final projec.docx

CHAPTER :1

INTRODUCTION

Sri indu college of engineering and tehnology

1. INTRODUCTION

1.1 General:

A hydraulic structure is a structure submerged or partially submerged in any body of water, which disrupts the natural flow of water. They can be used to divert, disrupt or completely stop the flow. An example of a hydraulic structure would be a dam, which slows the normal flow rate of the river in order to power turbines. A hydraulic structure can be built in rivers, a sea, or any body of water where there is a need for a change in the natural flow of water.

Hydraulic structures may also be used to measure the flow of water. When used to measure the flow of water, hydraulic structures are defined as a class of specially shaped, static devices over or through which water is directed in such a a way that under free-flow conditions at a specified location (point of measurement) a known level to flow relationship exists. Hydraulic structures of this type can generally be divided into two categories: flumes and weirs.

Hydraulic structures are used to positively control water flow velocities, directions and depths , the elevation and slope of the stream bed ,and the general configuration of a waterway including its stability and maintenance characteristics.

Many of these structures appear as specials and are expensive , which require careful and thorough hydraulic engineering judgment. Proper application of hydraulic structures can reduce initial and future maintenance costs by changing the character of the flow to fit the needs of a particular project , and by reducing the size and cost of related facilities .

The shape, size ,and other features of a hydraulic structure can vary widely for different projects ,depending upon the functions to be accomplished. Hydraulic design procedures must govern the final design of all structures. This may include model testing when a proposed design requires a configuration that differs significantly from known documented guidelines.

The engineers associated with the design ,construction and efficient working of the various types of hydraulic structures usually try to find out , in advance , how the structure would be have when it is actually constructed. For this purpose the engineers have to resort to experimental investigations. Such experiments are also necessitated in the case of the problems which cannot be solved completely simply by theoretical analysis. Obviously the experiments cannot be carried out on the full size of structures , which are proposed to be erected. It is essential to construct a small scale replica of the structure and the tests are performed on it to obtain the desired information.


1.2 HYDRAULIC MODEL INVESTIGATION:

In the science of hydraulics , many basic flow equations are available to predict the behaviour of the flow of fluids but while deriving them many assumptions are made, making it an ideal situation, which limits their application to only for certain simple situations. In the analysis of more complicated cases of turbulent flow, the difficulties and short comings connected with a theoretical solution are further increased and a mathematical treatment , if at all possible , may be extremely laborious and produce results which can be used safely after verification by experiments and experience.

The engineers associated with the design, construction and efficient working of the various types of hydraulic structures such as dams, spillways etc, usually try to find out ,in advance . how the structure would behave when it is actually constructed. For these purpose the engineers have to resort to experimental investigation. Such experiments are also necessitated in the case of problems which cannot be carried out on the full size hydraulic structures, which are proposed to be erected. It is then essential to construct a small scale replica of the structure is known as its model while the actual structure is called prototype.

MODEL:

The small scale replica of the structure .

PROTOTYPE:

Actual representation of any structure to its actual scale .


Fig shows a prototype of and its model.

Prototype:

Model:


Mostly the models are much smaller than the corresponding prototypes, but in some cases the models may be larger than the prototypes. The model tests are quite economical and convenient ,because the design, construction and operation of the model may be altered several times if necessary without incurring much expenditure till all the defects of the model are eliminated and the most suitable design is obtained. On the basis of the final results obtained from the model tests the design of the prototype may be modified and also it may be predict the behaviour of the prototype.

However , if the complete similarity between the model and prototype exist. The model test results can be utilized to obtain in advance the useful about the performance of the prototype.

1.3 TYPES OF MODEL STUDIES:

Two types of model studies are exist for the study of hydraulic model.

They are

1) Physical model studies

2) Numerical model studies

Understanding flows through open channels, whether natural water bodies such as rivers, lakes, or oceans or manmade structures is of crucial importance of addressing numerous hydraulic engineering problems. These include among the others, selection of suitable waste disposal sites, contaminant transport, and several other ecological problems induced by the presence and operation of hydropower plants in a natural environment. A prerequisite for arriving at such optimal solutions is that complex physics of open channel flows to be understand . These flows ,however, environments and it can involve multiple phases. For that reason, their understanding continues to present hydraulic engineers with a rather formidable challenhe.

Traditional approaches for studying natural river flows are based on field measurements and laboratory experiments. Owing to site and event specific concerns , field studies of natural open channel flows are very expensive, tedious and time consuming. Similar problem , although to lesser extent are associated with the laboratory physical model studies , which further suffer from scale effects owing to non similarity of one or more dominant non dimensional parameters .

The objective of this work is to develop an approach that does not exhibit any of the above short comings and can provide practicing engineers with a very effective tool for understanding natural river flows. To place this work in context, the following section present a brief review in area of physical and numerical modelling.


1.4 PHYSICAL HYDRAULIC MODEL:

A physical hydraulic model is a scaled representation of a hydraulic flow situation.

Physical hydraulic models are commonly used during design stages oto optimize a structure and to ensure a safe operation of a structure. They have an important further role to assist non engineering people during the “decision –making” process. A hydraulic model may help the decision makers to visualize and to picture the flow of field, before selecting a “suitable” design.

Why physical hydraulic model studies?

