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Barrage
& its hydraulic design
By: Vishal
Roll no.1130456
 CONTENTS
 INTRODUCTION
 OBJECTIVE
 LITERATURE REVIEW
 HYDRAULIC DESIGN
 CONCLUSION
 REFERENCES
INTRODUCTION
What is Barrage :
A barrage is a type of low-head, diversion dam which
consists of a number of large gates that can be opened
or closed to control the amount of water passing through
the structure, and thus regulate and stabilize river water
elevation upstream for use in irrigation and other
systems.
PRAKASAM BARRAGE (VIJAYWADA, AP )
LITERATURE REVIEW
 Historically, the first scientific attempt to study the science of subsoil hydraulics in
relation to the design of weirs on permeable foundations was made as early as
1895, in connection with the failure of Khanki Weir, in India. These historic
experiments were carried out by Lt. Col. Clibborn, Principal of Thomson Civil
Engineering College, Roorkee, during 1895–97. Because of these experiments, the
flow of water through the subsoil below the weir/barrage with its attendant
hydraulic gradients and uplift pressures has been recognized as the determining
factor in the design of the barrage (Government of India 1902). Until 1930, Bligh’s
Creep theory, which was no more than an imperfect adaptation of Col. Clibborn’s
work, held the field. It was realized eventually that the subject was more complex
than simple formula indicated. The years 1929 to 1935 were marked by special
activity with respect to subsoil hydraulics in relation to weir design, both in India,
the United States of America, Europe, and elsewhere and also various study
conducted on barrages by Parsons 1929; Terzaghi 1929; Khosla 1930; Khosla 1932;
Haigh 1935; Harza 1935; Lane 1935.
OBJECTIVES
 1.THE SUB-SURFACE CONSIDERATION FOR THE DESIGN
OF A BARRAGE
 2. STEPS FOR COMPUTING SEEPAGE PRESSURE, SEEPAGE
FORCE AND EXIT GRADIENT FOR A BARRAGE
 3. DETERMINATION OF WATERWAY OF A BARRAGE
 4. DIFFERENT PROTECTION WORKS FOR A BARRAGE
DESIGN OF BARRAGE
 THE DESIGN OF ANY HYDRAULIC STRUCTURE COMPRISES OF TWO
STEPS:
 • HYDRAULIC DESIGN, TO FIX THE OVERALL DIMENSIONS AND
PROFILES OF THE STRUCTURE ( DIMENSIONS ARE USUALLY FIXED
BY EMPIRICAL FORMULAE)
 • STRUCTURAL DESIGN, WHERE THE VARIOUS SECTIONS ARE
ANALYSED FOR STRESSES UNDER DIFFERENT LOADS AND
REINFORCEMENT OR OTHER STRUCTURAL DETAILS ARE WORKED
OUT.
 For barrages, there are two different sets of hydraulic
conditions exist :
 1. The first is due to sub-surface or seepage flow
conditions that occurs due to a water level difference
on the upstream and down stream of a barrage and it
is the maximum when the gates of a barrage are
mostly closed as during the low flow period of the
river.
 2. The other is due to surface flow conditions which
occur while the barrage gates are open during floods.
 Hydraulics of sub-surface flow
 The sub-surface flow below a barrage causes two definite
instability problems, as listed below and illustrated in Figure 1.
 1. Uplift forces due to the sub soil pressure that tends to lift
up the barrage raft floor, and
 2.Upward rising seepage forces through the river bed just
down stream of the solid apron causes sand particles to erupt
upwards and tends to ‘piping’ failure of the foundation.
 As seen from Figure 3, the distribution of sub-surface pressure, that is, the
pressure of the water held within the pores of the soil is such that it varies
from a maximum along the upstream river bed to a minimum at the
downstream river bed.
 The pressure head differential between the upstream and downstream is
expressed as a percentage and denoted by φ. A comparison of pressure
distribution below the barrage floor from Figs. 3(a) and 3(b) indicate that
the introduction of sheet piles reduce the pressure below the barrage raft
floor. In fact, the seepage paths increase due to the introduction of sheet
piles, consequently reducing the gradient of sub-surface pressure.
The pressure at any location of a certain
equipotential line is given by the following
expression
 Hu is the head of water on the upstream pool
above datum
 HD is the head of tail water above datum.
