ABSTRACTDesign, operation and refurbishment of hydraulic turbines, pumps or pump-turbine are strongly related to cavitation flow phenomena, which may occur in either the rotating runner-impeller or the stationary parts of the machine. This project presents the cavitation phenomena featured by hydraulic machinery in both pump and turbine mode, the influence of cavitation development on machine efficiency and operation are discussed.

ACKNOWLEDGMENTS

I would like to acknowledge my supervisor who gave me the necessary guidelines in writing this project.

NOMENCLATURE

A [m2] Area of the Flow Cross Section

NPSE [Jkg-1] = Net Positive Suction Energy

P [W] =Mechanical Power of the Machine

Q [m3s-1] =Discharge

g= [ms-2] =Acceleration Due to Gravity

n= [s-1] =Speed of Revolution

ps [Pa] =Absolute Static Pressure

pa [Pa] =Atmospheric Pressure

pv [Pa] =Vapor Pressure

χE = [-] Local Cavitation Factor

κ= [-] Cavitation Number

ρ [kgm-3] =Water Density.

σ [-] Thomas Number

CHAPTER 1

1.1 INTRODUCTION.

Design, operation and refurbishment of machineries are strongly related to cavitation flow phenomena, this may occur in either the rotating runner-impeller or the stationary

parts of a machinery. The economic trend to increase the specific power of the machine combined with the modern operating conditions to operate the machine over an extended range of discharge and specific energy challenges the scientific community to develop advanced knowledge of cavitation physics for this type of machineries. Cavitation occurs whenever the pressure in the flow of water drops to the value of the pressure of the saturated water vapour, pv (at the prevailing temperature); cavities filled by vapour, and partly by gases excluded from the water as a result of the low pressure, are formed. When these ‘bubbles’ are carried by the flow into regions of higher pressure, the vapour quickly condenses and the bubbles implode, the cavities being filled suddenly by the surrounding water. Not only is this process noisy, with disruption in the flow pattern, but – more importantly, if the cavity implodes against a surface, the violent impact of the water particles acting in quick succession at very high pressures, if sustained over a period of time, causes substantial damage to the (concrete or steel) surface, this can lead to a complete failure of the structure. Thus cavitation corrosion (pitting) and the often accompanying vibration is a phenomenon that has to be taken into account in the design of hydraulic structures, and prevented whenever possible (Knapp, Daily and Hammit, 1970; Galperin etal., 1977; Arndt, 1981).In this project i reviewed the broad definition of cavitation as it relates to hydraulic machineries most especially on centripetal pumps and turbinesCavitation in turbines cannot be explain generally but by the various types of turbines since each of them exhibit varying signs of cavitation and as such has varying ways of remedying it

1.2 CLASSES OF CAVITATION.

Cavitation is usually divided into two classes of behaviour: Inertial (Transient) cavitation is the process where a void or bubble in a liquid rapidly collapses, producing a shock wave. Such cavitation often occurs in pumps, propellers, impellers, and in the vascular tissues of plants. Non-inertial cavitation is the process in which a bubble in a fluid is forced to oscillate in size or shape due to some form of energy input, such as an acoustic field. Such cavitation is often employed in ultrasonic cleaning baths and can also be observed in pumps, propellers, etc.Since the shock waves formed by cavitation are strong enough to significantly damage moving parts, cavitation is usually an undesirable phenomenon. It is specifically avoided in the design of machines such as turbines or propellers.

1.3 TYPICAL SITUATIONS FAVORABLE TO CAVITATION

Typical situations in which cavitation can appear and develop within a flow can be described as follow;Wall geometry may give rise to sharp local velocity increases and resulting pressure drops within a globally steady flow. This happens in the case of a restriction in the cross-sectional area of liquid ducts (Venturi nozzles), or due to Curvature imposed on flow streamlines by the Local geometry (bends in pipe flow, upper sides of blades in propellers and pumps).Cavitation can also occur in shear flows due to large turbulent pressure fluctuations (see jets, wakes, etc.).The basic unsteady nature of some flows (e.g. water hammer in hydraulic control circuits, or ducts of hydraulic power plants, or in the fuel feed lines of Diesel engines) can result in strong fluid acceleration and consequently in the Instantaneous production of low pressures at some Point in the flow leading to cavitation. The local roughness of the walls (e.g. the

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concrete walls of dam spillways) produces local wakes in which small attached cavities may develop.As a consequence of the vibratory motion of the walls (e.g. liquid cooling of Diesel engines, standard A.S.T.M.E. erosion device) oscillating pressure fields are created and superimposed on an otherwise uniform pressure field. If the Oscillation amplitude is large enough, cavitation can appear when the negative oscillation occurs. Solid bodies that are suddenly accelerated by a shock in a quiescent liquid, particularly if they have sharp edges. The liquid acceleration needed to get round these edges produces low pressures even if the velocities are relatively small immediately after the shock.

1.4 THE MAIN EFFECTS OF CAVITATION IN TURBO MACHINERIES.

If a hydraulic system is designed to operate with a homogeneous liquid, additional vapor structures due to cavitation can be interpreted, by analogy with the case of mechanical systems, as mechanical clearances. The vapor structures are often unstable, and when they reach a region of increased pressure, they often violently— Alteration of the performance of the system (reduction in lift and increase in drag of a foil, fall in turbomachinery efficiency, reduced capacity to evacuate water in spillways, energy dissipation, etc.);— The appearance of additional forces on the solid structures;— Production of noise and vibrations;— Wall erosion, in the case of developed cavitation if the velocity difference between the liquid and the solid wall is high enough.

Thus, at first glance, cavitation appears as a harmful phenomenon that must be avoided. In many cases, the free cavitation condition is the most severe condition with which the designer is faced. To avoid the excessive financial charges that would be associated with this, a certain degree of cavitation development may be allowed. Of course, this can be done only if the effects of developed cavitation are controlled.

The negative effects of cavitation are often stressed. However, cavitation is also used in some industrial processes to concentrate energy on small surfaces and produce high pressure peaks. For this purpose, ultrasonic devices are often used. Examples of such positive applications include:— The cleaning of surfaces by ultrasonics or with cavitating jets,— The dispersion of particles in a liquid medium,— The production of emulsions,— Electrolytic deposition (the ion layers that cover electrodes are broken down by

Cavitation, accelerating the deposition process),— Therapeutic massage and bacteria destruction in the field of medical engineering,— The limitation of flow rates in confined flows due to the development of super cavities. Collapse since the internal pressure hardly varies and remains close to the vapor pressure. The collapse can be considered analogous to shocks in mechanical systems by which clearances between neighbouring pieces disappear.

