PLEASE NOTE THIS IS PART-1
By Referring or said Learning This Presentation You Can Clear Your Basics Fundamental Doubts about Fluid Mechanics. In this Presentation You Will Learn about Fluid Pressure, Pressure at Point, Pascal's Law, Types Of Pressure and Pressure Measurements.
Flow Equations for sluice gate.Introduces different flow equations to students which are widely utilized for the design of sluice gates connected to open channel.This tutorial will help to understand and articulate the basic flow equation utilized by designers all over the world.
Head losses
Major Losses
Minor Losses
Definition • Dimensional Analysis • Types • Darcy Weisbech Equation • Major Losses • Minor Losses • Causes Head Losses
3. • Head loss is loss of energy per unit weight. • Head = Energy of Fluid / Weight • Head losses can be – Kinetic Head – Potential Head – Pressure Head 6/10/2015 4Danial Gondal Head Loss
4. • Kinetic Head – K.H. = kinetic energy / Weight = v² /2g • Potential Head – P.H = Potential Energy / Weight = mgz /mg = z • Pressure Head – P.H = P/ ρ g 6/10/2015 5
5. • (P/ ρ g) + (v² /2g ) + (z) = constant • (FL-2F-1L3LT-2L-1T2) + (L2T-2L1T2)+(L) = constant • (L) + (L) + (L) = constant • As L represent height so it is dimensionally L. 6/10/2015 6 Dimensional Analysis
6. • However the equation (P/ ρ g) + (v² /2g ) + (z) = constant Is valid for Bernoulli's Inviscid flow case. As we are studying viscous flow so (P1/ ρ g) + (v1² /2g ) + (z1) = EGL1(Energy Grade Line At point 1) (P2/ ρ g) + (v2² /2g ) + (z2) = EGL2(Energy Grade Line At point 2) 6/10/2015 7 Head Loss
7. • For Inviscid Flow EGL1 - EGL2= 0 • For Viscous Flow EGL1 - EGL2= Hf 6/10/2015 8 Head Loss
8. MAJOR LOSSES IN PIPES
9. •Friction loss is the loss of energy or “head” that occurs in pipe flow due to viscous effects generated by the surface of the pipe. • Friction Loss is considered as a "major loss" •In mechanical systems such as internal combustion engines, it refers to the power lost overcoming the friction between two moving surfaces. •This energy drop is dependent on the wall shear stress (τ) between the fluid and pipe surface. 6/10/2015 10 Friction Loss
10. •The shear stress of a flow is also dependent on whether the flow is turbulent or laminar. •For turbulent flow, the pressure drop is dependent on the roughness of the surface. •In laminar flow, the roughness effects of the wall are negligible because, in turbulent flow, a thin viscous layer is formed near the pipe surface that causes a loss in energy, while in laminar flow, this viscous layer is non-existent. 6/10/2015 11 Friction Loss
11. Frictional head losses are losses due to shear stress on the pipe walls. The general equation for head loss due to friction is the Darcy-Weisbach equation, which is where f = Darcy-Weisbach friction factor, L = length of pipe, D = pipe diameter, and V = cross sectional average flow velocity.
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.
1. Introduction to Kinematics
2. Methods of Describing Fluid Motion
a). Lagrangian Method
b). Eulerian Method
3. Flow Patterns
- Stream Line
- Path Line
- Streak Line
- Streak Tube
4. Classification of Fluid Flow
a). Steady and Unsteady Flow
b). Uniform and Non-Uniform Flow
c). Laminar and Turbulent Flow
d). Rotational and Irrotational Flow
e). Compressible and Incompressible Flow
f). Ideal and Real Flow
g). One, Two and Three Dimensional Flow
5. Rate of Flow (Discharge) and Continuity Equation
6. Continuity Equation in Three Dimensions
7. Velocity and Acceleration
8. Stream and Velocity Potential Functions
PLEASE NOTE THIS IS PART-1
By Referring or said Learning This Presentation You Can Clear Your Basics Fundamental Doubts about Fluid Mechanics. In this Presentation You Will Learn about Fluid Pressure, Pressure at Point, Pascal's Law, Types Of Pressure and Pressure Measurements.
