waterhammer potential in pumps and systems

8/16/2019 Waterhammer Potential in Pumps and Systems

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Waterhammer Potential in Pumps and

Systems

by Dr. C. Samuel Martin,Waterhammer Consultant and Professor Emeritus, Georgia Tech, Atlanta,

GA

By definition waterhammer is a pressure (acoustic) wave phenomenon created by relatively sudden changes in the

liquid velocity. Although the name waterhammer may appear to be a misnomer in that it implies only water and the

connotation of a ‘hammering’ noise, it has become a generic term for pressure wave effects in liquids. Strictly

speaking, waterhammer can be directly related to the compressibility of the liquid. For relatively slow changes in

flow for which pressure waves have little to no effect the unsteady flow phenomenon is called surging.In pipelines, sudden changes in the flow (velocity) can occur as a result of 1) pump and valve operation in pipelines,

2) vapor pocket collapse, or 3) even the impact of water following the rapid expulsion of air out of a vent or a

partially open valve.Potentially, waterhammer can create serious consequences for pipeline designers if not properly recognized and

addressed by analysis and design modifications. There have been numerous pipeline failures of varying degrees andresulting repercussions of loss of property and life. Three principal tactics for mitigation of waterhammer are 1)alteration of pipeline properties such as lowering of pipe profile to increase local pressure or increasing pipe

diameter to reduce velocity, 2) implementation of improved valve and pump control procedures, and 3) design and

installation of surge control devices.

Waterhammer Basics For wave propagation in liquid-filled pipes the acoustic (sonic) velocity is modified by the pipe wall elasticity byvarying degrees, depending upon the elastic properties of the wall material and the relative wall thickness. The

expression for the wave speed a is

(equation 1)

where ρ is the liquid mass density of the liquid, K is the bulk modulus of the liquid, E is the elastic modulus of the

pipe wall, D is the inside diameter of the pipe, and e is the wall thickness. The pressure change associated with the

rapid velocity change across a waterhammer (pressure) wave is the well-known Joukowsky equation

(equation 2 )

Waterhammer Potential in Systems with Pumps The potential for waterhammer in pipeline systems can be directly related to changes in the rate of flow relative tothe system response characteristics. Clearly, rapidly operating control valves or sudden reversal of flow through

pumps with check valves can lead to waterhammer. Valves can either be a source of waterhammer or even a meansof mitigating it. Obviously, transients occur with every pump start-up, normal shutdown, or sudden loss of power to

the driver—often an electrical motor. For pump start-up the system experiences mostly pressure rise, while for

shutdown and power loss there is depressurization. The latter phenomenon in itself may not be consequential unlesslocal pressures fall to vapor pressure, leading to the growth of a vapor cavity, which will normally collapse.


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Experience shows that waterhammer is usually not a problem with pump start-up if the pipeline has no voids

(neither gas nor vapor), but is filled with liquid. Likewise, pump power failure will typically not be a problem if the

minimum pressure in the system due to this depressurization does not fall to vapor pressure.

Pump Start-up In many installations pumps are periodically shut down and restarted, generating pressure excursions of various

degrees. The normal start-up of centrifugal pumps against a closed pump discharge control valve or seated check

valve does not typically yield consequential waterhammer pressures provided the pipeline system is free of voids.The torque and power requirements for higher specific speed mixed flow pumps and axial flow pumps is an issue for

pump start-up against a closed valve, but waterhammer is normally not a concern for full pipe systems.

On the other hand, pipes containing voids can lead to waterhammer subsequent to pump start, depending upon the

rate of filling. The most serious waterhammer potential exists for systems with vapor or steam pockets that will be

collapsed suddenly as the void is extinguished. It is possible that the flow rate at the moment of void collapse canexceed the design flow if the pump runs out on its curve. Entrapped gases such as air can result in significant

pressure rise during pump start because of the so-called spring effect of the gas. The peak pressure, which is not

necessarily waterhammer, can attain values several times the driving pressure, depending upon the rate of pressurization.

