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Module 1: Los procesos de los ríos Modelos y Puente

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Physical River Models

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Lecture – 14: Physical River Models

Welcome all of you to this last class in the river engineering course and today, we will talk about physical river models okay, basically the experimental works what is necessary to do, understand the flow process, sediment process in rivers, so you say scale-down models. So to start that I will tell it that regarding the physical river models, we should have a knowledge of dimensions and similitudes that is what I have covered in fluid mechanics which is a MOOC course is available. So, please go through that 2 lectures on dimensions and similitudes that some component of that I will cover it here but more details of dimensional analysis and the similitudes, you can follow the MOOC course on the fluid mechanics designed by me. So, for you can look at that and more or less we are following river mechanics P.Y. Julien book and that is the physical river modelling concept what we will today, we will discuss it. And since it is a last class anyway, I am not going to more details of physical river models but I will try to develop a confidence in you on how to scale physical models for a river or a river reach. So, if you look at that I will show some case study of river physical models used for Indian rivers and then I will talk about the different type of similitudes as you know from basic similitudes like geometric similitudes, kinematic similitudes and the dynamic similitudes. And here we talk about 2 types of models; rigid bed models, mobile bed river models, so you can understand it, the one case there is sediment transport is dominated, so that is what is the physical river models and we can have a rigid bed models where the sedimentary process is not that dominated, so that case we can use the rigid bed models. So, we can divide into 2 parts, one is exact Froude similitudes, another for the tilted river models. Similar way the mobile bed river models will be a complete, incomplete models, I am not discussing much details here incomplete models, we will just discuss about complete mobile bed similitudes. Before trying these things to develop a river physical models, we should have an enough knowledge on river engineers, that knowledge will be help us to establish an appropriate river physical models.

And what is our objectives that we should try to understand it engineering point of view, it is
also a knowledge, the art of modelling we should follow it to have an appropriate model for a
river problems.
(Refer Slide Time: 04:05)Now, if you look at that very interesting lab setups what we have and there we are trying to
set up a small set of river model for Brahmaputra rivers, if you can look at the river
Brahmaputra, if you look at this braided loop and the flow is incoming and out goings. The
same concept when you talk about if you look at, this is what the prototype level which is
showing the satellite imagery and we are developing physical models okay, which in the lab
scale is a scale down models.
It is a scale down models and with a training work we can see these, there are geotubes are
there which are the training works, before implementing the geotubes, we can know it what is
the impact of the geotubes on river morphology that is what we conducted a study and try to
locate how the geotubes are effective for arresting the bank erosions. So, if you look at that
concepts and what we have done it that particle size of the d50 of the prototypes, this is the
prototype, this is the models is the same.
The river discharge is a 10,000 m3/s, we put a model is 10 lit/s, the river length of the island
is 6 kilometres, in the model scale is 1.73 m, width of the island is 2.5 kilometres and the
model level is 0.72 m. Now, if you look at the width of the right channels, width of the left
channels that is what we have given there, so this is a scale down model.
So, if you look at that geometry scale down models is there as well as the discharge the scale
down is there from 10,000 m3/s to 10 lit/s and it is a mobile bed condition, it is also mobile
bed conditions where the sediment, the bed load sediment process are happening it that is
what you can see it. So, we always have a scale down models from river to the laboratoryscales that is the scale down models. Today, we will discuss it how to develop a scale down
models that what we will discuss in more details.
(Refer Slide Time: 06:50)
Now, if you look at the similar one examples I will take it that physical river model study for
a bridge in a Brahmaputra rivers that means, this is the bridge proposed to be constructed, the
same models of the bridge and the piers, you can see it that is what is done it on a physical
model setups. So, this is the proposed road bridge on the Brahmaputra rivers, the same things
what if you look it, it is implement in physical models.
And these dots are representing bridge piers okay, this is what the main channels and other
channel formations are also there. So, this is the prototype, and this is the models. Now, let us
look at how about the scale down is happens it; here the design discharge is 99000 m3/s
which is close to 100 year return period flood, horizontal scale is 1:575, the vertical scale is
1: 65, river width 15 kilometres.