1.5 THE GENERAL CAUSES OF CAVITATION IN TURBO MACHINERY.

If the pressure in a hydraulic machinery (Pump or Turbine)Falls below the vapour pressure of the liquid at the prevailing temperature, then the liquid will the bubbles are carried

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downstream until they reach an area of higher pressure where they collapse or implode. This process has two serious consequences.If the bubbles collapse against a solid boundary (Impeller Blades; Vanes; etc.) the inrush of water causes high local impact forces which may cause fracture by fatigue. Alternatively the surfaces may become eroded or pitted and this is particularly the case when Cavitation is combined with Chemical attack from dirty water.The other consequence is that the flow patterns are disturbed by the presence of the bubbles. The area of line flow is reduced and eddies are formed giving rise to vibrations( If a Centrifugal Pump sounds as if it is pumping gravel, the pump is almost certainly cavitating). Associated with this is a loss of performance and efficiency. In severe cases the pump may stop delivering.

CHAPTER 2

2.1 CAVITATION IN CENTRIPETAL PUMPS

Fig 2.1 Cavitation on a centripetal pump

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In any discussion on centrifugal pumps various terms like vapor pockets, gas pockets, holes, bubbles, etc. are used in place of the term cavities. These are one and the same thing and need not be confused.

In the context of centrifugal pumps, the term cavitation implies a dynamic process of formation of bubbles inside the liquid, their growth and subsequent collapse as the liquid flows through the pump.

Generally, the bubbles that form inside the liquid are of two types; Vapor bubbles or Gas bubbles.

Vapor bubbles are formed due to the vaporisation of a process liquid that is being pumped. The cavitation condition induced by formation and collapse of vapor bubbles is commonly referred to as Vaporous Cavitation.

Gas bubbles are formed due to the presence of dissolved gases in the liquid that is being pumped (generally air but may be any gas in the system). The cavitation condition induced by the formation and collapse of gas bubbles is commonly referred to as Gaseous Cavitation.

2.2 Mechanism of Cavitation.

2.2.1 Step One: Formation of bubbles inside the liquid being pumped.

The bubbles form inside the liquid when it vaporises i.e. phase change from liquid to vapor. Vaporization of any liquid inside a closed container can occur if either pressure on the liquid surface decreases such that it becomes equal to or less than the liquid vapor pressure at the operating temperature, or the temperature of the liquid rises, raising the vapor pressure such that it becomes equal to or greater than the operating pressure at the liquid surface. For example, if water at room temperature (about 77 °F) is kept in a closed container and the system pressure is reduced to its vapor pressure (about 0.52 psia), the water quickly changes to a vapor. Also, if the operating pressure is to remain constant at about 0.52 psia and the temperature is allowed to rise above 77 °F, then the water quickly changes to a vapor.

Just like in a closed container, vaporization of the liquid can occur in centrifugal pumps when the local static pressure reduces below that of the vapor pressure of the liquid at the pumping temperature.

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2.2.2 Step Two: Growth of bubbles Unless there is no change in the operating conditions, new bubbles continue to form and old bubbles grow in size. The bubbles then get carried in the liquid as it flows from the impeller eye to the impeller exit tip along the vane trailing edge. Due to impeller rotating action, the bubbles attain very high velocity and eventually reach the regions of high pressure within the impeller where they start Collapsing. The life cycle of a bubble has been estimated to be in the order of 0.003 seconds.

2.2.3 Step Three: Collapse of Bubbles

Fig2.2.Collapse of bubbles

As the vapor bubbles move along the impeller vanes, the pressure around the bubbles begins to increase until a point is reached where the pressure on the outside of the bubble is greater than the pressure inside the bubble. The bubble collapses. The process is not an explosion but rather an implosion (inward bursting). Hundreds of bubbles collapse at approximately the same point on each impeller vane. Bubbles collapse non-symmetrically such that the surrounding liquid rushes to fill the void forming a liquid microjet. The micro jet subsequently ruptures the bubble with such force that a hammering action occurs. Bubble collapse pressures greater than 1 GPa (145x106 psi) have been reported. The highly localized hammering effect can pit the pump impeller. The pitting effect is illustrated schematically in the above figure. After the bubble collapses, a shock wave emanates outward from the point of collapse.  This shock wave is what we actually hear and what we call "cavitation".  The implosion of bubbles and emanation of shock waves (red color). In nutshell, the mechanism of cavitation is all about formation, growth and collapse of bubbles inside the liquid being pumped. But how can the knowledge of mechanism of cavitation can really help in troubleshooting a cavitation problem. The concept of mechanism can help in identifying the type of bubbles and the cause of their formation and collapse.

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2.3 IMPORTANT TERMS.

To enable a clear understanding of mechanism of cavitation, definitions of following important terms are explored.

2.3.1 Static Pressure, ps

The static pressure in a fluid stream is the normal force per unit area on a solid boundary moving with the fluid. It describes the difference between the pressure inside and outside a system, disregarding any motion in the system. For instance, when referring to an air duct, static pressure is the difference between the pressure inside the duct and outside the duct, disregarding any airflow inside the duct. In energy terms, the static pressure is a measure of the potential energy of the fluid.

2.3.2 Dynamic pressure, pd

A moving fluid stream exerts a pressure higher than the static pressure due to the kinetic energy (½ mv2) of the fluid. This additional pressure is defined as the dynamic pressure. The dynamic pressure can be measured by converting the kinetic energy of the fluid stream into the potential energy. In other words, it is pressure that would exist in a fluid stream that has been decelerated from its velocity ‘v’ to ‘zero’ velocity.

2.3.3 Total pressure, pt

The sum of static pressure and dynamic pressure is defined as the total pressure. It is a measure of total energy of the moving fluid stream. i.e. both potential and kinetic energy.

2.3.4 Velocity head

The head corresponding to dynamic pressure is called the velocity head.

Velocity head = pd / r g = (r v2 / 2) / r g = v2/2g

From the reading hm, of the manometer velocity of flow can be calculated and thus velocity head can be calculated. The pressure difference, dP (pt – ps) indicated by the manometer is the dynamic pressure.

dP = r v2 /2

Velocity head = dP / r g

2.3.5 Vapor pressure, pv

Vapor pressure is the pressure required to keep a liquid in a liquid state. If the pressure applied to the surface of the liquid is not enough to keep the molecules pretty close together, the molecules will be free to separate and roam around as a gas or vapor. The vapor pressure is dependent upon the temperature of the liquid. Higher the temperature, higher will be the vapor pressure.

