Transportation Of Gas By Means Of Pipe Distribution Engineering Essay

The system designed for the transit of gas media B by agencies of pipe distribution systems form a big group of rather standard technological systems which have late become an object of control mechanization to an of all time increasing extent.

Steady province analysis of gas webs is comparatively simple to implement but it is non frequently applied to operational gas transmittal systems. This is because in existent web, demands and force per unit areas vary more or less changeless and the system is ne’er at steady province. Fast transients are particularly of import in the event of compressor dislocations, or during peak ingestion periods.

Models for transeunt analysis of a pipe are based on the continuity and impulse equations. From a mathematical point of position, these equations for transeunt grapevine web analysis are a set of partial differential equations with force per unit area and mass or volumetric flow rate as the reliable variables, and with infinite and clip as the independent variables..The equations are fundamentally inflated, but can be transformed into parabolic if premises are made. The algorithms are available for work outing the partial differential equation are based on the implicit and expressed finite difference method or the method of characteristic. ( M.O.C ) . These methods have been shown to be successful in covering with transeunt flow in pipe webs and have been used for decennaries but they have disadvantages implicit in solution of the partial differential equations.

More so, the analogies between fluid and electrical webs have long been realised and they have been applied successfully in simulation of steady province pipe web systems. It is known from electrical circuit theory that relationships between electromotive force and current can be attributed to three basic elements, viz. , opposition, electrical capacity and induction. Similarly because of these basic analogies between electrical circuits and fluid webs, the same three basic elements are besides present in the fluid webs ( A.E. Fincham, London Research Station, British Gas, private communicating. )

The opposition consequence in a grapevine web is due to several factors, such as the raggedness and geometry of the pipes, the viscousness of the fluid and the fluid flow rate. The electrical capacity consequence of a grapevine web is straight attributed to the squeezability of fluid. The induction consequence of a grapevine is believed to be due to the kinetic energy of the fluid.

In 1936, Professor Hardy Cross of the University of Illinois developed a method for work outing webs which gained widespread usage and which later became know as the Hardy Cross ‘ Method.

Before the debut of web analysis techniques the lone method of work outing webs was test and mistake, doing an initial estimation of the flow in each pipe and doing arbitrary accommodations until a balance was achieved and a solution obtained.

However, both the ‘trial and mistake ‘ and Hardy cross ‘ Methods ‘ require big Numberss

of computation and are hence suited for merely little webs if manual solutions

are to be obtained. The development of computing machines and the addition in their computer science power made possible the analysis of big webs utilizing plans based on Hardy Cross ‘ Method.

The cardinal equation depicting steady province gas flow is derived from Bernoulli ‘s equation. The flow equations derived from Bernoulli ‘s equation are expressed in footings of the flow rates in the links and consist of nonlinear energy equations and additive continuity equations. The caput equations are formed of nonlinear continuity equations showing the flow rates in the links as a map of the nodal caputs ( utilizing Kirchhoff ‘s Torahs ) . Each of them is a set of nonlinear algebraic equations that can non be solved straight.

1.1 Industrial Application of Network Analysis

Network analysis can be found in many industrial sector, viz. below to reference ;

Application of H2O supply system.

Application of Network Analysis to Gas Station.

Power Plant Application.

1.2 Application of Water Supply System

The municipal H2O industry is a really complex industry on one manus and its demands to bring forth safe potable H2O. IT needs to supply first-class service to user. The difference between municipal H2O industry and other industry or service sector is that twelvemonth unit of ammunition H2O supply ca n’t be interrupted.

So pipe web H2O force per unit area analysis play a really of import function in municipal H2O technology planning design work.

There are four pipe web analysis methods.

Hardy cross Method

Best rank similar pipe length balance method

Newton Method

Flow Volume Balance Method.

By and large to simplify H2O force per unit area computation of pipe web analysis, we assume pipe web ‘s H2O flow is steady flow, therefore omit clip factor in act uponing flow volume

1.2.1 Application of Network Analysis to Gas Station.

Figure 1. Simple Gas Pipeline System

The natural gas enters the grapevine from a supply beginning and so is transported to one or more bringing points. The force per unit area in the grapevine is on the other order manus of valued Pisa depending on the single company or state standard force per unit area, and the grapevine pipe is on the order of two to four pess in diameter. Compressor Stationss are located about every 60 stat mis along the grapevine. The compressor Stationss are necessary to get the better of the gas force per unit area bead in the pipe. The compressor Stationss house the engines, gas turbine and the compressor.

