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Hosted by

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URS Corporation

21st Century Dam Design

Advances and Adaptations

31st Annual USSD Conference

San Diego, California, April 11-15, 2011

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On the CoverArtist's rendition of San Vicente Dam after completion of the dam raise project to increase local storage and provide

a more flexible conveyance system for use during emergencies such as earthquakes that could curtail the regions

imported water supplies.The existing 220-foot-high dam, owned by the City of San Diego, will be raised by 117

feet to increase reservoir storage capacity by 152,000 acre-feet. The project will be the tallest dam raise in the

United States and tallest roller compacted concrete dam raise in the world.

The information contained in this publication regarding commercial projects or firms may not be used for

advertising or promotional purposes and may not be construed as an endorsement of any product or

from by the United States Society on Dams. USSD accepts no responsibility for the statements made

or the opinions expressed in this publication.

Copyright 2011 U.S. Society on Dams

Printed in the United States of America

Library of Congress Control Number: 2011924673ISBN 978-1-884575-52-5

U.S. Society on Dams

1616 Seventeenth Street, #483

Denver, CO 80202

Telephone: 303-628-5430

Fax: 303-628-5431

E-mail: [email protected]

Internet: www.ussdams.org

U.S. Society on Dams

Vision

To be the nation's leading organization of professionals dedicated to advancing the role of dams

for the benefit of society.

MissionUSSD is dedicated to:

Advancing the knowledge of dam engineering, construction, planning, operation,

performance, rehabilitation, decommissioning, maintenance, security and safety;

Fostering dam technology for socially, environmentally and financially sustainable water

resources systems;

Providing public awareness of the role of dams in the management of the nation's water

resources;

Enhancing practices to meet current and future challenges on dams; and

Representing the United States as an active member of the International Commission onLarge Dams (ICOLD).

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Intelligent Flow Control 477

INTELLIGENT FLOW CONTROL AFTER LOAD REJECTION AT THE

JUNIPER RIDGE HYDROELECTRIC POWER GENERATION PROJECT

BEND, OREGON

Alden C. Robinson, PE1

Z. (Joe) Zhao, PE, Ph.D.

2

ABSTRACT

A new hydroelectric project with a long and large diameter steel penstock was designed

and constructed with a bypass system for the Central Oregon Irrigation District (COID).

During normal operation, flow passes through the turbine to generate electricity.However, for abnormal conditions or maintenance, flow will be switched to the bypass

system. There are two major requirements for the hydraulic system. First, the flow rate

downstream of the hydroelectric facility must remain constant always. Second, transientpressures in the hydraulic system after load rejection must be properly controlled. To

meet these requirements, intelligent flow controls are required. In order to design andimplement a proper flow control scheme, numerical modeling of the entire hydraulic

system was performed. The numerical modeling helped evaluate various flow conditionsin the system with three goals: 1) control the discharge downstream of the powerhouse by

adjusting turbine wicket gates and valves; 2) compute the highest hydraulic pressures

including positive transient pressures along the entire hydraulic system such that they arelower than the allowable design values of the penstock and the associated components;

and 3) compute the lowest hydraulic pressures including negative transient pressures

along the entire hydraulic system such that vacuum conditions are not induced. Thesechallenges were successfully resolved by COID at the Juniper Ridge Hydroelectric Power

Generation Project in 2009-2010 and are described herein.

INTRODUCTION

The Juniper Ridge Hydroelectric Power Generation Project is a 5-MW hydroelectric

project located in central Oregon between the City of Bend and the City of Redmond.

This is an Engineer, Procure and Construct (EPC) project constructed by a team led by

Slayden Construction Group, Inc. The team includes Sunrise Engineering Inc. for civildesign, CFM Engineers Inc. for electrical/control design and Burke Electrical Inc. as an

electrical contractor. The project mainly consisted of a hydraulic system, powerhouse,

substation, switchyard and site improvements. Two of the important project requirementsspecified by COID are to maintain downstream flow rate and to control transient

pressures in the hydraulic system. These two requirements were met by installing various

valves and flow controls in the hydraulic system. The flows and pressures in thehydraulic system were evaluated first and the penstock and valves were designed and

1President/CEO, Sunrise Engineering Inc., 25 East 500 North, Fillmore, Utah 84631, [email protected] Engineer/Manager, Sunrise Engineering Inc., 12227 South Business Park Dr., Draper, Utah

84020, [email protected]

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478 21st Century Dam Design Advances and Adaptations

selected accordingly. The hydraulic system, the flow and pressure evaluation techniques,

the flow and pressure evaluation results and design considerations are discussed herein.