The basic idea to know it discharge intensity variations upstream afflux due to the bridge, so
if you look at that we before implementing a bridge projects, we do a physical river models to
know it how much of discharge intensity variations are there, how much of scour formations
will be there at different bridge piers. What could be the upstream afflux will be there
because of this construction of this bridge.
So, this type of the prototype to models we do it in the laboratory to know it the flow and
sediment transport processes, what is happening in the model scale and that basis we predictit what could be the scenario in real river conditions that is what we do a scale down models.
We remember here we have used the horizontal scale and vertical scales are the different that
means, is a distorted models, this is what; distorted models were the horizontal scales and
vertical scales are the different.
Why we do follow basically the different distorted models for example, if you look at these
rivers as you can see that the length of these rivers can be in terms of 100 km, width is 15 km
and the depth of the flow maximum will be the 30 m that means, it is a kilometre orders in
the plan form dimensions, one is 100 km, another is 15 km but depth when you talk about 30
m.
If it is that the scale we cannot use a geometrical similarity models, exact models because we
cannot represent the same scale in the vertical direction and the horizontal direction because
of the river dimension that is what many of the times we talk about the scale issues okay,
because the scale, the dimensions of the river in terms of length, width and depth that is what
is very considerable, so we need to have a distorted models. That means, we will have a
vertical scale and the horizontal scales are the different mostly, the vertical scales are the
finer scale than the horizontal scales, which will be the coarser scale.
(Refer Slide Time: 10:58)
Now, if you look at 3 dimensional models which is a CWPRS Pune, central water power
research stations in Pune. If you look at this Kosi barrage, you can see this Kosi barrage and
abutment, all leads are there, so it is try to know it how this flow is varying it that is what is at
the physical models levels. The same way if you look at this Kosi rivers where we lot ofstudy has been done for the Kosi barrage like putting the different type of river training
works, what is effectiveness of river training works to protect the river banks and this is what
the river flowing.
So, if you look at that we conduct a series of physical based models for the Kosi barrage as
well as Kosi rivers, same way when we talk about hydraulic structures like Indira Sagar dam,
a 3d models we prepare it, exactly a scale down 3d models, Punatsangchhu II 3d models.
Similar way this is the port and this is the back water at Poompuhar embankments.
So, if you look it that way always we conduct a physical river models to try to understand it
at the structure, how the flow process are happening it, this is a 3 dimensional models, this is
2 dimensional models representing the plan forms, river training, how we have to have a river
trainings and you also have a back water for this condition. So, we do the physical river
models, central water power research stations Pune is leading in our country to do physical
river models.
(Refer Slide Time: 12:53)
Now, if you look at that what, how you do the hydraulic similitudes, that means we have a
prototype, we have the models, we try to do a scale downs that is the reasons, prototypes
conditions which we give a subscript of the p is a full scale conditions, field conditions, m is
in the hydraulic models conditions built in the laboratory. The the ratio between the model to
prototypes.That means, what we do it if any parameters like a length; length of prototypes by the length
of models that what will give length ratio. So, we define in the scale on this, we define this
the scale of this by this length of prototype by the length of model. So, if you look at that
most of the cases we do the studies in on the earth, so considering that if we first look at the
gravitational accelerations of the prototypes and models, the gp and gm’s they are equals.
That is the reasons the scale ratio for the gravitational acceleration field, it is comes out to be
1, so if you are using the same fluids, same water or same liquid whatever is there, the same
liquids you are doing any physical models, so the basic proportions like a density ratio,
acceleration due to gravity, ratio of dynamic viscosity, kinematic viscosity, unit weight ratio
all becomes 1.
So, the condition is that we are using the same fluid, so you are using the same fluid, so then
our model ratios will be the same. The most of the times as I said it we cannot do a total
geometric similarity models because we have a lot of constraint like the length, the physical
limitations in terms of space, water discharge, instrumentation accuracy, how accurate
instruments we have to measure the velocity, measure the flow depth, measure the turbulence
properties, measure the sediment.
