Alphabet Weirs: From Grade Control over Fish Migration · PDF fileAlphabet Weirs: From Grade Control over Fish Migration to Scour Control MASTER THESIS 747_08 WL Rapporten

Alphabet Weirs: From Grade Control over Fish Migration to Scour Control

MASTER THESIS

WL Rapporten747_08

FORM: F-WL-PP10-2 Version 02 VALID AS FROM: 17/04/2009

MASTER THESIS

TANVIR AHMED

Academic Tutor: Dr. – Ing. habil. F. Molkenthin, BTU Cottbus

Institutional Tutor: Patrik Peeters, Flanders Hydraulics Research

Time period: March to August, 2011

15 August, 2011

Alphabet Weirs: From Grade Control over Fish Migration to Scour Control


This publication must be cited as follows:

Ahmed, T. (2011). Alphabet weirs: From grade control over fish migration to scour control. A report submitted in partial fulfillment of the requirements for the MSc study program entitled: EuroAquae Hydroinformatics and Water Management. Version 2.0. WL Rapporten, 747_08. Flanders Hydraulics Research: Antwerp, Belgium

Waterbouwkundig Laboratorium

Flanders Hydraulics Research

Berchemlei 115

B-2140 Antwerp

Tel. +32 (0)3 224 60 35

Fax +32 (0)3 224 60 36

E-mail: [email protected]

www.watlab.be



Abstract

This research is based on details literature study both on common and special shape of weirs with the guidelines on how to model these weirs within the hydrodynamic software package MIKE 11 developed by DHI Water and Environment.

Weirs are hydraulic structures which act as a barrier across the direction of flow for the purposes of measuring flow, increase upstream water head, flow diversion, protect river banks, reduce erosive energy and allow for fish passage, grade control, river rehabilitation and restoration etc. The shapes vary from rectangular horizontal weirs over V-notch, oblique, ogee, curved, labyrinth & piano key weirs to alphabet weirs.

In-stream rock weirs of alphabet shape (U, A and W shape) are now being famous because of their interesting shapes and functionality. The traditional concrete structures are expensive, resulting in poor fish habitat and less naturally accepted which lead to the development of U-, A- and W-weir. Alphabet weirs can be used to establish grade control, reduce stream bank erosion, energy dissipation, increase aquatic habitat etc.

The in-stream rock weirs of alphabet shape are not a very old concept and the design and guidelines of these structures are not based on the physical process. More experimental study is required and qualitative field investigation should incorporate with numerical model with wide range of scenario to better understand the physics for proper design of alphabet weirs.

Accuracy of MIKE 11 to calculate upstream flow depth in rectangular channel is evaluated by incorporating broad-crested weir and alphabet weirs. These simulations were performed only for free flow condition. Laboratory experiments data used to model these weirs. The analytical outcomes following the weir equations derived for broad-crested weirs and alphabet weirs are compared with results obtained with MIKE 11 using the Broad Crested Weir option as well as Weir Formula 2. For both the weirs, MIKE11 gives good agreement while comparing with analytical results and the observed data.

Weirs of different shapes can possible to model in MIKE 11 if stage-discharge expressions are well determined with a weir coefficient.


Acknowledgements

All praises are due to the Almighty Allah Who has provided me with the opportunity to complete this research.

This project could have never been completed without the encouragement and valuable help of some important personalities. I wish to express my heartfelt and sincere gratitude to my institutional supervisor Mr. Patrik Peeters, who gave me the opportunity to work in Flanders Hydraulic Research as an intern to complete my master thesis. Mr. Patrik spent much time on reviewing the chapters of this thesis and offering direction and assistance throughout all phases of this research project.

I would like to have some special words to my academic tutor Dr.- Ing. Habil. Frank Molkenthin, BTU Cottbus for his constructive suggestions about the fourth semester research project.

I also want to give thanks to Dr. Christopher Thornton from Colorado State University, who provided the valuable resources regarding the topic.

A very special thank to my wife who accompanying me throughout the research and graduation program and give me moral support. Finally a big thank goes to my parent for their encouragement.


Preface

This thesis has been submitted in partial fulfillment of the requirements for the MSc study program entitled: EuroAquae Hydroinformatics and Water Management. The program is sponsored by the European Commission and consists of three course based semesters at a combination of the following participating universities:

Newcastle University (Newcastle Upon Tyne, UK) Budapest University of Technology and Economics (Budapest, Hungary) Brandenburg University of Technology (Cottbus, Germany) University of Nice - Sophia Antipolis (Nice, France) Technical University of Catalonia (Barcelona, Spain)

The fourth and final semester involves a research thesis and was carried out by the author of this report, Tanvir Ahmed, at the Flanders Hydraulics Research located in Antwerp, Belgium.

Alphabet Weirs: From grade control over fish migration to scour control

Euroaquae Hydroinformatics and Water Management Flanders Hydraulics Research I


Contents

Abstract ............................................................................................................................................. IV

Acknowledgements ............................................................................................................................ V

Preface .............................................................................................................................................. VI

Contents .............................................................................................................................................. I

List of tables ...................................................................................................................................... III

List of figures ..................................................................................................................................... IV

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

2 Weir Flow ..................................................................................................................................... 4

2.1 Free weir flow .................................................................................................................................. 4

2.1.1 Discharge over weir ................................................................................................................... 7

2.1.2 Energy dissipation by hydraulic jump ......................................................................................... 9

2.2 Free flow versus drowned or submerged flow ................................................................................ 9

2.3 Stage-Discharge Expression ........................................................................................................ 10

2.3.1 Free Flow conditions ................................................................................................................ 10

2.3.2 Submerged Flow conditions ..................................................................................................... 11

2.3.3 Side weir flow conditions .......................................................................................................... 11

3 Common weir types ................................................................................................................... 13

3.1 Standard Broad-Crested Weir....................................................................................................... 13

3.2 Standard Sharp-Crested Weir....................................................................................................... 17

3.3 V-Notch Weir ................................................................................................................................. 20

3.3.1 Weir for Fish Passage Facility .................................................................................................. 25

3.4 Oblique weirs ................................................................................................................................ 26

3.5 Ogee weirs .................................................................................................................................... 29

4 Alphabet weirs ........................................................................................................................... 33

4.1 U-weir ............................................................................................................................................ 34

4.2 A-weir ............................................................................................................................................ 40

4.3 W-weir ........................................................................................................................................... 42

4.4 Field Investigation Results of Alphabet Weirs by Reclamation (2007) ......................................... 44


Euroaquae Hydroinformatics and Water Management Flanders Hydraulics Research II


4.4.1 Flow Pattern over Alphabet Weir .............................................................................................. 44

4.4.2 Sediment Deposition and Erosion Patterns .............................................................................. 45

4.4.3 Scour Pool Location and Dimension ........................................................................................ 45

4.4.4 Numerical Analysis of Rock Weirs by Johnson (2011) ............................................................. 45

4.5 Limitation of Alphabet weirs .......................................................................................................... 48

4.6 Stage-discharge Expression for Alphabet Weir ............................................................................ 48

5 Modelling Weir flow with mike 11 .............................................................................................. 53

5.1 Literature review for MIKE 11 Weir Flow Calculation .................................................................... 53

5.2 Selection of MIKE 11 Weir Type and Weir Equation .................................................................... 56

5.3 Development of Model .................................................................................................................. 57

5.3.1 Broad-crested weir ................................................................................................................... 57

5.3.1.1 Option 1: Broad-crested weir ..................................................................................... 58

5.3.1.2 Option 2: Weir Formula 2 (Honma) ............................................................................ 59

5.3.1.3 Result Analysis for Broad Crested Weir ..................................................................... 61

5.3.2 Alphabet Weir........................................................................................................................... 64

5.3.2.1 Result Analysis of Alphabet Weir ............................................................................... 69

6 Conclusion ................................................................................................................................. 73

7 List of references ....................................................................................................................... 75

8 Appendix .................................................................................................................................... 77

8.1 Notations ....................................................................................................................................... 77


Euroaquae Hydroinformatics and Water Management Flanders Hydraulics Research III


List of tables

Table 1: Cv for Values of CdLh/A .............................................................................................................. 15

Table 2: Cd for Square Edge upstream weir ............................................................................................. 15

Table 3: Cd for Round Edge upstream weir .............................................................................................. 16

Table 4: Cd equation developed by Govinda Rao and Muralidhar (1963) ................................................ 16

Table 5: Ce for sharp crested weir (Kindsvater and Carter) ..................................................................... 20

Table 6: Classification and limits of applications of V-notch sharp-crested weir ...................................... 22

Table 7: Input Data for Broad Crested Weir (Bos, 1989) ......................................................................... 58

Table 8: Analytically determined weir coefficient and upstream water level ............................................ 60

Table 9: Output of Analytical and Model Results for Broad-Crested Weir ............................................... 63

Table 10: Input Data for Alphabet Weir .................................................................................................... 65

Table 11: Analytically determined weir coefficient and upstream water level .......................................... 67

Table 12: Analytically composite weir coefficient and upstream water level ............................................ 68

Table 13: Model Results for Alphabet Weir .............................................................................................. 72


Euroaquae Hydroinformatics and Water Management Flanders Hydraulics Research IV


List of figures

Figure 1: Mildura weir, Murray River at north-western Victoria .................................................................. 1

Figure 2: V-notch weir ................................................................................................................................ 2

Figure 3: Labyrinth weir built on Ute dam, USA ......................................................................................... 2

Figure 4: U-shaped rock weir ..................................................................................................................... 3

Figure 5: Free weir flow .............................................................................................................................. 4

Figure 6: Flow over broad-crested weir under free flow condition ............................................................. 5

Figure 7: Hydraulic Jump forms downstream of the weir ........................................................................... 5

Figure 8: Energy of a fluid particle ............................................................................................................. 6

Figure 9: Specific energy diagram ............................................................................................................. 7

Figure 10: Hydraulic jump interpreted by specific energy .......................................................................... 7

Figure 11: Free flow (L) and submerged flow (R) in weir ......................................................................... 10

Figure 12: Schematic plan for side weirs ................................................................................................. 11

Figure 13: Dimension sketch of side weir (Cross section and Water surface profile) .............................. 12

Figure 14: Flow over broad crested weir .................................................................................................. 13

Figure 15: Broad-crested weir in the field ................................................................................................ 13

Figure 16: Cv values as a function of the area ratio α1CdA ∗ A ................................................................ 14

Figure 17: Cd for flat topped weir for different values of p*w .................................................................... 17

Figure 18: Flow over sharp crested weir .................................................................................................. 18

Figure 19: Sharp-crested weir in the field ................................................................................................ 18

Figure 20: Sharp crested rectangular weir ............................................................................................... 18

Figure 21: Kb for rectanguler sharp crested weir ..................................................................................... 20

Figure 22: V-notch sharp crested weir ..................................................................................................... 21

Figure 23: V-notch in the field .................................................................................................................. 21

Figure 24: Values of Kh for V-notch sharp-crested weir ........................................................................... 22

Figure 25: Ce for fully contracted V-notch weirs ....................................................................................... 23

Figure 26: Ce for partially contracted V-notch weirs ................................................................................. 23

Figure 27: V-shaped broad-crested weir .................................................................................................. 24

Figure 28: Cd – h/L relation for different notch angle of V-shaped broad-crested weir ............................ 25

Figure 29: δ/L – h/L relation for different notch angle of V-shaped broad-crested weir ........................... 25

Figure 30: Different views of V-notch fish passage .................................................................................. 26

Figure 31: Flow behaviour of oblique weir ............................................................................................... 27

Figure 32: Flow velocity vetor in oblique weir .......................................................................................... 28

Figure 33: Free flow over oblque weir ...................................................................................................... 28

Figure 34: Flow over submerged oblique weir ......................................................................................... 29

Figure 35: Outflow from a free-falling weir, properly ventilated from below ............................................. 30

Figure 36: Ogee Weir ............................................................................................................................... 30

Figure 37: Chart gives weir coefficient at design head HD for vertical-faced ogee-crested weirs. ........... 31

Figure 38: Chart gives discharge coefficients for vertical-faced ogee-crested weirs at heads Ht other than design head Hd ......................................................................................................................................... 31


Euroaquae Hydroinformatics and Water Management Flanders Hydraulics Research V


Figure 39: Instream Rock weir of Alphabet shape ................................................................................... 34

Figure 40: U-weir ...................................................................................................................................... 35

Figure 41: Cross-section, profile and plan view of U-weir (Rosgen 2001) ............................................... 36

Figure 42: U-weir and constructed bankfull bench ................................................................................... 37

Figure 43: U-weir: Flow is directed to maintain centre channel (blue line) ............................................... 37

Figure 44: Application of U-weir for bridge and channel stability ............................................................. 38

Figure 45: U-weir for step restoration (Rosgen 2001) .............................................................................. 38

Figure 46: Rock vane ............................................................................................................................... 39

Figure 47: J Hook: Constructed on the right bank, directs flow to centre of the channel and reduce bank

erosion ...................................................................................................................................................... 39

Figure 48: Plan, profile and section view of J-Hook vane ........................................................................ 40

Figure 49: Cross-section, profile and plan view of A-weir (Rosgen 2006) ............................................... 41

Figure 50: A-weir ...................................................................................................................................... 42

Figure 51: Cross-section, plan and profile view of W-weir ....................................................................... 43

Figure 52: W-weir ..................................................................................................................................... 43

Figure 53: Free (L) and Submerge (R) flow over rock weir ...................................................................... 44

Figure 54: Lemhi River: before failure (L) and after right arm failure (R) ................................................... 44

Figure 55: Longitudinal profile of sediment deposition and pool patterns ................................................ 45

Figure 56: Field Photo and Corresponding Numerical Modelling Results ................................................ 46

Figure 57: Modeled Water Surface Elevation .......................................................................................... 47

Figure 58: Plan View: Velocity Vectors and wetted Area ......................................................................... 47

Figure 59: Thalweg Profile View and Velocity Magnitude ........................................................................ 48

Figure 60: Scale model of U‐ L , A M and W‐weir R ............................................................................. 48

Figure 61: Scaled Alphabet weir under testing condition ......................................................................... 49

Figure 62: U‐weir geometry ....................................................................................................................... 49

Figure 63: A-weir geometry ...................................................................................................................... 50

Figure 64: W-weir Geometry .................................................................................................................... 51

Figure 65: The weir property page of MIKE 11 ........................................................................................ 54

Figure 66: Definition sketch of weir flow in MIKE 11 ................................................................................ 55

Figure 67: Weir Modelling, Type: Broad Crested Weir ............................................................................. 59

Figure 68: Weir Modelling, Type: Weir Formula 2 .................................................................................... 59

Figure 69: Longitudinal Profile of Water Surface Elevation ...................................................................... 61

Figure 70: Measure Vs Simulated Water Level (Option: Broad Crested Type) ....................................... 62

Figure 71: Measure Vs Simulated Water Level (Option: Weir Formula 2) ............................................... 62

Figure 72: Increasing Channel Width: Width 5 m (Top) and Width 20 m (Bottom) .................................. 64

Figure 73: Alphabet Weir Modelling by Weir Formula 2 (Honma) ............................................................ 66

Figure 74: Longitudinal Profile of Water Surface Elevation ...................................................................... 69

Figure 75: Observed Vs Simulated Water Level: a) U-weir b) A-weir and c) W-weir ............................... 70

Figure 76: Observed Vs Simulated Water Level by composite weir equation: a) U-weir b) A-weir and c) W-weir ...................................................................................................................................................... 71


EuroAquae Hydroinformatics and Water Management

Flanders Hydraulics Research 1


1 Introduction

Weirs are hydraulic structure which date back from the ancient time. Weirs structures are placed into a stream (river, small streams, irrigation canal etc) perpendicular to the flow direction and control the flow depth and discharge in some way. These structures act as a barrier, raise the water level and cause water to pool (retain) in the upstream, especially at low flows. Downstream of the structure, higher flow velocities can cause scour.

Weirs enhance diverse flow conditions and provide additional roughness to the stream, which reduces the energy loss rate of the river and reduces its erosive capacities (Meneghetti, 2009). Weirs are also applied to convey the flow away from the banks towards the centre of the river and so to decrease the velocity gradient adjacent to the bank (bank protection) (Rosgen, 2006). Also for diverting water into irrigation canals, weirs are often used. Other useful purposes of weirs are grade, sediment and scour control. To make it more environmental friendly weirs should have the facility of fish passage for safe migration of fishes.

Different types of weirs are being used depending on their purposes and can be differentiated according to their shape and type of materials used.

Figure 1 shows the Mildura weir located on the Murray River at Mildura in north-western Victoria, Australia which provides stable pool for diversion of water.