HYDRAULIC SYSTEM

The Juniper Ridge Hydroelectric Power Generation Project was constructed within asection of an existing COID irrigation canal. Inflow to the canal is diverted from and

regulated through a gate at the Deschutes River near the City of Bend. The hydraulic

system consists of a forebay with diversion structure, 2.5-mile long108-inch diametersteel penstock with air/vacuum relief valves, 5-MW vertical Francis turbine/generator

unit with tailrace, and a bypass pipeline with energy dissipation valve-stilling basin

followed by the existing canal. The penstock splits before it enters the powerhouse. Themain penstock continues to the turbine/generator unit while the bypass pipeline continues

around the powerhouse to an energy dissipation valve. Flow discharges from the

hydroelectric facility to the canal downstream. A schematic diagram of the presenthydraulic system is shown in Figure 1.

Figure 1. System Schematic Diagram

Currently the total static head from the intake to the tailrace is 126 feet (ft) and the design

flow rate is 500 cubic foot per second (cfs). However, the project was designed and

constructed using the design criteria set for a possible future upgrade. Under a possiblefuture condition, the penstock will be extended upstream for approximately 4,600 ft,

increasing the total static head to 173 ft and the flow rate will remain at 500 cfs. For this

presentation, only the present condition is discussed. Figure 2 shows the end of thepenstock, the powerhouse and the bypass stilling basin under construction.

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Figure 2. Construction of Project

Excavated from the basalt rock in the existing canal, the forebay is approximately 200-ft

long by 60-ft wide and 24-ft deep. The diversion structure was designed with a normal

entrance of water to the penstock through a trash rack, and an auxiliary entrance throughan overflow weir.

The penstock system was designed to offer years of service. The 13,497-ft long, 108-inchdiameter, 3/8-inch thick steel penstock from the forebay to the powerhouse is

polyurethane-lined and coated. Each of the 40-ft long sections of steel pipe was

fabricated at the Portland Facility of Northwest Pipeline Company and welded together at

the project site. Six sets of air release/vacuum valves were installed along the penstock at

selected locations. Pipe access man-ways were typically installed at 2,000-ft intervals.There are three irrigation turnouts along the entire penstock. Before the penstock enters

the powerhouse, a bifurcation anchored to basalt rock splits the flow to: either a 108-inchdiameter section to the powerhouse or a 78-inch diameter section to the bypass structure.

In the powerhouse, the penstock is connected to an 84-inch diameter turbine shut-off

valve (TSV) immediately upstream of the turbine /generator unit. Flow through theturbine discharges to the tailrace after the hydraulic energy is extracted by the runner of

the turbine/generator unit. In the bypass structure, the 78-inch diameter bypass pipe is

connected to a 78-inch diameter bypass shut-off valve (BSV) before entering a 42-inchdiameter ring-jet-type-fixed-cone valve (FCV). FCV is used to dissipate energy in

conjunction with a stilling basin during bypass operations. The vertical Francis unit was

provided by The James Leffel & Co. The generator is a vertical brushless synchronoustype provided by Hyundai-Ideal. TSV, BSV and FCV were provided by Rodney Hunt.Normal flow controls are performed by the turbine wicket gates and FCV. TSV is used

for emergency shut-off and normal maintenance of the turbine/generator unit. BSV is for

the maintenance of FCV.

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FLOW CONTROL REQUIREMENTS

The two major requirements for the hydraulic system are: 1) the flow rate downstream of

the hydroelectric facility must remain constant whether or not the turbine/generator unit

is operational; and 2) transient pressures in the hydraulic system must be controlled to a

reasonable level. In order to meet these requirements, intelligent flow controls arerequired.

Flow Control for Discharge Conditions

When the turbine/generator unit is operational, flow at the powerhouse discharges

through the turbine to the tailrace. Alternatively, flow discharges to the bypass pipe lineand through FCV to the stilling basin when the turbine/generator unit trips off line or is

down for maintenance. During normal operations, flow through the system is controlled

by the turbine wicket gates and FCV. During abnormal conditions, TSV is used for flowcontrol. Because the flow characteristics of the turbine wicket gates, TSV and FCV are

not identical, maintaining a constant flow downstream of the powerhouse throughoperation of these gates and valves becomes a challenge. For example, closing the turbine

wicket gates and opening FCV at the same rate will not result in a steady-state flowdownstream of the powerhouse.