It is a well established and widely accepted fact among the hydraulic engineering professionals that the physical hydraulic scale model test is not only a choice but an essential tool for testing hydraulic structures before its construction due to its ability to solve complex hydraulic problems which otherwise cannot be solved analytically or computer modelling even with modern computing facility. The main objectives of physical hydraulic model study are:

To develop conceptual layout of overall headworks structures To verify and optimize the initial design of hydraulic structures with respect to cost

and operation To reveal potential demerits of a proposed hydraulic design of various structures and

explore solutions To use as supplementing tool to numerical modelling To research for innovations in hydraulic structures design

Similarly, the main advantages of physical hydraulic modelling are:

It involves comparatively small investment but has huge return It can save the project from unexpected failure It raises the confidence level of both designer and investor It can propose solutions for improvement of defects, if any in new as well as

constructed projects

1.5 VALUE OF PHYSICAL MODEL STUDIES:

Although our ability to model hydraulic performance analytically and computationally is constantly improving, physical models are still an extremely valuable tool. Physical models are often the most feasible and most economical way to incorporate three-dimensional


complexity. Physical models can also include the effects of physical processes that may not be understood well enough to be accurately incorporated into computer simulations.

1.6 CONSTRUCTION OF MODEL:

Selection of the type of model (2D or 3D) based on the type of problem to be handled. Selection of scale ratio for the model based on the discharge available at the site of

model relative to the prototype. If the depth of water available at the model in such way that it has a significant effect

on the velocities measured,then the model has to be distorted. Selection of the material for the construction of the different components of the

structure so that the component serves the purpose assigned to it . Selection of the site in the laboratory such that the water can be conveyed from the

reservoir to the site conveniently .

A variety of types of supporting maps and datasets are required for the development, update, use and proper understanding of hydrologic and hydraulic models. This section outlines the available datasets, provides information on how to obtain each relevant datasets, and provides specific guidance on the use of each dataset.

Experiments:

A series of experiments will be conducted to inspect the occurrence of negative pressure on the structure which may cause the cavitations phenomenon.

Importance of model scale:

An important consideration in the design of a physical model is the selection of an appropriate scale. A model that is larger than necessary will be uneconomical, while a model that is too small may make it difficult to simulate and measure the important physical processes. Modelling experience and a good understanding of the important physical processes in a given flow situation are used to ensure that the correct scale is selected for a physical model study.

Most model studies use water as both the prototype and model fluid. This can lead to scale distortions in the model results, because although we scale down the size of the structures and the flow rates and velocities, we do not scale the physical properties of the working fluid. If the scale is too small, physical properties of the fluid, such as viscosity or surface tension, can have a disproportionately large effect on model performance.


1.7 NUMERICAL MODEL STUDIES:

The above studies are based on numerical equations developed for example to study the cavitations susceptibility on spillway profile of hydraulic structures. Based on the results obtained y Falvey on the incipient cavitation index for spillways surfaces a numerical model will be developed. The model will calculate the cavitations index at various elevations on the spillway surface at suitable interval for various discharges under free flow and gated conditions. It also determines the elevations which have the potential to cavitate under the various discharges and gated conditions.

1.8 ADVANTAGES OF MODEL TESTING:

A hydraulic model may help the decision makers to visualize and to picture the flow of field , before selecting a “suitable” design

The model tests are quite economical. The model tests are very convenient. The design, construction and operation of the model may be altered several

times if necessary. Based on model test results the behaviour of the prototype, can be assessed. By model testing one can obtain optimum design of the parameter.


CHAPTER: 2

LITERATURE REVIEW


2. LITERATURE REVIEW

2.1 CLASIFICATION OF MODELS:

There are many types of models in use which are classified based on different parameters which are presented below:

1. Physical/ chemical classification:

Based on physical/ chemical properties models can be classified as

(i) single phase/ multi phase models (for water and oil phases)(ii) transport modelling (dispersion, advection)(iii) geochemical modelling

2. Classification based on geometry:

The following are the models varying with respect to geometry,

(i) 2-dimensional model(ii) 3-dimensional model(iii) Quasi 3-D model

3. Classification based on algorithm:

Models can be classified based algorithm as following,(i) analytical method(ii) finite differences(iii) finite element method

4. Classification based on distortion:

Distortion of amodel can be geometry distortion, configuration distortion, material or hydraulic distortion. Depending on the distortion model can be classified into two types

(i) distorted model(ii) undistorted model


5. Classification based on bed available :

Based on the type of bed provided in the model , models can be divided as

(i) models with fixed bed (ii) models with movable bed

2.2 DESCRIPTION OF DIFFERENT TYPES OF MODELS

Based on similarity in geometry:

2D model(Two-dimensional model):

Two dimensional models are used for the investigations of basic flow problems at spillways, outlets ,etc., where in all parallel planes the flow is either completely or at least approximately identical.

3D model(Three-dimensional model):

A 3D model is an exact replica of the original structure. It includes each and every minute parameter of the prototype. A solution for a 3d model can be directly applied to the prototype. It deals with every problem of a structure like flow pattern, power regulator, etc.

Quasi 3-D model(Three-dimensional model- Two-dimensional model):

Three dimensional models combined with two dimensional sections of the main part of the structure are used when problems of satial flow must be solved and the flow in one plane is simultaneously investigated.


Based on the bed available:

Models with fixed bed:

Models with fixed beds are used mainly when the problems of bed –load transport and local scour are not studied or relavant, and when problems of water levels and flow patterns only investigated.

Models with movable beds:

Models with movable beds are used if sediment transport, scour and deposition are involved.

Based on distortion:

Distorted model:

A distorted model is one which has its one or more characteristics not similar to the corresponding characteristics of prototype. Thus, in order to predict the performance of a prototype, the laws of distortion has to be applied by providing horizontal and vertical scale ratios or by changing its configuration or material or by adopting different discharges, velocity and time.

Undistorted models:

An undistorted model is one in which all the characteristics of prototype are represented similarly in the model without any distortion in all the aspects viz, geometric , configuration, hydraulic and material distorations.


