Control de Ariete Tesis

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    The easiest and least expensive way to control

    water hammer in irrigation and drainage network of

    Sivand DamReza Gharehkhani, Sayed Abbas Mousavi, Fatemeh Kazemi

    Abstract-Water hammer pressure occurs in pipelines of

    under pressure and it is based on pressure regulation, flow

    velocity and changes of location, time of fluid motion. In some

    hydraulic systems under pressure, such as water transmission

    lines, oil or water distribution systems and piping leading to the

    turbine, water tunnels, gravity flow and pumping systems, water

    hammer phenomenon is caused in various risks by creating a

    fast and damped transient wave, sometimes destructive power of

    these wave pressures are so, which would bring about serious

    consequences, burst in pipeline systems and distribution

    networks, failures and broken valves, control valves and pumpsare examples of the impact. In this study for simulation of

    transmission lines in stable and unstable hydraulic conditions,

    we use the two software of Bentley Company with the names of

    WaterGems and Hammer. Results from the model indicated that

    the phenomenon of water hammer occurs when valves are

    closing and for harness of this phenomenon we used the

    simplest way with regarding to the parallelism of the two lines

    together. Thus, a connection pipe were used that connected with

    the two main pipes in several points. In this method, during the

    occurrence of water hammer, every line serves as a repository

    for other lines.

    Keywords-Water hammer effect, Water hammer control,

    connection pipe, easiest way

    INTRODUCTION

    Water hammer is the formation of pressure wave as a

    result of sudden change in liquid velocity in a piping

    system. The water hammer phenomena usually explained

    by considering by ideal reservoir pipe-valve system in

    which the steady flow with velocity ! is stopped by an

    instantaneous valve closure. In other say it occurs when

    the fluid flow start or stop quickly or is forced to make a

    rapid change in direction, for example quick closing the

    valves and stoppage of a pump can create water

    hammer[4,12]

    Background of the Investigations

    Joukowsky[6] published the basic theory of water

    hammer. He achieved acceptable relationship for increase

    pressure, fluid density, velocity and wave speed changes.

    - Reza Gharekhani : Technical head office in irrigation and drainage

    network of Sivand Dam. E-mail: [email protected]

    - Sayed Abbas Mousavi: project manager in irrigation and drainagenetwork of Sivand Dam (pars garma company). E-mail:

    [email protected]

    -Fatemeh Kazemi: Technical Expert in Parese banaye shirazCompany.E-mail: [email protected]

    g

    VaH

    =

    H : Increased pressure on the basis of water head(m)

    A : wave velocity (m / s)

    V : velocity change of liquid in the pipe line (m / s)

    G: acceleration of gravity (m / s ^ 2)

    Joukowsky also studied and investigated the emission

    of waves in the pipeline and their reflections, means the

    time it takes a wave to go to the boundaries of reflection

    and return[6].

    In 1960s and development of computer industry a new

    era started in studying and analyzing the phenomenon of

    water hammer. Stritter and Whily[9] showed that with the

    aim of computer they can solve very difficult and

    sophisticate problems and so analyzing of water hammer

    that in that era was exclusive to the few number ofexperienced people, proposed for the most of engineers.

    Parmakian (1950-1963) stated that the aggregation of

    high pressure waves are dangerous and recommended

    that for ensuring and having enough safety from danger

    of the wave it should prevented from vacuum separation

    in system[8].

    In the research by Anton [1] water hammer analysis for

    control of water in underground mines had been done.

    Field measurement are comprised with a computer

    simulation analysis of a transient during power failure to

    the pump. The result show that the method of

    characteristic is an acceptable method for water hammeranalysis of mine pumping systems.

    In the research by Don[5], two procedure for solving

    the basic transient flow had been comprised . one of them

    is based on a numerical procedure using the method of

    characteristics (MOC). Another is referred to the wave

    characteristics method ( WCM). The results show that the

    MOC and WCM are both capable of accurately solving

    for transient pressures. The WCM will normally require

    fewer calculations and faster execution times. Because of

    the difference in calculation requirements and the

    comparable accuracy of two techniques, the use of the

    WCM will be more suitable for analyzing lang pipe

    network.

    Advances in Environmental Sciences, Development and Chemistry

    ISBN: 978-1-61804-239-2 417

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    Cannizzaro [3]discussed on the failure of the water

    column in transmission flows and creating a large

    pressure rise within the pipeline.

