = 1.5 to 1.9 t

Say Tapron 0.700 m

U/S Wing Wall

On the powerhouse side the spillway is separated by a divide pier and no wing wall

is provided on the powerhouse side. However, on the opposite side a wing wall

is recommended.

For an un‐flumed non‐meter fall, the side wall may be splayed at 45o from U/S edge

of crest and carried into the berm for about 1 meter.

In our case the fall / spillway is flumed therefore curved wing wall with radius of

5 to 6 times H subtending an angle of 60o at center and carried tangentially into

the berm may be provided.

Radius of Wing Wall Rwing 10.845 m = 5 to 6 H

Say Rwing 11.000 m

U/S FLOOR LENGTH

The U/S floor length is the balance length obtained by subtracting the length of crest,

length of D/S glacis and Length of D/S Floor from the total floor length calculated

by Khosla's theory.

Safe Exit Gradient by Khosla

Type of Soil

Shingle

Coarse Sand

Fine Sand

Safe Exit Gradient

0.25 to 0.20

0.20 to 0.17

0.17 to 0.14

Maximum static head is caused when the water is stored upto the crest level on the

U/S side and no water at D/S side. Although this condition will not be for prolonged

durations however, for design pupose this condition is valid.

Maximum Static Head

Maximum Static Head Hmax 206.857‐200.821

Maximum Static Head Hmax 6.037 m

Depth of D/S Sheet Pile dpd/s 5.000 m

Safe Exit Gradient GE 0.200 = 1 / 5

Factor 0.200*5.000/6.037

Factor 0.1657

From the table 7.248

Total Floor Length Required

" " " " bfloor 7.248*5.000

Total Floor Length Required bfloor 36.242 m

max /d sH HWL BL

max

/

1.E

d s

HG

dp

1

/.floor d sb dp

Already Provided Length 29.287 m

Balance Floor Length Lbalance 6.955 m

Horizontal Length of U/S Glacis lu/sglacis 2.359 m

U/S Horizontal Floor Length Lu/s

Floor 4.596 m (provided)

Add the remaining balance floor length to the stilling basin length

Length of Basin Lbasin 14.800 m

Say Lbasin 15.000 m (provided)

Total Floor Length b 36.442 m (provided)

Assume

Nominal Thickness of U/S Floor 1.00 m

Thickness at End of D/S Floor 1.20 m

RESIDUAL PRESSURES

Assume three sheet piles i.e. one sheet pile each at the start and end of concrete floor

and one intermediate sheet pile.

For U/S Pile Line

Total Length of Floor b 36.442 m

Depth of U/S Pile Line d 4.000 m

9.111

(1+SQRT(1+9.111^2))/2

5.083

1/3.14*ACOS((5.083‐2)/5.083)

0.293 i.e. 29.26%

0.707 i.e. 70.74%

1/3.14*ACOS((5.083‐1)/5.083)

0.203 i.e. 20.31%

where

where

b

d

11 2cosE

21 1

2

E

1C 1100C E

11 1cosD

21 1

2

D

0.797 i.e. 79.69%

For Intermediate Pile Line

Depth of Intermediate Pile Line d 4.000 m

Floor Length U/S of Pile b1 4.596 m

Floor Length D/S of Pile b2 31.846 m

1.149 7.962

4.774 ‐3.250

1/3.14*ACOS((‐3.250‐1)/4.774)

0 850 i e 84 96%

D1D 1

100D D

11

b

d 2

2

b

d

2 21 21 1

2

2 21 2

1

1 1

2

2

1 11 1cosE E

2

1 11 1cosC C

2

1 11cosD D

1 2

1

2E 0.850 i.e. 84.96%

1/3.14*ACOS((‐3.250+1)/4.774)

0.656 i.e. 65.63%

1/3.14*ACOS((‐3.250)/4.774)

0.738 i.e. 73.84%

For D/S Pile Line

Total Length of Floor b 36.442 m

Depth of D/S Pile Line d 5.000 m

7.288

(1+SQRT(1+7.288^2))/2

4.178

1/3.14*ACOS((4.178‐2)/4.178)

0.325 i.e. 32.54%

where

where

2

2C

2D

b

d

3

11 2cosE

21 1

2

3E

3

11 1cosD

21 1

2

1/3.14*ACOS((4.178‐1)/4.178)

0.225 i.e. 22.49%

CORRECTIONS FOR φC1

a). Correction at C1 for Mutual Inteference of Piles

Depth of Pile No. 2 D 3.000 m

Depth of Pile No. 1 d 3.000 m

Total Floor Length b 36.442 m

Distance Between Piles b' 4.096 m

Correction 19*SQRT(3.000/4.096)*((3.000+3.000)/36.442)

Correction 2.677 i.e. 2.68% +ve

Since the point C1 is in the rear in the direction of flow, the correction is +ve.

b). Correction at C1 Due to Thickness of Floor

Correction ((79.69%‐70.74%)/(203.870‐199.870))*1.00

2

3D

19'

D d DCorrection

b b


c). Correction Due to Slope at C1

Correction at C1 due to slope is nil, as this point is neither situated at the start nor

at the end of a slope.

Therefore Corrected φC1 75.66%

CORRECTIONS FOR φE2

a). Correction at E2 for Sheet Pile Lines

Since E2 is in the forward direction of flow as compared to Pile no. 1 therefore the

correction will be ‐ve.