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2.4 Types of Pump Cavitation

The classification of pump cavitation varies from scientist to scientist. The cavitation phenomenon is classified into five types which are inclusive of the various scientist opinions;

2.4.1 Suction Cavitation (Due to low NPSH):  Suction Cavitation occurs when the Net Positive Suction Head Available to the pump is less than Net Positive Suction Head Required (The pressure required to operate a pump satisfactorily and avoid cavitation is called Net Positive Suction Head). In other words when water enters a pump, its velocity increases causing a reduction in pressure within the pumping unit. If this pressure falls too low, the water will vaporise, forming bubbles entrained in the liquid. These bubbles collapse violently as they move to areas of higher pressure.

Symptoms

i. The pump sounds like it is pumping rocks.ii. High Vacuum reading on suction line. iii. Low discharge pressure/High flow

Causes

i. Clogged suction pipe.ii. Suction line too longiii. Suction line diameter too smalliv. Suction lift too high.v. Valve on Suction Line only partially open

2.4.2 Re-circulation Cavitation (Suction Recirculation Cavitation and Discharge Recirculation Cavitation.):

This is caused by low flow rate through the pump. There are twotypes which may occur together or separately:

i. Suction Recirculation CavitationFluid entering the pump suction nozzle is reversed, resulting in high velocity vortexes either in or near the impeller eye, in the suction nozzle, or in the pipe close to the suction nozzle.  High velocities result in low localized pressures, local pressures may drop below the vapor pressure of the fluid, resulting in cavitation.Cavitation damage observed on the pressure side of the inlet vanes, near the impeller eye, is a sign of suction recirculation, and therefore this observation is diagnostic.  When looking into the eye of the impeller, the pressure side of the inlet vanes is on the underside of the vane, and therefore may only be observed using a mirror.Noise due to suction recirculation cavitation can be distinctive from other cavitation noise, and is therefore diagnostic. 

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Suction recirculation cavitation noise is reported to be a loud popping, crackling, hammering, or knocking sound, with highest intensity detected at the suction nozzle.

ii. Discharge Recirculation CavitationAt low flow rates fluid leaving the impeller discharge side or the pump discharge nozzle, reverses, resulting in high velocity vortexes between the two flow directions, causing localized low pressure areas.  Pressures may drop below the vapor pressure of the fluid resulting in cavitation.  Recirculation cavitation damage also occurs on the discharge side of the impeller periphery, at the cutwater(s), inside the discharge nozzle, or in the pipe close to the discharge nozzle.Noise due to discharge recirculation cavitation is generally less noisy than suction side recirculation.  Discharge recirculation cavitation noise is heard mostly at the pump discharge nozzle, and there will not be the loud popping or crackling noise heard when suction recirculation is occurring.

In general however, pumps with lower pump specific speed (Ns) and lower suction specific speed (Nss), are more resistant to recirculation cavitation.

2.4.3 Incipient Cavitation:To understand incipient cavitation so terms will be defined

i. NPSHi (Net Positive Suction Head Inception):That Fluid pressure, as measured at the pump suction nozzle, at which all cavitation inside the pump is suppressed.

ii. NPSHR (Net Positive Suction Head Reception): The fluid pressure, as measured at the pump suction nozzle, at which a 3% drop in dP occurs (Presuming the 3% drop in dP  is caused by cavitation).

  Incipient Cavitation is commonly used to describe that cavitation occurring inside a pump from the NPSHR  3% value, up to the incipient point.  However, it must be pointed out that incipient cavitation occurs at all points below the incipient point, including pressure values below the NPSHR  3% value.  Incipient cavitation occurs in most pumps at all times.  The cause is turbulence created by the impeller, resulting in localized pressure below the vapor pressure of the pumpage.  In the general pump market, the ubiquitous presence of incipient cavitation appears to cause little damage and little loss of performance, therefore the concept is not commonly discussed.  Although this fact may partially be due to under-reporting, the fact remains that incipient cavitation damage is not a common topic except in specific markets.  The topic is interesting to those markets where high energy suction pumps are used.  HVAC cooling towers and chilled water systems are well known to have incipient cavitation problems. High margins of NPSHA over NPSHR can result in increasingly severe incipient cavitation damage, the higher the margin, the more damage that will occur, until the NPSHi value is reached, which is usually unachievable.  The

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Hydraulic Institute and others have established general recommended margins of NPSHA to address this problem.

2.4.3.1 Factors indicating incipient cavitation are:i. Heavy weight liquids such as water, and especially when these liquids are at cooler

temperatures, for water this would be 1500 F. or less.  Actually water is one of the worst actors in regards to cavitation damage in general.

ii. Certain ranges of Pump Specific Speed.iii. High Suction Specific Speeds (Nss > 9500).iv. Systems with high dP values.v. Systems with high margins of NPSHA over NPSHR .

Incipient cavitation is strongly linked to the Suction Specific Speed of a pump, the higher the suction specific speed, the more likely that incipient cavitation may become a problem.  High Suction Energy pumps require larger margins of NPSHA over NPSHR, some report this margin as 2-5 times NPSHA over NPSHR , some authorities report values up to 20 times NPSHA over NPSHR .  Confused?  There are no well defined simple ways to understand and know how to apply these pumps except by experience.  You need extra margin of NPSH, and yet if you supply too much NPSH then incipient cavitation becomes a problem.  For some pumps, a small margin works well, for other pumps higher margins are required. The reason for this confusion involves the test methods for NPSHR.  This test sets NPSHR at a point when a 3% drop in dP across the pump occurs as pump inlet pressure is reduced.  For low suction energy pumps and low suction specific speed pumps, that 3% drop in dP represents a small but detectable amount of cavitation.  But high suction energy and high suction specific speed pumps are much more efficient at moving water through the impeller, so that a 3% dP drop represents a large amount of cavitation that can damage the pump severely and quickly. 

2.4.4 Vane Passing Syndrome Cavitation: Cavitation resulting when the impeller vane tip to cutwater clearance is too small, resulting in excessive turbulence each time a vane passes the cutwater, resulting in cavitation and also pulsation.  The location of cavitation damage is diagnostic.  Typical cavitation type damage may be observed on the centre of the cutwater, impeller vane tips, discharge edge of the impeller shroud, and possibly to the pump casing downstream of the cutwater, and directly behind the cutwater.Engineering specifications may attempt to preclude this problem by not allowing pump manufacturers to supply pumps with the largest impeller diameter available for a given pump family.  This is not a recommended practice for engineers because it presumes that a pump manufacturer will provide a pump with vane passing syndrome without the manufacturer knowing of the problem, or if they know, they are not telling the customer.  Perhaps the practice is understandable in view of the behaviour of some pump manufacturers.

