Diversion headworks are structures constructed at the head of a canal to divert river water into the canal. They include components like weirs, barrages, canal head regulators, divide walls, fish ladders, and guide banks. The objectives are to raise water levels, control silt entry, regulate water flow, and allow fish passage. Proper site selection and design are needed to prevent failures from subsurface water flow, uplift pressure, hydraulic jumps, or scouring during floods. Remedies include increasing seepage lengths, adding sheet piles, and using thicker impervious floors.
Types- selection of the suitable site for the diversion headwork components
of diversion headwork- Causes of failure of structure on pervious foundation- Khosla’s theory- Design of concrete sloping
glacis weir.
Any hydraulic structure which supplies water to the off taking canal known as headwork. Storage head work is that stores water when it is available and supplies when needed.
Types- selection of the suitable site for the diversion headwork components
of diversion headwork- Causes of failure of structure on pervious foundation- Khosla’s theory- Design of concrete sloping
glacis weir.
Any hydraulic structure which supplies water to the off taking canal known as headwork. Storage head work is that stores water when it is available and supplies when needed.
This presentation covered Diversion head work topic. Details topics selection of the suitable site for the
diversion headwork- different parts of
diversion headwork- Causes of failure of
structure on pervious foundation- Khosla’s
theory- Design of concrete sloping glacis weir covered.
This presentation is covered topic of cross drainage work. In which topics necessity of Cross drainage structures, their types and selection,
comparative merits and demerits, design of
various types of cross-drainage structure:aqueducts, siphon aqueduct, super passage
siphon, level crossing and other types covered.
Defination Headworks is a civil engineering term for any structure at the head or diversion point of a waterway. It is smaller than a barrage and is used to divert water from a river into a canal or from a large canal into a smaller canal.
This presentation covered Diversion head work topic. Details topics selection of the suitable site for the
diversion headwork- different parts of
diversion headwork- Causes of failure of
structure on pervious foundation- Khosla’s
theory- Design of concrete sloping glacis weir covered.
This presentation is covered topic of cross drainage work. In which topics necessity of Cross drainage structures, their types and selection,
comparative merits and demerits, design of
various types of cross-drainage structure:aqueducts, siphon aqueduct, super passage
siphon, level crossing and other types covered.
Defination Headworks is a civil engineering term for any structure at the head or diversion point of a waterway. It is smaller than a barrage and is used to divert water from a river into a canal or from a large canal into a smaller canal.
chapter-3.pptx: CHANNEL HEADWORKS AND CANALSmulugeta48
Purposes:
Raises water level in the river
Regulates supply of water into the canal
Controls the entry of silt into the canal
Provides some storage for a short period
Reduces the fluctuations in the level of supply in river
Temporary diversion head works
Consists of a bund constructed across river to raise the water level in the river and will be damaged by floods.
2. Permanent diversion head works
Consists of a permanent structure such as a weir or barrage constructed across river to raise water level in the river.River section at the site should be narrow and well-defined.
Should have a large commanded area.
Site should be such that the weir (or barrage) can be aligned at right angles to the direction of flow in the river.
Good foundation should be available at the site.
Site should be easily accessible by road or rail.
Overall cost of the project should be a minimum
A water distribution system is a part of water supply network with components that carry potable water from a centralized treatment plant or wells to consumers to satisfy residential.
Topics:
1. Types of Diversion Head Works
2. Weirs and Barrages
3. Layout Diversion Head Works
4. Causes of Failures of Weirs and Barrages on Permeable Foundations
5. Silt Ejectors and Silt Excluders
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Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Courier management system project report.pdfKamal Acharya
It is now-a-days very important for the people to send or receive articles like imported furniture, electronic items, gifts, business goods and the like. People depend vastly on different transport systems which mostly use the manual way of receiving and delivering the articles. There is no way to track the articles till they are received and there is no way to let the customer know what happened in transit, once he booked some articles. In such a situation, we need a system which completely computerizes the cargo activities including time to time tracking of the articles sent. This need is fulfilled by Courier Management System software which is online software for the cargo management people that enables them to receive the goods from a source and send them to a required destination and track their status from time to time.
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CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
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Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
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The proposed project is developed to manage the automobile in the automobile dealer company. The main module in this project is login, automobile management, customer management, sales, complaints and reports. The first module is the login. The automobile showroom owner should login to the project for usage. The username and password are verified and if it is correct, next form opens. If the username and password are not correct, it shows the error message.