Figure 1: Mildura weir, Murray River at north‐western Victoria

Bos (1989) contains a detailed discussion of the well known broad-crested and sharp-crested weirs with their (straight lined) crests perpendicular to the flow direction. Both weirs types can serve particularly well for flow estimations based on a rating curve relating the flow discharge to the measured water level above the weir crest. In addition to a horizontal crest, V-notch as well as parabolic crest shapes among others are used. Another weir type especially designed for measuring flow discharges is the so-called crump weir. Figure 2 shows a V-notch weir, located in Espoo, southern Finland to measure runoff.

So-called oblique weir is placed obliquely to the flow resulting in an increase of effective length of the weir beyond the channel-width (Samani, 2010). Ogee or so-called horse-shoe weirs and labyrinth weirs (or a combination of both) as well as piano key weirs (PKW) serve the same purpose. Given a certain upstream water level and crest height, a higher discharge capacity is obtained, which is referred to as higher (weir) efficiency (Tuyen, 2006). The geometric features of the PKW make it an interesting solution for dam rehabilitation (Labyrinth, 2011). Figure 3 shows a labyrinth weir built on Ute dam in USA, which is able to discharge very high flow.





Figure 2: V‐notch weir

Figure 3: Labyrinth weir built on Ute dam, USA

In-stream rock weirs are becoming more and more important for river restoration and rehabilitation. These weirs can be A-, W-, J- or U-shaped and are often referred to as alphabet weir. In stream rock weirs can be used to establish grade control, reduce stream bank erosion, provide energy dissipation, increase aquatic habitat and allow fish passage (Thornton, 2011). Figure 4 shows a U-shaped rock weir, constructed in Frank Cocher Memorial Park, Pennsylvania, USA,





Figure 4: U‐shaped rock weir

In addition to in-stream weir applications, so-called side weirs are often installed as water intake structures. In the following chapter, a general introduction to weir flow is given. Next, standard broad-crested and sharp-crested weirs as well as V-notch, oblique and ogee weirs are briefly discussed. Following, alphabet weirs, their hydraulic performances and practical uses are covered in more detail. The report concludes with guidelines on how to model these weir structures within the hydrodynamic software package Mike 11.





2 Weir Flow

2.1 Free weir flow

When water flows over a weir, a transition occurs from subcritical (high water depth, low flow velocity) through critical to supercritical flow (low water depth, high flow velocity). The difference between the two states of flow can be understood by the effect of gravity. The ratio between inertial forces to gravity forces is known as the Froude number ( ⁄ ), where V is the mean flow velocity, g is the acceleration of gravity and D is the hydraulic depth. Hydraulic depth is defined as the cross-sectional area normal to the direction of flow in the channel divided by the width of the free surface. For rectangular channels this is equal to the depth of the flow section. If F<1, the flow is subcritical where the gravity forces dominate and the flow has low velocity. When F>1, the flow is super critical where inertia forces dominate and flow has high velocity. When the Froude number equals 1, the flow is termed as critical flow (Chow, 1959).

The phenomenon of flow changing from subcritical to supercritical is known as a hydraulic drop, where a rapid change of flow from high stage to low stage occurs and which is generally caused by abrupt change in channel slope or cross section. A reverse curve usually forms at the transitory region, connecting the water surface before and after the drop. The point of inflection of the reverse curve marks the approximate position of the critical depth at which the flow passes from subcritical to supercritical (Chow, 1959). Depending on the downstream condition a hydraulic jump is formed somewhere at the downstream side of the weir where the flow changes back from supercritical to subcritical. Hydraulic jump is a rapid change of flow from low stage to high stage. The specific energy before the jump is greater than the specific energy after the jump. So overall, a certain amount of energy is dissipated during hydraulic jump. Figure 5 and Figure 6 shows the different states of flow over a weir under free flow (Section 2.2) condition. Figure 7 shows the hydraulic jump forms downstream of a weir in the field condition.

Figure 5: Free weir flow





Figure 6: Flow over broad‐crested weir under free flow condition

Figure 7: Hydraulic Jump forms downstream of the weir

To understand the flow over weir and the energy dissipation due to hydraulic jump at the downstream part of the weir, the concept of Bernoulli’s equation and specific energy is important. The Bernoulli’s equation was obtained for a frictionless steady flow of incompressible fluid. It states that, along a streamline (Chanson, 1999),

V2g Z P

ρg Constant 1





Figure 8: Energy of a fluid particle

Where V, Z, P, ρ, g are the fluid velocity, altitude, pressure, density and the gravitational acceleration (Figure 8). The constant, right hand side of the equation [1] is expressed in meters and the total head in a streamline is defined as (Chanson, 1999):

H V 2g Z Pρg 2

The first term (V 2g) is known as the velocity head, the second term (Z) is known as the elevation head

and the last term (P ρg) is known as the pressure head. The second and third term together are often called the piezometric head (Chanson, 1999).

Specific energy is defined as the average energy per unit weight of water at a channel section as expressed with respect to channel bottom. Since the piezometric level coincides with the water surface, the piezometric head with respect to the channel bottom is given as (Bos, 1989):

Z Pρg h, the water depth 3

So, the specific energy head can be expressed as:

H h V2g 4

Where, H = Specific energy head, h = water depth and V = mean channel velocity. Equation [4] can be written as:

H hQ

2gA 5

Where, Q = total discharge and A = cross-sectional area of flow. For a given channel section and a constant discharge (Q), the specific energy (H) in an open channel section is a function of water depth (h) only. Plotting this water depth (h) against the specific energy (H) gives a specific energy curve as shown in Figure 9 (Bos, 1989).





Figure 9: Specific energy diagram

The curve shows that, for a given discharge and specific energy there are two ‘alternate’ depths of flow. One depth is for subcritical flow condition and another depth is for supercritical flow condition. At point C, the specific energy is a minimum for a given discharge and the two alternate depths coincide. This depth of flow is known as the critical depth of flow. For subcritical flow the depth of flow is greater than critical depth and for supercritical flow the depth of flow is less than the critical depth (Bos, 1989).

For flow over a weir, when the flow state changes from subcritical to supercritical with the occurrence of critical flow condition, it causes a small energy loss (Chanson, 1999). On the other hand, there is significant amount of energy loss, when the flow state changes from supercritical to subcritical by forming hydraulic jump (downstream of weir). The concept of specific energy for hydraulic jump due flow over downstream side of a weir is explained in (Figure 10). ∆H is the total energy dissipation due a hydraulic jump which is described briefly in Section 2.1.2.

Figure 10: Hydraulic jump interpreted by specific energy

2.1.1 Discharge over weir

If the weir is designed that there are no significant energy losses in the zone of acceleration upstream of





the control section and flow over the weir is critical; so according to Bernoulli’s equation while water is flowing from section 1 to 2, then (Figure 6):

H H 6

or

H H hV

2g 7

or

2g H h.

8

The flow over the channel is Q and Area of the rectangular control section is Ac, and,

L ∗ h 9

Where L is the width (across the direction of flow) of the control section (weir)

So,

Q A V 10

Or

Q A 2g H h.

11

Bos (1989) showed that, the critical depth hc can be expressed as:

h 23H 12

Finally Equation [11] can be shown as:

Q2

3

2

3g

.

LH . 13

In the above equation, the effect of head loss, viscosity, turbulence, the non-uniformity of flow due to curvature is not taken into consideration. But in reality these effects do occur and they must therefore be accounted for by the introduction of a discharge coefficient Cd. The Cd value depends on the shape and type of the weir (Bos 1989).

Q C2

3

2

3g

.

LH . 14

The above is equation is one of the forms of stage-discharge expression over a weir. In practice it is not possible to measure the energy head above the weir crest. So only water head, h above the weir crest is used by neglecting the energy head, H. Some investigators incorporated a correction coefficient Cv for neglecting the energy head, other don’t.

Bos (1989) mentions also an equation for sharp crested weirs following the principles of orifice flow (Equation [15]).

Q C2

32g . Lh . 15

This equation is used by many investigators for sharp crested as well as broad crested weirs replacing Ce by Cd. It is important to note that the power coefficient of ‘h’ is dependent on the type of the control section. For rectangular control section it is 1.5.





2.1.2 Energy dissipation by hydraulic jump

The transition from supercritical to subcritical flow, however, is characterized by a strong dissipative mechanism which is termed as hydraulic jump. The flow within the hydraulic jump is very complicated. It is characterized by large scale turbulence and hence, a very effective way for energy dissipation downstream of the weir. A hydraulic jump destroys much of the kinetic energy of the flow. The total energy loss (or the total head loss) due to hydraulic jump downstream of a weir (Flowing from section 3 to 4 in Figure 6) can be expressed by the following expression (Chanson, 1999):

H H ∆H 16

Where ∆H is the energy or head loss due to jump, and H1 and H2 are the upstream and downstream energy head of the jump respectively. Assuming hydrostatic pressure distribution and taking channel bed as a datum, by applying the Bernoulli equation, the above Equation [16] becomes:

V

2gh

V

2gh ∆H 17

V1 and h1 are the upstream velocity and water depth of the hydraulic jump and V2 and h2 are the downstream velocity and water depth of the jump which are described in the Figure 6.

Neglecting the drag force on the fluid, the continuity and momentum equations provide a relationship between the upstream and downstream flow depth as (Chanson, 1999):

h 2

2

218

Here, B is the channel width. In dimensionless term the above equation can be written as (Chanson, 1999):

h

h 1

21 8 1 19

Where Fr1 is the Froude number, upstream of the jump and as it is super critical condition, so Fr1>1. From the energy Equation [16] the head loss can be expressed as (Chanson, 1999):

∆4

20

Or in dimensionless term the energy loss can be written as (Chanson, 1999):

∆1 8 3

16 1 8 121

So, Equation [20] and [21] represent the energy dissipation due to hydraulic jump downstream of the weir.

2.2 Free flow versus drowned or submerged flow

Depending on the downstream water level, a weir can flow under free flow or submerged flow conditions. Free flow exists when the tail water level is at or below the crest level. On the other hand submerged weir flow exists when the tail water depth is above the crest level of the weir. In submergence flow, the difference between the downstream water level and the crest level is known as depth of submergence. For free flow the discharge is only dependent on the upstream water level of the weir and for submerged flow discharge is dependent on the upstream and in some extend also on the tail water level downstream of the weir. In practice, for depths of submergence equal or less than 0.7 times the critical depth, the flow is often considered as free flowing for calculating discharges while for greater levels of submergence the discharge





needs to be determined by considering both the upstream and tail water level (Goon, 1973). An advantage of submerged flow over a weir is that there is less energy loss (i.e. no free hydraulic jump or something like that) but higher head at both sides of the weir and discharge calculation is less easy (Borghei et al, 2003). Figure 11 shows free and submerged flow over a weir. The difference between upstream energy head (H) and the downstream energy head (Hd) is the available energy loss above the weir. The ratio between Hd and H is termed the submergence ratio above the weir.

Figure 11: Free flow L and submerged flow R in weir

When critical flow occurs at the control section of a weir, the upstream water level is independent of the tailwater level; then the flow over the weir is called modular. The fundamental condition for critical flow is that the available loss of head between the channel cross-sections where the upstream energy head, H and the downstream energy head, Hd are to be determined, is just sufficient to satisfy the requirement for critical flow to occur at the control section (Bos, 1989). According to Herchy (1995), in the simple and usual case where the downstream water level is below some limiting condition and where it does not affect the upstream head, there is a unique relation between head and discharge. This condition is termed as free flow or modular condition. On the other hand, if the tailwater level affects the flow, the weir is said to drowned or submerged and operated in the non-modular condition. For non-modular condition, an additional downstream measurement of head and a reduction factor is required to be applied to the modular or free flow discharge equation (see later). When the flow in the non-modular condition increases until the weir is almost or wholly submerged, the weir no longer performs as a discharge measuring device (Herschy, 1995)

2.3 Stage-Discharge Expression

2.3.1 Free Flow conditions

The (empirical or theoretical) relationship between the water surface stage (i.e. water depth) and corresponding flow discharge is termed as stage-discharge (stage-discharge) relation or rating curve or simply rating equation. Stage-discharge reliability and accuracy are dependent upon a structure placed in a stable section of the channel where a critical control depth may be maintained over a spectrum of discharges (Thornton, 2011). Many formulas have been developed to calculate discharges over weirs. For free flow conditions most of the formulas can be expressed in the following general form:

Q C L h . 22

Where Q(f) is the (free) flow discharge, C is the weir coefficient, L is the effective length of the weir crest across the direction of flow and h is the measured water level above the weir crest (Chow, 1959). The above equation can be seen as another form of equation [Section 2.1.1] in which the water head H is replaced by the water level h and a correction coefficient is added to account for this.

The accuracy of Equation [22] depends on the (empirical) determination of the weir coefficient which incorporates the relative depth and width of the approach channel and the roughness of the weir crest (Thornton, 2011) as well as other aspects like shape and orientation of the crest, weir size etc. It is important to note that the power coefficient of ‘h’ is dependent on the type of the control section. For rectangular control section it is 1.5.





2.3.2 Submerged Flow conditions

According to Chow (1959), submergence of a weir reduces its discharge capacity. In literature, different possibilities can be found to account for submerged flow conditions, e.g. Villemonte (1947) proposed the following expression

Q k 1 s . Q 23

Where, Qs= discharge for submerged flow, Qf= discharge for free flow, s = submergence ratio ( ⁄ ), hd and h are downstream and upstream water depth above the weir crest. The constant k and the exponent m, which account for the interaction effects, can be determined separately for each weir type.

The above formula can be expressed in the following general form:

Q R Q 24

Where, R is the reduction factor. Another possibility for determining submerge discharge is (MIKE 11 Reference Manual, 2007):

Q C L h p h h 25

Here, L= effective length of the weir, p = weir height. C2 is the second weir coefficient and calculated as:

C 32 √3C 26

C is the free flow weir coefficient, discussed in the previous section.

2.3.3 Side weir flow conditions

A side weir is a hydraulic structure which located in to a side channel to divert water from the main or parent channel when the water level in the main channel exceeds the specified limit. Water discharges freely over the side weir same as for conventional weirs. The main common function of side weir is to divert water from the main channel when the downstream flow capacity of the main channel being exceeded because of flood, storm water etc. In navigable canals side weir can be provided to maintain constant water level by means of discharging excess water. For the same purpose side weirs can be used in irrigation canal where side weirs provide a safety valve to prevent the canal banks being overtopped. Side weirs in irrigation canals can also be used where water is pumped from a main canal. The most common use of side weirs in UK is at combined sewer overflow where peaks flow is discharged in to the environment in a controlled manner (Richard, et al 2003). The schematic plan for side weir has shown in Figure 12.

Figure 12: Schematic plan for side weirs

Flow conditions in side weirs are more complex than the standard conventional weir. So it is not possible to obtain general stage-discharge equations like the weir which discussed previously. The flow behaviour of side weirs are as follows (Richard, et al 2003):





1. The flow is strongly three-dimensional with the weir tending to draw flow from the surface layers adjacent to the weir, while the remainder of the flow near the bed and along the opposite side of the channel is less strongly affected and continues within the onward channel.

2. Flow passing over the weir at oblique angle which is not constant. The higher the velocity, the oblique angle is more.

3. The water level in the parent channel is not constant which may vary depending on the flow condition of the channel. As a result the head in the side weir may vary with distance and causes a change in the rate of outflow per unit length of weir.

4. The oblique flow over weir and non-uniform flow velocity in the main channel cause complex flow behaviour in the side weir which difficult to analyse and cannot provide simple assumption to develop discharge equation.

Bos (1989) discussed the stage-discharge relation of side weirs. The flow of the main channel is assumed subcritical for derived this expression. The theory derived by Bos (1989) is only applicable if the area of water surface drawdown perpendicular to the centre line of the channel is small in comparison with water surface width of this channel. In other words, if y- p < 0.1B (Figure 13).

Figure 13: Dimension sketch of side weir Cross section and Water surface profile

Bos (1989) derived the discharge expression for side weirs which is expressed as:

Q CL y p . 27

Where L is length of the side weir. For standard broad or sharp-crested weir, the discharge coefficient ‘C’ can be expressed as:

C C g.

28

Or

C C 2g . 29

For side weirs, the Cd value is suggested to reduce to 5% for broad-crested weir and 10% for sharp-crested weir (Bos, 1989).





3 Common weir types

The edge or surface of the weir over which the water flows, is known as the weir crest. There are different types of weirs which are mainly named according to their crest shape. The sheet of water overflowing the weir crest is called ‘nappe’.

The most common types of weirs are described in the following sections.