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2.4.5 Flow turbulence:

We would prefer to have liquid flowing through the piping at a constant velocity. Corrosion or obstructions can change the velocity of the liquid and any time you change the velocity of a liquid you change its pressure. Good piping layouts would include :

i. Ten diameters of pipe between the pump suction and the first elbow. ii. In multiple pump arrangements we would prefer to have the suction bells in separate

bays so that one pump suction will not interfere with another. If this is not practical a number of units can be installed in a single large sump provided that :

iii. The pumps are located in a line perpendicular to the approaching flow. iv. There must be a minimum spacing of at least two suction diameters between pump

centre lines. v. All pumps are running. vi. The upstream conditions should have a minimum straight run of ten pipe diameters to

provide uniform flow to the suction bells. vii. Each pump capacity must be less than 15,000 gpm.viii. Back wall clearance distance to the centreline of the pump must be at least 0.75 of the

suction diameter. ix. Bottom clearance should be approximately 0.30 (30%) of the suction diameter x. The minimum submergence should be as follows:

Table 2.1 Minimum submerge

FLOW MINIMUM SUBMERGENCE

4,500 M3/HR 1.2 METERS

22,500 M3/HR 2.5 METERS

40,000 M3/HR 3.0 METERS

45,000 M3/HR 3.4 METERS

55,000 M3/HR 3.7 METERS

2.5 DETECTING CAVITATION.

1. Diagnose Cavitation by Sound    Low level cavitation in pumps may be inaudible, but higher levels generate distinctive sounds that we hear and call cavitation.  This sound can be a diagnostic clue to the experienced practitioner.  Cavitation makes different sounds depending on the equipment and conditions, and according to the type of cavitation.  Some descriptions of cavitation sounds are;

Pumps (water or similar weight liquids)

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i. Crackling or sizzlingii. Small steel shot rapidly striking against metal.iii. Hissing, rushing, swishing, or a static like sound similar to radio or television static.iv. Recirculation cavitation can produce loud knocking, hammering, or crackling sounds.

Valves (Valve disc riding close to seat)i. High pitch squealii. High pitch singing

Valves (High Flow)    The sound of high flow rate through a full open valve such that there is a very high pressure differential (dP) across the valve, and regardless if there is cavitation occurring or not, can be similar to the sound of cavitation in a pump, or the sound may be described as a swishing, rushing, or hissing sound. 

    Experienced persons may be able to diagnose cavitation by its unique sound qualities.  Cavity collapse has specific sound qualities that distinguish cavitation from sounds made by entrained gas bubbles, and also from the sound of failed bearings and other machinery noises. 

1. The trained ear may be able to distinguish just by the sound if cavitation is the source or not.

2. Cavitation sounds can start and stop quickly in response to changes in flow rate.3. Cavitation sounds exhibit precise repeatability, the noise is always the same under

identical conditions.     Gas bubbles entrained in the flow and not originating from cavitation, moving through a pump or valve, make a softer and lower frequency sound than cavitation because of the immense difference in energy levels.  Sound from entrained gasses may not react to variations in flow rate quickly or with precise repeatability as cavitation sounds do.

2. Diagnose Cavitation by Visual Examination of DamageVisual examination of supposed cavitation damage to pump components is often the best way to determine exact cause.  The key observation is usually the location of the damage. 

Severe discharge recirculation cavitation has damaged the discharge side of the impeller, specifically the vane tips and the outer edges of the front and rear vane shrouds. Moreover, discharge recirculation creates cyclic axial thrust loads that can fatigue the shaft, and in this case, the impeller attaching bolt, causing fatigue failure of the bolt.  The impeller bolt can be the weakest axial component in overhung end suction pumps, so the bolt fails instead of the shaft.

Suction cavitation has damaged the leading edge and suction side of the vane, and also damage is observed on "corner" surfaces leading into the vane. Suction cavitation in a pump was severe enough that cavities formed in the fluid before the fluid reached the impeller.  When the fluid reached the leading edge of the vanes and surrounding areas, the cavities collapsed onto the vane and surrounding areas eroding the impeller material. 

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If the pressure side of the vanes were damaged, (back side of the vane that can only be seen with a mirror), then suction recirculation cavitation would have been the cause.Again, the suction cavitation was severe enough that cavities occurred in the pumpage before the pumpage reached the pump.  When pressure increased in the area just ahead of the vane leading edge the cavities collapsed onto the vane causing the observed damage.

2.6 EFFECTS OF CAVITATION IN PUMPS.

Fig.2.3 Cavitation effect on a pump

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Cavitation can destroy pumps and valves, and cavitation causes a loss of efficiency in pumps immediately, and also a continuously increasing loss of efficiency as the equipment degrades due to erosion of the pump components by cavitation.  Therefore It is important to understand the phenomena sufficiently to predict and therefore reduce cavitation and damage from cavitation, and also to detect practical solutions to cavitation problems.

2.7 Cavitation Enhanced Chemical Erosion:   Pumps operating under cavitation conditions become more vulnerable to corrosion and chemical attack.  Metals commonly develop an oxide layer or passivated layer which protects the metal from further corrosion.  Cavitation can remove this oxide or passive layer on a continuous basis and expose unprotected metal to further oxidation.  The two processes (cavitation & oxidation) then work together to rapidly remove metal from the pump casing and impeller.  Stainless steels are not invulnerable to this process. 

2.8 Pump materials Selection:  There is no metal, plastic, or any other material known to man, that can withstand the high levels of energy released by cavitation in the forms of heat

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and pressure.  In practice however,  materials can be selected that result in longer life and customer value in their ability to withstand cavitation energies, so that attention to pump construction materials is valuable and productive.    Where cavitation is not a problem or not predicted to be a problem, common materials such as cast iron and bronze are suitable for pump construction.  There are millions of cast iron and bronze pumps that work fine for 20 years or more without any problem even though many of those pumps experience some cavitation. 2.9 FACTORS THAT INDICATE THE USE OF HIGH RESISTANCE MATERIAL. 

i. Corrosive Pumpage - Water with chlorine, salt water, or other oxidizers.  A metal that normally has no problem with erosion by a specific chemical can become vulnerable to that chemical If cavitation occurs.  Cavitation can eat away the protective surface oxide layers of a metal that protect the metal from corrosion.  Even stainless steel can experience chemical erosion if the passivated surface layer of the stainless steel is continuously removed by cavitation thus exposing unprotected metal to the oxidizing agent.

ii. Low Flow Rate - Long term operation at low flow rates can result in both types of Recirculation Cavitation.

iii. Low NPSHA - Long term operation with marginal or insufficient NPSHA.iv. Heavy Weight (High Density) Liquids - Heavy liquids such as water cause more

damage in cavitation situations.  Water molecules are small and dense, water weights 8.33 lbs./gallon.  Since density is highest at cooler temperatures, water and similar liquids are more of a problem at temperatures below 1500 F.

v. High Specific Speed Pumps (Ns>9000)vi. High Suction Specific Speeds (Nss>9500)vii. Systems with high dP values across the pump.viii. Systems with high margins of NPSHA over NPSHR .  In these situations

reducing NPSH may reduce or practically eliminate the cavitation damage.