ESTIMATION OF SEEPAGE DISCHARGE
Total seepage flow q is:
 q = Nf .Δq
 Δq m3/s per metre width, discharge between two
stream line per meter
 Nf is the no of flow channels
 The quantity Δq is governed by Darcy’s law
 Δq = k (Δh/ Δ s) Δ n
 k is the coefficient of permeability
 Δh is the potential drop between two equipotential lines
 Δs is the potential length along the stream line of flow net
‘square’ and Δn is the length normal to the stream line and
pressures the other length of the ‘square’.
 Δs = Δn
 Δh = Hdiff / Nd
 q = Nf k Hdiff / Nd
 Hdiff is the head difference between upstream pool
and downstream tail water level
 Nd is the number of equipotential drops between the
the upstream and the downstream river bed.
SEEPAGE FORCE
 An expression for the seepage force ΔF acting on the cylindrical
elementary volume may be expressed as:
 ΔF = p. ΔA - (p + Δp).ΔA
 This expression yields
 ΔF = -Δp. ΔA
 Thus, the seepage force per unit volume of soil is given as:
 ΔF / (ΔA.Δl) = -Δp /Δl =-ρ g.ΔH/Δl
 At the exit end, where the stream line meets the river
bed surface (B in Figure 5), the seepage force is
directed vertically upwards and against the weight of
the volume of solid held in the soil. If the seepage
force is great enough, it would cause sand-boiling,
with the ejection of sand particles causing creation of
pipe-like voids through the river bed
 In order to provide safety against piping-failure at the exit
end, the submerged weight (w) of the solid should be at least
equal to the seepage force. This may be expressed as:
 w = (1-e)(ρs-ρ) g≥-ρg ΔH/Δl
 w is the submerged weight of the solids assuming a void ratio
ratio e. ρs and ρ stand for the density of the solids and water
 The equation then simplifies to
 -ΔH/Δl ≤(1-e) (G-1)
EXIT GRADIENT AT THE END OF IMPERVIOUS
FLOOR.
 FACTOR OF SAFETY FOR DIFFERENT TYPES OF SOILS SHALL BE AS FOLLOWS
 COARSE SAND : 5 TO 6
 FINE SAND : 6 TO 7
 GE = {H/d} X [1/π√]
  = (1 + √1+ 2 )/2
  = b/d
 b = LENGTH OF BARRAGE
 d = DEPTH OF DOWN STREAM CUT OFF
 H = HEAD OF WATER
 THE DEPTH OF D/S CUT OFF ALONG WITH THE TOTAL LENGTH OF IMPERVIOUS FLOOR
SHOULD BE SUFFICIENT TO REDUCE THE EXIT GRADIENT TO WITHIN SAFE LIMITS.
COMPUTATION OF DISCHARGE
 THE DISCHARGE SHALL BE OBTAINED FROM THE FOLLOWING FORMULA:
 Q = CLH3/2;
 WHERE
 Q = DISCHARGE IN CUMECS,
 C - COEFFICIENT OF DISCHARGE
 L = CLEAR WATERWAY OF THE BARRAGE IN M, AND
 H = TOTAL HEAD CAUSING THE FLOW IN M.
LENGTHOF WATERWAY
 LACEY’S WATERWAY IS GIVEN BY THE FOLLOWING
FORMULA:
 L = 4.83 √Q
WHERE Q = DESIGN FLOOD DISCHARGE IN CUMECS FOR 50
YEAR FREQUENCY FLOOD.
SCOUR DEPTH:
 SCOUR IS LIKELY TO OCCUR IN ERODIBLE SOILS SUCH
AS CLAY,SILT,SAND.
 THE DEPTH OF SCOUR MAY BE CALCULATED FROM THE
LACEY’S FORMULA WHICH IS AS FOLLOWS.
 AS PER Cl. 19.1 OF I.S:6966(PART I) -1989.