Flow Equations for sluice gate.Introduces different flow equations to students which are widely utilized for the design of sluice gates connected to open channel.This tutorial will help to understand and articulate the basic flow equation utilized by designers all over the world.
Head losses
Major Losses
Minor Losses
Definition • Dimensional Analysis • Types • Darcy Weisbech Equation • Major Losses • Minor Losses • Causes Head Losses
3. • Head loss is loss of energy per unit weight. • Head = Energy of Fluid / Weight • Head losses can be – Kinetic Head – Potential Head – Pressure Head 6/10/2015 4Danial Gondal Head Loss
4. • Kinetic Head – K.H. = kinetic energy / Weight = v² /2g • Potential Head – P.H = Potential Energy / Weight = mgz /mg = z • Pressure Head – P.H = P/ ρ g 6/10/2015 5
5. • (P/ ρ g) + (v² /2g ) + (z) = constant • (FL-2F-1L3LT-2L-1T2) + (L2T-2L1T2)+(L) = constant • (L) + (L) + (L) = constant • As L represent height so it is dimensionally L. 6/10/2015 6 Dimensional Analysis
6. • However the equation (P/ ρ g) + (v² /2g ) + (z) = constant Is valid for Bernoulli's Inviscid flow case. As we are studying viscous flow so (P1/ ρ g) + (v1² /2g ) + (z1) = EGL1(Energy Grade Line At point 1) (P2/ ρ g) + (v2² /2g ) + (z2) = EGL2(Energy Grade Line At point 2) 6/10/2015 7 Head Loss
7. • For Inviscid Flow EGL1 - EGL2= 0 • For Viscous Flow EGL1 - EGL2= Hf 6/10/2015 8 Head Loss
8. MAJOR LOSSES IN PIPES
9. •Friction loss is the loss of energy or “head” that occurs in pipe flow due to viscous effects generated by the surface of the pipe. • Friction Loss is considered as a "major loss" •In mechanical systems such as internal combustion engines, it refers to the power lost overcoming the friction between two moving surfaces. •This energy drop is dependent on the wall shear stress (τ) between the fluid and pipe surface. 6/10/2015 10 Friction Loss
10. •The shear stress of a flow is also dependent on whether the flow is turbulent or laminar. •For turbulent flow, the pressure drop is dependent on the roughness of the surface. •In laminar flow, the roughness effects of the wall are negligible because, in turbulent flow, a thin viscous layer is formed near the pipe surface that causes a loss in energy, while in laminar flow, this viscous layer is non-existent. 6/10/2015 11 Friction Loss
11. Frictional head losses are losses due to shear stress on the pipe walls. The general equation for head loss due to friction is the Darcy-Weisbach equation, which is where f = Darcy-Weisbach friction factor, L = length of pipe, D = pipe diameter, and V = cross sectional average flow velocity.
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.
1. Introduction to Kinematics
2. Methods of Describing Fluid Motion
a). Lagrangian Method
b). Eulerian Method
3. Flow Patterns
- Stream Line
- Path Line
- Streak Line
- Streak Tube
4. Classification of Fluid Flow
a). Steady and Unsteady Flow
b). Uniform and Non-Uniform Flow
c). Laminar and Turbulent Flow
d). Rotational and Irrotational Flow
e). Compressible and Incompressible Flow
f). Ideal and Real Flow
g). One, Two and Three Dimensional Flow
5. Rate of Flow (Discharge) and Continuity Equation
6. Continuity Equation in Three Dimensions
7. Velocity and Acceleration
8. Stream and Velocity Potential Functions
HEAP SORT ILLUSTRATED WITH HEAPIFY, BUILD HEAP FOR DYNAMIC ARRAYS.
Heap sort is a comparison-based sorting technique based on Binary Heap data structure. It is similar to the selection sort where we first find the minimum element and place the minimum element at the beginning. Repeat the same process for the remaining elements.
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.