2.10 Material Resistance The Materials below are listed in the order of their ability to withstand Cavitation Erosion, Cast Iron having the lowest resistance and Stellite the highest resistance to cavitation damage.

i. Cast Iron ii. Leaded Bronze iii. Cast Carbon Steel iv. Manganese Bronze v. Monel vi. Cast Iron - CA-15, CA6-NM, CF-8M vii. Stainless Steel (Cast Precipitation, Cast Duplex)viii. Cast Nickel Aluminum Bronzeix. Titanium

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x. Cast Carburized 12% Chromium Stainless, Chrome-manganese austenitic Stainless.

xi. Stellite

Fig. 2.4 Impeller cavitation regions

2.11 Equaations

2.11.1 NPSH and Suction Specific Speed In designing a pumping system, it is essential to provide adequate NPSH available for proper pump operation. Insufficient NPSH available may seriously restrict pump selection, or even force an expensive system redesign. On the other hand, providing excessive NPSH available may needlessly increase system cost.

Suction specific speed may provide help in this situation.

Suction specific speed (S) is defined as:

Where N = Pump speed RPM GPM = Pump flow at best efficiency point at impeller inlet (for double suction impellers divide total pump flow by two). NPSHR = Pump NPSH required at best efficiency point.

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g

P

g

P vapourP

rr

g

V

g

P

g

V

g

P PPSS

22

22

rr

g

V

g

P

g

V

g

P PvapourSS

22

22

rr

LfSScatmospheri HHg

V

g

Pz

g

P

2

2

rr

g

PHHz

g

PNPSH vapour

Lfcatmospheri

available rr

For a given pump, the suction specific speed is generally a constant - it does not change when the pump speed is changed. Experience has shown that 9000 is a reasonable value of suction specific speed. Pumps with a minimum suction specific speed of 9000 are readily available, and are not normally subject to severe operating restrictions, unless the pump speed pushes the pump into high or very high suction energy.

2.11.2 Net Positive Suction Head (NPSH).. No cavitation

2.11.3 Cavitation Number:

• for cavitation-free operations

2.12 PREVENTING CAVITATION IN PUMPS.

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2.12.1 For vaporization problems (cavitation) :

There are two possibilities to cure vaporization problems;

2.12.2 Increase the suction head

1. Raise the liquid level in the tank 2. Raise the tank 3. Put the pump in a pit 4. Reduce the piping losses. These losses occur for a variety of reasons that include :

i. The system was designed incorrectly. There are too many fittings and/or the piping is too small in diameter.

ii. A pipe liner has collapsed. iii. Solids have built up on the inside of the pipe. iv. The suction pipe collapsed when it was run over by a heavy vehicle. v. A suction strainer is clogged. vi. Be sure the tank vent is open and not obstructed. Vents can freeze in cold

weather vii. Something is stuck in the pipe, It either grew there or was left during the last

time the system was opened . Maybe a check valve is broken and the seat is stuck in the pipe.

viii. The inside of the pipe, or a fitting has corroded. ix. A bigger pump has been installed and the existing system has too much loss for

the increased capacity. x. A globe valve was used to replace a gate valve. xi. A heating jacket has frozen and collapsed the pipe. xii. A gasket is protruding into the piping. xiii. The pump speed has increased.

5. Pressurize the tank 6. Install a booster pump

2.12.3 Lower the fluid temperature

1. Injecting a small amount of cooler fluid at the suction is often practical. 2. Insulate the piping from the sun's rays. 3. Be careful of discharge recirculation lines, they can heat up the suction fluid.

2.12.4 Reduce the N.P.S.H. Required

1. Use a double suction pump. This can reduce the N.P.S.H.R. by as much as 27% or in some cases it will allow you to raise the pump speed by 41%

2. Use a lower speed pump 3. Use a pump with a larger impeller eye opening. 4. If possible install an Inducer. These inducers can cut N.P.S.H.R. by almost 50%. 5. Use several smaller pumps. Three half capacity pumps can be cheaper than one large

pump plus a spare. This will also conserve energy at lighter loads.

On the other hand to cure cavitation in the various types of cavitation in pumps;

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2.12.5 For suction cavitation:

1. Remove debris from suction line. 2. Move pump closer to source tank/sump 3. Increase suction line diameter. 4. Decrease suction lift requirement 5. Install larger pump running slower which will decrease the Net Positive

Suction Head Required by the pump(NPSHR).6. Increase discharge pressure. 7. Fully open Suction line valve.

2.12.6 For discharge cavitation:

1. Remove debris from discharge line.2. Decrease discharge line length 3. Increase discharge line diameter.4. Decrease discharge static head requirement. 5. Install larger pump, which will maintain the required flow without discharge

cavitating. 6. Fully open discharge line valve.

2.12.7 For Recirculation cavitation:

1. Designing the pump for lower suction-specific speeds and limiting the range of operation to flow capacities above the point of recirculation.

2. Raising the suction head.

CHAPTER 3

CAVITATION IN TURBINES.

Fig.3.1 Cavitation on a turbine wheel

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3.1 INTRODUCTION.According to Bernoulli’s principle (derived by the Swiss mathematician Daniel Bernoulli), as the flow velocity of the water increases at any given elevation, the pressure will drop. There is a danger that in high-velocity sections of a reaction turbine, especially near the exit, the pressure can become so low that the water flashes over into small vapour bubbles, which then collapse suddenly. This so-called cavitation leads to erosion pitting as well as to vibrations and must be avoided by the careful shaping of all blade passages and of the exit passage or draft tube.

The cavitation phenomenon occurs when, at any point, the water pressure drops below its corresponding vapour pressure. This will create bubbles and the fluid will rush into the cavities left by the bubbles causing a species of water hammer.The resulting cavitation that occurs in the turbine not only impairs the turbine performance but it may also damage the machine itself.The signs of cavitation are:i. Milky appearance of the water at the exit of draft tube.ii. Vibrations and noise.