 R = 0.473 (Q/f)1/3
WHEN LOOSENESS FACTOR IS MORE THAN 1
 R = 1.35 (q2/f )1/3
 WHEN LOOSENESS FACTOR IS LESS THAN 1
Where
 R = DEPTH OF SCOUR BELOW THE HIGHEST FLOOD LEVEL
 Q= HIGH FLOOD DISCHSRGE IN THE RIVER IN CUMECS
 q = INTENSITY OF FLOOD DISCHARGE IN m3 per m width
 f = 1.76 (mr)1/2
 where mr is average particle size of soil grain
 EXTENT OF SCOUR IN A RIVER WITH ERODIBLE BED MATERIAL VARIES AT DIFFERENT
PLACES ALONG A BARRAGE. THE LIKELY EXTENT OF SCOUR AT VARIOUS POINTS ARE AS
FOLLOWS
• LOCATION RANGE MEAN
 U/S OF IMPERVIOUS FLOOR 1.25 TO 1.75 R 1.5 R
 D/S OF IMPERVIOUS FLOOR 1.75 TO 2.25 R 2.0 R
 WHERE R = DEPTH OF SCOUR
 IF THE CONCENTRATION FACTOR IS TAKEN INTO ACCOUNT IN FIXING DEPTH OF CUT
OFFS.
 THESE SHOULD BE SUITABLY EXTENDED IN TO THE BANKS ON BOTH SIDES UP TO AT
LEAST TWICE THE DEPTH
CUT OFFS
 The Cut offs can be provided in RCC, Steel Sheet pile or
 These are the barriers provided below the floor both on U/s
and D/s
 The main purpose is to increase the seepage path and also
prevent piping action below the floor.
 The depth of Sheet pile depends on the safety factor
for the design
 THE U/S AND D/S CUT OFFS SHOULD GENERALLY BE
PROVIDED TO CATER FOR SCOUR UPTO 1.0 R AND 1.25R
RESP.
 PROTECTION WORKS
 U/s block protection:
 PERVIOUS PROTECTION COMPRISING OF C.C. BLOCKS OF
ADEQUATE SIZE LAID OVER LOOSE STONE SHALL BE PROVIDED
JUST BEYOND THE U/S END OF THE IMPERVIOUS FLOOR.
 THE C.C. BLOCKS SHALL BE GENERALLY BE OF 1500 MM X 1500
MM X 900 MM SIZE.
 THE LENGTH OF U/S BLOCK PROTECTION SHALL BE EQUAL TO ‘D’.
D/S BLOCK PROTECTION:
 IT SHALL COMPRISE OF C.C.BLOCKS OF ADEQUATE SIZE LAID OVER
A SUITABLY DESIGNED INVERTED FILTER FOR THE GRADE OF
MATERIAL IN THE RIVER BED.
 THE C.C. BLOCKS SHALL GENERALLY NOT SMALLER THAN 1500 X
1500 X 900 MM SIZE TO BE LAID WITH GAPS OF 75 MM WIDTH,
PACKED WITH GRAVEL.
 THE LENGTH OF THE D/S BLOCK PROTECTION SHALL BE EQUAL TO
1.5 D
 The downstream block protection is laid on a graded inverted
filter designed to prevent the uplift of fine sand particles
upwards due to seepage forces. The filter should roughly
conform to the following design criteria.
 Where d15 and d85 represent grain sizes. dx is the size such that
x% of the soil grains are smaller than that particle size. Where
x may be 15 or 85 percent.
CONCLUSION
 Barrages are the most important diversion headworks which
are if appropriately designed will create lots of opportunities
in terms of irrigation, regulation, power projects. But there
seems to be a lot of uncertainties such as:
Non- homogeneity of the foundation soil, Difference in the packing
and pore space, Local intrusion of impervious material like clay
beds or very porous material, Faults and fissures in sub-soil
formation,
 So mere design on the basis of empirical formulae will not
lead us to effective design. Therefore it becomes necessary for
us to conduct model studies of structure before prototype
construction.
REFERENCES
 Khosla, A. N. (1930). ‘‘Stability of weirs and canal works: An application of the new
theory of hydraulic gradient.’’ Paper No. 140, Punjab Engineering Congress, Punjab,
India.
 Parsons, H. D. (1929). ‘‘Hydraulic uplift in previous soils.’’ Paper No.1713, Trans.
ASCE.