To find the minimal force per unit area countries within an bing web and hence the demand for support of these countries. Having established the superficial demand for support it ‘s necessary to be satisfied that burden informations and burden growing rates are accurate and that there are no interruptible tonss on the system. These are normally big and by definition may non be taking gas during peak demand periods. The optimal strategy for support will be based on the least cost solution but the web analysis plan ca be used for determine the technology demands of alternate option ; for illustration, increasing of the sizes of certain brinies during a reclamation plan could be a cheaper manner of supplying support than, state, a new feeder chief.

Network design for new lodging development is normally carried out in concurrence with a fiscal assessment. During the design procedure different pipe size combinations are tested against overall cost of each combination, leting the least cost solution to be found.

2. ) Aim, Input Requirements and Output Requirement of Network Analysis

2.1 ) Aims of Network Analysis

The aim of web analysis when applied to gas supply systems are to:

To find the flow all the pipes

To find the force per unit area at all the pipes junction.

Normally these aims are met when we have values for the followers:

The fixed force per unit areas at all supply points.

The tonss or off takes from the system.

Other possible restraints such as the minimal force per unit area at any points in the web

Remember that the end product from any web analysis merely every bit good as the input informations, so it ‘s worthwhile looking at the input and end product demand.

2.2 ) Input signal demands for Network Analysis

Flow Equation

Although non purely input informations, the flow equation, which is built into the web theoretical account, must be chosen to accommodate the web conditions.

As we saw in the faculty Gas Flow in round Pipes ‘ the existent signifier of the equation used varies depending on the preferable method for ciphering the value of the clash ; the method chosen will impact the values of the changeless K and exponent N.

Pipe Diameter

For each pipe in the web the internal diameter signifiers portion of the changeless K, which is relative to 1/d5. So an mistake of 1 % in the input value of diameter will bring forth a 5 % mistake in the value of K. This in bend would take to a 2.5 % mistake in a flow computation.

Accurate values for the internal diameter of each pipes in the web are hence of import, nevertheless the undermentioned points highlight the troubles associated with accomplishing the needed truth:

Nominal diameters are non good indicant of the true internal diameter because they ‘re merely a appellation. For hard-hitting steel grapevines the designated size is the outside diameter ; the existent internal diameter must be determined utilizing an accurate thickness

There is a difference in diameter between cavity dramatis personae and spun Fe pipes of the same nominal diameter due to the fabrication procedure. Many older gas distribution webs were constructed utilizing these types of pipe. The places of these pipes, within a web non normally known with any grade of certainty although some indicant may be obtained from the day of the month at which there are laid.

The internal status of the pipe will impact the existent diameter peculiarly where beds of graduated table have accumulated around the exterior of the pipe or sedimentations have partly filled the pipe

Pipe Length

In the low force per unit area flow equation, the pipe force per unit area loss and hence mistake will 1 in the value of K. nevertheless, since pipe lengths are determined from informations recorded at the clip of laying, or by scaling from record programs, the mistakes are likely to be equally distributed positively and negatively throughout the web. Such mistakes are likely to be self call offing on distribution webs of a sensible size.

2.3 ) End product Requirements

The primary demand of the end product from any web analysis plan is that it should accurately stand for the existent web. This can be achieved by ;

Guaranting the input is every bit accurate as possible: the end product can non be considered earnestly if the input is fishy. A database of information about all the pipes in a web can be used as the input to the plan. This will include accurate information on new pipes, obtained at the clip of laying, plus verification informations on pipes diameters, stuff, status, etc obtained whenever an bing chief is excavated for any ground: –

Occasional burden monitoring exercising to measure the truth of premise made in finding the burden informations. His is achieved by mensurating flows in pipes providing known as Numberss of clients ; it is expensive and hence done infrequently.

Conducting force per unit area studies over a chiseled country where entire tonss can be accurately assessed from metre readings in the country.

Using informations from force per unit area and flow studies to use accurate efficiency factors to the pipes within the study country.

3. Network Analysis Methods and Rules

Pipe Network simulates steady flow of liquids or gases under pressure.A It can imitate H2O system, long grapevines with different diameter pipes in series, parallel pipes, groundwater flow into a slotted good screen, dirty vapor extraction good design, and more.A Enter flows at nodes as positive for influxs and negative for escapes. A Inflows plus escapes must sum to 0.A Enter one force per unit area in the system and all other force per unit areas are computed.A All Fieldss must hold a figure, but the figure can be 0.A

Fig 2 Simple Pipe Network

Equation and Methodology

The pipe web computation uses the steady province energy equation, Darcy Weisbach or Hazen Williams clash losingss, and the stalwart cross method to find the flow rate in each pipe, loss in each pipe, and node force per unit areas. Minor losingss ( due to valves, pipe decompression sicknesss, etc. ) can be accounted for by utilizing the tantamount length of pipe method.