Cavitation in turbines varies in the different types and it can be reported as follow;

3.2 FRANCIS TURBINES

3.2.1 Type of Cavitation

In the case of a Francis turbine and for the design operating range, the type of cavity developing in the runner is closely driven by the specific energy coefficient ψ, the flow coefficient ϕ influencing only the cavity whirl. High and low values of ψ correspond to a cavity onset at the leading edge suction side and pressure side of the blades respectively.

Fig.3.2. Inlet edge cavitation, Francis turbine.

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This type of cavitation is not very sensitive to the value of the Thomas number and it can lead to a severe erosion of the blades. Traveling bubble cavitation takes place for the design value of ψ, at the throat of the runner flow passage, close to the outlet and corresponds to low flow angles of attack. This type of cavitation as shown in the figure below, is very sensitive to the content of cavitation nuclei and to the value of the Thomas number.

Fig.3.3 Travelling bubble cavitation in a Francis turbine runner.

For this reason, the plant NPSE is determined with respect to this type of cavitation. The drop of the η-σ curve is noticed when cavities extend up to the runner outlet in both types of cavitation. Depending on the value of the flow coefficient ϕ, a whirl cavity develops from the hub of the runner to the centre axis of the draft tube in the bulk flow, as shown in the figure below;

Fig.3.4 Cavitation whirls at low and high discharge operation, in a Francis turbine discharge ring.

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The size of the cavity is dependent of σ, but the vortex motion depends only on the flow coefficient values. The whirl development is mainly concerned with the stability of machine operation, since it is the main source of pressure fluctuations in the hydraulic installation. At low flow regime, it can be observed that complex flow recirculation at the inlet of the runner leading to vortex cavitation attached to the hub and extending up to the blade to blade passage.

Fig.3.5 Inter blades cavitation vortices in a Francis turbine runner.

This type of turbine operation corresponds usually to off- design operation. However this operation cannot be avoided during for instance the reservoir filling up period of a new hydro-power generation scheme

3.2.2 Efficiency Alteration

The setting of a Francis turbine is determined according to the risk of efficiency alteration, which is higher for high discharge, or high load, operating conditions as it can be seen from the expression of the cavitation factor χE . Therefore, the runner is usually designed in such a way that this corresponds to the development of travelling bubble outlet cavitation. This type of cavitation is very sensitive to the content of cavitation nuclei and to the value of the Thomas number. For this reason, the plant NPSE is determined with respect to this type of cavitation.

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Fig.3.6 Influence of free stream nuclei content on efficiency cavitation curves.

However, many tests carried out for Francis turbine of different specific speeds confirm a strong influence of cavitation nuclei content combined with the test head on the efficiency alteration phenomenon by cavitation. Nuclei content does not only influence cavitation inception, but also the development of bubble travelling cavities.

Moreover, test head influence is found to be more related to an effect of the active nuclei content than of the Froude effect. According to the Rayleigh Plesset stability analysis the lower radius limit of an active nucleus depends directly on the test head value leading to more or less active nuclei for a given nuclei distribution.

3.2.3 Cavitation Erosion

Typical runner areas where cavitation erosion can be observed are shown below.

Fig.3.7 Typical eroded areas of a Francis runner.

In general severe cavitation erosion damages are observed in Francis runners on the blade suction sides, shaded area A or downstream in the blade to blade channel, shaded area B

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The cause of these types of erosion is due to unexpected leading edge cavitation development and can only be corrected by reshaping the inlet edge. However, wall erosion can be mitigated by welding a layer of cavitation resistant alloy. In case of development of travelling cavitation bubble at the runner outlet region, a "frosted" area can be observed at the shaded area C, which usually leads to barely visible erosion and is easily controlled but the Thomas cavitation number. Finally, low load inter-blade cavitation vortices, can lead to erosion of the runner hub wall, shaded area D and the machine casing, leading to an erosion risk even though the head could be low. This type of cavitation is driven by the flow shear layer in this gap and it is not very dependent of the Thomas cavitation number.

3.3 KAPLAN AND BULB TURBINES

3.3.1 Type of Cavitation

Runners of Kaplan and bulb turbines are axial with adjustable blade pitch angle and the control of both the guide vane opening and the blade pitch angle allows optimized operation of the machine, so called "on cam" operation. For the design operating range a cavity development takes place at the hub of the runner in the figure below

Fig3.8. Hub cavitation development for a Kaplan runner

This type of cavitation is very sensitive to the Thomas number. Any effect of the water cavitation nuclei content is observed for this type of cavitation. However, the air entertainment can have a great influence on the extent of this cavity. Since the blades are adjustable, the runner is not shrouded and, then as shown in the figure below, tip clearance cavitation takes place in the gap between the blades and the machine casing, leading to an erosion risk even though the head could be low.

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Fig.3.9 Cavitation development fors

This type of cavitation is driven by the flow shear layer in this gap and it is not very dependent of the Thomas cavitation number. Since the blades are adjustable, the runner is not shrouded and then tip clearance cavitation takes place in the gap between the blades

3.3.2 Efficiency Alteration

The efficiency alteration for a Kaplan and bulbs turbines is mainly due to the development of hub cavitation. This hub cavity reaches the blade trailing edge, an efficiency drop will be observed.

Fig.3.10 Efficiency cavitation curve for a Kaplan Turbine.

This type of cavitation as mentioned is very sensitive to the Thomas number and determines the plant NPSE of the machine. Depending on the head of the machine limited development of tip clearance cavitation can be admissible for plant NPSE, especially for the case of Kaplan or bulb turbines, a strong influence of the Thomas cavitation number on the runway speed will be noticed

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3.3.3 Cavitation Erosion

Typical Kaplan runner areas where cavitation erosion can be observed are reported below.

Fig.3.11 Typical eroded areas of a Kaplan runner.

The most critical area where cavitation erosion is observed are the blade tips and the machine casing, shaded area A and B. This erosion is due to the development of tip clearance cavitation, which can take place even at plant NPSE. Either for lasting operations at high head or at low head erosion takes place at the suction side or the pressure side of the runner inlet, dashed area D or E respectively. This type of erosion is caused by inlet edge cavitation. Erosion corresponding to dashed area F or G can occur during lasting low head operation. Finally, for high load operation conditions erosion can be observed at the outlet of the runner at the suction side, shaded area C.

