This document discusses seepage pressure and flow through earthen dams. It explains that seepage pressure is the force per unit volume exerted by flowing water on the soil, acting along the flow line. It describes how flow nets can be used to determine seepage pressure at any point. The document also discusses the phreatic line (seepage line) and how its position within a dam is important for stability. It provides details on analyzing seepage flow through homogeneous earthen dams using confocal parabolas with a common focus.
OPEN CHANNEL FLOW AND HYDRAULIC MACHINERY
Open channel flow: Types of flows – Type of channels – Velocity distribution – Energy and momentum correction factors – Chezy’s, Manning’s; and Bazin formula for uniform flow – Most Economical sections. Critical flow: Specific energy-critical depth – computation of critical depth – critical sub-critical – super critical flows
Non-uniform flows –Dynamic equation for G.V.F., Mild, Critical, Steep, horizontal and adverse slopes-surface profiles-direct step method- Rapidly varied flow, hydraulic jump, energy dissipation
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
OPEN CHANNEL FLOW AND HYDRAULIC MACHINERY
Open channel flow: Types of flows – Type of channels – Velocity distribution – Energy and momentum correction factors – Chezy’s, Manning’s; and Bazin formula for uniform flow – Most Economical sections. Critical flow: Specific energy-critical depth – computation of critical depth – critical sub-critical – super critical flows
Non-uniform flows –Dynamic equation for G.V.F., Mild, Critical, Steep, horizontal and adverse slopes-surface profiles-direct step method- Rapidly varied flow, hydraulic jump, energy dissipation
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
WEIRS VERSUS BERRAGE
TYPES OF WEIRS
COMPONENT PARTS OF A WEIR
CAUSES OF FAILURE OF WEIRS & THEIR REMEDIES
DESIGN CONSIDERATIONS
DESIGN FOR SURFACE FLOW
DESIGN OF BARRAGE OR WEIR
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
WEIRS VERSUS BERRAGE
TYPES OF WEIRS
COMPONENT PARTS OF A WEIR
CAUSES OF FAILURE OF WEIRS & THEIR REMEDIES
DESIGN CONSIDERATIONS
DESIGN FOR SURFACE FLOW
DESIGN OF BARRAGE OR WEIR
Uniform Flow: Basic concepts of free surface flows,
velocity and pressure distribution,
Mass, energy and momentum principle for prismatic and non-prismatic channels,
Review of Uniform flow: Standard equations,
hydraulically efficient channel sections,
compound sections,
Energy-depth relations:
Concept of specific energy, specific force,
critical flow, critical depth,
hydraulic exponents, and
Channel transitions.
Explained in such a way that the reader could have a visual and interactive approach towards understanding Electric flux. With good number of diagrams.
Bligh’S CREEP THEORY
LIMITATIONS OF BLIGH’S THEORY
LANE’S WEIGHTED CREEP THEORY
KHOSLA’S THEORY AND CONCEPT OF FLOW NETS
COMPARISON OF BLIGH’S THEORY AND KHOSLA’S THEORY
23Network FlowsAuthor Arthur M. Hobbs, Department of .docxeugeniadean34240
23
Network Flows
Author: Arthur M. Hobbs, Department of Mathematics, Texas A&M Uni-
versity.
Prerequisites: The prerequisites for this chapter are graphs and trees. See
Sections 9.1 and 10.1 of Discrete Mathematics and Its Applications.
Introduction
In this chapter we solve three very different problems.
Example 1 Joe the plumber has made an interesting offer. He says he has
lots of short pieces of varying gauges of copper pipe; they are nearly worthless
to him, but for only 1/5 of the usual cost of installing a plumbing connection
under your house, he will use a bunch of T- and Y-joints he picked up at a
distress sale and these small pipes to build the network shown in Figure 1. He
claims that it will deliver three gallons per minute at maximum flow. He has
a good reputation, so you are sure the network he builds will not leak and will
cost what he promises, but he is no mathematician. Will the network really
deliver as much water per minute as he claims?
408
Chapter 23 Network Flows 409
Figure 1. A plumber’s nightmare.
Example 2 We want to block access to the sea from inland town s on
river R. We can do this by dropping mines in the river, but because the river
spreads out in a wide delta with several outlets, the number of mines required
depends on where we drop them. The number of mines required in a channel
ranges from a high of 20 mines in R to a low of 1 in some channels, as shown
in Figure 2. In that figure, each channel is shown with a number indicating
how many mines will block it. What is the smallest number of mines needed to
block off s’s access to the sea, and where should the mines be placed?
Figure 2. Delta system of river R and numbers of mines
needed to close channels.