3.1 Standard Broad-Crested Weir

The broad-crested or flat topped weir is a standard flow measuring device with a horizontal crest perpendicular to the direction of flow. The upstream edge of the weir should be rounded to avoid flow separation. Downstream of the horizontal crest there may be a vertical face or a downward slope, which is dependent on the submergence ratio under which the weir should operate at modular flow. The horizontal crest length or width of the weir should not be less than 1.45 H. Here H is the total energy head above the upstream crest of the weir (Bos, 1989). In broad crested weir the pressure may be assumed as hydrostatic as the stream lines run parallel to each other for a short distance. To obtain this, the length in the direction of flow of the weir crest (w) is restricted to the total upstream energy head over the crest (H) as (0.07≤H/L≤0.50) (Bos, 1989). Figure 14 and Figure 15 show the flow over a broad crested weir.

Figure 14: Flow over broad crested weir

Figure 15: Broad‐crested weir in the field

The most general form of free flow discharge expression over a weir is already mentioned in Section 2.3.1.





Q C L h . 30

Where, C is the weir coefficient, L is the effective length of the weir and h is the head above the weir crest. From the concept of Bernoulli’s equation, According to Bos (1989), the weir coefficient, C is expressed as follows:

C C C g.

31

The Cd is introduced to account for head loss due to viscosity, turbulence and the non-uniformity effects. Cd is a function of upstream energy head, H and the crest length, w is the weir length in the direction of flow (weir width) and can be calculated by the Equation [32] (Bos, 1989) .

C 0.93 0.10H

w32

The correction coefficient Cv is introduced as, the water depth h above the weir crest is considered instead the of the energy head H, i.e. the velocity head v2/2g is ignored (Bos 1989).

The Cv value can be derived from the Figure 16 (Bos 1989) or from Table 1 (Herschy, 1995).

Figure 16: Cv values as a function of the area ratio √α C A∗A

A* = Imaginary wetted area at the control section (L*h).

A = Wetted area at the head measurement station

α1 = velocity distribution coefficient (can be taken as unity for practical purposes)





Table 1: Cv for Values of CdLh/A

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.08

0.1 1.003 1.004 1.004 1.005 1.006 1.006 1.007 1.008 1.008 1.009

0.2 1.010 1.011 1.012 1.013 1.014 1.015 1.016 1.018 1.019 1.020

0.3 1.021 1.023 1.024 1.026 1.028 1.030 1.032 1.034 1.036 1.038

0.4 1.040 1.042 1.044 1.046 1.049 1.051 1.054 1.056 1.059 1.061

0.5 1.064 1.067 1.070 1.073 1.076 1.080 1.082 1.086 1.090 1.093

0.6 1.097 1.101 1.105 1.110 1.115 1.120 1.125 1.130 1.135 1.140

0.7 1.144 1.150 1.156 1.163 1.170 1.177 1.184 1.192 1.200 1.208

0.8 1.218 1.226 1.236 1.246 1.225

Azimi and Rajaratnam (2009) ignored velocity head correction from the discharge equation, so that the weir coefficient can be written as:

C C g.

33

They developed new equation for Cd by regression analysis with the experimental observation of Cd from the previous researches. The new Cd equations were derived for square and round edged upstream weirs. They differentiated the flat topped weir in to 3 categories on the basis of h/w ratio such as long crested, broad crested and short crested weir. The derived values for square edge upstream weirs are shown in Table 2.

Table 2: Cd for Square Edge upstream weir

Type h/L Cd

Long Crested 0<h/w<0.1 1.04 ⁄ .

Broad Crested 0.1<h/w<0.4 0.95 0.38 0.89

Short Crested 0.4<h/w<2 0.767 0.215 ⁄

Azimi and Rajaratnam (2009) also developed correlated equation for Cd for round crested weir (Table 3).





Table 3: Cd for Round Edge upstream weir

Type h/L Cd

Long Crested 0<h/w<0.1 1.16 h

whh p

.

Broad Crested 0.1<h/w<0.4 0.90 0.146

Short Crested 0.4<h/w<2 0.90 0.176

Govinda Rao and Muralidhar (1963) has studied extensively the variation of weir coefficient with h/w ratio. The weir coefficient can be expressed as:

C C 2g . 34

In their study they subdivided the flat topped weir in to three categories such as long crested, broad crested and sharp crested and developed Cd equations for each sub category (Table 4).

Table 4: Cd equation developed by Govinda Rao and Muralidhar 1963

Type h/L Cd

Long Crested 0<h/w≤0.1 0.5 0.1

.

Broad Crested 0.1<h/w≤0.4 0.5 0.05

.

Short Crested 0.4<h/w≤1.5 0.5 0.11

Johnson (2000) studied the discharge coefficient both for sharp and broad crested weir. All the data for his study were for fully aerated flow. In his study the weir coefficient can be expressed as:

C C2

32g . 35

Johnson (2000) developed equation for Cd for flat topped weir which is a function H w,

Where, H = Total upstream energy head and w = Width of the weir

Many researchers ignored the velocity head and developed equation as a function of h/w or h/p (p is the height of weir) as energy head, H is not possible to easily measured in the field. In his study Johnson (2000) also showed that there are considerable amount of change if velocity head is neglected. He developed a best fitted curve for flat topped weir, where discharge coefficient plotted against H/w for different weir dimension (p*w) which is shown in Figure 17.





Figure 17: Cd for flat topped weir for different values of p*w

The discharge coefficient, Cd and free flow discharge, Qf can be measured in an iterative way. At first Cd

is derived from Figure 17 by considering the measured upstream head (h) instead of the upstream energy head (H). Then the trial free flow discharge, Qf is calculated from the general form of discharge equation (Equation [30]). From this trial Qf, the trial upstream energy head (H) can be calculated by summing up the measured upstream head with the velocity head, where:

H h 36

Again Cd is taken from the Figure 17 with the new H/w ratio and again discharge is calculated. These processes will be repeated until the discharge value no longer considerable changes.

3.2 Standard Sharp-Crested Weir

Another discharge measurement structure with good accuracy is the sharp crested weir or thin plate weir (Figure 18 and Figure 19). The crest length in the direction of flow is very thin (recommended equal or less than 0.002 m) that it has no effect in stage-discharge relation. The downstream edge of the notch is bevelled if the weir is thicker than 2 mm. The bevelled surface should not less than 45°. For even a very small head, the nappe is completely free from the weir body after passing the weir (Bos 1989). Figure 18 and Figure 19 show the flow over sharp crested weir.

Depending on the weir opening, the sharp crested weir has been categorised into two parts (Bos, 1989):

- Fully contracted weirs: Weir width (L) is less than the channel width (B) (L/B < 1). Fully contracted weir may be use where the channel section is not rectangle (Figure 20).

- Full width weir: Weir and channel width are the same (L/B = 1). It is also known as suppressed sharp crested weir (Figure 20).





Figure 18: Flow over sharp crested weir

Figure 19: Sharp‐crested weir in the field

Figure 20: Sharp crested rectangular weir

For free flow discharge calculation over sharp-crested weir, Chow (1959) illustrated Rehbock formula for calculating the general discharge co-efficient by the following equation,

C 3.27 0.40h

p37

Here, h is the upstream head measured above the weir crest and p is height of the weir. The effective





length of the weir may be calculated as,

L L 0.1Nh 38

L’ is the measured length of the crest and n is the number of contraction. Chow (1959) also inscribed Rouse indication that Equation holds up to h/p = 5 but can be extended to h/p with fair approximation. Equation [37] is valid for discharge measures in cubic ft/sec.

Zhang et.al (2003) showed another forms of Rehbock formula where the weir coefficient can be expressed as:

C C 2g . 39

Where,

From Rehbock I (1920)

C 0.605 0.08 40

And from Rehbock II (1920)

C 0.611 0.08 41

Both of the equation [40] and [41] are valid for is valid for 0.025<h<0.60. Zhang, et.al (2003) also reported Bazin (1886) formula where the Cd form is expressed as:

C3

20.405

0.003

h1 0.55

h

h p42

The above is equation is valid for 0.08≤h≤0.55.

For the basic stage-discharge relation for sharp-crested weir, Bos (1989) showed the expression of weir coefficient, C as:

C C 2g . 43

Where, Ce is the effective discharge coefficient. Bos (1989) reported the Kindsvater and Carter (1987) formula to compute the free flow discharge Qf, where the most general form of discharge equation is changed in to the following form:

Q C L h . 44

Where, Le = L + kb and he = h + kh.

Kb and kh represent the combined effect of viscosity and surface tension. Empirical value of Kb can be calculated from the Figure 21 which is function of the ratio L/B. Where L is the effective weir length across the direction of flow and B is width of channel. The recommend constant positive value for Kh is 0.001. The effective discharge coefficient, Ce is a function of L/B and h/p and can also be calculated from the Table 5.





Figure 21: Kb for rectanguler sharp crested weir

Table 5: Ce for sharp crested weir Kindsvater and Carter

L/B Ce L/B Ce

1.0 0.602 + 0.075 h/p 0.5 0.592 + 0.011 h/p

0.9 0.599 + 0.064 h/p 0.4 0.591 + 0.0058 h/p

0.8 0.597 + 0.045 h/p 0.3 0.590 + 0.0020 h/p

0.7 0.595 + 0.030 h/p 0.2 0.589 - 0.0018 h/p

0.6 0.593 + 0.018 h/p 0.1 0.588 - 0.0021 h/p

0 0.587 - 0.0023 h/p

3.3 V-Notch Weir

V- notch is a most precise discharge measuring device for wide range of flow. V-notch is a type of sharp crested weir, place perpendicular to the sides and bottom of a straight channel. It is also frequently referred as a Thomson weir.

In the literature by Bos, 1989, there are two types of V-notch sharp crested weir, i) partially contracted and ii) fully contracted. In partially contraction weir, the weir contraction along the sides of the weir are not fully developed due to the proximity of walls and/or bed of the approach channel. One the other hand, in fully contracted weir has an approach channel whose bed and sides are sufficiently remote from the edges of the V-notch to allow for a sufficiently great approach velocity component parallel to the weir face so that contraction is fully developed. A graphical view of V-notch sharp crested weir is shown in Figure 22 and Figure 23.





.

Figure 22: V‐notch sharp crested weir

Figure 23: V‐notch in the field

The two types of V-notch can be subdivided by the following limitations which are shown in Table 6 (Bos, 1989). These limitations are based on the parameters h, p and B (Figure 22).





Table 6: Classification and limits of applications of V‐notch sharp‐crested weir

Partially Contracted weir Fully contracted weir

h/p ≤ 1.2 h/p ≤ 0.4

h/B ≤ 0.4 h/B ≤ 0.2

0.05 < m < h ≤ 0.6 m 0.05 < m < h ≤ 0.38 m

P ≥ 0.1 m P ≥ 0.45 m

B ≥ 0.6 m B ≥ 0.90 m

From the same concept of rectangular sharp crested weir, the stage-discharge equation for V-notch sharp crested weir can be written as ([45]) (Bos, 1989):

Q C 815 2gtan θ 2 h

. 45

Apart from the constant part, the V-notch equation has the same structure as the sharp and broad-crested weir. The power function is different because the control section is not rectangular any more. Here θ is the induced angle between sides of the notch. The above Equation [45] has been modified by Kindsvater and Carter (1957) which is applicable to both fully and partially contracted V-notch sharp-crested weirs.

Q C 815 2gtan θ 2 h

. 46

Here he = h + kh, where kh represent the combined effect of fluid properties. Empirical defined values of kh can be derived from the Figure 24, which is a function of notch angle θ (Bos, 1989).

Figure 24: Values of Kh for V‐notch sharp‐crested weir

The effective coefficient of discharge (Ce) is a function of h/p, p/B and θ. For fully contracted V-notch weir Ce is a function of notch angle θ only and can be calculated from Figure 25.





Figure 25: Ce for fully contracted V‐notch weirs

Again for partially contracted weir Ce is a function of both h/p and p/B and can be derived from the Figure 26 for 90° notch angle only (Bos, 1989).

Figure 26: Ce for partially contracted V‐notch weirs

Besides the V-notch sharp crested, there is V-shaped broad-crested weir which can be used to measure large and small discharges with high accuracy. A comprehensive study with different notch angle has been carried out Boiten (1980) at the Wageningen branch of the Delft hydraulics laboratory with the notch angle of 90°, 120° and 150°. In longitudinal direction, the V-shaped broad-crested weir is similar to the broad-crested weir with horizontal crest. It has the combined advantages of V-notch sharp-crested weir and horizontal broad-crested weir. The stage-discharge relation in V-shaped broad-crested weir is being influenced by downstream water level only at very high submergence ratio (80%) (Boiten, 1980). A V-shaped broad crested weir is shown in Figure 27:





Figure 27: V‐shaped broad‐crested weir

Depending on the purpose, the V-shaped broad-crested weir can be either fixed or moveable. Fixed crest will be used if there is no need of regulate flows. For irrigation, if the structure is used to regulate and measure flows, then construction will be carried out as a movable vertical sliding overflow structure. In movable weir the supporting crest can be raised or pushed down according to the desired crest level (Boiten, 1980).

According to the magnitude of head h, there are two types of flow possible in the V-shaped broad crested weir (Boiten, 1980).

- Under normal condition the flow type is called “less than full” where the weir width is unrestricted, the cross-sectional wet area in the control section is triangular. This is the case when H≤1.25Hb, Hb is the height of the triangle

- In exceptional circumstances the flow type is referred to as “more than full” where the weir width is restricted by vertical side walls. In this case H≥1.25Hb.

The stage-discharge relationship is developed from the same phenomena of broad-crested weir with rectangle control section which discussed before. The derived discharge equation for V-shaped broad-crested weir is shown in Equation [47] which for less than full flow (Boiten, 1980).

Q C C 45

. g2

.tan θ

2 h . 47

Cv is calculated from Equation [48] and Cd is derived from the Figure 28 (Boiten, 1980).

CH

h

. 48

For more than full flow, the discharge equation is:

Q C C 23

.g . B h 0.5H . 49

This equation is used for exceptionally high free flow discharge. In this case Cv value is calculated as:





CH 0.5H

h 0.5H

. 50

The Cd value is derived from the combination of Figure 29 and from the following equation:

Q 1 2δ

L

L

B1

δ

L

L

H

51

δ expresses the combined effects of boundary layer development and centripetal forces.

Figure 28: Cd – h/L relation for different notch angle of V‐shaped broad‐crested weir

Figure 29: δ/L – h/L relation for different notch angle of V‐shaped broad‐crested weir

3.3.1 Weir for Fish Passage Facility

Fish are migrating towards upstream and downstream in a river, lake or stream to complete their life cycle. Fish movement can be stopped in a channel when there are hydraulic structure (dam, culvert,





weir) act as an obstacle. A fish passage is a waterway which allows the passage of different species of fish through a particular obstruction. Fish passage facility over dams, weirs and culvert is an important consideration in fish bearing stream. An effective fishway attracts fish to enter the fish passage, pass through and exit safely with a minimum cost, time and energy.

One of the important types of fish way is weir fishways. It consists of chain of weirs which are settled down one after another, each weir is slightly higher than the downstream next downstream weir. Water pools are created between two consecutive weirs.

Fish can take rest in the pool or can pass the fish way. For the convenient pass of fishes over the weir, one of the possibilities to make the crest is V-shaped. Throughout the Netherland, in small creeps pool-types (weir fishway) fishways with V-shaped over falls have been applied. Design discharges have range from 0.35 to 5.50 m3/s. The typical plan, profile and front view of V-shaped fish passage shows in the Figure 30.

Figure 30: Different views of V‐notch fish passage

3.4 Oblique weirs

Besides the weir which is placed perpendicular to the direction of flows, some weirs are placed obliquely to the direction of flow. In oblique weir the effective length of the weir is increased beyond the channel width which increases the flow for certain water level at the upstream or decreases water head at the upstream for a certain discharge. When flow passing over the weir, it flows perpendicular to the weir. The flow accelerates when it reaches the weir and decelerate when leaves the weir. For sharp crested oblique type weir, maximum velocity observe above the weir crest while in broad crested type oblique weir the maximum velocity observe just behind the weir. The flow behaviour of the downstream side of the oblique is complex which causes turbulence properties that contribute to the dissipation of energy. Circulation of flow occurs behind weir and also flow convergence and separation are observed two opposite sides of the bank of the stream in the downstream side of the weir. For free flow condition, the accurate measurement is difficult as the flow behind weir highly turbulent and very complex. As a result higher head loss and energy dissipation occurs in compare to submerged flow. The flow behaviour over an oblique weir is shown the Figure 31 (Tuyen, 2006).