Hardy Cross Method and Torahs.

The Hardy Cross method is besides known as the individual way accommodation method and is a relaxation method. The flow rate in each pipe is adjusted iteratively until all equation is satisfied. The method is based on two primary physical Torahs ;

The amount of pipe flows into and out of a node equals the flow come ining or go forthing the system through the node.

Hydraulic caput ( i.e. lift caput + force per unit area caput, Z+P/S ) is single-valued. This means that the hydraulic caput at a node is the same whether it is computed from upstream or downstream waies.

Equations.

Pipe flows are adjusted iteratively utilizing the undermentioned equation,

until the alteration in flow in each pipe is less than the convergence standards.

n=2.0 for Darcy Weisbach losingss or 1.85 for Hazen Williams losingss.

Clash Losses, H

Our computation gives you a pick of calculating clash losingss H utilizing the Darcy-Weisbach ( DW ) or the Hazen-Williams ( HW ) A method.A The DW method can be used for any liquid or gas while the HW method can merely be used for H2O at temperatures typical of municipal H2O supply systems.A HW losingss can be selected with the bill of fare that says “ Roughness, vitamin E ( m ) ” .A The undermentioned equations are used:

If laminar Flow

If disruptive flow

If to the full disruptive flow

Where

“ log ” is basal 10 logarithm and “ In ” is natural logarithm.

A = Pipe country [ L2 ] .

C = Hazen Williams coefficient. Selectable as last point in drop-down bill of fare stating “ Roughness, vitamin E ”

D = Pipe diameter [ L ]

vitamin E = Pipe raggedness [ L ] . All pipes must hold the same raggedness.

f = Moody clash factor, used in Darcy Weisbach clash loss equation.

g = Acceralation due to gravity = 32.174 ft/s2 = 9.8066 m/s2

H = caput losingss in pipe [ L ] . Can besides be expressed in the force per unit area units [ P ] .

K = Constant in Hazen Williams equation of calculating H

K = Minor loss coefficient.

L = Pipe length [ L ] .

Leq =Equation length of pipe for minor losingss [ L ] .

n = Constant uses in Hardy Cross Equation.

P = Node force per unit area [ P ] . Can besides be expressed in length units [ L ] .

Q = Flow rate through a pipe, or into or out of node [ L3/T ] .Also know as discharge or capacity.

Re = Reynolds figure.

S = Specific weight of Fluid ( i.e. weight denseness ; weight per unit volume ) [ F/L3 ] . Typical units are N/m3 or Ib ( force ) /ft3. Note that S= ( mass denseness ) ( g ) .

V = Kinematics viscousness of fluid [ L2/T ] . Grecian missive “ nu ” . Note that Kinematics viscousness is tantamount to dynamic ( or absolute ) viscousness divided by mass denseness. Mass denseness = S/g.

V = speed in pipe [ L/T ] .

Z = Elevation of node [ L ] .

Z+P/S = Hydraulic caput [ L ] . Besides known as piezometric caput. Can besides be expressed in force per unit area units [ P ] .

Pressure Calculation

After calculating flowrate Q in each pipe and loss H in each pipe and utilizing the input node lifts Z and known force per unit area at one node, force per unit area P at each node is computed around the web:

Pj = S ( Zi -Zj – Hpipe ) + Pi where node J is down-gradient from node I. S = fluid weight denseness [ F/L3 ] .

Minor Losingss

Minor losingss such as pipe cubituss, decompression sicknesss and valves may be included by utilizing the tantamount length of pipe method ( Mays, 1999 ) . Equivalent length ( Leq ) may be computed utilizing the following reckoner which uses the expression Leq=KD/f. degree Fahrenheit is the Darcy-Weisbach clash factor for the pipe incorporating the adjustment, and can non be know f in front of clip. A moderately value to utilize is f=0.02, which is the default value. We besides recommend utilizing f=0.02 even if you select Hazen-Williams losingss in the pipe web computation. K values are from Mays ( 1999 ) .