When a customer search for a automobile, if the automobile is available, they will be taken to a page that shows the details of the automobile including automobile name, automobile ID, quantity, price etc. “Automobile Management System” is useful for maintaining automobiles, customers effectively and hence helps for establishing good relation between customer and automobile organization. It contains various customized modules for effectively maintaining automobiles and stock information accurately and safely.
When the automobile is sold to the customer, stock will be reduced automatically. When a new purchase is made, stock will be increased automatically. While selecting automobiles for sale, the proposed software will automatically check for total number of available stock of that particular item, if the total stock of that particular item is less than 5, software will notify the user to purchase the particular item.
Also when the user tries to sale items which are not in stock, the system will prompt the user that the stock is not enough. Customers of this system can search for a automobile; can purchase a automobile easily by selecting fast. On the other hand the stock of automobiles can be maintained perfectly by the automobile shop manager overcoming the drawbacks of existing system.
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2. • Diversion Headworks:
• Types- selection of the suitable site for the
diversion headwork- components of diversion
headwork- Causes of failure of structure on
pervious foundation- Khosla’s theory- Design
of concrete sloping glacis weir
3. Diversion Head-Works
• The works which are constructed at the head
of the canal in order to divert the river water
toward the canal, so as to ensure a regulated
continuous supply mostly silt free water with
certain minimum head into the canal, are
known as diversion headworks.
5. Objectives of Diversion Head Works
• The Following are the objective of Diversion
Head works
• To Raise the water level at the head of canal.
• To form a storage by construction of dykes on
both side of banks of the river so that water is
available throughout the year.
• To control the entry of silt into the canal and to
control the deposition of silt at the head of canal.
• To control the fluctuation of water level in the
river during different seasons.
10. Selection of Site for Diversion Head
Works
• The following points should be considered to
select a site for this diversion headworks.
• The river should be straight and narrow at the
site
• The elevation of site should be higher than the
area to be irrigated for gravity flow.
• River banks at site should be well defined and
stable.
• Valuable land upstream of the barrier like
weir or barrage should not be submerged.
11. Selection of Site for Diversion Head
Works
• Material of construction should be locally
available.
• Roads or railway communication to the site is
essential to carry the material of construction.
• Site should be close to the cropland to
minimize loss of water due to seepage and
evaporation of canal.
• The site should provide a good foundation for
construction of weir or barrage.
15. Components of Diversion Headworks
• The components of diversion headworks are:
• Weir or barrage
• Canal head regulator
• Divide Wall
• Fish Ladder
• Scouring Sluices Under sluices
• Silt excluder
• Silt ejector.
• Marginal embankment or dikes
• Guide bank
• Silt pocket or trap.
16. Weir or Barrage
• Weir is a solid obstruction placed across the
river. Its main function is to raise the water
level so that water can be diverted by canal to
crop field due to difference of head.
• Barrage is practically a low weir with an
adjustable gate over this low weir. Heading up
of water is affected by gate.
25. Types of Weir
• Weir may be of different types based on material of
construction, design features and types of soil
foundation as:
• Vertical Drop Weir
• A crest gate may be provided to store more water
during flood period. At the upstream and downstream
ends of impervious floor cut off piles are provided.
Launching apron are provided both at upstream and
downstream ends of floor to safeguard against
scouring action. A graded filter is provided
immediately at the downstream end of impervious
floor to relieve the uplift pressure. This type of weir is
suitable for any type of foundation.
29. Types of Weir
• Sloping Weir of Concrete:
• This type is suitable for soft sandy foundation.
It is used where difference in weir crest and
downstream riverbed is not more than 3 m.
Hydraulic jump is formed when water passes
over the sloping glacis. Weir of this type is of
recent origin.
32. Types of Weir
• Parabolic Weir:
• A parabolic weir is almost similar to spillway
section of dam. The weir body wall for this
weir is designed as low dam. A cistern is
provided at downstream.
34. Types of Weir
• Dry Stone Slopping Weir:
• It is dry stone or rock fill weir. It consists of
body wall and upstream and downstream dry
stones are laid in the form of glacis with some
intervening core wall.