So, what is accuracy that also matters to design the scale, the scale does not mean it that we
can do very, very finer scale unless otherwise you have a highly accurate instrumentations
with us. So, similar way we should implement the boundary conditions, upstream and
downstreams like these flow models, if you look at the proposed road bridge, this is the
bridge structures and this is the guide bunds and you can see that how the flow things will
happen.
So, in this case we need to know it what could be the upstream conditions, what it could be
the boundary conditions, when you develop the physical models these 2 conditions also
should be satisfied.
(Refer Slide Time: 16:22)Now, if you look at what you are doing it as I said it, the vertical scales zr directions, so
basically what you have any models you put it okay, in a 3 dimensions, you have a xr, you
have a zr which is vertical directions and we have the yr. So, most of the times we try to look
it whether you want to do a 3 dimensional models, then you need to locate all these
component; zr, yr, xr.
The z is vertical ratio, y is a lateral ratio, xr is the longitudinal ratio, longitudinal length ratio,
ratio of the longitudinal directions. When you do exact geometric similitude, okay that means
your vertical length case is equal to the horizontal length scales that means, your xr is equal to
yr equal to zr okay which can be done it for a smaller scale, it is exact similitudes, similitudes,
that means you are not distorting it.
You are not talking about like a 3d models of a hydraulic structure like a dam structure, we
can have all these conditions satisfied okay. So, the ratios can be also satisfy xr, yr and zr and
this is the conditions when you have that is the length ratio called geometric similitudes, we
call geometric similitudes but many of the times as I said it the vertical scale of the rivers are
much lesser, vertical depth of the rivers are much lesser as compared to width or in
comparison to the length.
So, we do the vertical scales different than the lateral scales in that case, we have a model
distortions will happen that when the vertical scales are not equal to the horizontal scales. The
distortions factors yr/zr, that length ratio in the yr directions by zr is a ratio in vertical
directions, so vertical scale is not equal to z scale. In this is the case if you want to estimatethe flow area in case of exact geometric similitudes, area will be the square of the lengths
okay, the square of the length ratio, the volume will be the cube of the length ratio.
But that is what will be substitute in case of volume, you will have xr, yr, zr product of these,
the horizontal surface and the cross section surface will you can interpret, it will be like this.
So, basically when you use a distorted models, you use xr, yr, zr’s are the different otherwise,
if you have exact similitude models, you use the Lr. So for that, area will be the Lr2 and the
volume will be the Lr3.
But in case of when you are using xr, yr, zr’s are the different in a distorted models, then your
area will be different depending upon whether is a horizontal surface or the cross sectional
surface. In horizontal surface you will have xr and yr and in the cross section surface you will
have a zr, yr.
(Refer Slide Time: 20:23)
The volume will be xr, yr, zr, so please give a attentions to these which is the ratios and now if
you look at basic next similitude is called kinematic similitude, as we discussed in
dimensional and similitude analysis and similitude analysis in fluid mechanics, it is the same
concept. That means is this is just here we are taking example the flow past a cylinders. This
is the original cylinders or you can say is a bridge piers and the flow is coming in which is a
cylindrical shape.
This is the prototype levels how the stream lines are happening, how the velocity
distributions are happening it. The same geometry kinematic similitude we have to do it, thescale down this the diameter of this bridge piers, which is a cylindrical bridge piers to this
shape and then we can have a scale for velocity components. And so that the streamline
patterns, the velocity ratio that is what will be maintain it, the length ratio, the time ratio and
the velocity space go whatever is there that what can maintain it.
So, if you look at that part that means we are introducing whenever kinematics similitude that
the parameter involving length and time that is velocity, accelerations and kinematic
viscosity, it is that is also will have the same Vr we given as a Vp/Vm. So, you have a tr will be
the time scales, will be ratio of the time scale will be tp/tm, if you look at that and basic
properties as you know it, the velocity is equal to length by time and you know it velocity
divided by the time will be the accelerations.