2.3 THEORY OF SIMILARITY:

The research on scale models is based on the theory of similarity. The theory of similarity shows:

How the model experiments should be theoretically and methodologically prepared. What requirements the model must fulfil to depict reality on a reduced scale as

faithfully as possible. Parameters to be measured during experiments. How to the research results must be processed. To what phenomenon the obtained results are applied and what is the extent of their

validity.

THEORY OF SIMILARITY HAS TWO PARTS:

Physical analysis Dimensional analysis

PHYSICAL ANALYSIS:

In a physical analysis , the flow conditions are said to be similar to those in the prototype if the model displays “similarity of form(geometric similarity), similarity of motion(kinematic similarity), and similarity of forces(dynamic similarity)”.

2.4 TYPES OF SIMILARITES:

There are three types of similarities to be established for complete similarity to exist between model and its prototype. After establishing complete similarity between model and prototype, the results from model studies can be used to predict the behaviour of prototype. The similarities are as below:-

GEOMETRIC SIMILARITY KINEMATIC SIMILARITY DYNAMIC SIMILARITY


GEOMETRIC SIMILARITY:

Geometric similarity exists between the model and the prototype if the ratios of corresponding length dimensions in the model and the prototype are equal. Such a ratio is defined as scale ratio.

Length scale ratio = Lr= lp/ lm = dp/dm = Hp/Hm

Where the p-refer for p-prototype and m- model parameters respectively. Length , depth and height are the parameters involved in geometric similitude.

KINEMATIC SIMILARITY:

Kinematic similarity implies that the ratios of prototype characteristic velocities to model velocities are the same

Velocity scale ratio:

Vr =vp/vm =(V1)p/(V1) m =(V2) p/(V2)m

Kinematic similarity can be determined if flow nets for the model and prototype are geometrically similar, which is turn means that by mere change in scale the two flow nets –one for the model and other for the prototype-one can be superimposed.

Kinematic similarity exists between the model and prototype if

The paths of the homologous moving particles are geometrically similar, and If the ratios of the velocities as well as acceleration of the homologous particles are

equal.

DYNAMIC SIMILARITY:

Dynamic similarity exists between the model and prototype which are geometrically and kinematically similar if the ratio of all the forces


acting at homologous points in the two systems viz., the model and prototype, are equal . Thus for flows to be dynamically similar, the ratios of the various forces acting on the fluid particles in one flow system should be equal to the ratios of similar forces at corresponding points in the other flow system.

Dynamic similarity implies that the ratios of prototype forces to model forces are equal

Force:

fR =(f1)p/(f1)m =(f2)p /(f2)m

Work and power are other parameters involved in dynamic similitude.

In the problems concerning fluid flow, the forces acting may be any one , or a combination of the several of the following forces:

Inertia forces Fi

Friction or viscous forces Fv

Gravity forces Fg

Pressure forces Fp

Elastic forces Fe

Surface forces Fs

Inertia force( Fi):

It is equal to the product of mass and acceleration of the flowing and acts in the direction opposite to the direction of acceleration. It is always existing in the fluid flow.

Friction force(Fv):

It is equal to the product of shear stress due to viscosity and surface area of flow. It is present in fluid problems where viscosity is having important role.

Gravity force (Fg):

It is equal to the product of mass and acceleration due to gravity of the flowing fluid. It is present in case of open surface flow.

Pressure force(Fp):

It is equal to the product of pressure intensity and cross sectional area of the flowing liquid. It is present in case of pipe flow.


Surface flow(Fs):

It is equal to the product of surface tension and length of surface of the flowing fluid.

Elastic force(Fe):

It is equal to product of elastic stress and area of the flowing liquid.

Notes :

1. Geometric similarity is not enough to ensure that the flow patterns are similar in both model and prototype (i.e. kinematic similarity).

2. The combined geometric and kinematic similarities give the prototype to model ratios of time , acceleration, discharge, angular velocity .

For flowing liquid ,the above mentioned forces may not always be present. And ,also the forces,which the present in a fluid flow problem,are not magnitude. There are always one or two forces which dominates the other forces. These dominating forces govern the flow of fluid.

Inertia force is the force of resistance offered by an inert mass to acceleration . according to Newton,s second law of motion, the magnitude of inertia force is equal to the product of particle mass and particle acceleration and its direction opposite to the direction of the acceleration of the particle.the conditions are required for complete dynamic similarity are developed from the newton’s second law of motion. If in a certain system of flowing fluid, a fluid particle of mass M is subjected to acceleration “a”. The inertia force of the particle mass “Ma”.

Again, if all the above noted forces exist in the system under construction, then the resultant force∑F,along on the particle, which is the vectorial sum of all the forces acting on the particle ,will be equal to the inertia force of the particle i.e.

∑F = Fv + → Fg+ → Fp + → Fe + → =(Ma )


For complete dynamic similarity to exist between and its prototype,the ratio of inertia forces of the two systems must be equal to the ratio of the resultant forces. Thus the following relation between the forces acting on model and prototype develops:

In addition to the above noted condition for complete dynamic similarity, the ratio of the inertia forces of the two systems must also be equal to the ratios of individual component forces i.e..the following relationships will be developed.

It may thus be mentioned that when two systems are geometrically, kinematically and dynamically similar, then they are said to be completely similar or completely similitude exists between the systems. However, as started implies geometric and kinematic similarities and hence if two systems are dynamically similar, they said to be completely similar. Moreover . As indicated later, for complete similitude to exist between the two systems viz. model and prototype, the dimensionless and ∏ terms, formed out of the complete set of variables involved in that phenomenon, must be equal.

2.5 DIMENSIONLESS NUMBERS:

Dimensionless numbers are those numbers which are obtained by dividing the inertia force by viscous force or gravity force or pressure force or surface tension force or elastic force. As this is a ratio of one force to the other force, it will be a dimensionless number.