Pump Shutdown Normal shutdown of pumps is often accomplished by initial closure of pump discharge valve, followed by stopping

of the pump driver. If the control valve time of closure is properly chosen to a) preclude vapor formation from too

rapid closure, or b) to prevent high reverse flow from too slow closure, waterhammer can be avoided.For relatively short systems with large static lift, check valve slamming is a possibility if the liquid column has a

quicker response than the valve. Swing check valves or other designs are frequently employed in pump discharge

lines, often in conjunction with slow acting control valves. A check valve should open easily, have a low head lossfor normal positive flow, and create no undesirable transients by its own action. For short systems, a slow

responding check valve can lead to waterhammer because of the high reverse flow generated before closure. A

spring or counterweight loaded valve with a dashpot can 1) give the initial fast response followed by 2) slow closureto alleviate the unwanted transient. The proper selection of the load and the degree of damping is important,

however, for proper performance. Check valve slam is also a possibility from stoppage or failure of one pump of

several in a parallel system, or resulting from the action of an air chamber close to a pump undergoing power failure.

Check valve slam can be reduced by the proper selection of a dashpot. Mitigation of waterhammer is possible by a)special check valve designs that allow for faster response, b) counterweights or springs to accelerate the initial valve

motion, and c) dashpots to cushion the final valve motion to reduce mechanical shock and valve slamming, which

can lead to waterhammer.Pump Power Failure The loss of the driving torque, yielding in an unbalanced torque and resulting in a drop in rotational pump speed,

consequentially produces flow reduction and pressure decrease. The potential of waterhammer in pumping systems

is most often related to pump power failure because of the possibility of vapor pocket formation and subsequentcollapse. This scenario should be investigated for systems since the consequences can be serious. In many

installations remedies for waterhammer mitigation have to be evaluated. Possible solutions are 1) increase in

rotating moment of inertia (flywheel), 2) installation of surge protection devices, and 3) alterations in valve

operating procedure or valve motion.

Pump and System VariablesThe importance of pump and system variables can be defined by simple investigation of a) the unbalanced angular

momentum equation for the pump and its driver, and b) the momentum relationship for the liquid column in the pipeunder deceleration subsequent to loss of driver torque. In general, the equation for angular momentum can be

expressed by

(equation3)

where TM is the driver (motor) torque, T is the resisting fluid torque, WR 2 is the total moment of inertia of all

rotating parts (motor, pump and entrained liquid, shaft, and possibly flywheel), g is gravitational acceleration, w and


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N are the rotational speed in rad/sec and rpm, respectively, and t is time. For loss of power to an electric motor TM =

0 in Eq. (3), yielding the rate of pump deceleration in terms of the unbalanced fluid torque T

(equation4)The significance of the moment of inertia WR 2 is apparent from Eq. (4). Moreover, the rate of rotor decelerationdN/dt is also influenced by the torque delivered by the pump at the corresponding speed N and flow Q. For

simplicity the coupling of the fluid system can be represented by linear momentum for a liquid column of length L.

For an uniform pipe of diameter D, cross-sectional area A, and instantaneous flow Q

(equation5)

where H is the level of the hydraulic grade line (HGL), x is the distance along the pipe, and f is the Darcy-Weisbach

resistance coefficient. Equation (5) is valid for both compressible flow (waterhammer) and incompressible (rigid

column). To demonstrate the effect of liquid column deceleration, we consider a short pipe of uniform diameter andinsignificant friction for which the effect of waterhammer is minimal, reducing Eq. (5) to

(equation6 )

where ³H is the static head on the system. For analysis of pump power failure problems Eq. (4) is required to assess

the change in pump speed, while the change in flow can only be determined from Eq. (5) alone for relatively short

pipe systems for which elastic effects are not important. Most analyses require consideration of the liquid and pipe

elasticity by the method of characteristics (MOC).

Abnormal Pump (Four Quadrant) Characteristics

The performance characteristics discussed up to this point correspond to pumps operatingnormally. During a transient, however, the machine may experience either a reversal in flow,

or rotational speed, or both, depending upon the situation. It is also possible that the torque and

head may reverse in sign during passage of the machine through abnormal zones of

performance. The need for characteristics of a pump in abnormal zones of operation can best be described with

reference to Figure 1, which is a simulated pump power-failure transient.