    In another research, [10] results show that water

    hammer effect is more in larger and bigger diameter of

    pipe line. Water hammer effect in the pvc pipe is greater

    than the water hammer effect in steel pipe. The

    prevention method of water hammer effect which installthe bypass pipe with non return valve had prove that the

    method is successfully to reduce the water hammer effect

    in the pipe line. The mean pressure is reducing about

    33.33% after installing the prevention method. This

    method is useful in the household usage as the non return

    valve is not an expensive method.

    Consequences from the water hammer phenomenon

    low and high pressures

    Non-steady flow can be caused high or low pressures.

    Excess pressure can damage the pumps, valves and otherpipeline equipment or cause fracture in lines. Low

    pressure causes the release of dissolved air of the fluid

    and if the pressure reaches the vapor pressure of the fluid

    leads to intense evaporation. Low pressure inside the

    pipes (plus the pressure due to external loading) can lead

    to pipe failure. The vapor cavity-closure can also cause

    extreme shock pressure that the system will be impaired.

    Vibration

    Vibration of non-steady flow in pipelines can cause

    significant effects on pipelines. Intense vibration of non-

    steady flows results from where that some alternating

    currents causes agitation of pipeline equipment in

    frequencies close to their natural frequency. In this case,

    the stresses and large deformations (with sound) occurs

    that may impair the system.

    Vacuum induction

    Rapid condensation and vaporization causing a vacuum

    induction that it is one of the lasting effects of the non-

    steady currents. Vapor cavity usually forms when fluid

    pressure by dynamic or statistic factors is equal to or less

    than vapor pressure. These holes are expanded by low

    pressure. When the pressure around these cavities

    increases over the vapor pressure, the cavities disappears

    and fall down. This creates noise, vibration and possible

    damage to the hard surfaces.

    Shock waves from collapsing vapor cavities can create

    pressure fluctuations and causes vibrations in system.

    Such vibrations can cause screws to loosen, Fatigue of

    connections, loose or breaking belts and damage to the

    pipes. If vapor cavities near the hard borders (such as

    plumbing) fall down, erosion is likely and this causes

    premature repair or replacement of pipe, valves, pumps,turbines, etc. Vapor induction can reduce system

    performance such as increased pump head loss reduction,

    reducing power generation in turbines and reducing the

    flow through the valves.

    Location and causes of water hammer

    The possibility of water hammer phenomenon that its

    formation mechanism depends on changing in velocity

    and pressure of flow exists in fluid transfer systems.

    Water hammer occurs in pipes for water transmission,water distribution networks, oil pipelines or fluid

    transmission in industries, turbine water flow in pipes or

    in open streams such as the failure of a dam failure, the a

    huge wave of water downstream along the path and flows

    by gravity or pumping flow systems.

    The accident occurred due to different causes that the

    most important are:

    - Reduce or increase the velocity and flow with

    maneuver of control valves in water, oil pipelines and

    - Reduce or increase the velocity and flow with

    opening and closing of control valves in water pipe

    turbines.

    - Setup or failure of pumps and turbines.

    - When switching or increase and decrease in flow and

    velocity in gravity flow with using control systems.

    - Power failure in pumping systems.

    - Existence of changes in flow path, including

    increasing and decreasing pipe diameter or existence of

    blind pipes.

    Calculation of water hammer (Water Hammer)

    One of the important factors for the calculation of

    water hammer is the calculation of wave velocity. Wave

    velocity in the pipe is obtained from the relationship

    based on m/s that is called Olivy relationship:

    )2

    1(*)/(*)/(1

    +

    =

    tDEK

    K

    a

    Where ! is Poisson's ratio (dimensionless), D is

    the pipe diameter (mm), t is the thickness of the pipe

    wall in terms of (mm), P is the density of water

    (kg/m3), E is modulus of elasticity of pipe, K is

    modulus of elasticity of water equal to 19/2 GPa. E

    values for pipes GRP are 30 to 50 GPa based on the

    type of material production.

    Water hammer in pipes under gravity pressure

    Gravity transmission lines are called networks that

    in which fluid flow from a source with a higher level

    toward a destination or consumer with lower leveldue to topography condition of pipeline approach is

    established by gravity and with the help of gravity.