Example 3 At Major University, Professor Johnson is asked to hire graders
for 100 sections spread among 30 different courses. Each grader may work for
one, two, or three sections, with the upper bound being the grader’s choice,
but the number actually assigned being Professor Johnson’s choice. Professor
Johnson contacts the potential graders, learns from each both his choice of
number of sections and which courses he is competent to grade, and makes a
table showing this information, together with the number of sections of each
course being offered. Because the real problem is too large to use as an example
here, Table 1 gives a smaller example. How should the assignment of graders
be made?
In this chapter, we begin with Example 1, solve Example 2 on the way to
solving Example 1, and then solve Example 3 by using the theory developed.
Many more kinds of problems are solved using the methods of this chapter in
the book Flows in Networks by Ford and Fulkerson [4].
410 Applications of Discrete Mathematics
Course Course Course Course Max # Sec.
1 2 3 4 Wanted
Student 1 yes yes no no 3
Student 2 yes no yes yes 2
Student 3 no yes yes yes 3
# Sec. Needed 3 1 1 2
Table 1. Graders and courses.
Flow Graphs
In Example 1, we have a network of pipes th.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
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.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
2. When flow occures through soil it exerts thrust on the soil particle along the
direction of flow. As the direction of any flow line changes from point to point,
which is defined by the tangent at any point, it is necessary to obtain pressure
per unit volume of the soil mass. Which is explained below.
SEEPAGE PRESSURE:
Seepage Pressure at any point, Seepage through Earthen Dam
etc.
A.
3. Flow nets are useful in the determination of the seepage pressure a
t any point along the flow path.
Consider the cubical element with all the sides equal t
o a. Let h, be the piezometric
The total force on = P, = ay,h,
The total force on = P,= y,h,
The differential force acting on the element is
P , - P , = P , = @ y , h , - h , )
Since (h, - h,) is the head drop Ah, we can write
2
� tJ,. I, 3
P, = y A h = a - y _ = a 'i y
3 w
' w w
where @' is the volume of the element. The force per unit volume o
f the element is, therefore,
This force exerts a drag o
n the element known a
s the seepage pressure. It has the dimension
of unit weight, and at any point its line o
f action is tangent to the flow line. The seepage pressure is
a very important factor in the stability analysis of earth slopes. If the line o
f action o
f the seepage
force acts in the vertical direction upward a
s o
n a
n element adjacent t
o , the
f
o
r
c
e that is acting downward t
o keep the element stable is the buoyant unit weight o
f the element.
When these two forces balance, the soil will just b
e a
t the point o
f being lifted
in the soil mass
head acting on the left face and h2 is the the head at the right face,
Left
Right
= net force acting on the element is,
downstream
up causing failure.
This force is acting along the gradient i.e. slope of the Stream Line
4. SEEPAGE FLOW THROUGH HOMOGENEOUS EARTH DAMS
In almost all problems concerning seepage beneath a sheet pile wall or through the foundation of a
concrete dam all boundary conditions are known. However, in the case o
f seepage through an earth
dam the upper boundary or the uppermost flow line is nor known. This upper boundary is a free
water surface and will b
e referred t
o a
s the line o
f seepage or phreatic line. The seepage line may
therefore be defined as the line above which there is no hydrostatic pressure and below which there
is hydrostatic pressure. In the design of all earth dams, the following factors are very important.
I. The seepage line should not cut th
e downstream slope.
2. The seepage loss through the dam should b
e the minimum possible.
The two important problems that are required to be studied in the design of earth dams are:
I . The prediction of the position o
f the line of seepage in the cross-section.
2. The computation o
f the seepage loss.
If the line of seepage is allowed t
o intersect the downstream f
a
c
e much above the toe, more o
r
less serious sloughing may take place and ultimate failure may result, This mishap can b
e prevented
b
y providing suitable drainage arrangements on the downstream side of the dam.
The section of an earth dam may b
e homogeneous or non-homogeneous. A homogeneous
dam contains the same material over the whole section and only one coefficient of permeability
may b
e assumed t
o hold f
o
r the entire section. In the non homogeneous or the composite section.
two or more permeability coefficients may have t
o be used according to the materials used in the
section. Following is the skemetic diagram of a homogeneous dam with seepage line.
B.