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
Online aptitude test management system project report.pdfKamal Acharya
The purpose of on-line aptitude test system is to take online test in an efficient manner and no time wasting for checking the paper. The main objective of on-line aptitude test system is to efficiently evaluate the candidate thoroughly through a fully automated system that not only saves lot of time but also gives fast results. For students they give papers according to their convenience and time and there is no need of using extra thing like paper, pen etc. This can be used in educational institutions as well as in corporate world. Can be used anywhere any time as it is a web based application (user Location doesn’t matter). No restriction that examiner has to be present when the candidate takes the test.
Every time when lecturers/professors need to conduct examinations they have to sit down think about the questions and then create a whole new set of questions for each and every exam. In some cases the professor may want to give an open book online exam that is the student can take the exam any time anywhere, but the student might have to answer the questions in a limited time period. The professor may want to change the sequence of questions for every student. The problem that a student has is whenever a date for the exam is declared the student has to take it and there is no way he can take it at some other time. This project will create an interface for the examiner to create and store questions in a repository. It will also create an interface for the student to take examinations at his convenience and the questions and/or exams may be timed. Thereby creating an application which can be used by examiners and examinee’s simultaneously.
Examination System is very useful for Teachers/Professors. As in the teaching profession, you are responsible for writing question papers. In the conventional method, you write the question paper on paper, keep question papers separate from answers and all this information you have to keep in a locker to avoid unauthorized access. Using the Examination System you can create a question paper and everything will be written to a single exam file in encrypted format. You can set the General and Administrator password to avoid unauthorized access to your question paper. Every time you start the examination, the program shuffles all the questions and selects them randomly from the database, which reduces the chances of memorizing the questions.
An Approach to Detecting Writing Styles Based on Clustering Techniquesambekarshweta25
An Approach to Detecting Writing Styles Based on Clustering Techniques
Authors:
-Devkinandan Jagtap
-Shweta Ambekar
-Harshit Singh
-Nakul Sharma (Assistant Professor)
Institution:
VIIT Pune, India
Abstract:
This paper proposes a system to differentiate between human-generated and AI-generated texts using stylometric analysis. The system analyzes text files and classifies writing styles by employing various clustering algorithms, such as k-means, k-means++, hierarchical, and DBSCAN. The effectiveness of these algorithms is measured using silhouette scores. The system successfully identifies distinct writing styles within documents, demonstrating its potential for plagiarism detection.
Introduction:
Stylometry, the study of linguistic and structural features in texts, is used for tasks like plagiarism detection, genre separation, and author verification. This paper leverages stylometric analysis to identify different writing styles and improve plagiarism detection methods.
Methodology:
The system includes data collection, preprocessing, feature extraction, dimensional reduction, machine learning models for clustering, and performance comparison using silhouette scores. Feature extraction focuses on lexical features, vocabulary richness, and readability scores. The study uses a small dataset of texts from various authors and employs algorithms like k-means, k-means++, hierarchical clustering, and DBSCAN for clustering.
Results:
Experiments show that the system effectively identifies writing styles, with silhouette scores indicating reasonable to strong clustering when k=2. As the number of clusters increases, the silhouette scores decrease, indicating a drop in accuracy. K-means and k-means++ perform similarly, while hierarchical clustering is less optimized.
Conclusion and Future Work:
The system works well for distinguishing writing styles with two clusters but becomes less accurate as the number of clusters increases. Future research could focus on adding more parameters and optimizing the methodology to improve accuracy with higher cluster values. This system can enhance existing plagiarism detection tools, especially in academic settings.
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.
Literature Review Basics and Understanding Reference Management.pptxDr Ramhari Poudyal
Three-day training on academic research focuses on analytical tools at United Technical College, supported by the University Grant Commission, Nepal. 24-26 May 2024
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.