Flow Controls for Transient Conditions

The hydraulic system must be operated safely when switching flow between the power

generation portion and the bypass portion of the hydraulic system. When the flow issteady, pressures within the hydraulic system remain constant at every location of the

system. However, when the flow conditions in the hydraulic system are being changed orare unsteady, a hydraulic transient (or water hammer) condition is created. During the

transient period from one steady condition to another, transient pressures are induced.

Transient pressure at a location in the hydraulic system is the change in pressure thatfluctuates around the steady-state pressure. If the total pressure, equal to the sum of the

steady-state and transient pressure, becomes too large, the allowable pressure of the

hydraulic system may be exceeded, possibly causing the penstock or the associated

equipment to fail. On the other hand, if the total pressure becomes too low, a vacuumcondition may be induced in the hydraulic system and possibly cause failure, especially

for sections of the penstocks exposed above the ground surface.

There are many scenarios when transient conditions may occur. One example is when the

turbine/generator load is rejected due to electrical grid problems. In this scenario the

turbine wicket gates or TSV need to be closed relatively quickly to avoid a prolongedover-speed of the turbine/generator unit. However, the faster the turbine wicket gates

close, the more rapidly the flow rate will decrease, resulting in higher pressure fluctuation

in the hydraulic system. Therefore, specifying an appropriate closing time for the turbinewicket gates becomes critical to the safe design and operation of the turbine/generator

unit and the hydraulic system.

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Several methods of controlling transient conditions are often used in hydroelectric power

generation facilities such as: increasing the closing and opening times of control valves,increasing the pressure class of pipelines, limiting pipe wave velocities, and use of

pressure relief valves, surge tanks and air chambers, etc. (Tullis, 1989). For the Juniper

Ridge Hydroelectric Power Generation Project, FCV acts as both a bypass and pressure

relief valve. When the turbine wicket gates or TSV are being closed, FCV opens todischarge flow as well as release transient pressures.

THEORETICAL CONSIDERATIONS

Due to the importance of flow controls for discharge and transient conditions, it is critical

to understand the flow and transient characteristics in the hydraulic system for its design,construction and operation.

Flow Rates

Flow Rates Controlled by TSV and FCV:

TSV is located immediately upstream of the turbine/generator unit. The main purpose ofTSV is for normal maintenance and emergency shut-off of the flow. TSV is a butterfly

valve, which consists of a disc mounted on a shaft that rotates in a cylindrical body. The

disc is oriented parallel to the flow to minimize any restriction when open or is positionedat a right angle to the flow to provide full closure.

FCV is located at the end of the bypass pipe to dissipate energy in conjunction with thestilling basin during bypass operations. FCV consists of a valve body with a deflector

cone, a cylinder gate, and a hydraulic actuator. Moving the cylinder gate sleeve upstreamand downstream over the valve body opens and closes the valve. The fixed internal cone

spreads the conical discharge jet in such a way that the surface area of the jet and area

that entrains air increase rapidly. When closed, the movable cylinder seals against theouter edge of the fixed cone. Typically, the valve discharge is sprayed into the air to

dissipate energy. For this project, two additional features were added to the valve, which

include a hood to restrain the spray of water into the air and a power spring attached to

the movable cylinder gate to force FCV open in case the hydraulic actuator fails.

Flow rates through the butterfly valve and the fixed cone valve are calculated by the

following general equation:

(1)

where:

Q= flow rate in cubic feet per second (cfs)Cd= coefficient of discharge

A= internal area of valve in square feet (ft2)

g = acceleration due to gravity (32.2 ft/s2)

H= net head across valve (ft)

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For a selected valve the internal area of valve A is known. The coefficient of discharge,

Cd, at various disc positions in degrees (0 degree for complete closure and 90 degree for100 percent opening) for TSV or at various gate strokes (percent opening) for FCV are

provided by the manufacturer. The Cdparameter at various gate strokes (percent opening)

for FCV is shown as an example in Figure 3.

Equation (1) shows that the flow rate Q is only a function of the head H for a

selected valve. The flow rate during the opening and closing of a valve can be calculated

using the corresponding head across the valve at various opening positions. However, thehead across a valve is related to the flow rate in the valve. Therefore, the computation of

flow rate at various valve openings is not straightforward.