5. k Phreatit line (seepage line)
[Basie parabola
'
'
'
Discharge f
a
c
e
Figure Basic parabola and the phreatic line for a homogeneous earth dam
1
B
DIRECTRIX
F
(CASAGREDE METHOD)
A
A'
C D
FD=y0
O O'
P'
P
X
Y
6. 4.20 FLOW NET CONSISTING OF CONJUGATE CONFOCAL PARABOLAS
As a prelude t
o the study of a
n ideal flow net comprising o
f parabolas a
s flow and equipotential
lines, i
t i
s necessary t
o understand th
e properties o
f a single parabola. The parabola ACV illustrated
in , is defined as the curve whose every point is equidistant fr
o
m a point F called the focus
and a line DG called the directrix. If w
e consider a
n
y point, say, A, o
n the curve, w
e can write F
A =
AG, where the line AG is nonnaJ to the directrix. If F is th
e origin o
f coordinates. and the
coordinates of point A are (x, y), we can write
AF =he+y = A G = x + y
y - }
o
r x =
2
%
where. y
,, = F
D
Eq. ) i
s the equation of the basic parabola. If th
e parabola intersects the y-axis at C
, w
e
can write
( )
FC= C
E =y,
Similarly f
o
r th
e vertex point V
, the fo
c
a
l distance a
, i
s
FV= VD=a,=y02 ( )
Figure illustrates the ideal flow net consisting of conjugate confocal parabolas. All the
parabolas have a common focus F.
The boundary lines of such a
n ideal flow net are:
Figure
1
(1
2
2
7. ingbyV.Murthy x [] Untitled1
E
Discharge
fa
c
e
Directrix
- - - - E
V D
i
'
•
f.
i
s
{
8
-
,
; r e ,
G w , ' , t i s
x
h
B
Figure Ideal flownet consisting of conjugate confocal parabolas
2.
8. I . Th
e upstream face AB, a
n equipotential line, i
s a parabola.
2. T
h
e downstream discharge fa
c
e F
V, a
n equipotential line, is horizontal.
3. ACV, the phreatic line, is a parabola.
4. BF, the bottom flow line, i
s horizontal.
T
h
e known boundary conditions a
r
e only three i
n number. They are, the two equipotential
lines AB and F
V, and th
e bottom fl
o
w line B
F
. Th
e t
o
p fl
o
w line ACV i
s t
h
e one that is unknown. Th
e
theoretical investigation of Kozeny ( 1 9 3 1 ) revealed that the flow net f
o
r such an ideal condition
mentioned above with a horizontal discharge fa
c
e FV consists of two families of confocal parabolas
with a common focus F. Since the conjugate confocal parabolas should intersect a
t right angles t
o
each other, all the parabolas crossing the vertical line F
C should have their intersection points lie o
n
this line.
which is unknown and
9. Method of Locating Seepage Line
The general method of locating the seepage line in an
y homogeneous dam resting on an
impervious foundation may be explained with reference to Fig 3(a). As explained earlier, the
focus F of the basic parabola is taken as the intersection point o
f the bottom flow line B
F and the
discharge face E
F. In this case the focus coincides with the toe of the dam. One more point is
required t
o construct the basic parabola. Analysis of the location of seepage lines by
A. Casagrande has revealed that the basic parabola with focus F intersects the upstream water
surface at A such that AA ' - 0 . 3 m, where m is the projected length of the upstream equipotential
line AB on the water surface. Point A is called the corrected entrance point. The parabola APSV
may now be constructed a
s per Eq. ). The divergence of the seepage line from the basic
parabol a is shown as A P and S
D in Fig. 3(a). For dams with flat slopes, the divergences may
be sketched by eye keeping in view the boundary requirements. The error involved in sketching
b
y eye, the divergence on the downstream side, might be considerable if the slopes are steeper.
ure -
( 1
10. B'
h
8
A A'
I
,
f
' . '
, o ,
p
<
' " �
1
'y- 83.�ic parabola
'
F V
(a)
0.4
0.3
? o »
a
0.I
0
30°
(b)
60
° 90
° 120° 150°
B-Slope of discharge face
180°
�
�
........_,
•
i
----•
Figure Construction of seepage line
3.
T
11. Seepage 335
Example
The cross section of an earth dam is shown in Figure 7.35. Calculate
the rate of seepage through the dam [q in m3/(min ∙ m)] by (a) Dupuit’s
method; (b) Schaffernak’s method; (c) L. Casagrande’s method; and
(d) Pavlovsky’s method.
25 m 2
2
Impermeable layer
b
c
30 m
k =3 ×10–4
m/min
a
a΄
0.3 ×50
=15 m
1 1
5 m
60 m
5 m
10 m
50 m
Figure 7.35
Seepage through an earth dam.
Ref: Adv. Soil Mechanics - B.M.Das
x
y
x
y
'
'
Yo
Directrix
Focus