Figure 31: Flow behaviour of oblique weir

Tuyen (2006 ) also found from his experiment that discharge coefficient of oblique weir is higher than the perpendicular weir for same channel width and water depth upstream of the weir which is the reason behind of lower water head upstream of the oblique weir than the perpendicular weir with same width of the channel width and discharge. If the oblique angle of the weir is increased, the discharge coefficient of the weir will slightly decrease and the discharge capacity of the weir will increase. Tuyen (2006) did not derive any direct equation for Cd but showed graphical representation of Cd with specific discharge and other weir parameters.

Borghei, et al. (2003) has done very comprehensive study on sharp crested oblique weir. In the laboratory setup, to check the accuracy of measurement, the study was started with 0° oblique angle, which acted as a sharp crested plain weir. He compared his result with previous researchers and found less than 1% of difference in result which meant the equipment and results are suitable for further analysis. Both the free flow and submerged flow analysis were performed. From the study it has come out that oblique weir can be used precisely as flow measuring device with less water head in compare to plain weir. The discharge of the oblique weir can be calculated in the same way like the standard sharp crested weir where the general discharge coefficient can be written as:

C C2

32g . 52

And free flow discharge is calculated by the same discharge formula:

Q CLh . 53

Cd can be calculated by the following equation:

C 0.701 0.121B L 2.229B L 1.663 hp 54

Where,

B = stream width, L = effective length of the weir, h = upstream water depth above the weir crest and p = weir height.

The tests were performed between the oblique angle 29° to 64° with h/p ratio between 0.08 to 0.2 and head greater than 40 mm. The result showed that for oblique angles <45°, Cd increases with increasing head (h/p increase) but the rate slows as oblique angle increases. Again for oblique angles>45°, Cd decreases with increasing head (h/p increase) and for oblique angle equals to 45°, Cd can be taken as constant value (0.605) for all values of h/p. It has been recommended to use oblique weir for small values of h/p as low values of h/p increases the efficiency of oblique weir and high values should not be





designed as it decreases the oblique effect.

Borghei, et al. (2003) also dealt with submerged flow over oblique weir. The general formula for submerged flow is:

Q RQ 55

Where Qs is the submerged discharge flow and R is the reduction factor. The results for submerged flow have been analysed using the same procedure as free flow. Qf can be calculated by using free formula (Equation [53]) and the discharge coefficient (Equation [54]). R can be calculated by the following equation:

K 0.008 L B 0.985 0.161 L B 0.479h

h56

hd is the downstream water depth above the weir crest. After that submerged discharge can be calculated by Equation [55].

Samani (2010) recently studied analytically the behaviour of flow over oblique weir for emerged (free flow) flow and submerged flow condition for different oblique angles. He assumed that the flow over an oblique weir has an arbitrary angle (β) between the approach and normal direction (Figure 32).

Figure 32: Flow velocity vetor in oblique weir

With this assumption and by considering the energy and continuity equations, he developed a discharge equation (Equation [57]) for an oblique weir for free flow. The flow over oblique weir under free flow condition has shown in Figure 33. Samani’s (2010) developed discharge equation is different from general form of discharge equation that have discussed in the previous sections.

Figure 33: Free flow over oblque weir

In this equation a new measurement hw is required, which is over weir flow depths. Samani, 2010

Q C 2gbh h ph h

h p h57





developed a polynomial relation of Cd with L/B ratio. The equation of free flow discharge coefficient is:

C 0.014 LB 0.002 L

B 0.946 58

Samani (2010) also developed submerged discharge equation for the oblique weir by using the momentum principle.

Q C1

2B 2g ∗ h h 1 1

cosφ 2p ∗ h p h p 59

Where, submerged discharge and discharge coefficient are denoted as Qs and Cds respectively and hd is downstream water depth above the weir crest. The flow over submerged oblique weir has shown in

Figure 34. From sensitive analysis it found that Cds is related to L/B, h/p as well as hd/h. For a certain L/B ratio, Cds increases with increasing h/p and hd/h. The developed equation for submerged discharge coefficient is:

C 2.3 LB

. hp

. hh

.60

Figure 34: Flow over submerged oblique weir

3.5 Ogee weirs

The ogee-crested weir has been one of the most studied hydraulic structures because of its superb hydraulic characteristics. Its ability to pass flows efficiently and safely, when properly designed, with relatively good flow measuring capabilities, has enabled engineers to use it in a wide variety of situations (Savage et al. 2001).

The ogee-crested weir is developed in a manner which will not produce any undesirable nappe variation normally associated with weirs except the sharp-crested weir. A shape is designed that force the nappe to follow a single path for any discharge and make the weir consistent for flow measurement (Figure 36). Its crest profile conforms closely to the profile of the lower surface of a ventilated nappe flowing over a rectangular sharp-crested weir (Figure 35) (Loftin, 1999)





Figure 35: Outflow from a free‐falling weir, properly ventilated from below

Figure 36: Ogee Weir

The shape of this nappe, and therefore of an ogee crest, depends on the head producing the discharge. Consequently, an ogee crest is designed for a single total head (energy head), called the design head HD. When an ogee weir is discharging at the design head, the flow glides over the crest with no interference from the boundary surface and attains near-maximum discharge efficiency (Loftin, 1999).

For flow at heads lower than the design head, the nappe is supported by the crest and pressure develops on the crest that is above atmospheric but less than hydrostatic. When the weir is discharging at heads greater than the design head, the pressure on the crest is less than atmospheric, and the discharge increases over that for ideal flow. The pressure may become so low that separation in flow will occur (Loftin, 1999).

Weir coefficient, C is a function of the approach velocity, which varies with the ratio of height of weir p to actual total head Ht, where discharge is given by Equation [61] (Loftin, 1999).

Q CLH . 61

Where, C is the weir coefficient, L is the effective length of the weir, across the direction of flow and H is the total energy head.





H h H h v2g 62

Where, h is the measured water level above the weir crest and Hv is the velocity head.

Figure 37 shows the design discharge coefficient, Cd for an ogee weir with a vertical upstream face for discharge at design head Hd. When the total head is other than the design head, the coefficient changes from the coefficient given in Figure 37. Figure 38 gives values of the weir coefficient C as a function of the ratio Ht/HD, where Ht is the actual head being considered and HD is the design head (Loftin, 1999).

Figure 37: Chart gives weir coefficient at design head HD for vertical‐faced ogee‐crested weirs.

Figure 38: Chart gives discharge coefficients for vertical‐faced ogee‐crested weirs at heads Ht other than design

head Hd

The weir coefficient, CD or C and the discharge, Q can be measured in an iterative way. At first CD or C is derived from the Figure 37 or Figure 38 by considering the measured upstream head (h) instead of the upstream energy head. Then the trial discharge, Q is calculated from the general form of discharge





equation (Equation [61]). From this trial Q, the trial upstream energy head (H) can be calculated by summing up the measured upstream head with the velocity head, where:

H h 63

Again the weir coefficient is taken from the Figure 37 or Figure 38 with the corrected total head and again discharge is calculated. This process is repeated until the discharge value no longer changes considerably (Loftin, 1999).





4 Alphabet weirs

In-stream rock weirs are becoming important for river restoration and rehabilitation. These weirs can be A, W, J and U shaped (Thornton, 2011) and are generally termed as alphabet weirs. In stream rock weirs can be used to establish grade control, reduce stream bank erosion, provide energy dissipation, increase aquatic habitat and allow fish passage (Thornton, 2011). Grade control provides a local base level to a river, and through time the river can adjust to the new base level, creating an equilibrium slope between grade control structures (Meneghetti, 2009). The alphabet weirs can be constructed with boulders, logs or combination of both. To prevent scour under the structure, geotextile fabric is required (Thornton, 2011).

These structures share the following common characteristics (Reclamation, 2007):

Loose rock construction materials (individually placed or dumped rocks with little or no concrete)

Extents spanning the width of the river channel and An abrupt change in the water surface elevation at low flows.

River spanning loose-rock structures share common performance objectives, which include the ability to withstand high flow events and preserve functionality over a range of flow conditions. Functionality is often measured by a structure’s ability to maintain upstream water surface elevation and/or downstream pool depths. Vertical drop height, lateral constriction, size of rock material, and construction methods are common design considerations for these structures (Reclamation, 2007).

Castro (2000) stated that rock weirs redirect stream flow to the centre of the stream channel and disrupt the velocity gradient in the near-bank region. They utilize a low weir section pointed upstream to force water flowing over the weir into a hydraulic jump. Flowing water turns to an angle perpendicular to the downstream weir face causing the flow to be directed away from the stream bank. The weir effect continues to influence the bottom currents even when submerged by flows greater than the channel-forming discharge

For stream bank stabilization there is a need for a softer form of bank protection as a substitute of the hard procedure by means of natural materials and this method is getting popularity by using natural materials. The traditional river structures do not meet the entire desire objective for river stabilization and restoration (Rosgen, 2006). ‘Soft’ typically refers to banks that have not been hardened by the application of riprap or similar practices (Meneghetti, 2009). The properly designed river structure should maintain a stable width-depth ratio, maintain shear stress to move largest size particle to maintain stability, decrease near bank velocity, shear stress, maintain channel capacity, ensure channel stability during floods, allows fish passage, provide safe passage of boat, improve fish habitat, be visually compatible with natural channels, be visually compatible with natural channels etc. The use of rip-rap, gabions, concrete lined channels, bin walls, interlocking blocks, groyens, Kelner Jacks, spur dikes, rock jetties, reinforced revetment, sheet piling, log cribs, concrete check dams and loose rock check dams are not only expensive but also lead to either on-site failures or problems immediately up or downstream of the structures, resultant poor fish habitat and less natural appearance. To minimize this type of problems, led to the development of cross-vane (A- and U- weir) and W-weir in the early 1990’s (Rosgen 2006). Figure 39 shows alphabet weir in a stream constructed by different shape of rocks and their alignment. A-weirs, also called double drops consist of two distinct crests. U-weirs (sometimes called V-weirs) contain a single crest in which the throat is perpendicular to the flow. Older U-weir structures tended towards design of a narrow throat, sometimes with the arms meeting at a point. W-weirs consist of one or more U-weirs, typically with a narrow, or no, throat (Reclamation, 2007).

Thornton (2011) stated that design and performance of criteria for site application rock weir type structures are often anecdotal or qualitative in nature and based upon the experiences of the design team. According to Reclamation (2007), the design, effectiveness, and performance of these types of structures have not been well documented. Recently some empirical relationships have been developed with the large numbers of laboratory data and efforts have taken to link these relationships with field engineering practices and lacking.





General monitoring of in-stream restoration projects provides some information pertaining to success and failure rates, they usually do not provide enough detailed information to determine the physical processes associated with the success or failure of a given structure geometry. As a result, current design methods are based upon anecdotal information applicable to narrow ranges of channel conditions. Methods and standards based upon predictable engineering and hydraulic performance criteria currently do not exist (Reclamation, 2007).

Figure 39: Instream Rock weir of Alphabet shape

4.1 U-weir

The U-weir resembles to the English alphabet letter “U”. The U-weir is widely known as cross vane. It spans the entire width of a channel and is used to divert erosive flow away from the both bank as well as provide some level of local grade control via a central section that crosses the stream either at bed level or at required bed level (Meneghetti 2009). A U-weir operated in Frank Kocher Memorial Park, Pennsylvania, USA is shown in figure Figure 40. The cross-section, profile and plan view of a U-weir, also called cross vane, is shown in Figure 41.





Figure 40: U‐weir

According to the Maryland Department of the Environment (2000), when U-weirs are constructed and spaced properly, it can simulate the natural pattern of pools and riffles occurring in undisturbed streams while forming gravel deposits which fish use as spawning grounds. According to Puckett (2007), the U-weirs provides a drop structure that creates a downstream pool for habitat and allows for a drop in bed elevation thereby allowing energy dissipation and lower bed slopes upstream and downstream where sinuosity is restricted. It is unique in that it acts as a weir, vane, and drop structure all in one. The upward sloping arms of the rock vane are similar to those of single arm vanes used to protect the outer stream bank of a curve where velocities increase.

The structure should only extend to the bankfull stage elevation and the slope of the weir (profile angle) should vary from 2 to 7% (Figure 41). If the bank is higher, a bankfull bench is constructed and the structure is integrated within the bench. The use of a cross-Vane is shown in Figure 42 where a bankfull bench is created adjacent to a terrace bank. The practices angle between the weir arm and the intercepted bank is normally between 20° to 30° where 20° angle provides the longest vane length and protects the greatest length of stream bank (Rosgen 2001).

According to Rosgen (2001), the U-weir serves the following purpose in to the stream:

i. It’s a grade control structure that decreases the shear stress, velocity and stream power near the bank but increases the energy in the centre of the channel (Figure 43).

ii. Its reduce bank erosion, create a stable width/depth ratio, maintain channel sediment transport capacity and sediment competence.

iii. The U-weir also provides for the proper natural conditions of secondary circulation patterns, commensurate with channel pattern, but high velocity gradients and boundary stresses are shifted from the near bank region.





Figure 41: Cross‐section, profile and plan view of U‐weir Rosgen 2001





Figure 42: U‐weir and constructed bankfull bench

Figure 43: U‐weir: Flow is directed to maintain centre channel blue line

iv. When bridges are constructed on a skew to the channel and/or placed on an outside bend, can produce abutment scour and embankment erosion. This problem can be solved by placing of an offset U-weir in the upstream of reach of the bridge. The vane on the outer bank in the bend has a flatter slope and smaller angle (20°), while the vane arm on the inside bank has a steeper slope and a larger angle (30°)





Figure 44: Application of U‐weir for bridge and channel stability

As a grade control structure, the cross vane is used to maintain base level in both riffle/pool channels rapids-dominated stream types and in step-pool channels (Figure 45). The U-weir can also be used for stream habitat improvement structure due to (Rosgen 2001):

i) An increase in bank cover due differential raise of the water surface in the bank region, ii) The creation of holding and refuge cover during both high and low flow periods in the deep

pool, iii) The development of feeding lanes in the flow separation zones (The interface between fast

and slow water) due to the strong downwelling and upwelling forces in the center of the channel and

iv) The creation of spawning habitat in the tail-out or glide portion of the pool.

Figure 45: U‐weir for step restoration Rosgen 2001

It is already mentioned that U-weir or cross vane acts as a unique combination of a vane, weir and drop structures. Probably the design concept of cross vane comes from the single vane where two single vane starts from the both banks of the stream and join together in the middle of the stream and give the shape of English alphabet ‘U’ or ‘V’.





The function of the vane is to reduce erosion and give stability of the river bank by divert water flow towards the centre of the stream. As like cross vane it also creates stream pool in the downstream sides. Vanes are linear structure; extend from the one side of the stream bank into the upstream direction of the stream (Figure 46). Vanes can also be constructed using logs or rocks. They normally extend out from the stream bank 1/3 of the bankfull width and are angled upstream from the bank between 20° to 30°.

Figure 46: Rock vane

There is another type of vane structures which is known as J-Hook vane. It is also directed upstream with a gentle slope and composed of natural materials like boulders, logs and root wads. The structure is designed to reduce bank erosion by reducing near bank slope, velocity, velocity gradient, stream power

and share stress (

Figure 47). Redirection of secondary cells from the near bank region does not cause erosion due to back-eddy re-circulation. The vane portion of the structures occupies 1/3 of the bankfull width as a normal vane and the hook portion occupies 1/3 of the centre portion (Rosgen 2006). The plan, profile and section view of J-Hook vane is shown in Figure 48.

Figure 47: J Hook: Constructed on the right bank, directs flow to centre of the channel and reduce bank erosion





Figure 48: Plan, profile and section view of J‐Hook vane

When J-Hook vane installed in a stream, maximum velocity, shear stress, stream power and velocity gradients are decreased in the near bank region and increased in the center of the channel. As a result sediment transport competence and capacity can also be maintained. The scour pool creates 1/3 of the centre channel, provides energy dissipation and holding cover for fish (Rosgen 2006).

4.2 A-weir

The A-weir resembles to the English alphabet letter “A”. It is also called as cross vane structure. The A-weir is similar to U-weir; the only difference, there is a horizontal sill or step placed perpendicular to flow and located in the middle of the structure. The cross-section, profile and plan view of the A-weir is shown in Figure 49 and an A-weir operated in the field is shown in the Figure 50.

The A- weir has the same function like the U-weir and it normally place in the high gradient stream channels. The extra horizontal sill which resembles it from “U” to “A” shape provides extra energy dissipation (Meneghetti, 2009).

In general, structural dimensions of A-weirs are consistent with U-weirs. No specific information was found on dimensions of the A-weir cross-arm. Reclamation (2007) has indicated that the cross-arm spans the entire width of the structure and is located in the center of the structure, downstream from the weir crest. The drop height of the cross-arm should be approximately half the drop height of the weir crest. The drop height is defined as the distance from the top of the weir rock at the crest to the stream bed just downstream of the crest.