These dimensionless numbers are also called non –dimensional parameters.

The following are the important dimensionless numbers:

i) Reynolds number ii) Froude’s numberiii) Euler’s numberiv) Mach’s number

i) The Inertia Force Ratio :

Inertia force = mass * acceleration

= ρ ×volume×(velocity/time)

=ρ × (velocity/time)×velocity

=ρ ×AV×V

=ρL2 V2

Since area A has the dimension as L2


ii) Reynolds number:

Since Fi = ρ L2V2

Fu = ρV2

FiFv

¿ρ L 2 V 2

μVL = [

ρVLμ

] =[ VLϑ

]

Where (μρ

) = ϑ the kinematic viscosity of the fluid.

This non –dimensional ratio VLϑ

is called “Reynolds number”(Re) in honor of O.Reynolds ,

a British physicist. Thus Reynolds number signifies the relative predominance of the inertia to the viscous forces occurring in the flow system. The larger the Reynolds number, the greater will be the relative magnitude of viscous force.

iii) Froude number (inertia-gravity force ratio):

Fi = ρ L2 V2

Fg = mass × acceleration due to gravity

=(ρ × volume) × g

= ρL 3 g

FiFg

= ρ L 2 V 2

ρL3 g=

V 2Lg

The square root of this ratio V

√ gL is known as “Froude number” after W.froude, a british

naval architect who first applied it to the practical problem of investigating the resistance to ships.

Froude number may also be interpreted as a ratio of mean velocity to the velocity of a small wave in quiet fluid. Its value equal to one is considered as critical value.


iv) Euler number(inertia –pressure force ratio):

Euler number =inertia force

pressure force

Inertia force Fi = ρ L2V 2

Pressure force Fp = pressure intensity × area

Where p-represents pressure intensity.

FiFg

= ρ L2 V 2

PL2 = ρV 2

P =

V 2

Pρ

The square root of this ratio V

√Pρ

is designated as Euler number named after swiss

mathematician .

Euler number is represented by the symbol “Eu ”. The reciprocal of this number viz (1/Eu ) is known as “Newton number”. Further ratio of pressure force to inertia force is known as “ pressure coefficient”.

v) Mach number(intensity- elasticity force ratio):

Mach number = intensity

elastcity forc e

Intensity Fi = ρ L2V 2

Elasticity force Fe = bulk modulus of elasticity × area

= (K × A ¿ =(K× L2)


Where K is the bulk modulus of elasticity of the flowing liquid.

FiFe

= ρ L2 V 2

KL2 = V 2

Kρ

= V 2

C2

Where C= √Kρ

,which represents the velocity of sound in that fluid medium whose K

and ρ are being considered.

The ratio (v2 / c2 ) is known as ‘ Cauchy number’. The square root of this ratio i.e (v/c) is known as “mach number”(Ma). As mach number represents a ratio of two velocities, its value equal to one ,is

considered as critical value. This is so because it amounts to the characteristics velocity of the phenomenon

becoming equal to the velocity of sound in that fluid medium . It becomes more significant when Ma < 1 , V< C the flow is termed as subsonic If Ma = 1 , V=C flow is considered to be sonic . When Ma >>1 flow is termed as hypersonic. However, when mach number relatively small say Ma <.4,the effect of

compressibility of the fluid can be together neglected.

vi) Weber number(inertia –surface tension force ratio ):

Weber number = inertia force

surface tension force

Inertia force Fi = ρ L2V 2

Surface tension force Fs = σL

Where σ represents surface tension.

The square root of this ratio is known as “Weber number” In analogy with the other numbers, a smaller weber number signifies larger

predominance of surface tension force and vice versa.

2.6 SIMILARITY LAWS OR MODEL LAWS:


The results obtained from the model tests may be transferred to the prototype by the use of model laws which may be developed from the principles of dynamic similarity. It may , however, be pointed out that .in the case of almost all the hydraulic structures, for which model studies are required to be carried out , it is quite rare that all noted forces are simultaneously predominant in the phenomenon. More ever, debarring certain exceptions , in most of the problems only one force in addition to the inertia force is relatively more significant than the rest of the forces, which may either not exists or may be negligible magnitude.

Under these circumstances the various model laws have been developed depending upon the significant influence of each of the forces on the different phenomena. In the derivation of these model laws, it has been assumed that for equal values of the dimensionless parameters the corresponding flow pattern in model and its prototype are similar.

1. Reynolds model law:

For the flows where in addition to inertia, viscous force is the only other predominant force, the similarity of flow in the model and its prototype can be established if the Reynolds number is same for both the systems. This is known as Reynolds model law, according to which

(Re)model = (Re)prototype

or

{ρ V Lμ }m = {ρ V L

μ }p

Applications:

Flow of incompressible fluid in closed pipe. Motion of submarines completely under water. Motion of aeroplane Flow around structures and other bodies immersed completely under moving fluids.


Some of the phenomena for which the Reynolds model law can be a sufficient criterion for similarity of flow in the model and the prototype are flow of incompressible fluid in closed pipes , motion of submarines completely under water , motion of air planes, and flow around structures and other bodies immersed completely under moving fluids.

1. Froude model law :

When the force of gravity can be considered to be the only predominant force which controls the motion in addition to the other force of inertia , the similarity of the flow in any two such systems can be established if the Froude number for both the systems is the same.

Applications:

Free surface flow’s flow over spillways sluices etc. Flow of jet from nozzle or orifice. Problems in which waves are likely to be formed on the surface.

Problems in which fluids of different mass densities flow over one another.