Modeling of transient fluid flow in the simple pipeline system
1. MODELING OF TRANSIENT FLUID
FLOW IN THE SIMPLE PIPELINE
SYSTEM
Submitted by:-
Aniruddha Singha (184104602)
2. What is Transient Flow
A transient is a temporary flow and pressure condition that occurs in a hydraulic system
between an initial steady-state condition and a final steady-state condition;
When velocity changes rapidly in response to the operation of a flow-control device(for
instance, a valve closure or pump start), the compressibility of the liquid and the elasticity of
the pipeline cause a transient pressure wave to propagate throughout the system;
In general, transients resulting from relatively slow changes in flow rate are referred to as
surges, and those resulting from more rapid changes in flow rate are referred to as water
hammer events. Surges in pressurized systems are different than tidal or storm
surges, flood waves, or dam breaks, which can occur in open-water bodies;
In general engineering practice, the terms surge, transient and water hammer are synonymous.
1
3. Methods for Formulation of transient flow
• Various methods have been developed to solve transient flow in pipes. These range from approximate equations to
numerical solutions of the nonlinear Navier-Stokes equations:
I. Arithmetic method—Assumes that flow stops instantaneously (in less than the characteristic time, 2L/a),
cannot handle water column separation directly, and neglects friction (Joukowski, 1898; Allievi, 1902).
II. Graphical method—Neglects friction in its theoretical development but includes a means of accounting for it
through a correction (Parmakian, 1963). It is time consuming and not suited to solving networks or pipelines with
complex profiles.
III. Method of Characteristics (MOC)—Most widely used and tested approach, with support for complex boundary
conditions and friction and vaporous cavitation models. It converts the partial differential equations(PDEs) of
continuity and momentum (e.g., Navier-Stokes) into ordinary differential equations that are solved algebraically
along lines called characteristics.
2
4. Common causes of transient flow
The most common causes of transient initiation, or source devices, are all moving
system boundaries.
• Sudden change of external flow demand at a junction due to fire demand or
valve closure;
• Sudden valve opening or closure;
• Pump Failure;
• Valves can be opened or closed with
the time varying change.
Fig:- Common Causes of Hydraulic Transients 3
5. Valves : A valve can start, change, or stop flow very suddenly. Energy
conservations increase or decrease in proportion to a valve’s closing or opening
rate and position , or stroke . Orifices can be used to throttle flow instead of a
partially open valve . Valves can also allow air into a pipeline and/or expel it,
typically at local high points.
(The problem that has been formulated for transient flow in pipelines is
due to closure of valve).
In pressurized networks, a steady-state condition or transient event at one
point in the system can affect all other parts of the system. Consequently,
computer models must consider every pipe that is directly connected to a
pressurized system, regardless of administrative or political boundaries.
4
6. Wave Propagation
The sequence of events following valve closure may be divided into four parts (Fig) as follows:
1. 0 < t ≤ L/a
When the valve is closed the flow velocity at the valve becomes zero. This increases the pressure at the valve by ΔH = -(a/g) ΔV.
and a positive pressure wave propagates towards the reservoir at the upstream. If a is the velocity of the pressure wave and L is
the length of the pipeline, then the wave front reaches the upstream reservoir at time t = L/a. At this time, along the entire length
of the pipeline, the pipe is expanded, the flow velocity is zero, and the pressure head is Ho + ΔH .
2. L/a < t ≤ 2L/a
Just as the wave reaches the upstream reservoir, pressure at a section on the reservoir side is Ho while the pressure at an adjacent
section in the pipe is Ho + ΔH. Because of this difference in pressure, the fluid flows from the pipeline into the reservoir with
velocity -Vo. Thus, the flow velocity at the pipe entrance is reduced from zero to -Vo.
3. 2L/a < t ≤ 3L/a
Since the valve is completely closed, a negative velocity cannot be maintained at the valve. Therefore, the velocity changes
instantaneously from −Vo to 0, the pressure drops to Ho − ΔH, and a negative wave propagates towards the reservoir
Behind this wave front, the pressure is Ho - ΔH and the fluid velocity is zero. The wave front reaches the upstream reservoir
at time t = 3L/a, the pressure head in the entire pipeline is Ho - ΔH, and the fluid velocity is zero.
.