Figure 49: Cross‐section, profile and plan view of A‐weir Rosgen 2006





Figure 50: A‐weir

Both the U- and A-weir are popular for boating features like kayakers. The invert portion (center 1/3, Figure 41 and Figure 49) of the structures creates a standing wave, but is associated with a “run” immediately downstream of the invert. As a result potential development of a dangerous recirculation pool that traps “swimming paddlers” is eliminated (Rosgen 2006).

4.3 W-weir

The W-weir resembles to the English alphabet letter “W” and was developed initially to control large rivers. The W-weir consists of four arms with center point facing downstream as shown in Figure 51. The two arm of the weir adjacent to the bank is designed similar to the cross vane where downstream central apex of the weir is built at approximately one half of the bankfull depth. Two downstream scour pools are formed on each upstream apex (Meneghetti, 2009). According to the Maryland Department of the Environment (2000), same like U-weirs when W-weir is constructed and spaced properly, it can simulate the natural pattern of pools and riffles occurring in undisturbed streams while forming gravel deposits which fish use as spawning grounds. The cross-section, profile and plan view of the W-weir is shown in Figure 51 and a W-weir operated in the field is shown in the Figure 52.

The objectives of the W-weir are (Rosgen 2006):

i) Provide grade control on large river ii) Enhance fish habitat iii) Provide recreational boating iv) Stabilize stream banks v) Facilitate irrigation diversion vi) Reduce bridge center pier and foundation scour vii) Increase sediment transport at bridge locations





Figure 51: Cross‐section, plan and profile view of W‐weir

Figure 52: W‐weir

Rosgen (2006) also reported that double W-weir is constructed on very wide river and/or where two center pier bridge design require protection. Two pools create in the downstream increase the holding, feeding and spawning areas for the fish habitat. The deep glide create upstream of the structure, adjacent to the bank due to increased depth and reduced velocity, also enhance the habitat of different ages of fishes.

As a grade control structures W-weir doesnot disrupt bed-load transport or fish migration because of the low invert level. The sloping crests and the nonuniform velocity distribution contribute to the generation of three-dimensional vortices downstream from the structure. This causes high turbulence zones with flow interactions in all three directions where two deep and partially separated scour holes are formed. On sand and fine gravel-bed rivers, it is very important to take account of the location and depth of the scour holes when designing the foundations of the weir to prevent undermining and failure (Bhuiyan, 2007).





4.4 Field Investigation Results of Alphabet Weirs by Reclamation (2007)

Field observations give (long term) data to understand the actual physical process on how the flow behaves due to the effects of a structure. Reclamation (2007) documented the flow processes over rock weirs of alphabet shape by details field investigation which includes 21 sites and consisting 127 structures. Some of the outcomes of these field investigations are described here.

4.4.1 Flow Pattern over Alphabet Weir

From the field investigation, it comes out that an increased velocity jet is visible downstream of the crest, extending 3 to 4 times the width of the structure. Rollers are frequently present even under submerged conditions. Figure 53 shows examples of submerged and free-flowing rock weirs in Rio Blanco, Colorado. If sediment buried the structure, this backwater effect was not evident. On the Rio Blanco, flow depths between structures appear to return to normal depth in most cases. Structures with voids still created a significant backwater effect.

Figure 53: Free L and Submerge R flow over rock weir

For structures on bends, the thalweg generally apporached the structures on the outside of the bend and then shifted to the throat (center of the sturcture) before continuing downstream. Structures on bends that did not appear to maintain the thalweg over the throat generally exhibited evidence of failure due to scour pool growth or flanking arround the structure arm.

FFF shows flow patterns at the site before and after failure of the right arm. After the right arm failed, the flow pattern returned to the original path on the outside of the bend. Upon a temporary repair to the strucutre, the main flow thread turned to pass over the throat.

Figure 54: Lemhi River: before failure (L) and after right arm failure (R)





4.4.2 Sediment Deposition and Erosion Patterns

Field studies indicated sediment deposition creating a ramp (inclined surface) beginning upstream of the structure and ending at the crest. Sediment tended to fill in the voids between header rocks and created a more solid wall. Structures with notches between the headers tended to maintain a low flow thread just upstream of the structure, while structures without gaps between the headers tended to create a plane bed upstream. Structures that were buried by large amounts of sediment did not contain a low flow thread despite the gaps between the headers.

Downstream pool depths and the amount of gravel within the pool varied between structures. In some cases, pools appeared completely filled with materials, while in others, the pool scoured down to bedrock (Reclamation, 2007).

On sites with multiple structures in series, the upstream structures tended to accumulate more deposition behind the crest and to have smaller scour pools than downstream structures. In the downstream end pools consisted entirely of exposed bedrock with little gravel deposition upstream of the crests or within the pools (Reclamation, 2007).

Structures along bends appeared to accelerate bar growth on the inside of the bend. Rocks forming asymmetric U-weirs typically located on bends appeared to protrude less into the flow and had more deposition upstream of the arms than structures on straight reaches. Similarly, on the downstream side of the arms, increased deposition occurred locally on the inside of the bend when compared to straight reaches (Reclamation, 2007).

4.4.3 Scour Pool Location and Dimension

Each structure that was not submerged/buried by sediment was characterized by a scour pool just downstream from the structure. The longitudinal location of the scour pool varied, but the maximum depth tended to occur at the end of the shortest arm of each structure. Lengths of the scour pools also varied but appeared to stretch approximately twice the length of the shortest arm. The lateral width of each pool tended to span the entire area within the structure arms. Isolated rocks were often observed at the maximum sour depths. At sites where bedrock control was present, the downstream pool often scoured down to the depth of bedrock. Many pools showed deposition at the downstream extent of the scour hole, resulting in a longitudinal profile depicted in Figure 55. Several structures no longer maintained depths in the scour pool because a substantial amount of material had been deposited in the scour pool location.

Figure 55: Longitudinal profile of sediment deposition and pool patterns

4.4.4 Numerical Analysis of Rock Weirs by Johnson (2011)

General monitoring of in-stream restoration projects provides some information pertaining to success and failure rates, it usually does not provide enough detailed quantitative information to determine the physical processes associated with the success or failure of a given structure geometry. As a result, current design methods are based upon anecdotal information applicable to narrow ranges of channel conditions. Complex flow patterns and performance of rock weirs are not understood, and methods and standards based upon predictable engineering and hydraulic performance criteria currently do not exist.





Without accurate hydraulics, designers cannot address the failure mechanisms of structures.

Flow characteristics such as jets, near bed velocities, recirculation, eddies, and plunging flow govern scour pool development can be replicated using a 3D numerical model. Numerical studies inexpensively simulate a large number of cases resulting in an increased range of applicability in order to develop design tools and predictive capability for analysis and design.

The 3 D numerical model U2RANS is used to investigate how variations in structure geometry affect local hydraulics, scour hole development, and overall structure performance. An automatic mesh generator was developed to expedite the process of generating 30 structure geometries in a simulated straight trapezoidal channel. Variations in structure geometry include: arm angle, arm slope, drop height, and throat width. Various combinations of each of these parameters are modeled at 3 flow rates: 1/3 bankfull discharge, 2/3 bankfull discharge and bankfull discharge. The numerical modeling focuses on how variations in structure geometry affect local flow patterns and scour development.

Figure 60 shows a U-Weir in the field and the corresponding water surface and velocity output from the 3D numerical model U2RANS. In the figure, entrained air reveals areas of high velocity and turbulence. The 3D model captured flow features including the draw down curve, hydraulic jump, and variations in velocity. Dry areas in the photograph, such as the protruding rocks in the upper left corner match the 3D model water surface. Figure 56 demonstrates the capability of three-dimensional numerical modeling to match field conditions.

Figure 56: Field Photo and Corresponding Numerical Modelling Results





Figure 57 shows a plan view with water surface elevation contours. The areas upstream and downstream of the structure show little lateral variation. The water surface drops rapidly over the structure and follows the weir crest topology.

Figure 57: Modeled Water Surface Elevation

Figure 58 shows surface velocity vectors. In the channel upstream and downstream of the structure water generally flows parallel to the banks. Over the weir, the flow paths rapidly converge and then slowly expand. A jet through the center of the channel creates abrupt lateral changes in velocity.

Figure 58: Plan View: Velocity Vectors and wetted Area

Figure 59 shows a vertical profile view for velocities along a longitudinal section of the thalweg. Water flows parallel to the bed upstream and downstream of the structure. The stream lines rapidly converge and diverge vertically through the structure. The velocity profile contains a jet midway through the water





column rather than the logarithmic profile of a typical river section

Figure 59: Thalweg Profile View and Velocity Magnitude

4.5 Limitation of Alphabet weirs

According to the Maryland Department of the Environment (2000), both U- and W- weirs should be avoided in channels with bedrock beds or unstable bed substrates, and streams with naturally well developed pool-riffle sequences. Castro (2000) stated that both U- and W- weirs perform well in gravel and cobble-bed streams and should not be used in sand-bed stream. He also added that U-weirs are not recommended to use in streams where flow width exceeds 30.5 meter and on the other hand W-weirs only be used on streams where bankfull channel width is greater than 30.5 meter.

No specific limitation has been found for A-weir. But as the design specification and purposes of U- and A-weirs are almost same, so the limitation of U-weir should also imply for A-weir.

4.6 Stage-discharge Expression for Alphabet Weir

Meneghetti (2009) developed the expression of calculating upstream water level or stage for U-, A- and W-weirs. A hydraulic testing program was performed by Meneghetti (2009) and Scurlock (2009) in which scaled, U-, A- and W-shaped rock weir structures were constructed at the laboratory of Colorado State Univesity, USA (Figure 60 and Figure 61). In total 31 tests were considered on 16 unique weir configuration to develop a stage-discharge relationship which were limited to 1/3 bankfull, 2/3 bankfull and bankfull discharges. For each configuration, a weir was built and the bed material was levelled to a slope prescribed by US Bureau of Reclamation. Construction of the physical model involved using a 16-ft (4.88 m) by 50-ft (15.24 m) flume to test the three different weir types. U-, A-, and W-weirs were built according to designs from Rosgen (2001) and Reclamation (2006). The tests were performed in rectangular cross-section, straight and gravel bed flume (Meneghetti, 2009).

Figure 60: Scale model of U‐ L , A M and W‐weir R





Figure 61: Scaled Alphabet weir under testing condition

An empirical approach and regression analysis were applied to develop stage-discharge relationships for U-, A and W-weirs. To develop this relation, a general form of a nonlinear power function relation is followed:

Y αQ 64

Where,

Yus = Upstream water depth

α = Discharge coefficient

β = Discharge exponent

To account for the unique geometry and variations in structure type of the U-, W and A-weirs, additional variables were added to Equation [64]. Effects of weir geometry and structure type on the depth of flow upstream of the weir were quantified by the use of two “compression factors.” These factors were ratios that described different aspects of weir geometry such as yn/LT, L/LA and LA/L. So the geometry of the U-, A- and W-weir are also important parameter in the head discharge expressions developed by Meneghetti (2009).

Weir arm length (LA) is defined as the length of the weir along the side of the flume. The angled weir are length (LAA) was defined as the length of the diagonal weir arm. The plan angle (θ) is the angle between the flume wall and LA. The profile angle (φ) is the angle between the horizontal plane and the weir arm that sloped downward from the tie in at bankfull elevation with the flume wall to the weir crest. For A- and U- weir the horizontal arm is one-third of the channel width. LB is the length of the angled arm with no profile angle included. A diagram detailing U- and A-weir geometry is displayed in Figure 62 and Figure 63.

Figure 62: U‐weir geometry





Figure 63: A‐weir geometry

It is important that the cross-arm of the A-weirs is not included to calculate total length calculations because the cross-arm was built at an elevation below the header rocks of the weir and the upstream water depth has no influences over it. So the total length of the U- and A-weir are same and can be calculated by the following equations.

L 2B3

SinθCosφ

B

365

Sin θB3

L66

CosφB3

Sin θL

67

LB3

Sin θ68

LB3

Sin θCosφ

69

Similar terminology is also used for the W-weirs. The outside angled weir arm length is termed as LAA-out, and the inside angled arm termed as LAA-in. Plan angle (θ) is measured as the angle between the stream wall and LAA-out. Outer profile angle (φ) is the angle measured between the horizontal plane and LAA-out that sloped downward from the tie-in at the flume wall to the weir crest. The inner profile angle (γ) is the profile angle of the inner angled arm. The recommended value γ is half the value of φ. A diagram detailing W-weir geometry is displayed in Figure 64. The equation for calculating total weir length for W-weirs is displayed as Equation [70] and [71].





Figure 64: W‐weir Geometry

L 2L 2L 70

or

L 2B4

SinθCosφ

2B4

SinθCosγ

71

Different combination of compression factors (Ratios that described different aspects of weir geometry such as yn/LT, LA/LAA and LAA/LA) were multiplied by Q and Yus in Equation [64] to improve the overall fit of the regression line to the experimented data and then unique expression to predict upstream water depth of each U-, A- and W-weir were developed. The expressions to predict the upstream water depth of U-, A- and W-weir are shown in the following equations (Meneghetti 2009):

For U-weir:

Y 0.830 Qy

L

. L

L72

For A-weir:

Y 0.847 Qy

L

. L

L73

For W-weir:

Y 0.955 Qy

L

. L

L74

Where,

yn = normal depth, LT = total weir length, LAA = angled weir arm length and LA = weir arm length

Yn can be calculated by the following equation:

Q1

nby S

by

b 2y75

Where

Yn = normal depth;





n = Manning’s roughness coefficient; Q = discharge; b = bottom width and; So = bed slope;

The above stage-discharge expressions developed by Meneghetti (2009) for different shapes of Alphabet weirs are not comparable with the general weir Equation [22]. Thornton et al. (2011) performed another study based on the same laboratory study and experimented data used by Meneghetti (2009) to develop general stage-discharge relationship for U-, A- and W-weirs. As mentioned earlier, in the laboratory testing program, total 31 tests were performed for three different conditions, 1/3 bankfull, 2/3 bankfull and bankfull conditions. All the tests were performed in subcritical and free flow conditions. Unique weir coefficients are developed for each type of weir and a composite weir coefficient is also proposed which is applicable to the U-, A- and W-weir. After comparing to the general form of the discharge equation (Equation [22]), the weir coefficient can be written as:

C 23C 2g . 76

For U-rock weir:

C 0.652d

p.

LB

.77

For A-rock weir:

C 22.109d

p.

LB

.78

For W-rock weir:

C 0.002d

p.

LB

.79

Where d50 is the median crest stone size, p is the average height of the weir, L is the effective length of the weir across to the direction of flow and B is the width of stream.

After comparing the predicting discharge with observed one, the coefficient of determination (R2) of U-, A- and W-weir were found as 0.970, 0.987 and 0.989 respectively.

The composite expression for Cd which is applicable for all the three types, U-, A and W weir is derived with the similar manner of the individual rock weir types. The composite rock weir coefficient is expressed as:

C 1.139d

p.

LB

.80

For the composite expression the R2 value slightly decreases to 0.964.





5 Modelling Weir flow with mike 11

MIKE 11 is a one dimensional modelling tools developed by Danish Hydraulic Institute (DHI), Water and Environment. MIKE 11 used for the simulation of flood, water quality and sediment transport in estuaries, irrigation system, channel and other water bodies. It’s fully dynamic modelling tool for simple and complex river and channel system.

The MIKE 11 hydrodynamic module (HD) uses an implicit, finite difference scheme for the computation of unsteady flows in rivers and estuaries. The module can describe sub-critical as well as supercritical flow conditions through a numerical scheme which adapts according to the local flow conditions (in time and space). Advanced computational modules are included for description of flow over hydraulic structures, including possibilities to describe structure operation.

The formulations can be applied to looped networks and quasi two-dimensional flow simulation on flood plains. The computational scheme is applicable for vertically homogeneous flow conditions extending from steep river flows to tidal influenced estuaries.

5.1 Literature review for MIKE 11 Weir Flow Calculation

This section describes the weir formulas (weir types), which are used in MIKE 11. This section has been derived from the MIKE 11 User Guide (2007) and Reference Manual (2007).

MIKE 11 includes descriptions for a wide range of structures which act as control points. The formulation of these features permits great flexibility since they range both in their degree of user-intervention and in their level of complexity. There are mainly three different types of weir options are available to model under MIKE 11.