    Advances in Environmental Sciences, Development and Chemistry

    ISBN: 978-1-61804-239-2 418

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    Factors causes water hammer in the gravity

    pipelines

    Sudden changes and pressure cause distribution of

    wave in pipelines and the occurrence of water

    hammer phenomenon. Considering that reservoir

    level is almost constant in gravity lines therefore it

    can be concluded that the water hammer in lines is

    summarized as follows:

    A- Sudden closing of taps on pipeline

    route

    B- Sudden opening of taps on pipeline

    route

    C- sudden fracture along the pipeline

    D- Cut or overload the downstream

    consumers that is associated with an increase or

    decrease in the current pipeline.

    The important point in relation to the gravity

    network of transmission lines is that separation of

    water column occurs less during water hammerphenomenon, because between upstream reservoir

    and nodes or downstream reservoir generally is a line

    which causes minimum pressure line become steady

    state in gravity system close to slope hydraulic line.

    However, where the ground suddenly falls to the

    lower elevation there is a possibility of water column

    separation phenomenon.

    The effect of pipeline profile and taps in gravity

    flows on water hammer rate

    - Positive pressure due to the maximum height

    difference of piezometric attenuation flow thatobtained from curve difference of maximum

    difference of piezometric height and profile

    evaluation of can provide with choosing the pressure

    bearing of the pipe and Characteristics of suitable

    work and also, if the pressure is higher than the

    nominal pressure can control it by safety valves and

    other safety measures.

    - Negative pressures that indicate vacuum

    induction and water column separation phenomenon

    cannot be easily controlled like positive pressures.

    The best and safest way is to inhibit negative

    pressure is to prevent its occurrence.

    - Negative pressures obtain from curve difference

    of minimum piezometric height and profile

    evaluation of line. So if in normal condition profile

    of the line is lower than the curve of minimum

    piezometric height, damaging effects of negative

    pressure and vacuum generation and separation of

    the water column in the line will not create. In design

    of gravity transmission pipelines whatever the

    pipeline profile has an upward concave cause that the

    curve of minimum piezometrc pressure locate above

    the profile of pipeline and possibility ofestablishment of negative pressures and destructive

    phenomenon of water hammer is reduced. However,

    in this case amount of positive pressure on the

    pipeline is considerable and only we should select

    proper nominal pressure of pipes and valves or can

    be controlled by a suitable buffer device.

    - In some of the designs that during the creation of

    water hammer only enter positive pressures on the

    pipeline and negative pressure does not occur due to

    the shape of the line profile, can be used a

    combination of two types of pipe for the transmissionline.

    - In gravity pipelines the main parameters

    determining hammer is the time to open and close

    TC valves. Therefore for analysis of the equations

    you should first select an assumed value of the TC,

    then the equation and the output results are

    investigated. So the minimum suitable time of

    closing that during which no serious danger threaten

    the pipeline and transmission system choose as a

    closing time of the taps.

    Almost in all kinds of taps during closing, amountof creating hammer during closing is about 85 to

    90% of low primary tap and the main hammer that

    causes damage occurs in about 10-15% of distal

    valve closure. For gravity systems of under

    pressure15-10% of the final closing of the valve

    should occurs in the time more thana

    LTr

    2= so

    water hammer pressure is reduced considerably[11].

    - In plans that the route of the pipeline is so long

    and the flow discharge capacity is considerable, inorder to reduce the time closing the valve operation

    can be carried out in two stages. So that 85 to 90% of

    tap sectional area will be operate at first and in a

    short time that can be calculated and for closing the

    remaining 10-15% should be done in a relative

    longer period and so the total time of closing is

    reduced.

    With using valves with electric or hydraulic

    steering (electric actuator) the opening and closing

    can be precisely controlled and regulated. In these

    taps with changing and reducing the operator the

    opening and closing time of the valves increase. Inpilot hydraulic taps we can control and regulate the

    opening and closing time by creating local pressure

    drop in the power steering line to the diaphragm and

    valve components[7].

    Existing methods for preventing hammer

    In order to avoid sudden shocks in pipes one way

    of controlling water hammer is selected according to

    the case arises in the design of water supply pipe

    networks, pumping stations and turbines.

    Basically in prediction of methods of preventingsudden strokes in pipes, pumping stations and water

    distribution networks, it is necessary to reduce the

    amount of height changing such as the energy

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    between tankers and location of taps and pumps,

    amount of time during wave movement and also

    changes in velocity. For this purpose the following

    methods suggested for preventing the hammer:

    - Use of safety valves

    - The use of check valves (to prevent water from

    back)

    - The use of buffer tanks

    - Flue pipes

    - Double orifice air valves

    What is important is the fact that basically designing

    water pipelines and networks and the choice of the

    roughness of the pipe lining and pressure drop should be

    done with care so to be able to withstand high pressures.