Some of the other phenomena for which the Froude model law can be sufficient criterion for dynamic similarity to be established in the model and the prototype are free surface flows such as flow over spillways, sluices etc, in which gravity is a motivation force, flow of jet from an orifice or nozzle ,problems in which waves are likely to be formed on the surface and problems in which fluids of different mass densities flow over one another.

Where the various quantities with subscript r represent the corresponding scale ratios.

Above equations may be used to obtain the scale ratios for various other physical quantities on the basis of Reynolds model law. Some of the scale ratios are shown in below table:

Descripton of quantities

Scale ratios Reynold’s law Froude’s law

Length Lr Lr

Velocity µr/ Lr ƥr Lr1/2 gr

1/2

Time Lr2ƥr/µr Lr

1/2 gr1/2

Acceleration µr2/ Lr

3 ƥr2 gr

Discharge Lrµr/ƥr Lr5/2 gr

1/2

Force µr2/ƥr ƥrLr

3gr


Work, Energy and Torque µr2Lr/ƥr ƥrLr

4gr

Pressure intensities µr2/Lr

2ƥr ƥrLrgr

Power µr3/Lrƥr

2 ƥrLr7/2gr

3/2

2. Euler Model Law:

In a fluid system where supplied pressures are the controlling forces in addition to the inertia force and the other forces are wither entirely absent or are significant, the dynamic similarities is obtained by equating the Euler number for both model and its prototype. This is known as Euler model law according to which

(Eu)model = (Eu)prototype

or vm/ (pm/ƥm) = vp/(pp/ƥp)

or vr/ (pr/ƥr) = 1

The above equation represents the primary relationship for the Euler model law which may be used to evaluate the scale ratios for various others physical quantities in accordance with Euler model law .

Euler model law may be contemplated as an essential requirement for establishing dynamic similarity in an enclosed fluid system where the turbulence is fully developed .so that the viscous force are insignificant , and also the forces of gravity and surface tension are entirely absent

APPLICATIONS:

In an enclosed fluid system where the turbulence is fully developed ,so that viscous forces ,gravity forces and surface tension forces are entirely absent

Mach Model Law:

If in any phenomenon only the forces resulting from elastic compression are significant, then the dynamic similarity between the model and its prototype may be achieved


by equating the mach number for both the system. This is known as ‘Mach Model Law’, according to which

(ma)model =(ma)prototype

or Vm/(km/ƥm) = Vp/(kp/ƥp)

or Vp/(kp/ƥp) = 1

The expression represented by the above equation may be considered as the basic relationship for mach model law from which the scale ratios for the other physical quantities may be derived.

The similitude based on mach model law finds extensive application in aerodynamic testing and in phenomenon involving velocities exceeding the speed of sound . in additional to this , it is also applied in hydraulic model testing for the case of unsteady flow, especially water hammer problems.

APPLICATIONS:

In aerodynamic testing. Phenomenon involving velocities exceeding the speed of the sound Hydraulic model testing for case of unsteady flow. Water hammer problems.

WEBER MODEl LAW :

When surface tension effects predominate in additional inertia force the pertinent similitude law is obtained by equating weber number for the model and its prototype .which is known as Weber-model law. Thus according to this model law

(We)model = (We)prototype

Or vm/(m/pm Lm) = vp/(p/ pp Lp )

Or vr/(r/pr Lr) = 1

The above equation may be considered as the basic equation for Weber model law, and the scale ratios for the various physical quantities may be derived with the help of this equation.

Some of the practical cases where surface tension forces dominate and accordingly the Weber model law can be the sufficient criterion for the dynamic similarity to be established between the model and the prototype are – flow over weirs involving very low head, very thin sheet of liquid flowing over a surface, capillary waves in channels etc.


APPLICATION:

Flow over weir involving very low heads. Very thin sheet of liquid flowing over a surface. Capillary waves in channel.

.

CHAPTER : 3

CASE STUDY ON

SANGAM BARRAGE


3. CASE STUDY ON PUICHINTHALA PROJECT

3.1 INTRODUCTION:

Pulichintala project on the river Krishna, estimated to cost Rs. 180 crore in 1988 impounds about 46 thousand million cubic feet (tm cft) of and directly benefits about 12 lakh acres of land in guntur & Krishna districts resulting in an additional yield of 3 quintals of paddy per acre per year. The additional benefit was estimated ar Rs. 120 crore per year in 1988. The project generates 150 megawatts (MW) of electricity which will benefit Nalgonda and guntur districts, the dam was 1290 metres long and 42 metres high is proposed to be built across the river krishna at Pulichintala village in Guntur district and nemalipuri village on other side of the river is Nalgonda district. The project is 120 km downstream project and above the prakasham barrage which goes waste into bay of bengal in August, September & October months in every year. The Pulichintala project which is a balancing reserviour with a capacity of 47 tm cft, doesnot have its own ayacut but strengthens the ayacutunder the prakasham barrage. The project does not have distributary canals, if pulichintala project becomes a reality, the ayacut under prakasham barrage need to depend on release of water from Nagarjuna sagar during nursery and transplantation of paddy periods the lower levels of water in nagarjuna sagar in august & september this year coupled with inadequate water in the prakasham barrage reserviour, transplantation of paddy in guntur and krishna district was delayed and the area under the paddy shrank. The pulichintala project will augment water in the prakasham barrage reserviour the surplus water impounded in the pulichintala reserviour will be released to the prakasham barrage reserviour with rapid development of 22 lakhs


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acre command area under the nagarjuna sagar project and constructions of dams in the upper reaches of krishna river in karnataka and maharastra , inflows into the prakasham barrage have been dwinding, dislocating the agricultural operations in the krishna delta . Incidentally the proposed project wil lreduce the road lenght between chennai & Hyderabad by about 40 km and improves water table in parts of guntur and nalgonda districts adjoining the reserviour.