Broad crested Weir Special Weir Weir Formula

The hydraulic description for both the broad-crested and special weir is similar. The weirs are modelled in MIKE 11 as control points at Q-points in the computational grid. Depending on the structure category, a relationship between the discharge and the upstream and downstream water levels is determined based on the flow condition, entrance and exit losses, and a critical flow correction factor. The flow regime (free or submerge flow) can be determined by the given upstream and downstream water level and the river discharge. The flow is known as zero flow if the weir is closed by a valve, or if both the upstream and the downstream water levels are below the structure crest level. Free flow is greater than the submerge flow. Initially the program assumes that the flow is free and the associated discharge is computed. If it is not a free flow then a submerged iteration is applied to determine the discharge. By comparing the free flow with submerge flow, the flow regime is determined finally as the smaller discharge is taken.

Figure 65 shows the different property of weirs in MIKE 11, which are needed to incorporate a weir in a channel. The brief description of weir properties and types of weirs and weir formulas use in MIKE 11 are documented in this section.





Figure 65: The weir property page of MIKE 11

Location: It includes the river name and chainage, where the weir is located as well as a string identification of the weir and the location type which may be regular, side structures or side structures plus reservoir.

Head Loss Factor: The factors determining the energy loss occurring for flow through hydraulic structures (only broad crested weir and special weir).

Geometry: This is only for broad crested weir and special weir. The weir can be specified by giving the specific geometry (Level-Width) or the weir geometry can be specified in the cross section editor.

Datum: Offset which is added to the level column in the level/width table.

Attribute: This option selects which type of weir or which weir formula will be applied to weir flow calculation. As mentioned already, in MIKE 11, there are three options to describe weir types:

i) Broad Crested Weir ii) Special Weir iii) Weir Formula

i. Broad Crested Weir

According to the manual, the standard formulations for flow over a broad crested weir are established automatically by the program on the basis of the weir geometry and the user specified head loss and calibration coefficients. These formulations assume a hydrostatic pressure distribution on the weir crests. Different algorithms are used for drowned flow and free overflow, with an automatic switching between the two.





ii. Special Weir

Special weirs are used to model a structure whenever the standard formulation for a broad crested weir is not sufficiently flexible. The special weir enables a user-defined relationship to be specified for critical flow and free overflow conditions. Two relationships are required, one for flow in positive direction and one for flow in negative direction. The h values correspond to water levels at the h-point upstream of the structure. From these user-defined relationships and from the energy loss relationship, a table relating the critical depth and the critical flow at the structure is derived. The derived relationship is also used during the computation to determine whether the flow is submerged or free overflow.

iii. Weir Formula

With the Weir Formula the discharge through a structure can be modelled by using standard weir formulas. In MIKE 11, there is an option to choose either any of the three weir formulas which are described below.

Figure 66: Definition sketch of weir flow in MIKE 11

Weir Formula 1

Weir formula 1 is based on a standard weir expression, reduced according to the Villemonte formula:

Q LC h h 1h h

h h

.

81

Where Q is discharge through the structure, L is the weir length, C is weir coefficient, k is the weir exponential coefficient, hus is upstream water level, hds is downstream water level and hw is weir level (Figure 66).

Weir Formula 2 (Honma)

Weir formula 2 is the Honma formula:

QC L h h h h for h h h⁄ 2 3⁄

C L h h h h for h h h⁄ 2 3⁄82

Where Q is the discharge through structure, L is the weir length, C1 is the first weir coefficient, C3 2⁄ √3C is the second weir coefficient, g is the acceleration due to gravity, hu is the upstream water

level, hd is the downstream water level and hw is weir level (Figure 66).

The first discharge equation is for free over flow and the second equation is for submerged flow over the weir.





Weir Formula 3 (Extended Honma)

Weir formula 3 is the extended Honma formula. The flow is calculated is three flow regimes called perfect, imperfect and submerged overflow. The choice of regime is defined by the ratio between downstream and upstream water depth above the crest.

Q

C Lh ⁄ for h h⁄ h h⁄ i

C ∝ h h⁄ β Lh ⁄ for other cases

C γ h h⁄ δ Lh h h ⁄ for h h⁄ h h⁄ s

C a h z⁄ b for all

83

Where L is the weir length, z is weir height above cross section invert, h is the upstream water level above the crest, h1 is the downstream water level above the crest, (h1/h)i is a user specified depth ratio limit between perfect and imperfect flow regime, (h1/h)s is a user specified depth ratio limit between imperfect and submerged flow regime. a, b, p, α, β, r, γ, δ and p are user specified parameters.

MIKE 11 simulation engine or user interface does not check if there is a continuous transition from one flow regime to the next. This has to be ensured by the user through proper selection of the parameters.

5.2 Selection of MIKE 11 Weir Type and Weir Equation

In this study, two types of weirs have been selected to be modelled by MIKE11 under free flow conditions. These are the i) standard broad crested type weir and ii) alphabet weirs. It is already discussed in the previous section that to model weir flow, several types of weir and weir equations are available. These are i) Broad Crested Weir, ii) Special Weir iii) Weir Formula 1, iv) Weir Formula 2 (Honma) and v) Weir Formula 3 (Extended Honma). The selection any of the option is the most important part to model weir and the selection is dependent on the available data and knowledge on weir equations.

For the first two types, i) Broad Crested Weir and ii) Special Weir, same types of geometrical data (weir width and height) is needed. For the Broad Crested type the program automatically calculates the head-discharge relationship by the internal algorithm and from the characteristics of broad-crested weir. But the Special Weir option cannot be applied unless the reliable user specified stage-discharge data is available for positive and negative flow.

The main parameter of the weir formulas is the weir coefficient. The weir coefficient for the general weir equation for free flow condition described in this study for different types of weir are only comparable with the Weir Formula 2. The free flow discharge equation for Weir Formula 2 (Honma) is:

Q C L h h h h 84

In this equation, the difference between the upstream water level (hu) and the weir crest (hw) is actually the water depth above the weir crest (h). So Equation [84] is the same equation like general weir Equation [22] and the weir coefficient C1 is actually the same as the weir coefficient C. So the formulas that have been discussed in this study to calculate the weir coefficient can be used for MIKE 11 Weir Formula 2 as an input.

The weir coefficient for Weir Formula 1 and Weir Formula 3 (Extended Honma) of MIKE 11 are not same as the weir coefficient of general stage-discharge equation as the form of equations is not same. Weir Formula 3 (Extended Honma) is based on different conditions and which also bit complicated as many user specified parameters are involved like a, b, p, α, β, r, γ, δ and p. The details of choosing the value of these parameters are not documented in the MIKE 11 reference manual. Again no guide lines of determine the weir coefficient for Weir Formula 1 and Weir Formula 3 are documented in MIKE11 reference manual.

By analyzing the different types of weir option available in MIKE 11, two types of weir option have been selected for weir modelling; type 1: Broad Crested Weir and type 2: Weir Formula 2.





5.3 Development of Model

To model the broad-crested and the alphabet weir (U-, A- and W-weir) data coming from experimental observations is used. The available data are the measured head/water level-discharge relationships and weir dimensions. These data’s are processed, so that it can be used in to MIKE 11 format. The objective of the modelling study is to develop a model with the input of experimental discharge data and corresponding geometry and then analyse the accuracy of the simulation results by comparing simulation water level with the experimental water level upstream of the weir.

For the modelling study, weir coefficient, C is calculated for the both type of weirs with the experimental data. With this weir coefficient, C and the general stage-discharge relationships ([22]), the predicted upstream water level of the weir has been calculated analytically. So, finally the experimental data is compared the modelled results and the analytical results.

The details of model development are given in the following sections.

5.3.1 Broad-crested weir

For broad-crested weir modelling, rating tables provided by Bos (1989) have been used. This table contains a series of stage-discharge relations for different weir heights of 0.2 meter, 0.4 meter and 0.6 meter. Among the series of data some random data have been selected which covered all the heights of weir and wide ranges of discharges. The discharge data are given as per meter width of the weir. So the design discharge for the model channel is recalculated by multiply by the weir width. The selected data for the model is applicable for weir width greater than 2 meter.

To model the broad-crested weir, a channel length of 100 meter is chosen with rectangular cross-section (width 5 meter). The weir width is considered same as the channel width. The upstream boundary condition (Chainage 0 meter) is the discharge which comes from the rating table provided by Bos (1989) after multiplying it with the weir width. The downstream boundary (Chainage 100 meter) is the water level which value is chosen very low (0.01 meter). In an intermediate position (Chainage 32 meter) the location of the weir is chosen. The Model is also simulated to see the effect of upstream water level by increasing the channel in to 20 meter when the weir width is same as 5 meter. The processed data for the model is shown in Table 7.





Table 7: Input Data for Broad Crested Weir Bos, 1989

Sl No

Water Depth above

weir crest h (m)

weir height p (m)

U/s waterLevelhus

Discharge per m width, q (m3/s)

Channel Width B (m)

Weir LengthL (m)

Weirwidth w (m)

Design Discharge Q (m3/s)

1 0.1 0.2 0.3 0.0521 5 5 1 0.2605

2 0.16 0.2 0.36 0.1099 5 5 1 0.5495

3 0.22 0.2 0.42 0.1827 5 5 1 0.9135

4 0.28 0.2 0.48 0.2691 5 5 1 1.3455

5 0.34 0.2 0.54 0.3681 5 5 1 1.8405

6 0.4 0.2 0.6 0.4788 5 5 1 2.394

7 0.46 0.2 0.66 0.6007 5 5 1 3.0035

8 0.5 0.2 0.7 0.6878 5 5 1 3.439

9 0.56 0.2 0.76 0.8271 5 5 1 4.1355

10 0.64 0.2 0.84 1.028 5 5 1 5.14

11 0.68 0.2 0.88 1.135 5 5 1 5.675

12 0.3 0.4 0.7 0.2859 5 5 1 1.4295

13 0.52 0.4 0.92 0.684 5 5 1 3.42

14 0.68 0.4 1.08 1.051 5 5 1 5.255

15 0.74 0.4 1.14 1.205 5 5 1 6.025

16 0.82 0.4 1.22 1.422 5 5 1 7.11

17 0.9 0.4 1.3 1.652 5 5 1 8.26

18 0.94 0.4 1.34 1.773 5 5 1 8.865

19 1 0.4 1.4 1.96 5 5 1 9.8

20 0.12 0.6 0.72 0.0675 5 5 1 0.3375

21 0.24 0.6 0.84 0.1982 5 5 1 0.991

22 0.4 0.6 1 0.4395 5 5 1 2.1975

23 0.5 0.6 1.1 0.6239 5 5 1 3.1195

24 0.6 0.6 1.2 0.8319 5 5 1 4.1595

25 0.78 0.6 1.38 1.262 5 5 1 6.31

26 0.88 0.6 1.48 1.53 5 5 1 7.65

27 0.98 0.6 1.58 1.817 5 5 1 9.085

It is mentioned already that to model broad-crested type weir two types of weir option have been selected; i) Broad-crested weir and ii) Weir Formula 2.

5.3.1.1 Option 1: Broad-crested weir

To test the Broad Crested Weir option, 27 separate simulations has been done with the upstream design discharge data from the Table 7. The downstream water level is always constant to 0.01 meter. The weir width is also fixed for all the simulation but with the different weir height given in the Table 7. In MIKE 11 it is important to press the button to calculate Q/h relations every time when the weir dimension changes (Figure 67). The program internally defines the Q-h relation for specific weir dimension (Section 5.1). Same number of simulations has also done by with same data in Table 7 but increase the channel length to 20 meter.





Figure 67: Weir Modelling, Type: Broad Crested Weir

5.3.1.2 Option 2: Weir Formula 2 (Honma)

Broad-crested weir is also modelled with the same data of discharge, weir width and height, described in the previous section by applying the Weir Formula 2 (Section 5.1). One of the main important parameter for Weir Formula 2 is the weir coefficient (C1) (Figure 68). It is explained in Section 5.2 that this weir coefficient (C1) is same as the weir coefficient (C) of the general weir Equation [22]. For broad-crested weir, several methods by several investigators to compute the weir coefficient, C has been documented (Section 3.1).

Figure 68: Weir Modelling, Type: Weir Formula 2

For modelling the broad-crested weir the prescribed equation by Bos (1989) is followed to determine the





weir coefficient. One of the main reasons for choosing Bos (1989) is that it considered the velocity head by incorporating a correction coefficient, Cv. Example of determining the weir coefficient, C is given below:

From Section 3.1, according to Bos (1989),

C C C 2

3

2

3g

.

Here, Cd is the discharge coefficient, Cv is the correction coefficient for neglecting velocity head and g is the gravitational acceleration. To determine C, at first, the value of Cd is determined by the following equation (Section 3.1),

C 0.93 0.10H

w

Where, H is the upstream energy head above the weir crest and w is the weir width. As H is not easily measurable, the upstream water head above the weir crest, h is used by. From the data in Table 7, for the first row, the Cd value is:

0.93 0.100.10

10.94

Cv is a function of . Where, L is the weir lenght, h is head above the weir crest and A is the wetted area at the head measurement station which is located just upstream of the weir side. So, for the first row of the data in Table 7,

C Lh

A 0.94 5 0.10

5 0.300.31

Cv is determined as 1.023 from Table 1 which is a function of . Finally the weir coefficient, C

1.023 0.94 2323 9.81

. = 1.639461.

The weir coefficient C is determined for the entire dataset and used as input for the MIKE 11 Weir Coefficient, C1. In spread sheet, with the value of weir coefficient, the predicted value of upstream side of the weir above the weir crest is calculated analytically by rearranging the general weir equation

( . ). So, for the above example, predicted head above the weir crest, .

.

.

0.100324 meter and the upstream water level above the channel bottom, 0.1003240.20 0.300324 meter. Here, p is the height of the weir.

All the values of C and analytically calculated upstream water level are shown in the Table 8.

Table 8: Analytically determined weir coefficient and upstream water level

Sl No

hus

measured

(m)

Q (m3/s)

Cd Cd bh/A Cv C hus

predicted

(m)

1 0.3 0.2605 0.94 0.313 1.023 1.639461 0.300324

2 0.36 0.5495 0.946 0.420 1.042 1.680569 0.362316

3 0.42 0.9135 0.952 0.499 1.061 1.722067 0.424109

4 0.48 1.3455 0.958 0.559 1.08 1.763952 0.485508

5 0.54 1.8405 0.964 0.607 1.093 1.796366 0.547574

6 0.6 2.394 0.97 0.647 1.11 1.83566 0.608233

7 0.66 3.0035 0.976 0.680 1.12 1.863655 0.670105

8 0.7 3.439 0.98 0.700 1.13 1.888001 0.710082





9 0.76 4.1355 0.986 0.727 1.14 1.91637 0.771109

10 0.84 5.14 0.994 0.757 1.156 1.959033 0.85058

11 0.88 5.675 0.998 0.771 1.163 1.978827 0.890333

12 0.7 1.4295 0.96 0.41 1.042 1.636699 0.712486

13 0.92 3.42 0.982 0.56 1.082 1.674207 0.950594

14 1.08 5.255 0.998 0.63 1.11 1.888648 1.076552

15 1.14 6.025 1.004 0.65 1.12 1.91712 1.133767

16 1.22 7.11 1.012 0.68 1.135 1.958276 1.207887

17 1.3 8.26 1.02 0.71 1.15 1.999842 1.280392

18 1.34 8.865 1.024 0.72 1.156 2.018159 1.317281

19 1.4 9.8 1.03 0.74 1.17 2.054569 1.369074

20 0.72 0.3375 0.942 0.16 1.007 1.606011 0.720884

21 0.84 0.991 0.954 0.27 1.018 1.62647 0.845794

22 1 2.1975 0.97 0.39 1.038 1.653748 1.013358

23 1.1 3.1195 0.98 0.45 1.051 1.670797 1.118554

24 1.2 4.1595 0.99 0.50 1.064 1.687846 1.223963

25 1.38 6.31 1.008 0.57 1.086 1.718534 1.413956

26 1.48 7.65 1.018 0.61 1.101 1.735583 1.519385

27 1.58 9.085 1.028 0.64 1.115 1.752632 1.624337

5.3.1.3 Result Analysis for Broad Crested Weir

The longitudinal profile from the model output shows the difference in water surface elevation between upstream and downstream side of the weir. The weir is located at the chainage 32 meter (Figure 69).

Figure 69: Longitudinal Profile of Water Surface Elevation

The measured upstream water level is compared with the analytically obtained as well as the within Mike 11 modelled water level. The model results show that both options do not give the exact solutions. The Upstream water level comes from the Broad Crested type option always give higher value for all the simulation compare to the result from the Weir Formula 2. Though both the outputs give reasonable results, when it is compared with measured upstream water level. When simulated water level with

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0[m]

-2.0

-1.0

0.0

1.0

2.0

3.0

[meter] 1-1-2011 00:00:00

BRANCH1 0 - 100

0 30 31 31 32 35 70 100





Broad Crested weir type option compare with the measured water level, the coefficient of determination (R2) value is 0.998 (Figure 70). On the other hand, for the case of Weir Formula 2, the R2 value is 0.999 (Figure 71). The analytical calculated upstream water level and the model computer upstream water level based on the same form of equation and the weir coefficient is also same for each calculation and they both give exactly the same value. The results are shown in the Table 9.