    Strategies to anticipate and deal with water hammer in

    pipelines, irrigation and drainage network project ofSivand Dam

    Before choosing one of the techniques for controlling

    the impact of stroking in the transmission line, the

    transmission line must be hydraulic modeling and with

    calculation of the potential stroke, finally the appropriate

    methods should be presented at the end due to the

    condition of the project.

    Sivand Dam Project of irrigation and drainage network

    has been designed and implemented as pipe networks.

    For transmission of water to the first part of the network

    it has been used from two parallel GRP pipes with adiameter of 1200 mm that receives water from an open

    reservoir and shall be transferred to the beginning of the

    network in length of 11800 meters. Because of the height

    difference between the reservoir and the water outlet area

    of agricultural land (about 36 meter) pipes went under

    pressure and it was necessary that investigate the hammer

    phenomenon and offer a proper method for controlling of

    that.

    It is necessary to precisely modelling part of hydraulic

    system like pipes, tanks and relief, safety and switching

    valves for analyzing water transmission line. In this

    regard, the pipeline is divided into a number ofcomputational reaches and necessary to be considered the

    pressure values at nodes and flow as input data plan in

    addition to the physical characteristics. The purpose of

    the model is to investigate the impact of hydraulic

    transients in pipelines transporting water results from

    closing of water taps.

    First we stimulate with WaterGems for normal

    conditions in steady state and then with Hammer for

    unsteady state of pipeline and results are presented as a

    graph.

    The model boundary conditions

    Due to the hydraulic studies conducted, water flow in

    the basin divider is designed as a free surface and the

    output structure is so that the water level is at a constant

    level of 1611 meters.

    Hydraulic modeling in stable condition

    It is prepared with entering the transmission line route

    profile and the placement of nodes and pipes on the

    hydraulic model of the transmission line in hydraulic

    stability conditions.

    Table 1: Names and computational nodes of main line

    water transfer project from km 0+000 to 11+800

    LabelElevation

    (m)

    Calculated

    Hydraulic

    Grade (m)

    Pressure

    (m

    H2O)

    J-1-A.V 1,609.00 1,610.30 1

    J-2-B.O 1,594.97 1,609.51 15

    J-3-A.V 1,596.95 1,609.22 12

    J-5-B.O&A.V

    1,578.97 1,603.78 25

    J-6-

    B.V&A.V1,576.68 1,602.47 26

    J-7 1,576.57 1,601.61 25

    J-8-B.O 1,575.34 1,600.63 25

    J-9-A.V 1,575.80 1,599.91 24

    J-10-A.V 1,576.20 1,599.38 23

    J-12-B.O&A.V

    1,573.90 1,596.65 23

    J-13 1,573.66 1,595.05 21

    J-14 1,573.00 1,594.98 22

    Table 2 Names and properties of water transmission

    pipe line project from km 0+000 to 11+800

    LabelLength

    (m)

    Pressure

    PipeHeadloss

    (m)

    HeadlossGradient

    (m/km)

    P-1 147 0.2 1.31

    P-2 605 0.8 1.31

    P-3 219 0.29 1.31

    P-4 2124 2.79 1.31

    P-5 2019 2.65 1.31

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    LabelLength

    (m)

    Pressure

    Pipe

    Headloss

    (m)

    HeadlossGradient

    (m/km)

    P-6 999 1.31 1.31

    P-7 649 0.85 1.31

    P-8 749 0.98 1.31

    P-9 549 0.72 1.31

    P-10 399 0.53 1.31

    P-11 999 1.31 1.31

    P-12 1084 1.42 1.31

    P-13 1213 1.59 1.31

    P-14 53 0.07 1.31

    Graph (1) Profiles of main line water transfer project

    from zero miles to km 11+800

    Figure 1 profiles and hydraulic gradient for water

    transmission line projects in stable hydraulic condition .

    With viewing the profile of basin divider from the

    place of the pipeline to km 11+800, it is observed that

    static pressure is up to about 5/36 meters of water.