37. Barrage
• When the water level on the upstream side of
the weir is required to be raised to different
levels at different time, then the barrage is
constructed. Practically a barrage is an
arrangement of adjustable gates or shutters at
different tiers over the weir. The water level
can be adjusted by the opening of gates.
39. Divide Wall
• The Divide Wall is a long wall constructed at right angle to the
weir or barrage, it may be constructed with stone masonry or
cement concrete. On the upstream side, the wall is extended
just to cover the canal regulator and on the down stream side,
it is extended up to the launching apron. The functions of the
divide wall are as follows,
• (a) To form a still water pocket in front of the canal head so
that the suspended silt can be settled down which then later
can be cleared through the scouring sluices from time to time.
• (b) It controls the eddy current or cross current in front of the
canal head.
• (c) It provides a straight approach in front of the canal head.
• (d) It resists the overturning effect on the weir or barrage
caused by the pressure of the impounding water.
41. Scouring Sluices or Under Sluices
• The Scouring sluices are the openings provided
at the base of the weir or barrage. These
openings are provided with adjustable gates.
Normally, the gates are kept closed. The
suspended silt goes on the depositing in front of
the canal head regulator. When the silt
deposition becomes appreciable the gates are
opened and the deposited silt is loosened with an
agitator mounting on a boat. The muddy water
flows towards the downstream side through the
scouring sluices. The gates are closed. But, at the
period of flood, the gates are kept opened.
44. Fish Ladder
• The Fish Ladder is provided just by the side of the
divide wall for the movement of fishes. Rivers are
important source of fishes. There are various types of
fish in the river. The nature of fish varies from type
to type. But in general, the tendency of fish is to
move from upstream to downstream in winters and
from downstream to upstream in monsoons. This
movement is essential for their survival.
45. Fish Ladder
• Due to construction of weir or barrage, this
movement gets obstructed, and is detrimental to
the fishes. For the movement of the fishes along
the course of the river, the fish ladder is essential.
In the fish ladder, the baffle walls are
constructed in the zigzag manner so that the
velocities of flow within the ladder does not
exceed 3 m/s. The width, length, and height of
the fish ladder depends on the nature of the river
and the type of the weir or barrage.
48. Canal Head Regulator
• A structure which is constructed at the head of
the canal regulator to regulate the flow of water
is known as canal head regulator. It consists of a
number of piers which divide the total width of
the canal into a number of spans which are
known as bays. The pier consists of a number of
tiers on which the adjustable gates are placed.
The gates are operated from the top by suitable
mechanical device. A platform is produced on
the top of the piers for the facility of operating
the gates. Again some piers are constructed on
the downstream side of the canal head to support
the roadway.
51. Silt Excluder
• When still pocket is formed in front of the canal
head by constructing the divide wall, then it is found
that the lower layer of water contains heavy silt and
the upper layer contains very fine silt. The fine silt is
very fertile and it may be allowed to enter the canal.
But the heavy silt causes sedimentation in the
pocket.. To eliminate the suspended heavy silt, the
silt excluder is provided. It consists of a series of
tunnels starting from the side of the head regulator
up to the divide wall.
52. Silt Excluder
• The tunnel nearest to the head regulator is
longest, and the successive tunnels decrease in
length, the tunnel nearest to the divide wall is
shortest. The tunnels are covered by R.C.C. Slab.
The top level of the slab is kept below the sill
level of the head regulator. So, the completely
clear water is allowed to flow in the canal
through the head regulator. The suspended
heavy silt carried by the water enters the silt
excluder tunnels and passes out through the
scouring sluices.
53. Silt Excluder
• Silt excluders are those works which are
constructed on the bed of the river, upstream
of the head regulator. The clearer water
enters the head regulator and silted water
enters the silt excluder. In this type of
works, the silt is, therefore, removed from the
water before in enters the canal.
55. Silt Ejectors
• Silt ejectors, also called silt extractors, are
those devices which extract the silt from
the canal water after the silted water has
• traveled a certain distance in the off-take
canal. These works are, therefore, constructed
on the bed of the canal, and little distance
downstream from the head regulator.
57. Marginal Embankments or dykes
• The marginal embankments or dykes are earthen
embankments which are constructed parallel to the
river bank on one or both the banks according to the
condition. The top width is generally 3 to 4 m and side
slope is generally 1 ½ : 1 to 2: 1. The height of the
embankment depends on the highest flood level. A
suitable margin is provided between the toe of the
embankment and the bank of the river. To resist the
effect of erosion on the embankment, wooden piles are
driven along the river banks throughout the length of
dyke. The length of the dyke is protected by boulders
pitching with cement grouting and the downstream
side is protected by turfing.