figure1.gif figure1.gif

Fig 1 -


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Figure 1A centrifugal pump is delivering liquid at a constant rate when there is a sudden loss of power from the prime

mover—in this case an electric motor. For the postulated case of no discharge valves, or other means of controlling

the flow, the loss of driving torque leads to an immediate deceleration of the shaft speed, and in turn the flow. Thefour curves are head (H), flow (Q), speed (N), and torque (T), expressed in percentage of the rated values. With noadditional means of controlling the flow, the higher head at the final delivery point will eventually cause the flow to

reverse (Q < 0) while the inertia WR 2 of the rotating parts maintains positive rotation (N > 0). Up until the time of

flow reversal the pump has been operating in the normal zone, albeit at reduced flow. In order to predict system

performance in regions of negative rotation and/or negative flow the analyst requires characteristics in these regionsfor the machine in question. Indeed, any peculiar characteristic of the pump in these regions could be expected to

have an influence on the hydraulic transients. It is important to stress that the results of such analyses are criticallygoverned by the following three factors: 1) availability of complete pump characteristics in zones the pump will

operate, 2) complete reliance upon dynamic similitude (homologous) laws during transients, and 3) assumption that

steady-flow derived pump characteristics are valid for transient analysis.

Eight possible zones of operation, four normal and four abnormal, will be

discussed here with reference to Figure 2, developed by Martin (Ref. 1).

In Figure 2 the head H is shown as the difference in the two reservoir

elevations to simplify the illustration. The effect of pipe friction may beignored for this discussion by assuming that the pipe is short and of relatively large diameter. The regions referred to

on Figure 2 are termed Zones and Quadrants, the latter definition originating from plots of lines of constant head andconstant torque on a flow-speed plane (Q - N axes), as shown in Figure 3. Quadrants I (Q > 0, N > 0) and III (Q < 0,

N < 0) are defined in general as regions of pump or turbine operation, respectively. It will be seen, however, that

abnormal operation (neither pump nor turbine mode) may occur in either of these two quadrants. A very detaileddescription of each of the eight zones of operation is in order. It should be noted that all of the conditions shown

schematically in Figure 2 can be contrived in a laboratory test loop using an additional pump (or two) as the master

Figure_2 Figure_3

Fig 2 & 3 - Click image for full-size

image


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and the test pump as a slave. Most, if not all, of the zones shown can also be experienced by a pump during a

transient under the appropriate set of circumstances.

Quadrant I . Zone A (normal pumping) in Figures 2 and 3 depicts a pump under normal operation for which all four

quantities—Q, N, H, and T are regarded as positive. In this case Q > 0, indicating useful application of energy. Zone

B (energy dissipation) is a condition of positive flow, positive rotation, and positive torque, but negative head— quite an abnormal condition. A machine could operate in Zone B by 1) being overpowered by another pump or by a

reservoir during steady operation, or 2) by a sudden drop in head during a transient caused by power failure. It is

possible, but not desirable, for a pump to generate power with both the flow and rotation in the normal positivedirection for a pump, Zone C (reverse turbine), caused by a negative head, and resulting in a positive efficiency

because of the negative torque. The maximum efficiency would be quite low due to the bad entrance flow condition

and unusual exit velocity triangle.

Quadrant IV . Zone H, labeled energy dissipation, is often encountered shortly after a tripout or power failure of a

pump, as illustrated in Figure 1. In this instance the combined inertia of all the rotating elements—motor, pump and

its entrained liquid, and shaft—has maintained pump rotation positive but at a reduced value at the time of flow

reversal caused by the positive head on the machine. This purely dissipative mode results in a negative or zero

efficiency. It is important to note that both the head and fluid torque are positive in Zone H, the only zone inQuadrant IV.

Quadrant III . A machine that passes through Zone H during a pump power failure will then enter Zone G (normal

turbining) provided that reverse shaft rotation is not precluded by a mechanical ratchet. Although a runawaymachine rotating freely is not generating power, Zone G is the precise mode of operation for a hydraulic turbine.

Note that the head and torque are positive, as for a pump but that the flow and speed are negative, opposite to thatfor a pump under normal operation (Zone A). Subsequent to the tripout or load rejection of a hydraulic turbine or the

continual operation of a machine that failed earlier as a pump, Zone F (energy dissipation) can be encountered. Thedifference between Zones F and G is that the torque has changed sign for Zone F, resulting in a braking effect,

which tends to slow the free wheeling machine down. In fact the real runaway condition is attained at the boundary

of the two zones, for which torque T = 0.