3.4 Causes of Cavitation in turbines

The liquid enters hydraulic turbines at high pressure; this pressure is a combination of static and dynamic components. Dynamic pressure of the liquid is by the virtue of flow velocity and the other component, static pressure, is the actual fluid pressure which the fluid applies and which is acted upon it. Static pressure governs the process of vapor bubble formation or boiling. Thus, Cavitation can occur near the fast moving blades of the turbine where local dynamic head increases due to action of blades which causes static pressure to fall. Cavitation also occurs at the exit of the turbine as the liquid has lost major part of its pressure heads and any increase in dynamic head will lead to fall in static pressure causing Cavitation.

3.5 Effects of Cavitation on turbines

The formation of vapor bubbles in cavitation is not a major problem in itself but the collapse of these bubbles generates pressure waves, which can be of very high frequencies, causing damage to the machinery. The bubbles collapsing near the machine surface are more damaging and cause erosion on the surfaces called as cavitation erosion. The collapses of smaller bubbles create higher frequency waves than larger bubbles. So, smaller bubbles are more detrimental to the hydraulic machines.Smaller bubbles may be more detrimental to the hydraulic machine body but they do not cause any significant reduction in the efficiency of the machine. With further decrease in static pressure more number of bubbles is formed and their size also increases. These bubbles coalesce with each other to form larger bubbles and eventually pockets of vapor. This

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disturbs the liquid flow and causes flow separation which reduces the machine performance sharply. Cavitation is an important factor to be considered while designing Hydraulic Turbines.

3.6 Avoiding Cavitation in turbines.

To avoid cavitation while operating Hydraulic Turbines parameters should be set such that at any point of flow static pressure may not fall below the vapor pressure of the liquid. These parameters to control cavitation are pressure head, flow rate and exit pressure of the liquid. The control parameters for cavitation free operation of hydraulic turbines can be obtained by conducting tests on model of the turbine under consideration. The parameters beyond which cavitation starts and turbine efficiency falls significantly should be avoided while operation of hydraulic turbines.Flow separation at the exit of the turbine in the draft tube causes vibrations which can damage the draft tube. To dampen the vibration and stabilize the flow air is injected in the draft tube. To totally avoid the flow separation and cavitation in the draft tube it is submerged below the level of the water in tailrace.

3.7 CAVITATION REPAIRS IN TURBINES.

3.7.1 APPROACH

The repair of cavitation pitting damage on turbines is an essential part of a hydro plant maintenance program. If left unrepaired, or if improperly repaired, the extent of damage will increase, usually at an accelerating rate, eventually leading to an extended and costly outage of the unit. "An effective repair program can minimize the adverse problems associated with cavitation pitting. The main objectives of such a program are:

i. Restoration of runner and other components within the turbine water passages to "as new" condition;

ii. Correction of any profile errors or irregularities which are responsible for the pitting; and

iii. Avoidance of blade shape distortion and its Effect to further damage.

As with any equipment, excessive repairs to a turbine can lead to reduction in its performance and useful operating life. Extensive weld repairs can result in runner Blade distortion, acceleration of further cavitation damage, and possible reduction of turbine efficiency. Also, extensive repair can cause residual stressing in the runner resulting in structural cracking at areas of high stress.

To maximize equipment life and to maintain high availability and good operating efficiency, cavitation pitting repairs should be done in a logical and methodical manner. The basic steps of such a repair program are as follows:

i. Inspection

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ii. Identify cause of pitting iii. Plan best approach to repairs iv. Perform repairs

"Thorough periodic inspection of equipment within a preventive maintenance program is a prerequisite to long-term reliability, and routine inspection for cavitation damage is no exception to this concept. Additionally, clear and concise inspection records assist in reporting the causes of cavitation pitting and monitoring the effectiveness of repair programs.

"Identifying the cause of cavitation pitting on turbine equipment is often a significant step toward mitigating the problem. In many cases, identification will be difficult and may not be conclusive; nevertheless, some attempt at ascertaining the cause of the damage is warranted and should not be overlooked.

"Prior to making repairs, consideration should be given to the options available for doing the work. There are two general approaches:

One is to restore the runner to original profiles; and the other is to perform runner modifications to eliminate or reduce the cause of the damage. Restoration to original profile is the most straightforward approach; however, in the long term, profile modifications will likely have increased benefits. "Once an approach to repair is established, implementation of the work using proper procedures and high quality workmanship will maximize the effectiveness of the repair program.

3.8 FREQUENCY OF INSPECTION AND REPAIR

3.8.1 Cavitation Damage Inspections

"Periodic inspection of a turbine for cavitation damage is an important part of turbine maintenance. Frequent inspections are particularly important during the initial period for operation of a new turbine or new runner, as they will enable cavitation damage to be detected at an early stage and remedial measures to be effected before pitting becomes extensive.

3.8.2 Cavitation Repairs

The frequency of turbine cavitation repairs will vary from plant to plant. The time between repairs will depend upon the rate of metal removal, the plant owner's philosophy for repairs, and other indirect factors.

Approaches for cavitation repairs are:

i. Make all repairs each inspection period. Many plant owners believe that this is good practice from a preventive maintenance point of view.

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ii. Repair only areas where cavitation damage is I/8 inch (3 mm) or deeper. Preparation of damaged areas even with only light surface "frosting" is usually done to a depth of at least 1/8 inch (3 mm).

iii. Repair areas on stainless steel overlay where pitting is 1/8 inch (3 mm) or deeper. On carbon steel, repair areas even with light damage using stainless steel weld material.

iv. Allow cavitation to progress to the maximum depth which can be repaired with two weld passes (about 3/8 inch [10 mm]).

i. Make repairs only when damage becomes so bad that it threatens to impair the strength of the turbine or when preparation of the damaged area may result in holes completely through the runner blade.

"Indirect factors which influence scheduling of repair work include:

ii. Availability of maintenance personnel

iii. System operating conditions such as requirements for peaking or standby capacity, transmission limitations, and unscheduled outages of other units

3.9 CAVITATION DAMAGE INSPECTION

Cavitation damage inspection should be made from both the draft tube area below the runner and from the stay ring/wicket gate area in the spiral (or semi-spiral) case.

"Inspection from the draft tube area should normally be done from a temporary maintenance platform installed below the runner. On units greater than about 12 foot (3.7 m) diameter when no repairs are planned, draft tube inspection may be made from a portable boat floating in the draft tube while water level is maintained below the bottom of the draft tube access door. Most areas of the runner which are susceptible to cavitation damage can be seen from the draft tube side. The leading edge of the blades, however, can best be inspected from the wicket gate area. On small units where access to the runner from the wicket gate area is poor, a polished metal mirror can be used for observing the leading edge area from the draft tube side.