58. Marginal Embankments or dykes
• The Marginal Bunds are constructed for the
following purposes.
• (a) It prevents the flood water or storage
water from entering the surrounding area.
• (b) It retains the flood water or storage water
within a specified section.
• (c) It Protects the towns and village from
devastation during the heavy flood.
• (d) It protects valuable agricultural lands.
60. Guide Bank
• When a barrage is constructed across a river which
flows through the alluvial soil, the guide banks must
be constructed on both the approaches to protect the
structure from erosion. It is an earthen embankment
with curved head on both the ends.
• The Guide Bank serves the following purposes.
• It protects the barrage from the effect of scouring and
erosion.
• It controls the tendency of changing the course of the
river.
• It controls the velocity of the flow near the structure.
63. Guide Bank
• Components of Guide Banks are
• Upstream curved head
• Downstream curved head
• Shank portion which joins upstream and
downstream curved end
• Sloping apron
• Launching apron
• Pile protection
65. Causes of Failure of weir or barrage
on permeable foundation
• The combined effect of surface flow and surface flow may
cause the failure of the weir or barrage.
• (i) Failure due to subsurface flow
• (a) By piping or undermining: The water from the
upstream side continuously percolates through the bottom
of the foundation and emerges at the downstream end of
the weir or barrage floor. The force of percolating water
removes the soil particles by scouring at the point of
emergence. As the process of removal of soil particles goes
on continuously, a depression is formed which extends
backwards towards the upstream through the bottom of
the foundation. A hollow pipe like formation thus develops
under the foundation due to which the weir or barrage
may fail by subsiding. This phenomenon is known as
failure by piping or undermining.
68. Causes of Failure of weir or barrage
on permeable foundation
• (b) By uplift Pressure: The percolating water exerts an upward pressure
on the foundation of the weir or barrage. If this uplift is not
counterbalanced by the self weight of the structure, it may fail by
rapture.
• 2. Failure by Surface Flow:
• (a) By Hydraulic Jump: When the water flows with a very high velocity
over the crust of the weir or over the gates of the barrage, then
hydraulic jump develops. This hydraulic jump causes a suction
pressure or negative pressure on the downstream side which acts in
the direction of uplift pressure. If the thickness of the impervious floor
is not sufficient, then the structure fails by rapture.
• (b) By Scouring During floods: The gates of the barrage are kept open
and the water flows with high velocity. The water may also flow with
very high velocity over the crest of the weir. Both the cases can result
in scouring effect on the downstream and on the upstream side of the
structure. Due to scouring effect on the downstream and on the
upstream side of the structure, its stability gets endangered by shearing.
72. Causes of Failure of Weir, and
Remedies
• If a weir is constructed on permeable soil, weir may fail
by piping, uplift force, suction caused by standing wave
and scouring on both upstream and downstream of the
weir.
• When hydraulic gradient or exit gradient exceeds the
critical value of soil, surface soil at down end starts
boiling first and is washed away by percolating water.
This process of removal or washing out of soil continuous
and eventually a channel in the form of pipe is formed by
seepage water. This is called piping which may cause the
failure of foundation. Similarly uplift force of percolating
water is acting on ther floor from bottom and if the
weight of floor is not enough to resist this uplift force,
floor may fail by cracking or bursting.
73. Causes of Failure of Weir, and
Remedies
• The main remedies against failure are:
• Path of percolation or creep length of seepage
water should be increased by providing sheet
piles at upstream, downstream or at
intermediate point to reduce the hydraulic
gradient.
• Floor thickness should be increased to
increase its self weight to balance the uplift
force.
74. Precautions Against Failure
• The following precautions can be taken to prevent
failure.
• (a) The length of the impervious layer should be
carefully designed so that the path of the percolating
water is increased consequently reducing the exit
gradient.
• (b) Sheet piles should be provided on the upstream
side and the downstream side of the impervious
floor to increase to the length of percolating water
so that the uplift pressure is considerable reduced.
• (c) The thickness of the impervious floor should be
such that the weight of the floor is a sufficient to
counterbalance the uplift pressure.