5
7. 4. 3L/a < t ≤ 4L/a
As soon as this negative wave reaches the reservoir, an unbalanced condition is created again at the
upstream end. Now the pressure is higher on the reservoir side than at an adjacent section in the
pipeline. Therefore, the fluid now flows from the reservoir into the pipeline with velocity Vo, and the
pressure head increases to Ho .At time t = 4L/a the wave front reaches the downstream valve, the
pressure head in the entire pipeline is Ho, and the flow velocity is Vo. Thus, the conditions in the pipeline
at this time are the same as those during the initial steady-state conditions except that the valve is now
closed.
Since the valve is completely closed, the preceding sequence of events starts again at t = 4L/a
Fig:- Pressure variation at valve
6
8. Formulation of problem
During the hydraulic shock (water hammer) in the metal pipe, the
velocity c of the pressure disturbance is usually three times greater than
the velocity v of the flow, which therefore, may be ignored in the
characteristic equations
𝑑𝑥
𝑑𝑡
= ± c (1)
In the simplified analysis, fluid viscosity is neglected, which means that
in the equation:
±
𝑔
𝑐
𝑑ℎ
𝑑𝑡
+
𝑑𝑣
𝑑𝑡
+
λ𝑣∣𝑑𝑣∣
2𝑑
= 0 (2)
7
9. The last member is cancelled, i.e.
λ𝑣∣𝑑𝑣∣
2𝑑
= 0 . Considering the reductions mentioned, simple pipeline system is
analysed as shown in Figures below
Fig:- Diagram x-t for the basic version
of the simple pipeline Fig:- Schematic diagram of pipe system
8
10. 1. Continuity Equation for Unsteady Flow
The continuity equation for a fluid is based on the principle of conservation of mass.
The general form of the continuity equation for unsteady fluid flow is as follows :
𝑎2 𝜕𝑄
𝜕𝑥
+ 𝑔𝐴
𝜕𝐻
𝜕𝑡
=0
2. Momentum Equation for Unsteady Flow
The equations of motion for a fluid can be derived from the consideration of the forces
acting on a small element, or control volume, including the shear stresses generated by
the fluid motion and viscosity. The three-dimensional momentum equations of a real
fluid system are known as the Navier-Stokes equations. Since flow perpendicular to
pipe walls is approximately zero, flow in a pipe can be considered one-dimensional, for
which the continuity equation reduces to
𝜕𝑄
𝜕𝑡
+ 𝑔𝐴
𝜕𝐻
𝜕𝑥
+R𝑄 ∣ 𝑄 ∣= 0
9
11. Data used for the problem
• The height of the water pressure in the tank, h = 100m
• The length of the pipe, l = 12000 m
• Number of pipes in the system, n = 4
• Pipe diameter, D = 900mm
• Pressure wave velocity, c = 1200 m/s
• Coefficient of friction resistance, f= 0.022
• Δx=l/n=3000 m
• Δt=6 sec
Initial values
ℎ1=100 at t=0,6,12………
ℎ2= 99.83 at t=0
10
12. ℎ3=99.50 at t=0
ℎ4= 98.70 at t=0
ℎ5=98.5 at t=0
Known values of discharge taken
Q(:,1)=2.63; Q(1,2)=1.89; Q(1,3)=0.6; Q(1,4)=0.2
11
13. Lax Scheme
The numerical scheme used in the problem is the Lax Scheme. This scheme is first-
order accurate, is easy to program and gives satisfactory results although sharp wave
fronts are slightly smeared.