So, if you use these 2 terms and try to look at the velocity and the length ratios as we deduct
that part and the accelerations as we can consider is a 1 okay. So, in that case we will get it
the Vr/zr5 = 1 which is the flow Froude numbers, V2/ρgh is a constant that is what you know
it. So, when you do this kinematic similarity, you needs to have the Froude similitudes
criteria. So, even if that the that is what is hold good at, that is what is indicating here that
you will have that conditions.
So, once this is the conditions is there, the Froude similitude criteria is there, you can
compute it time scales as well as the velocity scales. Now, we can go for the distorted models
where the time scales varies along the directions, the restricted to simulations 1D flow it
cannot account for the 2 dimensional, 3 dimensional convective and turbulence accelerations.
When you do the distorted model or tilted model, so it is not used to model the vorticity,
diffusion, turbulent mixings and the dispersions process. This distorted model you can use it
and most of the times when you talk about the river scales we have to use distorted models.
(Refer Slide Time: 24:00)Now, if you look at the dynamic similitudes that means, we are talking about as if you look at
the prototype of models okay, it is a scale down models. So, all the gates are also scale down,
flow properties are scale down such a way that if I take, a points which is having the force
because of inertia, the gravity force, friction force and the pressure force and force diagrams
like this. The force diagrams will be more like the same, the force diagrams will be the more
or less is same but only the magnitudes will be difference.
When you attain that then we call dynamic similitudes, then we call the dynamic similitudes
at that what each conditions happens it, that means it is a involving with a mass, that means
mass density, specific weight, dynamic viscosity when we try to have the ratio between the
model and prototypes, so that is what is the ratio of the densities and these mass ratios what is
there.
So, individual force acting on corresponding fluid element must have the same force ratio in
both the systems they have the same force ratio, exact similitudes of all force in hydraulic
structure is impossible, only at the full scales. So, when you look it to have an exact
similitudes, that means that geometric similitudes should be satisfied, kinematic similitudes
should be satisfied and the dynamic similitudes should be satisfied.
If these 3 condition is satisfied, looking all these equations we can know it, it is only possible
when you have a full conditions, which you cannot implement, the river the scale model you
can; cannot implement the full scale model for a rivers, it is impossible. So, we go for
distorting forces, how do we get it? We look at which are the forces negligible like whetherthe friction force is dominated, whether the inertia force is dominate, the gravity force or the
pressure force.
So, based on that we try to look at which is a dominated forces like most of the open channel
flow, the gravity plays the major roles. So, we try to look at the gravity is more impact when
you have an open channel flow or you look it where the viscosity or flow resistance play the
major roles that is way we try to look at which component of force we can use for the
prototype models which will be so the dominating forces, other in not a negligible forces like
other components always we can neglect it that is the strategy being followed for river
physical models.
(Refer Slide Time: 27:06)
Now, let us coming to the rigid bed models when you consider it like you have a hydraulic
structures, spillway, you have a fish ladder passage, where the sediment transport is not that
significant or you are not considering the sediment part that extensively, we are looking more
towards the flow structures. We try to move towards to understanding how the turbulence
behaviours are happening not considering the sediment part.
So, we can go for rigid bed models which is the fixed bed, as name implies the no sediment
transport that is what we consider it where the silt parameters is less than 0.03. So, you can
see a river flow where you have the shield parameter is lesser than 0.03, then you can
consider it is rigid bed model. So, basically what we try to look at resistance to flow should
be the same for model as well as the prototypes.So, it needs to have an exact geometric similitudes that means resistance of flow can be
neglected or you can have a distorted tilted models where a resistance to flow is important
that is what you have to consider. Exact geometric similitudes and Froude number similitudes
can be simultaneously maintain it when the resistance to flow can be neglected. So, you have
a geometric similitudes, you have the Froude number similitudes that is what we can
maintain it, it is possible to do it, only if the resistance to the flow can be neglected.