A balancing reservoir is proposed across river Krishna near Pulichinta Village in Guntur District ( 85.0 Km upstream of Prakasam barrage and 115.0 Km down stream of Nagarjuna Sagar Dam), for storing 45.77 TMC of water for stabilization of existing ayacut of 13.08 Lakh acres of Krishna delta and for early transplantation of paddy crop during June and July.Administrative approval for Rs. 681.604 Crores was accorded by the Government vide G.O.Ms. No. 208 dt. 18-11-2005. Revised administrative approval for Rs. 1281.0 Crores was accorded by the Government vide G.O.Ms.No. 90 dt. 04-08-2009. The construction of head works of the Project were entrusted to M/s Srinivasa Constructions Limited CR 18G JV, Hyderabad for their quoted amount of Rs. 268.87 Crores with a tender premium of less 18.4% and agreement concluded vide S.E’s agt. No. 1SE/2004-2005 Dt. 30/9/04.


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3.3 BENEFITS OF THE PROJECT:

1)Additional yield of Paddy can be achieved due to early transplantation of paddy crop, resulting an additional benefit to the ayactudars of Krishna delta every year.

2)Additional yield of pulses in Krishna delta resulting additional benefit every year.3)Coconut trees can be grown on the bunds of nursery tanks which gives annual

benefit.4)Pisci culture can be developed in the reservoir to give an additional income5)Hydro Electric power can be generated upto 120 MW.

• Administrative Approval = Rs. 681.604 Cr.• Revised Administrative approval = Rs. 1281.00 Cr.

(G.O.Ms. No.90 Dt.4-8-2009) Details of Rs. 1281.00 Cr a) Head works = Rs.390.00 Cr. b) Land Acquisition = Rs.264.13 Cr. c) R&R = Rs.364.72 Cr. d) Environment&Ecology(Forest) = Rs.109.73 Cr. e) Others( incl. establishment) = Rs.152.42 Cr. ------------------- = Rs.1281.00 Cr. -------------------

• Value of Work = Rs.314.96 Cr. (Agt. amount 268.87+ Supplemental items (Agt to be concluded)+Rs.46.09Cr) Supplemental items =SLB to DLB=22.45Cr.Raised trunnion=12.91Cr. & Extra stilling Basin=10.73Cr.

• Storage Capacity (Gross) = 45.77 TMC• Live Capacity = 36.23 TMC


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CHAPTER:4

PHYSICAL MODEL STUDIES


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4.1 Conversion of prototype discharge to model discharge:

Discharge of prototype is given in cumecs. It is converted to model discharge in cusecs by using conversion 1 cumec = 35.314 cusecs

Let Qp be discharge in prototype = 21240 cumecs = 750069.36 cusecs Qm be discharge in model Lr be scale = 1:100

Now, prototype discharge is converted to model discharge by using formula Qp = Qm/(Lr)2.5

Now the scale is fixed by trial and error method in such a way that model discharge should be 4 to 6 cusecs.

And now Lr is fixed, and all the prototype hydraulic particulars are converted to model hydraulic particulars by using Lr.

Particulars Prototype ModelMax. flood discharge 21240 cumecs 4.664 cusecsF.R.L/ M.W.L +35.000 m 29.633 w.r.t

crestlevel +36.340

Crest level +32.200 m 20.188U/S Floor levelD/S Cistern level

+31.000 m +28.970

23.7066

4.2 Estimation of discharge in Model:


Discharge is allowed in model by using notches.

Flow over notches:

A weir or notch is generally used for measuring the flow of liquids. A weir is an opening in the sidewall of a tank at top. The stream of liquid coming out the weir is known as a nappe, sheet, or vein. There is no difference between a notch and weir except that the former is a small structure and has sharp edges. A weir is generally an overflow structure, with a broad crest, built across an open channel. The terms air and weirs are used synonymously in general. The top of weir wall over which the liquid flows is known as the sill or crest. The head under which the weir is discharging is measured from the crest to the free surface.

Flow through rectangular notch:

Discharge over the rectangular notch of crest length ‘b’ and working under a head

’H’.

Q=2/3 cd b 2g H3/2

Where cd= coefficient of discharge which depends on length of weir, the head H, the

degree of sharpness of the edge etc. and is about 0.62. The actual value of the cd for a

particular notch should be obtained from experiments.End contractions:

If the length of the weir is less than the width of the channel, the nappe contracts at

the sides. The width of the nappe at the crest is less than the crest length b, and the weir is

said to have end contractions. Effective length, b’=b-0.1 n H

Where n= no. of end contractions.


Flow through triangular notch:

A triangular notch, also called a V-notch, is of triangular shape with apex down.

Q=8/15 Cd2g tan (1/2) H5/2

Where Cd=0.6 in general

.

The coefficient of contraction of a notch depends upon the length of the wetted perimeter. In

a triangular notch there is no base to contraction. The contraction is due to sides only.

Consequently the coefficient of discharge is fnotchesly constant in a triangular notch for all

heads. A triangular notch is very accurate for the measurement of low discharge.

Trapezoidal notch:

It has the shape of trapezium. Discharge through a trapezoidal notch is

Q =2/3 cd b 2g H3/2 + 8/15 Cd2g tan (1/2) H5/2.

Estimating of discharge by using rectangular 1 mt notch:

Here in pulichinntala model studies rectangular notch of 1 mt length will be used. By

using formula Q=2/3 cd b 2g H3/2 level of water to be maintained.

Notch tables will also be used to know the level of water to be maintained in notch so

as to have particular discharge in model.