 Garg N.K. (2002). “Optimal Barrage Design based on Subsurface Flow
Considerations” Paper No.128, ASCE
 https://en.wikipedia.org/wiki/Barrage
 IS 6966: Part1 (1989) ‘Guidelines for Hydraulic Design of Barrages and Weirs: Part-1
Alluvial Reaches (First revision)’, pub. By Bureau of Indian Standards, Manak
Bhawan, New Delhi
 nptel.ac.in/courses/105105110/pdf/m4l02.pdf

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Design of barrages

  • 1. Barrage & its hydraulic design By: Vishal Roll no.1130456
  • 2.  CONTENTS  INTRODUCTION  OBJECTIVE  LITERATURE REVIEW  HYDRAULIC DESIGN  CONCLUSION  REFERENCES
  • 3. INTRODUCTION What is Barrage : A barrage is a type of low-head, diversion dam which consists of a number of large gates that can be opened or closed to control the amount of water passing through the structure, and thus regulate and stabilize river water elevation upstream for use in irrigation and other systems.
  • 5.
  • 6.
  • 7. LITERATURE REVIEW  Historically, the first scientific attempt to study the science of subsoil hydraulics in relation to the design of weirs on permeable foundations was made as early as 1895, in connection with the failure of Khanki Weir, in India. These historic experiments were carried out by Lt. Col. Clibborn, Principal of Thomson Civil Engineering College, Roorkee, during 1895–97. Because of these experiments, the flow of water through the subsoil below the weir/barrage with its attendant hydraulic gradients and uplift pressures has been recognized as the determining factor in the design of the barrage (Government of India 1902). Until 1930, Bligh’s Creep theory, which was no more than an imperfect adaptation of Col. Clibborn’s work, held the field. It was realized eventually that the subject was more complex than simple formula indicated. The years 1929 to 1935 were marked by special activity with respect to subsoil hydraulics in relation to weir design, both in India, the United States of America, Europe, and elsewhere and also various study conducted on barrages by Parsons 1929; Terzaghi 1929; Khosla 1930; Khosla 1932; Haigh 1935; Harza 1935; Lane 1935.
  • 8. OBJECTIVES  1.THE SUB-SURFACE CONSIDERATION FOR THE DESIGN OF A BARRAGE  2. STEPS FOR COMPUTING SEEPAGE PRESSURE, SEEPAGE FORCE AND EXIT GRADIENT FOR A BARRAGE  3. DETERMINATION OF WATERWAY OF A BARRAGE  4. DIFFERENT PROTECTION WORKS FOR A BARRAGE
  • 9. DESIGN OF BARRAGE  THE DESIGN OF ANY HYDRAULIC STRUCTURE COMPRISES OF TWO STEPS:  • HYDRAULIC DESIGN, TO FIX THE OVERALL DIMENSIONS AND PROFILES OF THE STRUCTURE ( DIMENSIONS ARE USUALLY FIXED BY EMPIRICAL FORMULAE)  • STRUCTURAL DESIGN, WHERE THE VARIOUS SECTIONS ARE ANALYSED FOR STRESSES UNDER DIFFERENT LOADS AND REINFORCEMENT OR OTHER STRUCTURAL DETAILS ARE WORKED OUT.
  • 10.  For barrages, there are two different sets of hydraulic conditions exist :  1. The first is due to sub-surface or seepage flow conditions that occurs due to a water level difference on the upstream and down stream of a barrage and it is the maximum when the gates of a barrage are mostly closed as during the low flow period of the river.  2. The other is due to surface flow conditions which occur while the barrage gates are open during floods.
  • 11.  Hydraulics of sub-surface flow  The sub-surface flow below a barrage causes two definite instability problems, as listed below and illustrated in Figure 1.  1. Uplift forces due to the sub soil pressure that tends to lift up the barrage raft floor, and  2.Upward rising seepage forces through the river bed just down stream of the solid apron causes sand particles to erupt upwards and tends to ‘piping’ failure of the foundation.
  • 12.
  • 13.
  • 14.
  • 15.  As seen from Figure 3, the distribution of sub-surface pressure, that is, the pressure of the water held within the pores of the soil is such that it varies from a maximum along the upstream river bed to a minimum at the downstream river bed.  The pressure head differential between the upstream and downstream is expressed as a percentage and denoted by φ. A comparison of pressure distribution below the barrage floor from Figs. 3(a) and 3(b) indicate that the introduction of sheet piles reduce the pressure below the barrage raft floor. In fact, the seepage paths increase due to the introduction of sheet piles, consequently reducing the gradient of sub-surface pressure.
  • 16.
  • 17. The pressure at any location of a certain equipotential line is given by the following expression  Hu is the head of water on the upstream pool above datum  HD is the head of tail water above datum.
  • 18.