4.0 Newton Loop Method

Newton Loop Node Method: Is basically used in work outing the set of loop equation in steady province gas web. However, this method does non work out loop equation. The equations have to be transformed to an tantamount set of node equations, which are so solved to give the nodal force per unit area. The nodal force per unit areas are used to cipher the corrections to the chord flows, and the tree subdivision flows are obtained from them. The procedure is repeated continuously until the true solution is obtained. Figs 5 show the procedure to work out the web job. The procedure of doing a cringle flow synonymous to a chord flow in the web is rather complex.

Fig 3 Graph of gas

Where

Qt1, Qt2 aˆ¦Qt5 – Branch flow

QAC — Chord flux indistinguishable to flux in cringle Angstrom

QBC — Chord flux indistinguishable to flux in cringle B

Formulation of Equation for Steady State Analysis

The steady-state flow rate of gas in pipe is described by many expressions, but none are cosmopolitan. The effects of clash are hard to measure and are the chief ground for fluctuation in the flow expression. Most of the flow equation is derived from Bernoulli ‘s equation. The undermentioned general flow equation is the looks normally used for web analysis in the gas industry.

Where

Pb =base force per unit area, psia

D =inside pipe diameter, millimeter

P1 = upstream force per unit area, psia

Tb =base temperature, 0R

f =friction factor, dimensionless

P2 =downstream force per unit area, psia

Qb =gas flow rate at base status, SCF/hr

Tavg =average absolute temperature of fluxing gas,0R

G =specific gravitation of gas with regard to air, dimensionless

Zavg =average squeezability factor of gas at fluxing status dimensionless

( In most distribution system flow computation the value of this factor can be taken as 1.0 )

Nodal Formation

Kirchhoff ‘s first jurisprudence provinces that the algebraic sum the flow at any node is zero. This means that the burden at any node is equal to the amount of the subdivision flows into and out of the node.

Loop Formation

Kirchhoff ‘s 2nd jurisprudence province that the force per unit area bead around any closed cringle is zero. A closed cringle starts and coatings at the same node so there can be no force per unit area bead around the cringle.

Advantages and Disadvantages of Using Simulation theoretical accounts for Network Analysis.

Models are mathematical representations of a procedure. A theoretical account contains the cardinal elements of a system under survey. Most good theoretical accounts begin with the modeler interrupting down a complex procedure into a series of parts. There are many good theoretical accounts in the Today.

Simulations can take many signifiers from spreadsheets to three dimensional representations of things traveling a infinite. A simulation can be stochastic or deterministic. It is of import that the developer understandings the difference between these two types of stimulation.

The Newton Method is largely used in pipe work computation. In the multi-dimensional instance this method requires the solution of a system of additive algebraic equation in every loop, which in the instance of gas web, has a thin coefficient matrix. The Newton loop-node method basically solves the set of loop equation.

The advantages and disadvantages of simulation methods of work outing web analysis jobs can be summarised as follow.

Advantage

Enable the interior decorator to analyze the consequences of complex computation and assorted combination of design parametric quantities therefore geting at good net work design.

Enable the applied scientists to seek the many combinations of shrieking constellation and other design parametric quantity, which were impossible to make. Because of clip required making manually.

Give the ability to the design applied scientist to do alterations to the net work geometry. Loads, etc.

Reduce the cost of design, buildings, and care of shrieking net plants

Provides numerical mistake free computations and requires much less technology clip than those done manually. They design engineer therefore has the ability to see more alternate solutions, in so making, make better design in the same available clip.

Disadvantage

In the instance of the cringle method, the disadvantage of holding to specify the cringles in the webs which makes its application really complex and hard to work out?

Some premise is important for the development of theoretical accounts.

5.0 Analysis of Complex Pipe Networks with Multiple Loops and Inlets and Mercantile establishments

The techniques described antecedently for analysis of pipe flow are satisfactory if the pipe

system is simple, dwelling of one pipe or a combination of pipes in which the flow waies are all known unequivocally. In more complex systems, pipes might be combined in interrelated cringles in ways that make it hard to find even the way of flow in any given pipe. The cardinal relationships that we have derived up to this point – the energy and continuity equations and the relationships between flow and head loss in any given pipe – still use in such a system, but the sheer figure of equations that need to be satisfied to find the complete flow conditions is dashing. The conditions in such systems are normally solved with specialised computing machine plans designed specifically for that intent. However, before such plans were widely available, less sophisticated techniques were developed for analysing the systems. These techniques are easy programmed into a spreadsheet, so they provide a span between the really simple jobs that can be solved manually and the monolithic 1s that can be solved merely with particular package. In this subdivision, we explore these intermediate-scale techniques. These techniques, every bit good as more sophisticated 1s, let us to reply such inquiries as:

* For the given flow rates, what will be the head loss in each pipe?