4.3 Velocity studies at various points:

Velocity in model is determined by using pitot tube connected to manometer. Here kinetic energy of flow is converted to potential energy by rising of water level in

manometer.

Pitot tube:

The pitot tube is used to measure the local velocity at a given point in the flow stream and not the average velocity in the pipe or conduit.


Manometer:

Difference in manometer head h is calculated and velocity is detrmined by formula v=2gh

4.4 Determining the direction of flow of water in model:

It would be better if the flow of water in model is normal to axis of dam. Flow of water is checked by using potassium permanganate dye. If flow of water is not normal to transverse section of spillway, then guide banks are

to be provided so as to make flow normal to transverse section of spillway.


ELEVATION OF BARRAGE


Experiments:

Reservoir levels , tail water level, velocities of water at different points along with flow features were noted for

free flow conditions for different discharges i.e 100% discharge with all gates opened 75% discharge with all gates opened 50% discharge with all gates opened 25% discharge with all gates opened

By throttling all the gates uniformly for different discharges i.e 100% discharge at FRL condition 75% discharge at FRL condition 50% discharge at FRL condition 25% discharge at FRL condition


CHAPTER: 5

EXPERIMENTS AND ANLYSIS OF RESULTS

5. EXPERIMENTS AND ANALYSIS OF RESULTS

5.1 Selection of Site: -

A site suitable for the construction of 3D Model of Sangam Barrage was selected in the out-door field laboratory of Hydraulics Laboratory and the ground was cleared -off the Debris/Jungle and a leveled tray prepared to pave the way for the proposed model.


5.2 Development of Infra Structure: -

The infrastructure required for the model i.e., flumes, sumps, channels, shutters to carry the water into the model and Tail channels to connect re-circulation with main flumes (channel) are constructed at the model site. Necessary Pumps/Motors were arranged at the field laboratory for pumping of water for re-cycling during model experiments.

5.3 Construction of Model: -

A geometrically similar Composite/3D Model representing all design and field features of Sangam Barrage is constructed to a scale of 1:100 in the outdoor Hydraulics Laboratory based on the relevant technical information such as net levels on both upstream and downstream of Dam with pertinent features like piers, Gates, aprons, NOF’s on both sides of Dam, Training Walls etc. as furnished by the concerned authorities vide Drawing and the actual ground conditions are simulated in the model. Adequate gauge chambers are also provided on the upstream & downstream side of the dam to measure the water levels accurately.

Flow from U/S to D/s


5.4 Scope of 3-D Model Studies:

i) To confirm the adequacy of the vent way for passing an MFD of 750069.36 Cusecs (21240 Cumecs) with upstream floor level being at +31.000 m.

ii) To confirm the Energy Dissipation Arrangement provided on the downstream of the Dam.

iii) To Observe Velocities at different Chainages on the downstream of the dam along and across the River course for various discharges/flood flows.

iv) To observe the comprehensive flow features on the upstream and downstream i.e. cross–currents, eddy flows etc.


Dry Model - View from Down Stream

Down Stream


5.5 Hydraulic particulars:

Following are the Hydraulic Particulars pertaining to the Dam as per the Drawings

and Technical Information furnished by the Field Authorities.

Sl.

No.Parameter Value

1 MFD (Maximum Flood Discharge)21240 cumecs/

7,50,069.36 Cusecs

2 Full Reservoir Level +35.000 m

3 Crest Level of Barrage +32.200 m

4 Crest Level of Scour sluice +31.200 m

5 Number of Vents 54

6 Size of Vents 12 m x 2.8 m

7 Designed Flood Discharge +13182 cumecs

8 U/S MWL for 21240 cumecs +37.460 m

9 U/S MWL for 13182 cumecs +39.460 m

10 U/S Floor level +31.000 m

11 D/S Cistern Level +28.970 m

12 Thickness of Intermediate Piers 2.00 m

13 Number of scour vents 6

14 Dimension of Scour Vents 12 m x3.800m

15 Type of Gate Vertical lift

16 Catchment Area 50122 sq.Km


Experiments:

The proposed experiments were broadly divided into four setups as Series-I,

II,III and each setup is explained in sequential order with the main focus of the studies on the

following Hydraulic Parameters: -

1. To confirm the Adequacy of the Vent-way with 54 vents operative to pass the MFD 21240 Cumecs (7,50,069.000 Cusecs) with water level at + 37.460 m on the upstream of the Barrage.

2. To observe the efficacy of Energy dissipating arrangement provided Satisfactory or not.

3. To observe velocities on the downstream of the Barrage across the River course with corresponding tail water levels for various discharges/Flood flows.

4. To observe general flow features on the upstream and downstream of the Barrage i.e. Cross-Currents, Eddy Flows etc.


Side View of the Barrage When Model is running


5.6 EXPERIMENTS

Series – 1 All Vents Fully Opened Including Scour Bay

Setup – 3

In the first instance, as per the scheduled program, experiment was carried-out for MFD with corresponding Tail Water Level with all gates fully in open condition. A discharge corresponding to MFD i.e., 10619 Cumecs (3,75,000cusecs) considering 54 gates as operational was allowed into the model through a 3 feet long standardized Rehbock Notch fitted in a flume on the upstream of the model. After stabilization of flow, the Tail Water level at El. + 37.347 m at a distance of 320 m from the axis of the Barrage as per the rating curve furnished by the concerned authorities was maintained artificially by means of tail gate arrangement provided at the exit of the model. After total stabilized condition of flow throughout the model, observations were noted which are as follows: –

i) The Reservoir level realized on the upstream level of the was noted to be at +

31.000 m as against the full reservoir level of +35.000 m.