Quadrant II . The two remaining Zones—D and E—are very unusual and infrequently encountered in operation, with

the exception of pump turbines entering Zone E during transient operation. Again it should be emphasized that bothzones can be experienced by a pump in a test loop, or in practice in the event a machine is inadvertently rotated in

the wrong direction by improper wiring of an electric motor. Zone D is a purely dissipative mode that normally

would not occur in practice unless a pump, which was designed to increase the flow from a higher to lowerreservoir, was rotated in reverse, but did not have the capacity to reverse the flow (Zone E of Quadrant III — mixed

or axial flow), resulting in Q > 0, N < 0, T < 0, for H < 0. Zone E, for which the pump efficiency > 0, could occur in

practice under steady flow if the preferred rotation as a pump was reversed. There is always the question regardingthe eventual direction of the flow. A radial-flow machine will produce positive flow at a much reduced capacity andefficiency for N < 0 (Zone E of Quadrant II—reverse pumping) compared to N > 0 (Zone A of Quadrant I—normal

pumping), yielding of course H > 0. On the other hand, mixed and axial-flow machines create flow in the opposite

direction (Zone E of Quadrant III), and H < 0, which corresponds still to an increase in head across the machine in

the direction of flow.The transient scenario illustrated in Figure 1 can be related to Eqs. (4) and (5) by the slopes dN/dt and dQ/dt,

respectively. The slope of the pump speed curve, whether from analysis or measurement, can reveal the sign of the

pump torque—either positive or negative. For this example the pump torque remains positive (dN/dt < 0) until themachine enters Quadrant III at the runaway point—boundary between Zones G (turbining) and F (braking).

Pump Start-up with Gas or Vapor Void in Pipe Figure 4 is included to illustrate the difference between pressurization of a)

liquid alone, b) a gas void, and c) a vapor void in subcooled liquid. For the

idealized case of instantaneous opening of the valve at the reservoir tosimulate pump start-up, and assumption of no fluid friction in the pipe system,

the case of solid liquid results in a doubling of the imposed pressure difference HU - HD, due to the reflection off

the closed end. Figure 5 shows the results for a) solid liquid, b) entrapped air, and c) the most severe case of vaporvoid collapse, assuming rapid condensation in the fashion of liquid column separation analysis. Although the

analysis may not be valid when taken to the limit of no void, small amounts of entrapped air can potentially yield

results worse than the case of no gas. Obviously, the existence of even a small vapor bubble is clearly the worstsituation.

Figure_4 Figure_5

Fig 4 & 5 - Click image for full-

size image


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Mitigation of Waterhammer with Surge Protection and Valve Operation For many pump and pipe systems the loss of driving power to the pump or pumps can lead to vapor void formation

and subsequent waterhammer due to void collapse. Although occasionally optimal operation of a pump discharge

valve can prevent vapor formation, more commonly the problem can occur simply due to the pump deceleration andthe sensitivity to the inertia WR 2. If the potential vapor void problem (liquid column separation) can not be

alleviated by valve operation or by an increase in inertia, then surge protection should be considered. The type of

surge protection device most appropriate for the pump and system depends on a number of factors: liquid inquestion, restraints on admission of air, subsequent removal of air, allowance of negative pressure in general,

operational considerations, maintenance, and economics, to name a few. Experiences with three types of surge

protection devices will be presented to illustrate their effectiveness for the particular pump and system. Moreover,

the efficacy of analysis will be demonstrated by comparison of transient calculations with field measurements.

Air-Vacuum Breaker The introduction of air into a pipe subsequent to pump power failure is one of many possible

solutions to combat the possibility of liquid-column separation and collapse and the potentialdire consequences. There are questions regarding the modeling of the vacuum breaker or

other air admittance device as well as the handling of the air mass during the subsequent transient. Figure 6 depicts a

supply system delivering water to safety related cooling elements of a nuclear plant. Analysis indicated that liquid

column separation and serious waterhammer pressures would occur for pump power failure of two or more of the

five pumps. Following an evaluation of various protective measures — air chamber, flywheel, one way surge tank

— the efficacy of the more economical vacuum breaker scheme was assessed. In order to be comfortable with thecalculations based upon standard MOC calculations, site measurements of transient pressures were made.

Figure 7 is a graph showing plots of the 1) recorded and 2) calculated pressures at pump

discharge for a 200 mm check-valve type vacuum breaker shown in Figure 6, along withanalytical traces for 3) no surge protection (column separation), and 4) a 2000 ft3 air

chamber. In summary, the vacuum breaker was deemed a practical engineering solution even

though the peak pressure was still approximately 50% of that with column separation. Because of economics, the airchamber was not chosen notwithstanding its effectiveness in a significant further reduction of peak pressures.