Figure 3. Coefficient of Discharge for FCV

Flow Rates Controlled by Turbine Wicket Gates:

The turbine wicket gates were designed to control the flow in conjunction with FCV. It is

desirable to know the flow rate at various percent openings of the wicket gates or the

wicket gate rating curve. The wicket gate rating curve at the rated turbine speed wasprovided by the turbine manufacturer. Flow rates can be obtained from the rating curve

when the head across the turbine and the percent opening of the wicket gates are known

for the rated turbine speed of 300 rpm. However, similar to the case for valves, it is not

straightforward to obtain the flow rate because the head across the turbine is a relatedvariable. Furthermore, the turbine will not always remain at the rated speed during the

opening or closing of the wicket gates. For example, during load rejection, if the wicketgates are not closed promptly, the turbine speed will increase until the runaway speed isreached before it decreases when the turbine wicket gates are gradually closed. Manual

computation of flow rates during wicket gates closure after load rejection is a

complicated task and numerical modeling is necessary.

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4.2 Hydraulic Transient Pressures

Hydraulic transients are disturbances that occur in a fluid during a change from one

steady state to another. Transients will occur in every hydroelectric plant because

changes must be made (e.g. starting-up from standstill and shutting-down). Transient

pressures in a hydraulic system fluctuate until another steady state condition is reached.There are three methods to calculate hydraulic transient pressures (ASME, 1996): 1) rigid

column theory for slow changes in flow; 2) elastic theory for rapid changes in flow; and

3) numerical modeling for intermediate changes in flow.

When changes in flow are slow, transient pressures may be evaluated using rigid column

theory and the concept of water starting time Twas defined below (ASME, 1996):

= (2)

where: Tw= water starting time is defined as the time required for the water in the waterconduit system to accelerate from zero to rated velocity at rated head (sec)

L= length of water column from upstream free water surface to downstream free

water surface (ft)

V= rated velocity (ft/sec)g = acceleration due to gravity (32.2 ft/sec

2)

H= rated head (ft)

When changes in flow are rapid, compressibility effects must be taken into consideration.

Flow changes at the turbine or valves are propagated through the water column by

pressure waves with a celerity or velocity of propagation in the penstock, which dependson the characteristics of the penstock, and can be estimated. If the closure of the turbine

wicket gates or valves takes place in less time than is required for the wave to propagate

to a free surface and back, the closure is considered rapid. Pressure rise is nowcontrolled by the conversion of the kinetic energy in the moving water to pressure

energy. For a uniform diameter conduit, the following relationship is used to calculate the

pressure change for a rapic closure (ASME, 1996):

= - (3)

where:

= pressure change (ft)c = celerity or velocity of propagation (ft)

= change in flow velocity (ft/sec)g = acceleration due to gravity (32.2 ft/sec

2)

The negative sign - indicates that when the flow velocity decreases, the pressure

rises while when the flow velocity increases, the pressure drops.

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Equation (3) shows that for a certain hydraulic system (c is known) the transient pressure

head is proportional to the change in flow velocity. A large flow velocity change will

induce large transient pressures. Both pressure increases and decreases may be inducedand are dependent on whether the flow rate increases or decreases.

Changes of flow in most hydroelectric projects are intermediate (ASME, 1996). Thesesituations are best analyzed using special purpose computer programs. The following

basic partial differential equations of momentum and continuity for unsteady,

compressible flow in elastic conduits are solved with applications of appropriateboundary conditions using various computer programs (USACE, 1998):

Momentum: + + = 0 (4)

Continuity: + = 0 (5)

where:

= total head or energy grade (ft)Q = discharge (ft

3/sec)

x = distance along conduit (ft)

t = time (sec)

g = acceleration due to gravity (32.2 ft/sec2)

A= cross sectional area of the conduit (ft2)

D= diameter of the conduit (ft)f = Darcy-Weisbach friction factor

c = celerity of a compression wave travelling through the conduit and is a

function of modulus of elasticity of pipe wall, thickness of pipe wall anddiameter of the conduit

There are basically two computational schemes in use to solve the above partialdifferential equations for pressure transient calculations:

1. Method of characteristics, and

2. Method of implicit finite differences.

The first method is described by Wylie and Streeter (1993) and Chaudry (1988) while the

second method was originally described by Perkins et al. (1964). Details of these two

methods are described in various references (e.g., Zipparro and Hansen, 1993; Streeter,1971 and USACE, 1998) and will not be repeated.