* Will extra caput have to be supplied by pumps in order to obtain the coveted flows?

* How much will the flows rates change in assorted parts of the system if a new pipe is installed, linking two antecedently unconnected points, or to replace an older, smaller

pipe?

* How much will the force per unit area at a consumer ‘s tap bead if the fire water faucet outside his or her

place is in usage?

Solving the System of Equations

The methods used historically to work out pipe web jobs are “ relaxation ” techniques, in which a few of the variables are estimated, the others are computed, and the original estimations are revised based on algebraic uses of the computed variables. The numerical solution will, of class, depend to some extent on which equation is used to associate flow to head loss. With regard to shriek web analysis, the traditional attack is known as the Hardy Cross method. This method is applicable if all the pipe sizes ( lengths and diameters ) are fixed, and either the caput losingss between the recesss and mercantile establishments are known but the flows are non, or the flows

at each influx and outflow point are known, but the caput losingss are non. This latter instance is explored following. The process involves doing a conjecture as to the flow rate in each pipe, taking attention to do conjectures in such a manner that the entire flow into any junction equals the entire flow out of that junction. Then the caput loss around each cringle is calculated, based on the false flows and the selected flow vs. head loss relationship. Next, the system is checked to see if the caput loss around each cringle is zero. Since the initial flows were guessed, this will likely non be the instance. The flow rates are so adjusted in such a manner that continuity ( mass in peers mass out ) is still satisfied at each junction, but the head loss around each cringle is closer to zero. This procedure is repeated until the accommodations are satisfactorily little. The elaborate process is as follows.

1. Specify a set of independent pipe cringles in such a manner that every pipe in the web is portion of at least one cringle, and no cringle can be represented as a amount or difference of other cringles. The easiest manner to make this is to take all of the smallest possible cringles in the web.

2. Randomly choose values of Q in each pipe, such that continuity is satisfied a each pipe junction ( sometimes called nodes ) . Choose a mark convention for each cringle ; one easy option pick is to systematically specify Q to be positive if the ( false way of flow is clockwise with regard to loop under consideration. This convention means that the same flow in a given pipe might be considered positive when analysing one cringle, and negative when analysing another.

3. Calculate the caput loss in each pipe, utilizing the same mark convention for caput loss as for flow, so that hafnium in each pipe has the same mark as Q, when analysing any given cringle.

4. Calculate the caput loss around each cringle. If the caput loss around every cringle is zero, so all the pipe flow equations are satisfied, and the job is solved. Presumably, this will non be the instance when the initial, arbitrary conjectures of Q are used.

5. Change the flow in each pipe in a given cringle by I”Q. By altering the flow rates in all the pipes in a cringle by the same sum, we assure that the addition or lessening in the flow into a junction is balanced by the exact same addition or lessening in the flow out, so that we guarantee that the continuity equation is still satisfied. The fast one is to do a good conjecture for what I”Q should be, so that the caput loss around the cringle approaches nothing. To accomplish this, we assume that we can take a value of I”Q that is precisely what is needed to do the caput loss nothing, and so see how this value of I”Q is expected to be related to other system parametric quantities. The relationship is derived as follows. The Darcy-Weisbach equation can be written in the signifier:

Hfo =KQ2 ( 2 )

Hf1 =KQ2 = ( KQ+I”Q ) 2 ( 3 )

=KQ2 +KQo 1I”Q+higher order footings in I”Q ( 4 )

Assuming that the higher order footings are little compared to the first two, we can drop them from Equation 4. Following, we sum the caput losingss in all the pipes around the cringle being analyzed.

As noted antecedently, the initial conjecture of the flow rates is wholly arbitrary, every bit long as

continuity is satisfied at each junction. If one makes good conjectures for these flow rates, the job will meet rapidly, and if one makes hapless conjectures, it will take more loops before the concluding solution is found. However, any conjectures which meet the mass balance standard will finally take to the same, right concluding consequence.

Note that the premises for flow must be consistent for all the cringles in the system. That is, one time a flow rate and way are assumed for a given pipe, those same premises must be used for that pipe in every cringle that includes it. Finally, note besides that, if a pipe is portion of two or more different cringles, the rectification factors for all the cringles that contain it are applied to it.