So, the basically it is well suited for the 3D, 3 dimensional flow around the flow structures
where the sediment is not river but when the long river reaches like Brahmaputra or river
where flow resistance play the major force components, we cannot neglect it. In that times we
should do Froude number similitudes as well as resistance similitudes which basically the
manning’s equations or stricklers manning’s equations we can use it to satisfy for tilted and
distorted models.
(Refer Slide Time: 29:50)
Now, if you look at that exact Froude number similitudes as already you have discussed is
that we try to look it first the exact geometric similitudes should be there for the Froude
number criteria and which is what 3 dimensions. If the vertical accelerations are not
negligible that is what you need to have 2 dimensional models and these are the particular
well suited model for flow near the hydraulic structures, as I said that spillway structures or
sluices structures, so all these.
And you can have the length scale and the mass scales like this, you have a length, the time
and the mass scales using the fundamental dimensions we can consider it and we can deriveit, I do encourage you to follow dimensional analysis or similitudes to any fluid mechanics
courses to know it how to get it the mass ratio is a function of the length ratio or the that is
what you have to do it by considering this dimensions of the variables.
(Refer Slide Time: 31:05)
Now, if you look it there is a 2 conditions again is coming it that exact similitude imposes
constraint that usually difficult to work for modelling of the rivers, scaling the size of
roughness also its matters it. So, when you do a river models, what is the size of roughness
you will get it, this is a river which is the your prototype, and you have a scale models which
will be the few centimeters and you have in terms of meter, 10 m.
So you need to try to look at the resistance what you are saying it, are same orders okay, so if
you look it that way, the size of roughness elements according to length scale will maintain
the same resistance parameter as long as the Reynolds numbers, the grain Reynolds number
is greater than the 70 for both the models and the prototypes. This is the possible only very
coarse bed materials are put it on the bed streams.
The basically, here you can have a fine sand to represent that here put it either the boulders to
obtain, this is the model to obtain the same resistance. So, you try to know it how to do the
scaling, when we try to locate the similitudes of this part.
(Refer Slide Time: 32:51)Now, if you look at how you need to do it, as I said it we need to look at, as we discussed
earlier, near bed conditions will be drastically change because laminar sub layer thickness in
the hydraulic models is relatively too thick, in the hydraulic models is a relatively too thick
that is the reasons you require to scale down the laminar sub layer thickness ratios in terms of
shear velocity ratio, then the length ratio.
So, I just to repeat it that when you try to make it the flow behaviour, what is happening at
the river level, the same thing conditions you want to talk about near bed conditions at the
what is happening at the flume level at the laboratory scales, what we need to look at, what is
the thickness of laminar sub layers. The laminar sub layer thickness in a laboratory scales is
much thicker than the case of the laminar sub layers in a river.
So, we need to do a scale down of laminar sub layer thickness, so if you look at that way we
need to have, we cannot maintain exactly geometric similitudes, the length similitudes require
very small particles, the scale modelling produce very large laminar sub layer thickness in the
model. What I am trying to do it because I have been completing this course of these lectures,
physical river models it needs to have to have a lot of knowledge on the near bed conditions
what it happens in the river.
The same conditions whether you can prevail or you can maintain with a ratio at the flume
scale that is the very challenging task like the same concept like hydraulic smooth regimes,
resistance to flow increase as Reynolds numbers decreases, the resistance to flow will be
larger for the model than the prototype in case of hydraulic smooth regimes. So, we try to;river knowledge, mechanics knowledge what we have if you try to correlate it, you can see
that when you do a scale down models, there is an issue on change of the laminar sub layers
as well as the flow resistance.
The exact similitudes of near bed flow conditions cannot be preserved when the same fluid is
used, you just try to understand it, the viscous effect cannot be neglected, exact similitudes
would require different fluid for the models and the prototypes. That means, the river may
have the waters but you can do other materials where you can satisfy this the flow resistance
similitudes, that same ratio we can maintain it at the model levels and the compared to the
prototype levels.