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NUMERICAL MODELING

Model Description

The U.S. Army Corps of Engineers (USACE) computer program Water Hammer and

Mass Oscillation (WHAMO) has been developed to assist engineers in understandingand mitigating hydraulic transient by simulating water hammer and mass oscillation in

networks that convey fluids. The program determines time varying flow and head in a

network that may include pipes, valves, pumps, turbines, junctions and other elements.The WHAMO program is formulated in terms of a four-point implicit finite difference

representation of the governing partial differential equations (4) and (5).

Modeling Cases

Transient pressures along the penstock were analyzed using WHAMO for five scenarios,each under the present and future conditions during the design of the project. The worst

case scenario occurs when TSV is used for emergency shut-off. For the worst case, it isassumed that the electrical load is rejected due to trip-off, the turbine wicket gates cannot

be closed and FCV also cannot be opened normally (because of possible hydraulicsystem failure, loss of hydraulic pressure, or the power spring actuated FCV is disabled).

The peak transient pressure from this scenario was the highest among the ten scenarios

and was used in the design of the penstock and associated components of the hydraulicsystem. However, for the purpose of this presentation, only the following two cases under

the present condition are discussed.

Case 1. Shut-off of the turbine/generator unit due to turbine load rejection with active

bypass system turbine load rejected, turbine wicket gates closing at a specifiedstarting time and rate, and FCV opening at a specified starting time and rate.

Case 2. Shut-off of the turbine/generator unit due to turbine load rejection with inactive

bypass system turbine load rejected, turbine wicket gates closing at a specifiedstarting time and rate, and FCV not opening.

WHAMO Model Setup

Major Input Data:

The WHAMO program is relatively well-documented and easy to implement. Input datato the program include: node number, element of hydraulic system, geometric

information of penstock sections, friction loss coefficients, minor loss coefficients, valve

specifications and characteristics, turbine/generator specifications and characteristics,turbine operation status, and turbine and valve control schedule.

For this model, node Y is at the bifurcation just upstream of the powerhouse, node T isthe turbine wicket gates, and node F is FCV.

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Figure 4. Typical Discharge Rates through the Turbine, FCV and the Sum

(Scenario 1 0 sec Time Delay)

Figure 5. Typical Total Pressures at the Turbine, FCV and the Bifurcation


Because the total discharge rate exceeded the design rate of 500 cfs during the switching

of flow from the turbine to FCV, different controls were required to maintain the

discharge rate of 500 cfs. Therefore, a scenario 2 was simulated where FCV started toopen 40 seconds after the turbine wicket gates started to close. The resulting three flow

rate variations are shown in Figure 6. It shows that during the switching period the total

discharge rate remained less than 500 cfs and more uniform than in scenario 1.

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Figure 6. Typical Discharge Rates through the Turbine, FCV and the Sum


Correspondingly, the transient pressures at the turbine wicket gates (T) and FCV (F) rose

initially in response to the decrease of the total flow rate in the penstock, fluctuated and

then returned to the static pressure at the turbine wicket gates (T) and the steady-statelevels at FCV (F), respectively. The pressures immediately upstream of the turbine

wicket gates (T), FCV (F) and the bifurcation (Y) are shown in Figure 7. These transient

pressures were also small as expected because the designated turbine wicket gate closing

time (240 sec) is relatively long and FCV acted as a pressure relief valve.

Figure 7. Typical Total Pressures at the Turbine, FCV and the Bifurcation(Scenario 2 0 sec Time Delay)

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Case 2 Wicket Gates Being Closed and FCV Not Being Opened

In this case, the turbine/generator unit is being shut-off linearly in 240 seconds after load

rejection and FCV remains closed abnormally. The flow rate decreases through the

turbine (T), the zero flow rate through FCV (F) and the total flow rate are shown in

Figure 8. The flow rate vs. time curve shows that during the linear closing process of theturbine wicket gates the flow rate reduction through the turbine was not linear. Initially

the flow rate decreased slowly before eventually accelerating. This phenomenon is due to

the head loss across the wicket gates. As the wicket gates begin to close, the head lossacross the wicket gates is small compared to the head loss in the entire hydraulic system.

As the wicket gates continue to close and the head loss across the wicket gates increases

to a significant percentage of the total loss in the hydraulic system, the wicket gates canbegin to control the flow. The transient pressures at T, F and Y were significantly higher

than their respective steady-state levels as expected because FCV did not act as a pressure

relief valve in this case (Figure 9). After the turbine wicket gates were completely closed,the transient pressures fluctuated and returned to the static levels, which were higher than

the initial steady-state pressures.