  • 19. ESTIMATION OF SEEPAGE DISCHARGE Total seepage flow q is:  q = Nf .Δq  Δq m3/s per metre width, discharge between two stream line per meter  Nf is the no of flow channels
  • 20.  The quantity Δq is governed by Darcy’s law  Δq = k (Δh/ Δ s) Δ n  k is the coefficient of permeability  Δh is the potential drop between two equipotential lines  Δs is the potential length along the stream line of flow net ‘square’ and Δn is the length normal to the stream line and pressures the other length of the ‘square’.
  • 21.  Δs = Δn  Δh = Hdiff / Nd  q = Nf k Hdiff / Nd  Hdiff is the head difference between upstream pool and downstream tail water level  Nd is the number of equipotential drops between the the upstream and the downstream river bed.
  • 22.
  • 23. SEEPAGE FORCE  An expression for the seepage force ΔF acting on the cylindrical elementary volume may be expressed as:  ΔF = p. ΔA - (p + Δp).ΔA  This expression yields  ΔF = -Δp. ΔA  Thus, the seepage force per unit volume of soil is given as:  ΔF / (ΔA.Δl) = -Δp /Δl =-ρ g.ΔH/Δl
  • 24.  At the exit end, where the stream line meets the river bed surface (B in Figure 5), the seepage force is directed vertically upwards and against the weight of the volume of solid held in the soil. If the seepage force is great enough, it would cause sand-boiling, with the ejection of sand particles causing creation of pipe-like voids through the river bed
  • 25.  In order to provide safety against piping-failure at the exit end, the submerged weight (w) of the solid should be at least equal to the seepage force. This may be expressed as:  w = (1-e)(ρs-ρ) g≥-ρg ΔH/Δl  w is the submerged weight of the solids assuming a void ratio ratio e. ρs and ρ stand for the density of the solids and water  The equation then simplifies to  -ΔH/Δl ≤(1-e) (G-1)
  • 26. EXIT GRADIENT AT THE END OF IMPERVIOUS FLOOR.  FACTOR OF SAFETY FOR DIFFERENT TYPES OF SOILS SHALL BE AS FOLLOWS  COARSE SAND : 5 TO 6  FINE SAND : 6 TO 7  GE = {H/d} X [1/π√]   = (1 + √1+ 2 )/2   = b/d  b = LENGTH OF BARRAGE  d = DEPTH OF DOWN STREAM CUT OFF  H = HEAD OF WATER  THE DEPTH OF D/S CUT OFF ALONG WITH THE TOTAL LENGTH OF IMPERVIOUS FLOOR SHOULD BE SUFFICIENT TO REDUCE THE EXIT GRADIENT TO WITHIN SAFE LIMITS.
  • 27. COMPUTATION OF DISCHARGE  THE DISCHARGE SHALL BE OBTAINED FROM THE FOLLOWING FORMULA:  Q = CLH3/2;  WHERE  Q = DISCHARGE IN CUMECS,  C - COEFFICIENT OF DISCHARGE  L = CLEAR WATERWAY OF THE BARRAGE IN M, AND  H = TOTAL HEAD CAUSING THE FLOW IN M.
  • 28.
  • 29.
  • 30. LENGTHOF WATERWAY  LACEY’S WATERWAY IS GIVEN BY THE FOLLOWING FORMULA:  L = 4.83 √Q WHERE Q = DESIGN FLOOD DISCHARGE IN CUMECS FOR 50 YEAR FREQUENCY FLOOD.