    According to the technical report of consulting

    engineers, shows that the flow rate is about 3.5 cubic

    meters per second by PN6 GRP pipes with a diameter of

    1200 mm shall be transmitted to the network. Dynamicpressure of the flow path is from zero at the beginning of

    the path to about 3 atm.

    calculations and modeling results in unstable

    hydraulic conditions

    inputs to hydraulic hammer model of in HAMMER

    software

    Coefficients and necessary information relating to the

    characteristics of the pipe and fluid inside the pipe are

    presented to model the path of unstable modes in TableNo. (3)

    Table (3) the physical characteristics of GRP pipes

    MaterialYoung's ModulusPoisson's

    Ratio (109 lbf/ft2)(GPa)

    G.R.P1300.4

    fluid properties

    Pipe material: GRP

    Length of the transmission line: 11800 m

    Inner diameter: 1200 mm

    Wave velocity in the pipe: minimum 400 and

    maximum of 600 meters per second

    Partial pressure of water vapor: 10 - Mtrab

    Valves: Butterfly valves with a diameter of 1200 mm

    and 200 mm diameter air

    Water level in the basin divider

    Profile Transmission Line

    Flow rate for each pipeline 1.75 cubic meter per second

    Modeling is done in unstable hydraulic conditions for

    slow closing of switching valves at the times of 60, 90,

    150, 200 and 300 seconds. In Figure (2) to (9) profiles of

    pipelines and minimum and maximum blow pipes are

    shown at different times. It is observed with increasing

    valve closure time in the last 10% hit rate is decreased but

    never reach to zero

    Scenario: BaseProfile from R-1-B.V to J-14

    Distance along Pipe Walk(m)

    (m

    )

    E

    le

    va

    tio

    n

    1570.0

    1575.0

    1580.0

    1585.0

    1590.0

    1595.0

    1600.0

    1605.0

    1610.0

    1615.0

    0.0 2000.0 4000.0 6000.0 8000.0 10000.0 12000.0

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    .

    Figure 2: Closing the valve on the wave speed of 600

    meters per second for 200 seconds with no impulse

    control equipment

    . Figure 2 shows unsteady hydraulic condition when

    switching valve is closing in about 9+500 km in duration

    of 200 seconds. It can be seen that without any water

    hammer control equipment, dynamic pressure of pipeline

    reaches to about 10 atmospheres before the tap.

    Figure 3: Closing valve for 200 seconds at a speed of

    400 meters per second without any impulse control

    equipment.

    Figure (3) shows the increasing pressure result fromclosing of switching valve in around 9+500 km with

    wave speed of 400 meters per seconds without any water

    hammer control equipment. It is observed that with

    decreasing the wave speed from 600 to 400 meter per

    seconds, the amount of potential hit rate decrease about 2

    atm.

    Figure 4: Closing the tap for 90 seconds at a speed of

    400 meters per second without any impulse control

    equipment.

    As can be seen in Figure 4, if the switching valve

    closure time reduced from 200 to 90 seconds, pressure

    rise due to water hammer occurred slightly than the

    previous case (200 seconds) but the frontal of positive

    wave moved at about 4 km further upstream side of the

    valve.

    Figure 5: Closing of the tap in 60 seconds by taking ashort circuit between two pipes (wave velocity of 600

    meters per second)

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    In figure 5 it is observed in the case of a short circuit

    between the two pipelines, since the closure time of the

    valve at about 9+500 km has decreased (from 200 to 60

    seconds) than the time when it is not a connection

    between the two pipes but the increasing pressure of

    water hammer is reduced considerably or in other words

    the maximum pressure generated during the worst

    condition is approximate to working pressure of the pipe

    (that will not exceed 6 atm.).

    Figure (6): Tap closing in 60 seconds by taking a short

    circuit between two pipes.

    In Figure 6 it can be seen since the valve closure time

    has increased from 60 to 150 seconds, pressure reduction

    result from water hammer than the figure 5 is so small.

    Figure (7): The use of pressure reducing valve in km

    9+500 before switching valve

    (Wave velocity of 600 meters per second)

    Another way to reduce the impact of pressure is to use

    safety valves.

    As it is observed in fig.7 pressure reduction of water

    hammer in the time of using safety valves is about 1 atm

    in comparison with fig.6.

    But for observing the effect of slowly closure of

    switching valves in the last 10 to 15%, seven case was

    modeled, showed that if 90% of the tap close in 200

    seconds and the last 10 percent close in 100 seconds

    reducing the impact in comparison to the second case

    (Figure 3) is about one to one and a half atmosphere.