Figure 8. Typical Discharge Rates through the Turbine, FCV and the Sum(Case 2 FCV Not Open)

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Figure 9. Typical Total Pressures at the Turbine, FCV and the Bifurcation(Case 2 FCV Not Open)

Hydraulic Grade Line along Penstock:

The variations of flow rates and transient pressures with time at many selected locations

along the penstock were computed and obtained as described. At each location, themaximum and minimum transient pressures were read from the model outputs. Hydraulic

grade lines (HGL) were calculated at those locations along the penstock. The steady-state

HGL, the maximum HGL caused by the positive transient pressures and the minimumHGL caused by the negative transient pressures for Case 2 were plotted in conjunction

with the penstock centerline elevation in Figure 10. The maximum and minimumpressures along the penstock were used for the hydraulic system design to make sure themaximum pressures were less than the allowable pressure of the penstock and its

associated valves, and the minimum pressures were positive, resulting in a non-vacuum

condition along the penstock.

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Figure 10. Maximum and Minimum Piezometic Head along Penstock

(Case 2 FCV Not Open)

DISCUSSION AND CONCLUSIONS

WHAMO software provided a valuable tool for the understanding of the flow and

transient conditions in the hydraulic system. Discharge rates during the switching

between the hydroelectric and bypass portions of the system may be controlled bydelaying opening or closing of various valves. The 40-second opening delay for FCV

eliminated the 80 cfs flow surcharge and resulted in a more uniform downstream flow, as

a surcharge may have been significant enough to overtop the canal banks. For the JuniperRidge Hydroelectric Project, the surcharge was taken into consideration when the control

scheme of the unit was designed and implemented. The implemented control scheme fornormal operation resulted in discharge downstream of the facility similar to that in the40-second time delay case.

Significant transient pressures could be induced in the hydraulic system if not controlled

properly. The numerical modeling showed that the transient pressure upstream of theturbine wicket gates was largest when FCV could not be opened. Therefore, in addition to

the normal design in a typical bypass system, a power spring was added to FCV to force

it open when the other actuation systems malfunction. Negative transient pressures werealso observed in the hydraulic system. However, they were small compared to the steady-

state pressures such that vacuum conditions did not happen along the penstock.

Based on the analyses, the following conclusions are made:

1. An appropriate control scheme is required to avoid overflow and drain of theforebay and overtopping of the canal bank downstream of the hydroelectric

facility.

2. Flow rates downstream of the powerhouse can be controlled by adjusting the rate

and starting time of valve movements.

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3. Maximum positive transient pressures occur at the end of the penstock near the

turbine wicket gates and the control valves, and become less as they moveupstream to a free surface. Significant transient pressures may occur in the

hydraulic system and can be mitigated by controlling the movement of valves and

installation of pressure relief valves.

4.

Negative transient pressures along penstocks should be evaluated to prevent avacuum condition from happening, especially for long, thin and exposed pipes.

5. Special purpose software such as WHAMO is a valuable tool for the evaluation

and design of hydraulic system.

REFERENCES

ASME Hydro Power Technical Committee, The Guide to Hydropower Mechanical

Design. HCI Publications, Inc., 1996.

Chaudry, H.M., Applied Hydraulic Transients, VNR, New York, New York, 1988.

Perkiins, F.E., A.C. Tedrow, P.S. Eagleson, and A.T. Ippen, Hydro-Power Plant

Transients, Part II: Response to Load Rejection, Report No. 71, MIT Hydrodynamics

Laboratory, September 1964.

Tullis, J. Paul, Hydraulics of Pipelines, Pumps, Valves, Cavitations, Transients. John

Wiley & Sons Inc., 1989.

USACE, Water Hammer and Mass Oscillation (WHAMO) 3.0 Users Manual, U.S.Army Corp of Engineers Construction Engineering Research Laboratories ADP Report

98/129, September 1998.

Wylie, E.B., and V.L. Streeter, Fluid Transients, Prentice Hall, Englewood Cliffs, NewJersey, 1993.

Zipparro, Vincent J., and Hans Hasen, Editors, Davis Handbook of Applied Hydraulics,Fourth Edition, McGraw-Hill, Inc., New York, New York. 1993.

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