Initially, there was reluctance regarding air admittance via air vacuum valves because of concern regarding

problems with entrapped air during subsequent restarting of the pumps.

Air Chamber (Hydropneumatic Surge Tank) If properly designed and maintained, an air chamber can alleviate both negative and positive pressure problems in

pumping systems. They are normally located within or near the pumping station where they would have the greatest

effect. An air chamber solution may be quite effective in solving the transient problem, but quite expensive. Airchambers have the advantage that the tank—sometimes multiple—can be mounted either vertically or horizontally.

The principal criteria are available water volume and air volume for the task at hand. For design, consideration must

be given to compressed air supply, water level sensing, sight glass, drains, pressure regulators, and possible freezing.

Frequently, a check valve is installed between the pump and the air chamber. Since the line length between the pump and air chamber is usually quite short, check valve slamming may occur, necessitating the consideration of a

dashpot on the check valve to cushion closure. The assurance of the maintenance of air in the tank is essential—

usually 50% of tank volume, otherwise the air chamber can be quite ineffective.

Figure 8 shows the profile of a raw water pumping station and 2.5-mile long delivery pipe

consisting of 78-inch, 48-inch, and 72-inch diameter pipes to a reservoir at the watertreatment plant. Without the presence of any protective devices such as air chambers,

vacuum breakers, or surge suppressors, water hammer with serious consequences can be

shown to occur due to depressurization following sudden electrical outage of the plant. In this case of no protection

a large vapor cavity will occur at the first high point above the pumping station. This phenomenon, called water-column separation, can be mitigated by maintaining the pressures above vapor pressure. Air chambers may be

installed for this purpose, but they will often be quite large and expensive to accomplish the task. Provided the air

that is drawn in by the opening of air vacuum valves can be completely and slowly purged out of air-release valves,vacuum breakers can potentially solve the problem, however, at a much reduced cost.

Provided the air in the tank is maintained near the mid level by float control and a dedicated compressor, the air

chamber can adequately protect the pipe and pump from undesirable waterhammer. On one occasion when the air

chamber became nearly water solid due to improper float and compressor maintenance, pump power failure resultedin pipe rupture, ostensibly because of liquid column separation. Since the same situation could occur during

isolation of the air chamber for painting or other maintenance, consideration was given to alternate or standby surge

Fig 6 - Click imagefor full-size image

Fig 7 - Click image

for full-size image

Fig 8 - Click image

for full-size image


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protection. It was shown by analyses that vacuum breakers alone at the two main high points along the piping can

protect the force mains from the low pressure problem, but due to the return of the water column from the reservoir,

the pressure rise is quite severe. This necessitates the installation of a surge suppressor at the pump station, which in

conjunction with the vacuum breakers, can protect the line from column-separation type water hammer.

The results of PNET analysis are shown on Figure 8 in terms of minimum HGL envelope,indicating that the air chamber under proper operation protects the pipeline from negative

pressure. Figure 9 compares the measured values of pump manifold pressure with predicted

ones from computer code PNET for a three pump trip.

One-Way Surge Tank The purpose of a one-way surge tank is to prevent initial low pressures and potential water-column separation by

admitting water into the pipeline subsequent to a downsurge. The tank is normally isolated from the pipeline by one

or more lateral pipes in which there is one or more check valves to allow flow into the pipe if the HGL is lower inthe pipe than the elevation of the water in the open tank. Under normal operating conditions the higher pressure in

the pipeline keeps the check valve closed. The major advantage of a one-way surge tank over a simple surge tank is

that it does not have to be at the HGL elevation as required by the latter. It has the disadvantage, however, on onlycombating initial downsurges, and not initial upsurges.

Considerations for design are: 1) location of high points or knees of the piping, 2) check valve and lateral piping

redundancy, 3) float control re-filling valves and water supply, and other appurtenances. Maintenance is critical inorder to insure the operation of the check valve(s) and tank when needed.