    But the eight case was modelled for observing the

    effect results from slowly closure of switching valves in

    another location of transmission line, showed that if 90

    percent of the tap closure (km 3+100) took place in 200

    seconds and the other 10 percent took place in 100

    seconds, again, there will likely be a hit.

    CONCLUSION

    Due to the unstable conditions of hydraulic modeling

    results and comparison of various methods to control the

    impact from the economic view and the condition to

    ensure the operation of pipeline the following are

    discussed:

    1 - Almost in all types of valves during closing, the

    amount of water hammer caused by the closure is

    approximately 85 to 90 percent of the primary reducing

    tap and mainly the water hammer causing damage occurs

    in about 15-10% of distal valve closure. For under

    pressure gravity systems, 15-10% of the final closing of

    the valve should be applied in a time more than

    a

    LTr

    2= , in order to reduce water hammer pressure.

    2 - Using a short circuit( connection pipe) between two

    pipes that in case of occurrence of strokes, each pipe acts

    like a reservoir buffer for the pipe and in addition to cost

    reduction compared to control impulse safety valves or

    other techniques, the conditions of operation of the

    transmission line is easy.

    3 - One of the oldest method is to install pressure

    before the valve and so the operator should be trained

    according to the number of pressure and the maximum

    pressure should not be increased to a certain value to

    perform the operation of valve closure. Due to the error

    of manpower and the possibility of inattention of the

    owner this method is not recommended.

    4- Using power steering (electric actuator) or hydraulic

    valves that it can precisely control and regulate the

    opening and closing time. By changing and reducing the

    operator rounds, increases the time of opening and

    closing of the valve. In hydraulic pilot valves with

    creating local pressure drop in direction of hydraulic

    steering to the diaphragm and valve components can

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    control and regulate the opening and closing time of the

    valve.

    5 - The modeling results showed that safety valve

    control the potential water hammer so good.

    6- In total the cost of short circuit(connection pipe)

    between two pipes is less than the safety valves and

    power steering, also during the operation of this circuit itgives more flexibility to design and it is recommended to

    use short circuit between the two pipes in switching valve

    basin to control the water hammer phenomenon.

    REFRENCES

    [1] Anton Bergant., Angus, R. Simpson And Esad Sijahmozic., Water

    Hammer Analysis of Pumping Systems For Control of Water in

    Underground Mines. 4 th International Mine Water Congress,

    Ljubljana, Slovenia, Yugoslavia. September 1991.

    [2] Allievi, L., Theory of Water Hammer Ricardo Garoni, Rome,

    1925

    [3] Cannizzaro, D., Pezzigna.G., 2005. Energy Dissipation in Transient

    Gaseous Cavitation Journal of Hydraulic Engineering, ASCE, 131,

    724-732.

    [4] C.k. su, and c. camara, cavitation luminescence in a water

    hammer: up scaling sonoluminescence. Journal of physics of

    fluids, vol.15,pp- 1457-1461

    [5] Don J. Wood., Water Hammer Analysis Essential And Easy (

    and Efficient), Journal of Environmental Engineering, vol. 131,

    No.8, August 1.2005.ASCE, ISSN 0733-9372/2005/8-1123-1131

    [6] Joukowsky, N., Water Hammer, Proc. Am. Water Works Ass.,

    1904, v24,pp 338-424

    [7] Magazine NO 517, Vice President of Strategic Planning and

    Control: guidelines on the selection and design of control

    equipment and water utility of hammer. pp: 260-290, 2006

    [8] Parmakian, J., 1963. Water Hammer Analysis. Dover

    Publications, inc., New York, NY.

    [9] Streeter, V.L. And Wylie, E.B., Water hammer and surge

    control.Annual Review of Floud Mechanics, V6, paper 8054, pp57-73, 1974

    [10] Tan Wee Choon., Lim Kheng Aik., Lim Eng Aik., Thean Him.,

    Investigation of Water Hammer Effect Through Pipe line System

    international journal on Advanced Science Engineering

    information Technology. Vol. 2( 2012) No. 31SSN: 2088-5334

    [11] Taebi, A. And Chamani, M,. Urban Water Distribution Network.

    University OF Sfahan, Iran, pp: 330- 340, 2000.

    [12] Wood, F.M., History of Water Hammer , Dep. Civ. Eng., Queens

    Univ., Kingston, ont., C.E.Res.Rep. n 65.Apr 1970

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