(Refer Slide Time: 36:12)
Now, if you look at we can develop the length resource, considering the basic definitions of
the fluid properties, flow properties that is what is we can do it. If you look at this rigid bed
okay, exact one, tilted one and complete general ones okay, there is a 3 conditions. For a
mobile bed you can have a, m equal to i.e. sticklers coefficient m equal to 1/6 and you have,
when you have a grain particle size ratio that what is not equal to 1, you will have and you
have incomplete.
So, if you look at this tables, which clearly indicates that I can compute the geometric particle
diameters, the cross sections areas, the volume kinematic properties like a time, the flow and
the bed velocity, shear velocity, settling velocity, discharge unit bed loads okay, qbr stands for
unit bed loads which is we consider for the mobile bed.
(Refer Slide Time: 37:25)And if you look at next ones; the mass, the pressure, the shear stress, force and the
dimensionless number like slope, Darcy Weisbach, Fr values, flow Froudes, Reynolds
number, shield numbers, Grain Reynolds numbers, dimensionless diameters, this is these
states is a dimensional and the sediment densities. If you look at that I just encourage you
have the self-readings on these chapters to know it what is the scales and the exact and the
tilted case.
In case of the mobile bed we have a general, we have a different conditions of dimensionless
diameters and the incomplete part which we are not discussing here. So, if you try to look at
these things we can derive it and that is the modelling part.
(Refer Slide Time: 38:25)Now, I will be not going more details but I will just put it as an empirical nature but you try
to derive it, when you do the Froude similitudes for tilted river models, so we make a tilted
river models yr, length the vertical ratio and the lateral ratios are not equals, in case of the
tiltings you will have a case of xr the longitudinal directions ratio and the vertical directions
that not acceptable.
So, when vertical and lateral accelerations of water can be neglected with respect to
gravitation, so the basically it allows the different scale for flow depth and the sediment size,
again you can look it when you have a the grain Reynolds numbers is greater than 70s the
resistance to flow depends upon relative submergence that is what we discuss when you
talking about the resistance.
(Refer Slide Time: 39:36)
That way if you look at how you have to have a 2 equations to satisfy here, this is a flow
Froude numbers as well as the flow resistance equations. To satisfy both we are writing the
resistance equations in terms of flow Froude numbers here, as a flow Froude numbers is
equal to 1 and you have a dsr is not equal to 1, from the resistance to flow which is Darcy
Weisbach formulas we can establish exponent component is a functions of h/ds, the
submerged ratio.
And if you put in that equations, you will get it the flow Froude ratios are, is a function of zr,
xr and dsr and exponent of 2m, this m when you talk about manning stricklers equations, this
m is equal to 1/6 that is what if you remember the manning stricklers equations, we define them is a function of dx to the power 1/6 that is the power exponent point which m equal to the
1/6 that the instead of we can use m equal to 1/6.
(Refer Slide Time: 40:59)
So, in that case you will have the 3 criteria, just try to understand, so you have a 3 criteria’s
that means it will be mostly satisfy the Froude numbers, Mannings stricklers similitude
criteria. If you use all these equations, then you will get it in a distorted models you will have
a relationship like this. A tilted models you will have a not equal to that, satisfy the flow
Froude numbers, you will have a dsr relations.
Now, if you look at for these equations we have a 2 degree of freedoms, selecting from 3
parameters xr, zr and dsr we can consider that and change that value still, the model and
prototypes should satisfy these 2 conditions, as it follow these conditions we can have a say
that it is having the Froude and Manning stricklers similitude criteria.
(Refer Slide Time: 42:12)Now, if you look at this is what the notes is there for when you do the rigid boundary models,
we have to look at that when you have a roughness is typically increase with a
disproportionate large block of sticks are used to produce the stage discharge relationship
which are comparable to the prototypes okay that is we have to do it and most of the times as
it says that when you work with a distorted rigid boundary models you need to have intuitions
and judgment of experience okay of engineers that how it is matter is.