Figure 70: Measure Vs Simulated Water Level Option: Broad Crested Type

Figure 71: Measure Vs Simulated Water Level Option: Weir Formula 2





Table 9: Output of Analytical and Model Results for Broad‐Crested Weir

Sl No

Q (m3/s) hus

(m)

Observed

Spread sheet Model Result

hus(m)

Analytical

hus (m)

Option: Broad‐Crested

hus (m)

Option: Weir Formula 2

1 0.261 0.3 0.300 0.31 0.300

2 0.550 0.36 0.362 0.375 0.362

3 0.914 0.42 0.424 0.441 0.424

4 1.346 0.48 0.486 0.506 0.490

5 1.841 0.54 0.548 0.572 0.548

6 2.394 0.6 0.608 0.637 0.608

7 3.004 0.66 0.670 0.702 0.670

8 3.439 0.7 0.710 0.746 0.710

9 4.136 0.76 0.771 0.8111 0.771

10 5.140 0.84 0.851 0.898 0.851

11 5.675 0.88 0.890 0.942 0.890

12 1.430 0.7 0.712 0.738 0.712

13 3.420 0.92 0.951 0.987 0.951

14 5.255 1.08 1.077 1.166 1.077

15 6.025 1.14 1.134 1.236 1.134

16 7.110 1.22 1.208 1.327 1.208

17 8.260 1.3 1.280 1.418 1.280

18 8.865 1.34 1.317 1.463 1.317

19 9.800 1.4 1.369 1.531 1.369

20 0.338 0.72 0.720 0.735 0.720

21 0.991 0.84 0.843 0.876 0.843

22 2.198 1 1.003 1.068 1.003

23 3.120 1.1 1.102 1.191 1.102

24 4.160 1.2 1.199 1.315 1.199

25 6.310 1.38 1.370 1.542 1.370

26 7.650 1.48 1.462 1.67 1.462

27 9.085 1.58 1.553 1.799 1.553

When channel widh is increased from 5 meter to 20 meter and the weir size is same as before, then for the Broad Crested type option the upstream water level does not change but it effects the downstream water level which becomes bit lower than previous simulation. The same results also come from the Weir Formula 2 option by using the same weir coefficient. Figure 72 shows longitudinal profile of the simulation number 7 (Table 9); the upstream water level is 0.702 meter and downstream water level is 0.31 meter but when the channel width increased to 20 meter the upstream level does not change but downstream level decreased to 0.10 meter.





Figure 72: Increasing Channel Width: Width 5 m Top and Width 20 m Bottom

But, when the channel width changes, the weir coefficient also changes because, Cv and Cd will be changed, as these values are dependent on the gauge area (upstream wetted area of the weir) and the upstream water head. When weir coefficient will change, it will also reflect the analytical and modelled output water level. The scenario of greater channel width than weir length only can be modelled by Weir Formula 2, not by the broad crested weir option.

This situation with updated weir coefficient cannot be modelled in the study because it requires updated water level and discharge data for this scenario.

5.3.2 Alphabet Weir

The data comes from the laboratory tests from the Colorado University physical model and which are used by Meneghetti (2009) and Thorton (2011) to develop stage-discharge relation for alphabet weir (U-, A- and W-weir) are used in MIKE 11 to model alphabet weir.

Total 34 sets of data are available which covers all the U-, A- and W weirs. To model the alphabet weir, a channel length of 100 meter is chosen. The cross-sections are same as the rectangular cross-section (width 4.877 meter) which is constructed in the laboratory with the prescribed longitudinal slope. The alphabet weir geometry about the effective length of the weir across the direction of flow has been described in Section 4.6. With the equation ((Equation [65] and [71])) prescribed in Section 4.6, the total effective length of the weir is calculated for each U-, A- and W-weir. For alphabet weir the effective





length of the weir is always larger than the channel width.

The upstream boundary condition (Chainage 0 meter) is the discharge which comes from the laboratory experiment. The downstream boundary (Chainage 100 meter) is the water level which value is chosen very low (0.01 meter). In an intermediate position (Chainage 32 meter) the location of the weir is chosen. The processed data for the model is shown in Table 10.

Table 10: Input Data for Alphabet Weir

SL No

Weir Type

Slope m/m

Discharge Q (m

3/s)

U/S Water Level hus (m)

Avg. weir height p (m)

Water Deth above Weir Crest h (m)

ChanelWidthB (m)

PlanAngleѲ (°)

Profile Angle

φ (°)

Weir Length L (m)

Weir Rock Sized50 (m)

1 U 0.0047 0.377 0.182 0.134 0.048 4.877 24.99 3.54 9.305 0.175

2 U 0.0047 0.753 0.242 0.134 0.108 4.877 24.99 3.54 9.305 0.175

3 U 0.0047 1.133 0.269 0.134 0.135 4.877 24.99 3.54 9.305 0.175

4 U 0.0047 0.377 0.186 0.134 0.052 4.877 24.99 3.54 9.305 0.175

5 U 0.0047 0.753 0.244 0.134 0.110 4.877 24.99 3.54 9.305 0.175

6 U 0.0047 0.753 0.245 0.134 0.111 4.877 24.99 3.54 9.305 0.175

7 U 0.0047 0.963 0.261 0.134 0.127 4.877 24.99 3.54 9.305 0.175

8 U 0.0033 0.283 0.170 0.101 0.069 4.877 28.48 2.51 8.437 0.223

9 U 0.0033 0.566 0.222 0.101 0.120 4.877 28.48 2.51 8.437 0.223

10 U 0.0033 0.850 0.267 0.101 0.166 4.877 28.48 2.51 8.437 0.223

11 U 0.0021 0.184 0.158 0.101 0.056 4.877 25.38 1.70 9.206 0.254

12 U 0.0021 0.377 0.189 0.101 0.088 4.877 25.38 1.70 9.206 0.254

13 U 0.0021 0.566 0.223 0.101 0.121 4.877 25.38 1.70 9.206 0.254

14 U 0.0033 0.283 0.157 0.101 0.055 4.877 22.97 2.05 9.950 0.223

15 U 0.0033 0.566 0.207 0.101 0.106 4.877 22.97 2.05 9.950 0.223

16 U 0.0033 0.850 0.238 0.101 0.137 4.877 22.97 2.05 9.950 0.223

17 A 0.0021 0.184 0.181 0.129 0.052 4.877 29.99 1.02 8.129 0.254

18 A 0.0021 0.377 0.226 0.129 0.097 4.877 29.99 1.02 8.129 0.254

19 A 0.0021 0.566 0.254 0.129 0.125 4.877 29.99 1.02 8.129 0.254

20 A 0.0033 0.283 0.199 0.136 0.063 4.877 29.94 1.69 8.137 0.223

21 A 0.0033 0.566 0.233 0.136 0.097 4.877 29.94 1.69 8.137 0.223

22 A 0.0033 0.850 0.276 0.136 0.140 4.877 29.94 1.69 8.137 0.223

23 A 0.0047 0.377 0.200 0.136 0.064 4.877 26.52 2.4 8.901 0.175

24 A 0.0047 0.753 0.249 0.136 0.113 4.877 26.52 2.4 8.901 0.175

25 A 0.0047 1.133 0.297 0.136 0.161 4.877 26.52 2.4 8.901 0.175

26 W 0.0021 0.184 0.126 0.090 0.036 4.877 26.65 2.38 10.863 0.254

27 W 0.0021 0.377 0.171 0.090 0.080 4.877 26.65 2.38 10.863 0.254

28 W 0.0021 0.566 0.203 0.090 0.112 4.877 26.65 2.38 10.863 0.254

29 W 0.0033 0.283 0.150 0.101 0.048 4.877 23.16 2.76 12.385 0.223

30 W 0.0033 0.566 0.188 0.101 0.087 4.877 23.16 2.76 12.385 0.223

31 W 0.0033 0.850 0.224 0.101 0.122 4.877 23.16 2.76 12.385 0.223





32 W 0.0047 0.377 0.163 0.111 0.052 4.877 19.98 3.13 14.251 0.175

33 W 0.0047 0.753 0.205 0.111 0.094 4.877 19.98 3.13 14.251 0.175

34 W 0.0047 1.133 0.246 0.111 0.135 4.877 19.98 3.13 14.251 0.175

The characteristics of broad-crested weir and the rock type alphabet weirs are different. That’s why only option to model the alphabet weir is chosen the Weir Formula 2 (Honma). According to Thorton (2011) the weir coefficient, C is calculated for each type of U-, A- and W-weir (Equation [76] to [80]). The weir coefficient, length and average height of the weir are the main input parameters for weir modelling under Weir Formula 2 (Figure 73). The details calculation procedure to determine the weir coefficient, C for each type of alphabet weirs has been discussed in Section 4.6. Example of determining the weir coefficient, C is given below.

Figure 73: Alphabet Weir Modelling by Weir Formula 2 Honma

From Section 4.5, according to Thorton (2011),

C 23C 2g .

And for U-Weir,

C 0.652d

p.

LB

.

From Table 10, the data of the first row,

C 0.652 0.175 0.134

.9.305

4.877

.

0.79

So,

C 23 0.790 2 9.81 . 2.33

With the same manner the weir coefficient, C is calculated for the U-, A- and W-weir with the prescribed equation by Thorton (2011) as discussed in Section 4.6 (Equation [76] to [79]). This weir coefficient used as an input of MIKE 11 Weir Coefficient, C1. In spread sheet, with the value of weir coefficient, the predicted value of upstream side of the weir above the weir crest is calculated analytically by rearranging the general weir equation ( . ). For the above example, predicted head above the





weir crest, .

. .

.0.067 meter and the upstream water level with respect to channel

bottom, 0.067 0.134 0.201 meter. Here, p is the height of the weir. All the values of C and analytically calculated predicted upstream water level are shown in the Table 11.

Table 11: Analytically determined weir coefficient and upstream water level

SL No

Weir Type

p (m)

hus

measured

(m) Q L Cd C

hus

predicted

(m)

1 U 0.134 0.182 0.377 9.305 0.790 2.334 0.201

2 U 0.134 0.242 0.753 9.305 0.790 2.334 0.240

3 U 0.134 0.269 1.133 9.305 0.790 2.334 0.274

4 U 0.134 0.186 0.377 9.305 0.790 2.334 0.201

5 U 0.134 0.244 0.753 9.305 0.790 2.334 0.240

6 U 0.134 0.245 0.753 9.305 0.790 2.334 0.240

7 U 0.134 0.261 0.963 9.305 0.790 2.334 0.259

8 U 0.101 0.170 0.283 8.437 0.514 1.519 0.180

9 U 0.101 0.222 0.566 8.437 0.514 1.519 0.226

10 U 0.101 0.267 0.850 8.437 0.514 1.519 0.265

11 U 0.101 0.158 0.184 9.206 0.495 1.461 0.159

12 U 0.101 0.189 0.377 9.206 0.495 1.461 0.194

13 U 0.101 0.223 0.566 9.206 0.495 1.461 0.223

14 U 0.101 0.157 0.283 9.950 0.567 1.674 0.168

15 U 0.101 0.207 0.566 9.950 0.567 1.674 0.206

16 U 0.101 0.238 0.850 9.950 0.567 1.674 0.239

17 A 0.129 0.181 0.184 8.129 0.545 1.608 0.187

18 A 0.129 0.226 0.377 8.129 0.545 1.608 0.223

19 A 0.129 0.254 0.566 8.129 0.545 1.608 0.252

20 A 0.136 0.199 0.283 8.137 0.620 1.832 0.207

21 A 0.136 0.233 0.566 8.137 0.620 1.832 0.249

22 A 0.136 0.276 0.850 8.137 0.620 1.832 0.284

23 A 0.136 0.200 0.377 8.901 0.779 2.299 0.206

24 A 0.136 0.249 0.753 8.901 0.779 2.299 0.247

25 A 0.136 0.297 1.133 8.901 0.779 2.299 0.281

26 W 0.090 0.126 0.184 10.863 0.500 1.478 0.141

27 W 0.090 0.171 0.377 10.863 0.500 1.478 0.172

28 W 0.090 0.203 0.566 10.863 0.500 1.478 0.198

29 W 0.101 0.150 0.283 12.385 0.569 1.681 0.158

30 W 0.101 0.188 0.566 12.385 0.569 1.681 0.192

31 W 0.101 0.224 0.850 12.385 0.569 1.681 0.220

32 W 0.111 0.163 0.377 14.251 0.574 1.694 0.173

33 W 0.111 0.205 0.753 14.251 0.574 1.694 0.210

34 W 0.111 0.246 1.133 14.251 0.574 1.694 0.241





Thornton (2011) also formulated another composite general equation to calculate Cd (Equation [80]), which is applicable to all the U-, A- and W-weir (Section 4.6). With this composite equation, the weir coefficient, C and the corresponding predicted upstream water level (analytical) is also determined for the same data (Table 12).

Table 12: Analytically composite weir coefficient and upstream water level

SL No

Weir Type

p (m)

hus

measured

(m)

Q (m3/s)

L (m)

Cd

Composite C

Composite

hus

predicted

(m)

1 U 0.134 0.182 0.377 9.305 0.799 2.360 0.201

2 U 0.134 0.242 0.753 9.305 0.799 2.360 0.240

3 U 0.134 0.269 1.133 9.305 0.799 2.360 0.273

4 U 0.134 0.186 0.377 9.305 0.799 2.360 0.201

5 U 0.134 0.244 0.753 9.305 0.799 2.360 0.240

6 U 0.134 0.245 0.753 9.305 0.799 2.360 0.240

7 U 0.134 0.261 0.963 9.305 0.799 2.360 0.258

8 U 0.101 0.170 0.283 8.437 0.567 1.674 0.175

9 U 0.101 0.222 0.566 8.437 0.567 1.674 0.219

10 U 0.101 0.267 0.850 8.437 0.567 1.674 0.255

11 U 0.101 0.158 0.184 9.206 0.506 1.496 0.158

12 U 0.101 0.189 0.377 9.206 0.506 1.496 0.192

13 U 0.101 0.223 0.566 9.206 0.506 1.496 0.221

14 U 0.101 0.157 0.283 9.950 0.543 1.603 0.170

15 U 0.101 0.207 0.566 9.950 0.543 1.603 0.210

16 U 0.101 0.238 0.850 9.950 0.543 1.603 0.243

17 A 0.129 0.181 0.184 8.129 0.619 1.828 0.182

18 A 0.129 0.226 0.377 8.129 0.619 1.828 0.215

19 A 0.129 0.254 0.566 8.129 0.619 1.828 0.242

20 A 0.136 0.199 0.283 8.137 0.704 2.079 0.202

21 A 0.136 0.233 0.566 8.137 0.704 2.079 0.240

22 A 0.136 0.276 0.850 8.137 0.704 2.079 0.272

23 A 0.136 0.200 0.377 8.901 0.818 2.414 0.204

24 A 0.136 0.249 0.753 8.901 0.818 2.414 0.243

25 A 0.136 0.297 1.133 8.901 0.818 2.414 0.277

26 W 0.090 0.126 0.184 10.863 0.447 1.319 0.145

27 W 0.090 0.171 0.377 10.863 0.447 1.319 0.179

28 W 0.090 0.203 0.566 10.863 0.447 1.319 0.206

29 W 0.101 0.150 0.283 12.385 0.513 1.514 0.163

30 W 0.101 0.188 0.566 12.385 0.513 1.514 0.198

31 W 0.101 0.224 0.850 12.385 0.513 1.514 0.229

32 W 0.111 0.163 0.377 14.251 0.625 1.844 0.170

33 W 0.111 0.205 0.753 14.251 0.625 1.844 0.204

34 W 0.111 0.246 1.133 14.251 0.625 1.844 0.234





5.3.2.1 Result Analysis of Alphabet Weir

The longitudinal profile from the model output shows the difference in water surface elevation between upstream and downstream side of the weir. The weir is located at the Chainage 32 meter (Figure 69).

Figure 74: Longitudinal Profile of Water Surface Elevation

The measured upstream water level is compared with analytically determined water level and from the model output. The analytical output and model output based on the same weir equation and the same weir coefficient and they both give exactly the same results.

The model output results are compared with measured upstream water level. For W-weir the model output gives the best results. The coefficient of determination (R2) for U-, A- and W-weir is respectively 0.9761, 0.9486 and 0.9886 (Figure 75).