75. Precautions Against Failure
• (d) Energy dissipater blocks like friction
blocks, impact blocks, should be provided.
• (e) Inverted filter should be provided with
concrete blocks on the top so that the
percolating water does not wash out the soil
particles.
• Deep foundation like well foundation should
be provided for the barrage piers
80. Flow Net
• A flownet is a graphical representation of two-
dimensional steady-state groundwater flow
through aquifers.
• The method consists of filling the flow area with
stream lines and equipotential lines, which are
everywhere perpendicular to each other, making
a curvilinear grid.
• Stream Lines: The streamlines represent the paths
along which the water flows through the sub-soil.
• Equipotential lines: Equipotential lines are lines of
• equal hydraulic head.
82. Khosla’s Theory
• Khosla’s Theory and Concept of Flow Nets
• Many of the important hydraulic structures,
such as weirs and barrage, were designed on
the basis of Bligh’s theory between the periods
1910 to 1925. In 1926 – 27, the upper Chenab
canal siphons, designed on Bligh’s theory,
started posing undermining troubles.
Investigations started, which ultimately lead to
83. • Khosla’s theory. The main principles of this theory
are summarized below:
• (a) The seepage water does not creep along the
bottom contour of pucca flood as started by Bligh,
but on the other hand, this water moves along a set
of stream-lines. This steady seepage in a vertical
plane for a homogeneous soil can be expressed by
Laplacian equation:
84. Khosla’s Theory
• The equation represents two sets of curves
intersecting each other orthogonally. The resultant
flow diagram showing both of the curves is called a
Flow Net.
• Stream Lines: The streamlines represent the paths
along which the water flows through the sub-soil.
• Every particle entering the soil at a given point
upstream of the work, will trace out its own path and
will represent a streamline. The first streamline
follows the bottom contour of the works and is the
same as Bligh’s path of creep. The remaining
streamlines follows smooth curves transiting slowly
from the outline of the foundation to a semi-ellipse, as
shown below.
85. Khosla’s Theory
• Equipotential Lines: (1) Treating the downstream bed
as datum and assuming no water on the downstream
side, it can be easily started that every streamline
possesses a head equal to h1 while entering the soil;
and when it emerges at the down-stream end into the
atmosphere, its head is zero. Thus, the head h1 is
entirely lost during the passage of water along the
streamlines.
86. Khosla’s Theory
• Further, at every intermediate point in its path,
there is certain residual head (h) still to be dissipated
in the remaining length to be traversed to the
downstream end. This fact is applicable to every
streamline, and hence, there will be points on
different streamlines having the same value of
residual head h. If such points are joined together,
the curve obtained is called an equipotential line.
88. Khosla’s Theory
Every water particle on line AB is having a
residual head h = h1, and on CD is having a
residual head h = 0, and hence, AB and CD
are equipotential lines.
Since an equipotential line represent the
joining of points of equal residual head, hence
if piezometers were installed on an
equipotential line, the water will rise in all of
them up to the same level as shown in figure
below
90. Khosla’s Theory
• The seepage water exerts a force at each point in the
direction of flow and tangential to the streamlines as
shown in figure above. This force (F) has an upward
component from the point where the streamlines turns
upward. For soil grains to remain stable, the upward
component of this force should be counterbalanced by
the submerged weight of the soil grain. This force has
the maximum disturbing tendency at the exit end,
because the direction of this force at the exit point is
vertically upward, and hence full force acts as its
upward component.
91. Khosla’s Theory
• For the soil grain to remain stable, the
submerged weight of soil grain should be more
than this upward disturbing force. The
disturbing force at any point is proportional to
the gradient of pressure of water at that point
(i.e. dp/dt). This gradient of pressure of water at
the exit end is called the exit gradient. In order
that the soil particles at exit remain stable, the
upward pressure at exit should be safe. In other
words, the exit gradient should be safe.
92. Critical Exit Gradient
• This exit gradient is said to be critical, when
the upward disturbing force on the grain is
just equal to the submerged weight of the
grain at the exit. When a factor of safety equal
to 4 to 5 is used, the exit gradient can then be
taken as safe. In other words, an exit gradient
equal to ¼ to 1/5 of the critical exit gradient
ensured, so as to keep the structure safe
against piping.