Correction 2.677 i.e. 2.68% ‐ve

b). Correction at E2 Due to Thickness of Floor

Correction ((84.96%‐73.84%)/(203.870‐199.870))*1.00


c). Correction Due to Slope at E2

Correction at E2 due to slope is nil, as this point is neither situated at the start nor


Therefore Corrected φE2 79.50%

CORRECTIONS FOR φC2

a). Correction at C2 for Mutual Inteference of Piles

Since C2 is in the back direction of flow as compared to Pile no. 3 therefore the

correction will be +ve.





Correction 19*SQRT(4.000/31.846)*((3.000+4.000)/36.442)


b). Correction at C2 Due to Thickness of Floor

19'

D d DCorrection

b b

Correction ((84.96%‐73.84%)/(203.870‐199.870))*1.00


c). Correction Due to Slope at C2

Since the point c2 is situated at the start of a slope of 1 v : 2 h, i.e. an up slope in the

direction of flow; the correction is ‐ve.

Correction Factor for 2:1 Slope 6.50

Horizontal Length of Slope 2.359 m

Correction 6.50*(2.359/31.846)


Therefore Corrected φC2 69.22%

CORRECTIONS FOR φE3

a). Correction at E3 for Sheet Pile Lines

Since E2 is in the forward direction of flow as compared to Pile no. 1 therefore the

correction will be ‐ve.





Correction 19*SQRT(1.000/31.846)*((3.800+1.000)/36.442)


b). Correction at E3 Due to Thickness of Floor

Correction ((32.54%‐22.49%)/(200.821‐195.821))*1.20


c). Correction Due to Slope at E3

Correction at E2 due to slope is nil, as this point is neither situated at the start nor


Therefore Corrected φE3 29.69%

19'

D d DCorrection

b b

EXIT GRADIENT

Maximum Seepage Head Hmax 6.037 m

Depth of D/S Pile d 5.000 m


7.288

0.165

Exit Gradient GE 0.199 or 1 / 5.03

CHECK: GE ≤ 0.2 O.K.

SUB‐SURFACE H.G.L.

(m asl)Height / Elevation of Sub‐Soil H.G.Line above Datum

HGL

max

/

1.E

d s

HG

d

1

φC3 0.00% 0.000

φD3 22.49% 0.770

φE3 29.69% 1.017

φC2 69.22% 2.370

φD2 73.84% 2.529

φE2 79.50% 2.722

φC1 75.66% 2.591

φD1 79.69% 2.729

φE1 100.00% 3.424

(m) 3.424

(m asl) 203.433

(m asl) 206.857

FSL u/s and no flow d/s

FLOOR THICKNESS (By Sub‐Surface Flow Analysis‐STATIC CONDITIONS)

U/S Fl Thi k

204.450

205.803

205.962

206.156

206.024

Head

D/S Water Level

U/S Water Level

Flow Condition

U/S Pile Line

Intermediate Pile Line

D/S Pile Line

206.857

206.162

203.433

204.203

U/S Floor Thickness

U/S Residual Uplift Pressure

" " " " PC1 75.66%*2.987

U/S Residual Uplift Pressure PC1 2.260 m

U/S Floor Thickness (required)

" " " " tu/s 2.260/1.24

U/S Floor Thickness (required) tu/s 1.823 m

Provide tu/s 1.900 m

D/S Floor Thickness

D/S Residual Uplift Pressure

" " " " PE3 29.69%*2.987

D/S Residual Uplift Pressure PE3 0.887 m

D/S Floor Thickness (at end) (required)

" " " " tend 0.887/1.24

1 1 /.C C u sP Corrected Y

1

/ 1C

u s

Pt

G

3 3 /.E E u sP Corrected Y

3

1E

end

Pt

G

D/S Floor Thickness (required) tend 0.715 m

Provide tend 0.800 m

Floor Thickness at Pile No.2

Residual Pressure

" " " " PE2 79.50%*2.987

Residual Pressure PE2 2.375 m

Floor Thickness at Pile No.2 (required)

" " " " t2 2.375/1.24

Floor Thickness at Pile No.2 t2 1.915 m (required)

Provide t2 2.000 m

FLOOR THICKNESS (By Surface Flow Analysis‐DYNAMIC CONDITIONS)

2 2 /.E E u sP Corrected Y

2

2 1EP

tG

Unbalanced Head = HGL ‐ WSP

Floor Thickness = Unbalanced Head x 2/3 x 1/1.24

Location Distance HGL WSP UnbalancedThickness

(m) (m asl) (m asl) (m) (m)

End of Crest 8.255 206.082 206.382 ‐0.300

12.299 205.702 204.992 0.710 0.382

16.344 205.322 202.673 2.648 1.424

Start of Jump 20.388 204.942 199.977 4.964 2.669

Toe of D/S Glacis 20.942 204.890 200.847 4.043 2.174

24.042 204.598 201.679 2.919 1.570

27.142 204.307 202.261 2.046 1.100

30.242 204.016 202.757 1.259 0.677

33.342 203.724 203.160 0.564 0.303

End of Concrete Floor 36.442 203.433 203.433 0.000

Therefore;

Maximum Floor Thickness 2.700 m(at toe of D/S Glacis)

U/S Floor Thickness 2.000 m

Thickness at End of Floor 0.800 m

Deg Outfall Spillway Design

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