ii) Energy dissipation provided is working satisfactorily as the Jump is forming

with in the stilling basin.

iii) Velocities Heads for 50 % Discharge from the surface of water were

measured on the downstream of the Barrage at Chainages At end sill,

At Ch : 200m From end sill, ,

At Ch : 700 m from end sill and At U/S from the axis of the Barrage along

the River course and at different locations across the river, which are recorded

and shown in Annexure I.

iv) It was observed that the flow from the upstream of the Barrage is normal to

the axis of the Barrage (a general form of stream lined flow) and no skew

flows were observed.

v) Maximum velocity (for MFD) observed on the downstream of the Barrage is

of the order of 3.96 m/sec against the Vent No.3 at End sill from the axis of

the Barrage in the river course.

vi) The length and height (Elevation) of the Training Walls on both the flanks is

found to be sufficient for all flows and no cross-currents, eddy flows are

observed.


Series – 3 All Vents Fully Opened & SCOUR VENTS CLOSED(10% less on MFD)

Setup 4

After observing the above parameters, the experiment was continued with MFD 4778.5 Cumecs (1,68,750cusecs) with all gates fully open condition and scour vents closed, by maintaining the Tail Water Level After total stabilized condition of flow through the model, the flow features and velocities observed at various locations are shown in Figure and Annexure I and observations were noted which are as follows:-

i) The Tail water level realized at a distance of 320 m from the axis of the spillway is about +36.290 m.

ii) The Hydraulic Jump is forming within the stilling basin and hence the Energy dissipation provided is satisfactory.

iii) Velocities Heads for 25 % Discharge from the surface of water were


At Ch : 200 m From end sill, ,

At Ch : 700 m from end sill and At U/S from the axis of the Barrage along the River course

and at different locations across the river, which are recorded and shown in Annexure I.

from the axis of the Barrage along the River course and at two different locations across the river, which are recorded and shown in Annexure I.

iv) It was observed that the flow from the upstream of the dam is normal to the axis of the Barrage (a general form of stream lined flow) and no skew flows were observed.

v) Maximum velocity (for MFD) observed on the downstream of the Barrage is of the order of 3.71 m/sec against Vent No.15 at a distance of 500 m from the axis of the Barrage in the river course.

vi) The length and height (Elevation) of the Training Walls on both the flanks is found to be sufficient for all flows and no cross-currents, eddy flows are observed.

Series – 3 All Vents Fully Opened & SCOUR VENTS CLOSED (10% less on MFD)


Setup 3

After observing the above parameters, the experiment was continued with MFD 6371.4 Cumecs (2,25,000cusecs) with all gates fully open condition and scour vents closed, by maintaining the Tail Water Level After total stabilized condition of flow through the model, the flow features and velocities observed at various locations are shown in Figure and Annexure I and observations were noted which are as follows:-

i) The Tail water level realized at a distance of 320 m from the axis of the spillway is about +34.01 m.

ii) The Hydraulic Jump is forming within the stilling basin and hence the Energy dissipation provided is satisfactory.

iii) Velocities Heads for 30% Discharge from the surface of water were


At Ch : 200 m From end sill, ,

At Ch : 700 m from end sill and At U/S from the axis of the Barrage along the River course

and at different locations across the river, which are recorded and shown in Annexure I.

from the axis of the Barrage along the River course and at two different locations across the river, which are recorded and shown in Annexure I.

iv) It was observed that the flow from the upstream of the dam is normal to the axis of the Barrage (a general form of stream lined flow) and no skew flows were observed.

v) Maximum velocity (for MFD) observed on the downstream of the Barrage is of the order of 1.4 m/sec against Vent No.15 at a distance of 700 m from the axis of the Barrage in the river course.

vi) The length and height (Elevation) of the Training Walls on both the flanks is found to be sufficient for all flows and no cross-currents, eddy flows are observed.


Series 1. ALL VENTS FULLY OPENED INCLUDING SCOUR BAY

MFD =750000 Cusecs scale 1:100


Series 2. ALL VENTS FULLYOPENED &SCOUR VENTS CLOSED

MFD = 750000 Cusecs


Series 3. ALL VENTS FULLY OPENED & SCOUR VENTS CLOSED

MFD =750000 Cusecs 10% Less on MFD

sl no set up nQp Qm Q% Notch Head (c Notch F TWL maintained (mDepth Of Water (Depth Of Water (cTWL chamber FR 1 2 3 4 5 6 7 8 9 10 111 set up 1675,000.00 6.75 100% 22.39 82.74 36.9 7.89 7.98 89.282 set up 2 506250 5.062 75% 18.65 79 36 7.03 7.03 88.333 set up3 337500 3.375 50% 14.38 74.73 34.92 5.95 5.95 87.254 set up 4 168750 1.688 25% 9.15 69.5 33.52 4.55 4.55 85.85

.


CHAPTER: 6

CONCLUSION


6. CONCLUSION

i) The Water Level/Reservoir Level realized on the upstream of the barrage when MFD is passing through all the (54) Vents of the Spillway is observed to be at u/s MWL +37.460 m against the designed FRL of +35.000 m. Hence ventway provided is just sufficient to pass the MFD for 54 vents in operation.

ii) As reported, the functioning of Energy Dissipation Arrangement provided is satisfactory.

iii) The Maximum velocity observed is of the order of 3.71m/sec against

Vent No.3 at end sill from axis of the barrage for MFD under free flow condition with corresponding Tail Water Level of +37.347 m.

v) With the existing approach conditions the flow on the upstream of the barrage is observed to be stream-lined and normal to the dam axis devoid of any skewness.

v) The flow on the downstream of the barrage is also observed to be

stream-lined devoid of Cross-Currents or Eddy flows etc.


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