A large pumping station has been installed and commissioned to deliver water over a distance of over 20 milesthrough a 72-inch diameter steel pipe, (Ref. 2). Three three-stage centrifugal pumps, which run at a synchronous

speed of 720 rpm, have individual rated quantities of 18,000 gpm, heads of 530 feet, and power of 2500 hp. Initial

surge analysis indicated potential water-column separation. The surge protection system was then designed withone-way surge tanks as well as air-vacuum valves strategically located. Following design of the piping system with

respect to surge protection and installation of the pumping station and piping system, the surge protection was

checked by computer code PNET using MOC. An extensive test program was initiated in order to ascertain the

steady-state flows, pump and valve characteristics, and the level of surge protection. In particular, it was desired toinvestigate the efficiency of four one-way surge tanks and two on-line surge tanks. The test data were also useful in

order to know if the transient analysis could predict with a reasonable accuracy the performance of the future

projected pump station configuration of four and then, possibly, five pump operation.Figure 10 shows the variation of transient pump speed, pump flow, pump

manifold pressure, and pipeline pressure under an air vacuum valve which did

not operate for the indicated pump discharge cone valve closure curve. The

speed and flow curves show that the pump traversed through four zones (A, H,G, and F) and three quadrants (I, IV, and III) of pump operation.Finally, Figure 11 illustrates the effectiveness of the one-way and simple surge tanks in prevention of negative

pressures along the pipeline.

Preliminary Assessment of Potential Waterhammer The assessment of the potential of waterhammer prior to embarking on any detailed computer analysis can be

conducted by realization of the role of pump and system and operating conditions, as discussed previously. The

salient basic items are:

• Pump start-upWhat is the operational procedure for pump start-up?

What type of pump discharge valve is present?

What is the valve stroke time?

Is the pipe liquid solid or is there gas or vapor present?• Pump shutdown

What is the operational procedure for pump shutdown?

What type of pump discharge valve is present?What is the valve stroke time?

• Pump power failure

What is the operational procedure for pump power failure?

What type of pump discharge valve is present?

What is the valve stroke time?Does the pipeline have high points where liquid column separation could occur?

Fig 9 - Click image

for full-size image

Figure_10 Figure_11

Fig 10 & 11 - Click image for full-

size image


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Practicality of Computer Codes and Interpretation of Output There are numerous computer codes in industry, university, research labs, and from consultants. Most waterhammer

codes are based on MOC, which has been well developed and indeed tested against field and laboratory

measurements with adequate success, especially for those systems that are all liquid. The presence of gas, vapor, orsteam can significantly complicate the analysis, and for the case of condensation-induced waterhammer

computational results have considerable uncertainty.

Even for waterhammer analysis of routine systems with standard computer codes, prior understanding ofwaterhammer and experience with conducting analysis is essential. The proper input of data and final interpretation

of computer output must be stressed.

Benchmarking of computer codes by the Electric Power Research Institute (EPRI), as reported in Ref. 3, for

waterhammer problems in the nuclear industry has demonstrated the variability of computer results for well-posed

problems. Indeed, for liquid column separation for which experimental results were available, the output fromseveral commercial waterhammer codes was not encouraging with respect to comparison of codes. The EPRI

benchmarking emphasizes the role of experience and knowledge of the phenomenon of waterhammer in assessing

potential waterhammer.

References 1.Martin, C. S., “Representation of Pump Characteristics for Transient Analysis”, ASME Symposium on

Performance Characteristics of Hydraulic Turbines and Pumps, Winter Annual Meeting, Boston, November 13-18,

1983, pp. 1-13.

2.Martin, C. S. and Cobb, L., “Experience with Surge Protection Devices”, BHr Group International Conference on Pipelines , Manchester, England, March 24-26, 1992, pp. 171-178.

3.“Water Hammer Prevention, Mitigation, and Accommodation”, EPRI NP-6766, Final Report, Research Project

2856-3, July 1992, Volumes 1-6. Dr. C. Samuel Martin is a retired Professor in the School of Civil and Environmental Engineering at the Georgia

Institute of Technology. He has been an active researches in the field of fluid transients, two-phase flow, cavitation

and hydraulic machinery. Professor Martin has developed hydraulic transient analysis techniques for pump turbinesand has been published extensively. Professor Martin has been a consultant to numerous industries in the general

subject of hydraulics, but in particular in the specialty field of waterhammer and abnormal characteristics of pumps

and turbines. Dr. Martin received his Ph.D. in Civil Engineering from the Georgia Institute of Technology.


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Pump Zones of Operations

Figure 2


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Figure 3


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Gas Vapor Void in Pump

Figure 4

Figure 5


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Figure 6

Figure 7


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Pumping Station Hydraulic Profile

Figure 8


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Pressure Prediction Comparisons

Figure 9


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Figure 10


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Figure 11

waterhammer potential in pumps and systems

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