The partial derivatives as follows:-
𝜕𝐻
𝜕𝑡
=
𝐻𝑖
𝑗+1
− 𝐻𝑖
Δ𝑡
𝜕𝑄
𝜕𝑡
=
𝑄𝑖
𝑗+1
− 𝑄𝑖
Δ𝑡
𝜕𝑄
𝜕𝑥
=
𝑄𝑖+1
𝑗
− 𝑄𝑖−1
𝑗
2Δ𝑥
𝜕𝐻
𝜕𝑥
=
𝐻𝑗+1
𝑖
− 𝐻𝑖−1
𝑗
2Δ𝑥 12
14. In which
ഥ𝐻𝑖 = 0.5(𝐻𝑗+1
𝑖
− 𝐻𝑖−1
𝑗
) and
ത𝑄𝑖 = 0.5(𝑄𝑗+1
𝑖
− 𝑄𝑖−1
𝑗
)
Putting the above equations in Continuity and momentum equation we have,
𝐻𝑖
𝑗+1
=0.5(𝐻𝑖−1
𝑗
+𝐻𝑖+1
𝑗
)-0.5
𝑎2
𝑔𝐴
Δ𝑡
Δ𝑥
(𝑄𝑖+1
𝑗
− 𝑄𝑖−1
𝑗
)
and
𝑄𝑖
𝑗+1
=0.5(𝑄𝑖−1
𝑗
+𝑄𝑖+1
𝑗
)-0.5𝑔𝐴
Δ𝑡
Δ𝑥
(𝐻𝑖+1
𝑗
− 𝐻𝑖−1
𝑗
) − RΔ𝑡 ത𝑄𝑖| ത𝑄𝑖|
Fig:- Elementary mesh of
characteristics grid for internal
points
13
15. MATLAB Code
h = 100 ; %The height of the water pressure in the tank,m
l = 12000 ; %The length of the pipe,m
n = 4 ; % Number of pipes in the system,
D = 900/1000; %Pipe diameter, Pipe diameter,mm
c = 1200 ; % velocity of pressure wave,m/s
f= 0.022 ; % Coefficient of friction resistance,
g=9.8 ; %acceleration due to gravity,m/s^2
Q=2.63; %discharge in first node,m^3/s
A=(pi*D^2)/4; %Area of pipe,m^2
V=Q/A; %velocity of water,m/s
%hf=(f*l/n*V^2)/(2*g*D); %%head loss in second node by weisbach equation
hf=.345;
H=100; %head in first node
15
16. h1=99.83; h2=99.50; h3=98.7; h4=98.5; %%% head in each node,m
R=f/(2*D*A^2);
deltax=l/n; %dx
deltat=6; %dt
hh=zeros(8,5);
hh(:,1)=100; hh(1,2)=h1; hh(1,3)=h2; hh(1,4)=h3;
hh(1,5)=h4; %%head loss matrix
qq=zeros(8,5);
qq(:,1)=2.63; qq(1,2)=1.89; qq(1,3)=.6; qq(1,4)=.2;
qq(1,5)=.39; %%discharge matrix
t=0:6:42;
for i=1:7
for j=1:3
hh(i+1,j+1)=hh(i,j)+hh(i,j+2)-(c^2/(2*g*A))*(deltat/deltax)*(qq(i,j)-qq(i,j+2));
for k=1:8
q(k,j+1)=1/2*(qq(k,j)+qq(k,j+2))
end
qq(i+1,j+1)=1/2*(qq(i,j)+qq(i,j+2))-(g*A/2)*(deltat/deltax)*(hh(i,j)-hh(i,j+2))-R *q(i,j+1)*abs(q(i,j+1))*deltat
end
16
23. Conclusion
The construction of reliable and efficient piping systems represents a large
investment cost due to the number of protective elements to be installed to keep the
system safe from non-stationary phenomena;
The terms for one-dimensional fluid flow, with the introduction of assumptions and
simplifications, are quite complex, therefore MATLAB programs is used to calculate
fluid flow parameters;
In the numerical calculations advantage has been taken of the Lax Scheme which
can be used in the cases when frictional effects are very important. In this method
the values of the pressure heads and discharge flows are calculated on the basis of
the mean resistance of elementary pipe sections related to the flow value of the
preceding and following time steps.
14
24. References
Salmanzadeh M. (1993) “Numerical Method for Modeling Transient Flow in
Distribution Systems”, Islamic Azad University, Shoushtar;
Vataj G. & Berisha X. (2018) “MODELING OF TRANSIENT FLUID FLOW IN
THE SIMPLE PIPELINE SYSTEM”, University of Prishtina, Pristina, Kosovo;
Textbook of APPLIED HYDRAULIC TRANSIENTS by M. Hanif Chaudhry.
23