  • 31. SCOUR DEPTH:  SCOUR IS LIKELY TO OCCUR IN ERODIBLE SOILS SUCH AS CLAY,SILT,SAND.  THE DEPTH OF SCOUR MAY BE CALCULATED FROM THE LACEY’S FORMULA WHICH IS AS FOLLOWS.  AS PER Cl. 19.1 OF I.S:6966(PART I) -1989.  R = 0.473 (Q/f)1/3 WHEN LOOSENESS FACTOR IS MORE THAN 1
  • 32.  R = 1.35 (q2/f )1/3  WHEN LOOSENESS FACTOR IS LESS THAN 1 Where  R = DEPTH OF SCOUR BELOW THE HIGHEST FLOOD LEVEL  Q= HIGH FLOOD DISCHSRGE IN THE RIVER IN CUMECS  q = INTENSITY OF FLOOD DISCHARGE IN m3 per m width  f = 1.76 (mr)1/2  where mr is average particle size of soil grain
  • 33.  EXTENT OF SCOUR IN A RIVER WITH ERODIBLE BED MATERIAL VARIES AT DIFFERENT PLACES ALONG A BARRAGE. THE LIKELY EXTENT OF SCOUR AT VARIOUS POINTS ARE AS FOLLOWS • LOCATION RANGE MEAN  U/S OF IMPERVIOUS FLOOR 1.25 TO 1.75 R 1.5 R  D/S OF IMPERVIOUS FLOOR 1.75 TO 2.25 R 2.0 R  WHERE R = DEPTH OF SCOUR  IF THE CONCENTRATION FACTOR IS TAKEN INTO ACCOUNT IN FIXING DEPTH OF CUT OFFS.  THESE SHOULD BE SUITABLY EXTENDED IN TO THE BANKS ON BOTH SIDES UP TO AT LEAST TWICE THE DEPTH
  • 34. CUT OFFS  The Cut offs can be provided in RCC, Steel Sheet pile or  These are the barriers provided below the floor both on U/s and D/s  The main purpose is to increase the seepage path and also prevent piping action below the floor.  The depth of Sheet pile depends on the safety factor for the design  THE U/S AND D/S CUT OFFS SHOULD GENERALLY BE PROVIDED TO CATER FOR SCOUR UPTO 1.0 R AND 1.25R RESP.
  • 35.  PROTECTION WORKS  U/s block protection:  PERVIOUS PROTECTION COMPRISING OF C.C. BLOCKS OF ADEQUATE SIZE LAID OVER LOOSE STONE SHALL BE PROVIDED JUST BEYOND THE U/S END OF THE IMPERVIOUS FLOOR.  THE C.C. BLOCKS SHALL BE GENERALLY BE OF 1500 MM X 1500 MM X 900 MM SIZE.  THE LENGTH OF U/S BLOCK PROTECTION SHALL BE EQUAL TO ‘D’.
  • 36.
  • 37. D/S BLOCK PROTECTION:  IT SHALL COMPRISE OF C.C.BLOCKS OF ADEQUATE SIZE LAID OVER A SUITABLY DESIGNED INVERTED FILTER FOR THE GRADE OF MATERIAL IN THE RIVER BED.  THE C.C. BLOCKS SHALL GENERALLY NOT SMALLER THAN 1500 X 1500 X 900 MM SIZE TO BE LAID WITH GAPS OF 75 MM WIDTH, PACKED WITH GRAVEL.  THE LENGTH OF THE D/S BLOCK PROTECTION SHALL BE EQUAL TO 1.5 D
  • 38.  The downstream block protection is laid on a graded inverted filter designed to prevent the uplift of fine sand particles upwards due to seepage forces. The filter should roughly conform to the following design criteria.  Where d15 and d85 represent grain sizes. dx is the size such that x% of the soil grains are smaller than that particle size. Where x may be 15 or 85 percent.
  • 39.
  • 40. CONCLUSION  Barrages are the most important diversion headworks which are if appropriately designed will create lots of opportunities in terms of irrigation, regulation, power projects. But there seems to be a lot of uncertainties such as: Non- homogeneity of the foundation soil, Difference in the packing and pore space, Local intrusion of impervious material like clay beds or very porous material, Faults and fissures in sub-soil formation,  So mere design on the basis of empirical formulae will not lead us to effective design. Therefore it becomes necessary for us to conduct model studies of structure before prototype construction.
  • 41. REFERENCES  Khosla, A. N. (1930). ‘‘Stability of weirs and canal works: An application of the new theory of hydraulic gradient.’’ Paper No. 140, Punjab Engineering Congress, Punjab, India.  Parsons, H. D. (1929). ‘‘Hydraulic uplift in previous soils.’’ Paper No.1713, Trans. ASCE.  Garg N.K. (2002). “Optimal Barrage Design based on Subsurface Flow Considerations” Paper No.128, ASCE  https://en.wikipedia.org/wiki/Barrage  IS 6966: Part1 (1989) ‘Guidelines for Hydraulic Design of Barrages and Weirs: Part-1 Alluvial Reaches (First revision)’, pub. By Bureau of Indian Standards, Manak Bhawan, New Delhi  nptel.ac.in/courses/105105110/pdf/m4l02.pdf