Example of the Use of Simulation Methods for Network Calculation

Application to Water Supply System

Figure 4. Representation of Pipe Network

The pipe webs shown in Fig. 5 consist of 12 pipes, nine nodes, changing nodal demands, a reservoir, and a variable-head armored combat vehicle. The hourly fluctuation of nodal demands pattern used for the simulation is shown in Fig. 6

Figure 5. Hourly Variation of Nodal Demand

As a first measure to compare the H2O quality simulation modal, the convergence of the dynamic modal to a steady-state solution was verified. In order to make this, the modal was run for a long clip simulation period with stead-state flow solution to cipher the Cl concentrations in the web. It required 6 yearss of simulation period for the nodal concentration to make steady-state.

Since the Cl concentration in the web are maps of flows, the fake concentration from the two modals differ significantly in both clip and magnitude. The concentration at the nodes near the reservoir ( nodes 2, 3, 4 and 5 ) show less difference when compared with the concentration computed by standard theoretical account. The concentration at nodes near the armored combat vehicle ( nodes 6, 7, and 8 ) has important difference in clip and in magnitude.

The web is besides simulated without scattering. The differenced in the concentration profiles are undistinguished when compared with those with scattering. This is because the flow in the web is advection dominated and the scattering co-efficient is really little.

The upper limit and minimal operation conditions for a natural gas

transmittal grapevine with an internal diameter of 600mm is shown below.

If the natural gas is a representative southern North Sea Gas what is the Quantity of line battalion released at MSC when the flow rate alterations from Qmin to Qmax

Premises

The gas temperature is 150C

Zmax the maximal flow rate = 0.875

Zmin at the medium flow rate = 0.864

Datas

vitamin D = 600mm

Pin ( 1 ) = 70bar

Pin ( 2 ) = 70bar

Pout ( 1 ) = 60bar

Pout ( 2 ) = 50bar

L = 100Km ~ 100,000m

T = 150C ~ 288.15K

Zm ( 1 ) = 0.875

Zm ( 2 ) = 0.864

From

Substituting values

VS1=2.077m3

VS1=4.401m3

Therefore

Vlinepack = VS2 – VS1

= ( 4.401 – 2.077 ) M3

= 2.324m3

Where

vitamin D = Pipeline diameter [ m ]

Pin ( x ) = Pipeline recess force per unit area at point 1 or 2 [ saloon ]

Pout ( Y ) = grapevine mercantile establishment force per unit area at points 1 or 2 [ saloon ]

L = grapevine length [ m ]

T = Gas temperature [ K ]

Vs1 = grapevine volume at minimal flow rate

Vs2 = grapevine volume at maximal flow rate

6.0 Drumhead

Network analysis is used extensively for analyzing fluid and electrical webs in a figure of different industries, including the gas industry.

The primary aim of web analysis in the gas industry is to find the force per unit areas and flow in all the web pipes

Accuracy of input informations is of import for web analysis to be of value

End product from web analysis can be checked against to be of value.

Applications of web analysis in the gas industry include:

Designation of support strategies

Pressure optimization

Operational planning

Testing the web under specific conditions

Testing the web under specific conditions

Planing new webs.

7.0 REFERNCES

Analysis of flow Networks of Conduits Or Conductors, University III Eng. Exp.Sta. Balance ( 1936 ) .

Gas Flow In Circular Pipes Dr G.G Nasr Gas Engineering and Management. Module 3.University of Salford.

Fluid Mechanics, Douglas, Gasiorek & A ; swaffield 3rd erectile dysfunction. Longman Press. ( 1995 ) .

Journal of Hydraulic Engineering.Nov. 1998

hypertext transfer protocol: //www.lmnoeng.com/Pipes/PipeNetwork.htm A© 2001 LMNO Engineering, Research, and Software, Ltd. ( All Rights Reserved )

Accessed 10/11/2007

hypertext transfer protocol: //faculty.washington.edu/markben/CEE342… ( accessed 15/12/2007 )

Table of Content Page

1.0 INTRODUCTION 1

INDUSTRIAL APPLICATION OF NETWORK ANALYSIS 2

2.0 OBJECTIVES, INPUT REQUIREMENT AND OUTPUT REQUIREMENT

OF NETWORK ANALYSIS 4

2.1 OBJECTIVE OF NETWORK ANALYSIS 4

2.2 INPUT REQUIREMENTS FOR NETWORK ANALYSIS 4

2.3 OUT REQUIREMENT 5

3.0 NETWORK ANALYSIS METHODS AND RULES 6

4.0 NEWTON LOOP METHOD 8

5.0 ANALYSIS OF COMPLEX PIPE NETWORKS WITH MULTIPLE

LOOPS AND INLETS 11

6.0 SUMMARY 18