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0[m]

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

[meter] 1-1-2011 00:00:00

BRANCH1 0 - 100

0 10 20 30 31 31 32 35 40 50 60 70 80 90 100





Figure 75: Observed Vs Simulated Water Level: a U‐weir b A‐weir and c W‐weir

With the composite weir coefficient, the model results gives slightly better result only for A-weir. In these case the coefficient of determination (R2) for U-, A- and W-weir are 0.9679, 0.963 and 0.9825 respectively (Figure 76). The model results and analytical computed results give the exact value by using the combined weir coefficient.

All the results are shown in the Table 13.





Figure 76: Observed Vs Simulated Water Level by composite weir equation: a U‐weir b A‐weir and c W‐weir





Table 13: Model Results for Alphabet Weir

SL No

Weir Type

Q hus

measured

(m)

Model Result Analytical Result

hus predicted

(m) By Individual weir Equation

hus predicted

(m) By Composite Weir Equation

hus predicted

(m) By Individual weir Equation

hus predicted

(m) By Composite Weir Equation

1 U 0.377 0.182 0.201 0.201 0.201 0.201

2 U 0.753 0.242 0.240 0.240 0.240 0.240

3 U 1.133 0.269 0.274 0.273 0.274 0.273

4 U 0.377 0.186 0.201 0.201 0.201 0.201

5 U 0.753 0.244 0.240 0.240 0.240 0.240

6 U 0.753 0.245 0.240 0.240 0.240 0.240

7 U 0.963 0.261 0.259 0.258 0.259 0.258

8 U 0.283 0.170 0.180 0.175 0.180 0.175

9 U 0.566 0.222 0.226 0.219 0.226 0.219

10 U 0.850 0.267 0.265 0.255 0.265 0.255

11 U 0.184 0.158 0.159 0.158 0.159 0.158

12 U 0.377 0.189 0.194 0.192 0.194 0.192

13 U 0.566 0.223 0.223 0.221 0.223 0.221

14 U 0.283 0.157 0.168 0.170 0.168 0.170

15 U 0.566 0.207 0.206 0.210 0.206 0.210

16 U 0.850 0.238 0.239 0.243 0.239 0.243

17 A 0.184 0.181 0.187 0.182 0.187 0.182

18 A 0.377 0.226 0.223 0.215 0.223 0.215

19 A 0.566 0.254 0.252 0.242 0.252 0.242

20 A 0.283 0.199 0.207 0.202 0.207 0.202

21 A 0.566 0.233 0.249 0.240 0.249 0.240

22 A 0.850 0.276 0.284 0.272 0.284 0.272

23 A 0.377 0.200 0.206 0.204 0.206 0.204

24 A 0.753 0.249 0.247 0.243 0.247 0.243

25 A 1.133 0.297 0.281 0.277 0.281 0.277

26 W 0.184 0.126 0.141 0.145 0.141 0.145

27 W 0.377 0.171 0.172 0.179 0.172 0.179

28 W 0.566 0.203 0.198 0.206 0.198 0.206

29 W 0.283 0.150 0.158 0.163 0.158 0.163

30 W 0.566 0.188 0.192 0.198 0.192 0.198

31 W 0.850 0.224 0.220 0.229 0.220 0.229

32 W 0.377 0.163 0.173 0.170 0.173 0.170

33 W 0.753 0.205 0.210 0.204 0.210 0.204

34 W 1.133 0.246 0.241 0.234 0.241 0.234





6 Conclusion

Application

Weirs are hydraulic structures which are constructed in a river, stream or irrigation canal which act as a barrier across the direction of flow. The main purposes of the weirs are measuring flow, increase upstream water head, flow diversion, protect river banks, reduce erosive energy and allow for fish passage, grade control, river rehabilitation and restoration etc.

Common Types of Weirs

There is wide range of weirs available, differentiated according to their shape and the shape actually originated following specific purposes. The shapes vary from rectangular horizontal weirs over V-notch, oblique, ogee, curved, labyrinth & piano (key) weirs to alphabet weirs. The most common types of weirs are the rectangular broad-crested weir and sharp-crested weir, which can be used as flow control and flow measuring device. Sharp crested weir is useful for flow measuring and gives good rating equation. V-notch is the most precise flow measuring device in a wide range and the crest can be both sharp-crested and broad-crested. It is important to note that a weir cannot be work as a discharge measuring device in submerge flow condition. V-notch weir can be incorporated with other hydraulic devices for efficient fish passage facilities. To increase the efficiency of weirs, they can be placed obliquely across the direction of flow, so that the effective length of the weir increases which increases the flow for a certain upstream water level. Other solution to increase the effective length of the weir are curved, labyrinth, piano key shaped and alphabet weir crests. Except the sharp-crested weir, the other weirs produce variation of nappe; to minimise this undesirable nappe variation, the ogee crested weir has been developed.

Alphabet Weirs

In-stream rock weirs are getting popularity because of their interesting shapes and functionality. These structures are constructed by dumping rocks with little or no concrete. Most of these weirs are U, A and W shaped and generally termed as alphabet weirs. The traditional concrete structures are expensive, resulting in poor fish habitat and less naturally accepted which lead to the development of U-, A- and W-weir. Alphabet weirs can be used to establish grade control, reduce stream bank erosion, energy dissipation, increase aquatic habitat and allow fish passage. The alphabet weirs are recommended to construct in gravel bed channel.

The U- and A-weir are also known as cross vane and the main difference between the two is that in A-weir there is a horizontal sill or step placed in the middle of the weir structure which resembles the shape from U- to A. This extra sill provides extra energy dissipation and extra pool is created inside the sill. The shape of U or A makes it a combination of a weir, vane and drop structure. On the other hand, W- weir acts as two U or V-shaped weir places adjacently for comparatively wide channel so two pools created in the downstream increase the holding, feeding and spawning areas for the fish habitat. Because of the special shape the effective length of the alphabet weir is always greater than the channel width which increases the discharge capacity for a certain upstream water head.

Alphabet weir diverts erosive flow to the centre part of the channel and reduces the velocity gradient in the near bank region. There is a gentle profile angle which utilizes a low weir section pointed upstream to force water flowing over the weir into a hydraulic jump. When designed and spaced properly, these weirs can simulate the natural pattern of pool, run and riffles in the downstream of the structure which is good for different ages of fish habitat. Bridges constructed in on a bend or skew channel can produce abutment scour which can minimise by placing a U-weir in the upstream reach of the bridge. In a wide channel W-weir or double W-weir is placed where two centre pier bridge requires protection. As a grade control structure, the alphabet weir is used to maintain base level in both riffle/pool channels, rapids-dominated stream types and in step-pool channels.

The in-stream rock weir of alphabet shape is not a very old concept and the design guidelines of these weirs are not based on physical processes. The design, effectiveness and performance of these structures are not well documented. There is not enough research on sediment transport and turbulence. General monitoring and field investigation results can give the trend of success and failure





rates of these structures but do not give enough information to determine the real physical process associate with success and failure of a given structure geometry. As a results the alphabet weir in the application stage are not designed for a very wide channel with high flow velocities. Even for small flow the structures cause failure because of not properly design by considering hydraulics. More experimental study is required and qualitative field investigation should incorporate with numerical model with wide range of scenario to better understand the physics for proper design.

The main construction materials for alphabet weirs are rock stone by dumping one layer after another. One of the reasons may be the availability from the surroundings and it requires less efforts. Dumping of stone to make the alphabet shape is not good for high water level channel with high velocity. As the shape is one of most important thing for diverting erosive flow from the stream bank so other stable design construction material should take into consideration for wide range of flow.

Weir Coefficient

Weir coefficient, C is the most important parameter for stage-discharge relationship of weir. Its value depends on the type and shape of the weir as well as the equation used. When C value increases, it also increases the discharge capacity. On the other hand for a certain amount of flow, higher coefficient values lower the upstream water level. The procedure to determine the weir coefficient depends on the types of weirs and many experimental studies have been performed in details to determine its values. These studies are mainly empirical based. While considering any of the formula it is important to consider the limitation and condition of that equation. Most of the weir coefficients are function of weir dimension and head above the weir crest. So to get the correct discharge, the head should be measured in a proper guided way.

Modelling experience with Mike 11

The broad-crested weir and the alphabet weir are modelled only for free flow condition. Accuracy of MIKE 11 to calculate upstream flow depths in rectangular channel are evaluated.

In case of broad-crested weir, the option Weir Formula 2 gives slightly better results in compare to the inbuilt Broad-crested type option. For free flow conditions, the Weir Formula 2 is comparable with the general weir equation and the accuracy of the model results depends on the accuracy of weir coefficient. To calculate the weir coefficient, formulae mentioned by Bos (1989) have been chosen as it is considered the correction coefficient for ignoring the velocity head. While comparing with the measured water level, the simulated water levels give good agreement and for the both type of option the coefficient of determination (R2) are close to 1. With the same weir coefficient, the upstream water level of the weir determined analytically and the model results comes from the Weir Formula 2 exactly matches with the analytical results.

Where the channel width is larger than the weir width than it is justify to model broad crested weir with the Weir Formula 2.

To model alphabet shape weirs in MIKE 11, only Weir Formula 2 is considered. The proper geometry of the alphabet weir cannot be incorporated in MIKE 11 and the flow depth is determined by the stage-discharge equation associate with weir coefficient. To determine the weir coefficient, the only available formula developed by Thorton (2011) has been considered. For alphabet weir MIKE 11 produce exactly same upstream flow depths compare the analytical results. The model results also give satisfactory results in compare to measured water level. From the modelling study it can be said that weir of various shape can be possible to model in MIKE 11 if the stage-discharge expression are well determined with a weir coefficient.

The weir coefficient, developed by Thorton (2011) is comes from the laboratory experiments which is for narrow channel with low flow. This formula needs to be verified with real condition for wide range of discharges. After that it would be justified to use these equations for numerical simulation for various scenarios.

In MIKE 11, weir coefficient can also be used as a calibration parameter. If it is not possible to determine the weir coefficient manually before input it as a data, then one can starts as a trial value and compare the results with upstream measured water level and then can tune the value of weir coefficient. When the value of weir coefficient increases, it reduces the upstream water level and vice versa.





7 List of references

Azimi, A.H. and Rajaratnam.N. (2009). “Discharge Characteristics of Weirs of Finite Crest Lenght.” Journal of Hydraulic Engineering, Vol. 135, No. 12

Bhuiyan, F., Hey, R.D., Wormleaton, P.R. (2007). “Hydraulic evaluation of W-weir for river restoration”, Journal of Hydraulic Engineering, American society of civil of engineers, Vol. 133, No. 6, June 2007, pp. 596-609

Boiten, W. (1980). “The V-shaped broad-crested weir discharge characteristics”, Report on basic research, S 170-VI, Delft hydraulics laboratory

Borghei, S.M., Vatannia, Z., Ghodsian, M. and Jalili, M.R. (2003). “Oblique rectangular sharp-crested weir”, Proceedings of the institution of Civil Engineers, Water and maritime engineering 156, Issue WM2, pp. 185-191

Bos, M.G. (1989). “Discharge measurement structures”, Third edition, International institute for land reclamation and improvement, Wageningen, The Netherlands

Chanson, H. (1999). “The hydraulics of open channel flow”, An introduction, basic principles, sediment motion, hydraulic modeling, design of hydraulic structures, Butterworth-Heinemann.

Chow, V.T. (1959). “Open channel hydraulics”, Second edition, McGraw-Hill Kogakashua Ltd

Goon, H.J. (1973).”Submerged weir flow”, Design note 15, U.S. department of agriculture, soil conservation service, Engineering division, Design branch.

Govinda Rao, N.S., and Muralidhar, D.(1963). “Discharge characteristics of weirs of finite crest width.” La Houille Blanche, 5, 537-545

Herschy, R.W (1995). “Streamflow measurement”, Second edition, E & FN Spon, an imprint of Chapman & Hall, London, UK.

Johnson, C.H. (2011). “Numerical Analysis of River Spanning Rock U-weirs: Evaluating effects of structure geometry on local hydraulics.” Dissertation, Colorado State University, Department of Civil and Environmental Engineering, Fort Collins, Colorado.

Johnson, M.C. (2000). “Discharge coefficient analysis for flat-topped and sharp crested weir ”, Springerink, Journal of irrigation science, Volume 19, no 3, pp: 133-137.

Kindsvater, C.E. and Carter, R.W. (1957). “ Discharge characteristics of rectangular thin plate weirs”, Journal of the hydraulics division, American society of civil of engineers, Vol 83, No 6, pp. 1-36

Loftin, M.K. (1999). “Water Resources Engineering”, the McGraw-Hill Companies, Inc.

Meneghetti, A.M. (2009). “Stage-discharge relationships for U-, W- and A-weirs in unsubmerged conditions”, Master thesis, Colorado state university, Fort Collins, Colorado.

MIKE 11 User Guide (2007). “MIKE 11, A modelling system for Rivers and Channels, User Guide”, DHI Water and Environment

MIKE 11 Reference Manual (2007). “MIKE 11, A modelling system for Rivers and Channels, Reference Manual”, DHI Water and Environment

Labyrinth (2011). Labyrinth and piano key weirs, http://www.pk-weirs.ulg.ac.be, accessed July 2011. Maryland Department of the Environment (2000). “Maryland’s waterway construction guidelines”, The Maryland Department of the Environment Water Management Administration





Puckett, P.R. (2007). “The rock cross vane: A comprehensive study of an in-stream structure”, PhD thesis, North Carolina State University, USA Reclamation (Bureau of Reclamation). (2006). “Alphabet Weir Physical Model Design Write-Up”. Correspondence, July 2006. Reclamation (Bureau of Reclamation) (2007). “Qualitative Evaluation of Rock Weir Field Performance and Failure Mechanisms”, U.S. Department of the Interior, Bureau of Reclamation, Technical Service Center, Denver, Colorado, USA Richard, M., Brendan, B., Yann, G. and CE, R. (2003). “Hydraulic design of side weirs”, Thomas Telford publishing, Thomas Telford Ltd, London,UK

Rosgen, D.L. (2001). “Cross-vane, W-weir, and J-hook vane structures”, Their description, design and application for stream stabilization and river restoration, Wildland hydrology, Inc.

Rosgen, D.L. (2006). “Cross-vane, W-weir, and J-hook vane structures”,Description, design and application for stream stabilization and river restoration, Wildland hydrology, Inc.

Samani, A.R.K. (2010). “Analytical approached for flow over an oblique weir”, Transaction A: Civil engineering, Vol.17, No.2 pp.107-117, Sharif University of Technology.

Savage, B.M., Johnson, M.C. (2001). “Flow over ogee spillway: physical and numerical model case study”, Journal of hydraulic engineering, American society of civil of engineers, volume. 127, no. 8pp: 640-649

Tuyen, N.B. (2006). “Flow over oblique weirs”, MSc. Thesis, Section of hydraulic engineering, Faculty of civil engineering and geosciences, TU Delft, Delf University of Technology.

Swamee, P.K.(1988). “Generalized rectangular weir equations.” Journal of Hydraulic Engineering, American society of civil of engineers, Vol. 114, No 8, pp.945-949

Thornton, C.I., Meneghetti, A.M., Collins, K., Abt, S.R. and Scurlock, S.M. (2011). “Stage-discharge relationships for U-, A-, and W-weirs in un-submerged flow conditions”, Journal of the American Water Resources Association, American Water Resources Association, Vol. 47, No. 1

Zhang, X., Yuan, L., Peng, R. and Chen, Z. (2010). “Hydraulic Relations for Clinging Flow of Sharp-Crested Weir”, Journal of hydraulic engineering, American Society of Civil Engineers, pp: 385-390





8 Appendix

8.1 Notations

A Wetted area at the head measurement station

A* Imaginary wetted area at the control section

B Channel width

C Weir coefficient

Cd Discharge coefficient

Cds Submerge discharge coefficient

Ce Effective discharge coefficient

Cv Correlating coefficient for neglecting velocity head

Fr Froude number

g Gravitational acceleration

H Energy head

h Upstream water depth above the weir crest

hc Critical depth

∆H Energy dissipation due to hydraulic jump

hd Downstream water depth above weir crest in submerged flow

Hd Total energy downstream of the weir

Hv Velocity head

H Total energy head above the weir crest

Kb, Kh Combined effect of viscosity and surface tension

Ks Submerged coefficient

L Effective weir length across the direction of flow

p Weir Height

P Pressure

Ρ Density

V Mean channel velocity

Vc Critical flow velocity

Q Discharge

Qf Free flow discharge

Qs Submerged flow discharge





w Weir width in the direction of flow

Z Altitude

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