Adequate lighting is necessary for a thorough inspection--the stronger the light source the better. When the runner erection platform is in place, photographic-type lighting is optimum. For the wicket gate area, large portable battery powered lights are usually sufficient. A drop-cord-type light is also suitable for difficult areas. For safety, ground fault detectors are necessary in the power supply to the turbine water passages. Alternately, a low voltage direct current power source should be used.

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"The inspection should be thorough, covering not only the runner, but the draft tube liner, discharge ring, wicket gates, bottom ring, and headcover. The runner blades should be permanently numbered. The wicket gates may be identified by referencing them to the baffle vane.

"It is recommended that a checklist be prepared to ensure that all parts of the turbine are inspected, and that all areas of cavitation damage be recorded on sketches or in tabular form. The records should include the following:

Date of inspection

Number of hours of operation and the generation (kWH) since the previous repairs and/or inspection

Operation limits (i.e., net head, tail-water level, low flows, and any incidence and duration beyond these limits

Overall area of each area of pitting, as well as the average depth and maximum depth

Dimensions of damaged areas from the leading and trailing edge of the blades

Photographs of the damaged areas and of subsequent repairs

"When taking photographs, the blade number, the date of the inspection, and dimensions of the pitted area should be clearly marked on the blade for reference.

3.10 CAUSE OF PITTING

An important step in any effort to minimize cavitation damage is to identify the cause of the pitting. This requires careful examination of the extent and location of the pitting as well as a review of the operating history of the unit including operating heads and loading of the machine.

In analyzing cavitation damage, first check for local discontinuities in blade shape or profile in the area immediately upstream of the damaged surface. Also check whether or not the cavitation patterns are the same on each of the blades. If damage varies from blade to blade and there are no apparent discontinuities upstream, the problem may be on the overall blade profile or blade location. In this case, a template should be made of a cavitation-free blade or the one with the least pitting, and this template used to check the overall profile of the other blades for possible modifications. If the pattern of damage is very similar from blade to blade, and local profile discontinuities are not evident, the problem becomes more difficult and other factors such as method of operation, operating heads, etc., must be considered.

"The possibility that damage is not the result of cavitation should be investigated:

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Damage may be from corrosion, particularly if water has high oxygen content or high dissolved solids.

On carbon steel runners with stainless steel overlay, damage at the interface of carbon steel and stainless steel is likely to be partially due to galvanic action.

Large voids beneath overlay are caused by galvanic corrosion which will occur when there is a small hole in the overlay. The hole may be a defect in the weld overlay or from cavitation pitting which has penetrated the overlay.

If water contains large amounts of entrained solids, the damage may be caused by physical erosion rather than cavitation pitting.

"Input from the turbine manufacturer's hydraulic engineer in assessing the cause of pitting is always valuable. This is one reason for inspection at an early stage of operation. Even if damage is far less than the guaranteed amount, the manufacturer should be asked to report on the cause of the damage.

REFERENCE:

Chaudhry, M. H. [1987] Applied Hydraulic Transients, 2nd Ed., Van Nostrand Reinhold,New York.

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Cuenca, R. H. [1989] Irrigation System Design, Prentice-Hall, Englewood Cliffs, NewJersey.Diaz, J. E. [1972] Water Hammer Produced by Release of Air from Water Pipes, M. S.Thesis, Colorado State University, Ft. Collins, April.Hathoot, H. M., Abo-Ghobar, H. M., Al-Amoud, A. I., and Mohammad,F. S. [1994] Analysis and Design of Irrigation Laterals, J. Irrig. and Drainage Engr.,ASCE, 120(3), 534.James, L. G. [1988] Principles of Farm Irrigation System Design, Wiley, New York.Jensen, M. E. [1983] Design and Operation of Farm Irrigation Systems, ASAEMonograph No. 3, ASAE, St. Joseph, MI.Jeppson, R. W. and Davis, A. L. [1976] Pressure Reducing Valves in PipeNetwork Analyses, J. Hydraulics Div., ASCE, 102(HY7), 987.Marsden, N. J. and Fox, J. A. [1976] An Alternative Approach to the Problem ofColumn Separation in an Elevated Section of Pipeline, Second Int. Conf. on PressureSurges, Paper F1, BHRA Fluid Engineering, Cranfield, Bedford, England, Sept.Martin, C. S. [1976] Entrapped Air in Pipelines, Second Int. Conf. on PressureSurges, Paper F2, BHRA Fluid Engineering, Cranfield, Bedford, England, Sept.Martin, C. S., Padmanabhan, M., and Wiggert, D. C. [1976] Pressure WavePropagation in Two-Phase Bubbly Air-Water Mixtures, Second Int. Conf. on PressureSurges, Paper C1, BHRA Fluid Engineering, Cranfield, Bedford, England, Sept.McNown, J. S. [1954] Mechanics of Manifold Flow, Trans. ASCE, 119, 1103.Miller, D. S. [1984] Internal Flow Systems, Vol. 5, BHRA Fluid Engineering, Cranfield,Bedford, England.Scaloppi, E. J. and Allen, R. G. [1993] Hydraulics of Irrigation Laterals:Comparative Analysis, J. Irrig. and Drainage Engr., ASCE, 119(1), 91.Silva-Araya, W. F., and Chaudhry, M. H. [1997] Computation of EnergyDissipation in Transient Flow, J. Hydr. Engr., ASCE, 123(2), 108.Stockstill, R. L., Nielson, F. M., and Zitta, V. L. [1991] HydraulicCalcula-tions for Flow in Lock Manifolds, J. Hydr. Engr., ASCE, 117(8), 1026.Street, R. L., Watters, G. Z., and Vennard, J. K. [1996] Elementary FluidMechanics, 7th Ed., John Wiley, New York.Streeter, V. L. and Wylie, E. B. [1967] Hydraulic Transients, McGraw-Hill, NewYork.Talozi, S. A. [1998] Microirrigation Computer Simulation: Pressure Sensitivity toHydraulic Change, M. S. Thesis, University of California, Davis, August.Thorley, A. R. D. [1991] Fluid Transients in Pipeline Systems, D. & L. George,Barnet, England.U. S. Soil Conservation Service [1984] National Engineering Handbook, Sec. 15,Trickle Irrigation, (Ch. 7), 129 pp.Vigander, S., Elder, R. A., and Brooks, N. H. [1970] Internal Hydraulics ofThermal Discharge Diffusers, J. Hydraulics Div., ASCE, 96(HY1), 509.Watters, G. Z. [1984] Analysis and Control of Unsteady Flow in Pipelines, 2nd Ed.,Butterworths, Stoneham, Massachusetts.Weaver, D. L. [1972] Surge Control

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