• The submerged weight (Ws) of a unit volume
of soil is given as:
94. Khosla’s Method of independent variables for
determination of pressures and exit gradient for
seepage below a weir or a barrage
• In order to know as to how the seepage below the
foundation of a hydraulic structure is taking place, it is
necessary to plot the flow net. In other words, we must
solve the Laplacian equations. This can be
accomplished either by mathematical solution of the
Laplacian equations, or by Electrical analogy method,
or by graphical sketching by adjusting the streamlines
and equipotential lines with respect to the boundary
conditions. These are complicated methods and are
time consuming. Therefore, for designing hydraulic
structures such as weirs or barrage or pervious
foundations, Khosla has evolved a simple, quick and an
• accurate approach, called Method of Independent
Variables.
95. Khosla’s Method of independent variables for
determination of pressures and exit gradient for
seepage below a weir or a barrage
• In this method, a complex profile like that of a weir is
broken into a number of simple profiles; each of
which can be solved mathematically. profiles which
are most useful are:
• (i) A straight horizontal floor of negligible thickness
with a sheet pile line on the u/s end and d/s end.
• (ii) A straight horizontal floor depressed below the bed
but without any vertical cut-offs.
• (iii) A straight horizontal floor of negligible thickness
with a sheet pile line at some intermediate point.
96.
97. Khosla’s Method of independent variables for
determination of pressures and exit gradient for
seepage below a weir or a barrage
• The key points are the junctions of the floor and the
pole lines on either side, and the bottom point of
• the pile line, and the bottom corners in the case of a
depressed floor. The percentage pressures at these key
• points for the simple forms into which the complex
profile has been broken is valid for the complex
profile
• itself, if corrected for
• (a) Correction for the Mutual interference of Piles
• (b) Correction for the thickness of floor
• (c) Correction for the slope of the floor
98. (a) Correction for the Mutual interference of
Piles
The correction C to be applied as percentage of head due to this effect, is given
by
Where,
b′ = The distance between two pile lines.
D = The depth of the pile line, the influence of which has to be determined on
the neighboring pile of depth d. D is to be measured below the level at
which interference is desired.
d = The depth of the pile on which the effect is considered
b = Total floor length
The correction is positive for the points in the rear of back water, and
subtractive for the points forward in the direction of flow. This equation
does not apply to the effect of an outer pile on an intermediate pile, if the
intermediate pile is equal to or smaller than the outer pile and is at a
distance less than twice the length of the outer pile.
100. (a) Correction for the Mutual interference of
Piles
• Suppose in the above figure, we are considering the influence of
the pile no (2) on pile no (1) for correcting the pressure at C1.
Since the point C1 is in the rear, this correction shall be positive.
While the correction to be applied to E2 due to pile no (1)
shall be negative, since the point E2 is in the forward direction
of flow. Similarly, the correction at C2 due to pile no (3) is
positive and the correction at E2 due to pile no (2) is negative.
101. (b) Correction for the Thickness of Floor
• In the standard form profiles, the floor is
assumed to have negligible thickness. Hence,
the percentage pressures calculated by
Khosla’s equations or graphs shall pertain to
the top levels of the floor. While the actual
junction points E and C are at the bottom of
the floor. Hence, the pressures at the actual
points are calculated by assuming a straight
line pressure variation.
103. (b) Correction for the thickness of floor
• Correction for the slope of the floor a correction is applied for
a slopping floor, and is taken as positive for the downward
slopes, an negative for the upward slopes following the
direction of flow. Values of correction of standard slop such
as 1 : 1, 2 : 1, 3 : 1, etc. are tabulated in Table below
104. (b) Correction for the thickness of floor
• The correction factor given above is to be multiplied
by the horizontal length of the slope and divided by
the distance between the two pile lines between
which the sloping floor is located. This correction is
applicable only to the key points of the pile line fixed
at the start or the end of the slope.
105. Exit gradient (GE)
• It has been determined that for a standard form
consisting of a floor length (b) with a vertical cutoff
of depth (d), the exit gradient at its downstream end
is given by
106. Important Questions
• Explain Khosla’s method of independent variables.
• Explain the term ”Diversion Head Work” and
clearly mention its different functions.
• Explain Bligh’s Creep Theory in details.
• What is weir? How does it differ from a barrage
structure?
• What are the functions of a canal head regulator?