Patent Publication Number: US-2022220957-A1

Title: Method and system for damping flow pulsation

Description:
FIELD AND BACKGROUND OF THE INVENTION 
     The present invention, in some embodiments thereof, relates to flow control and, more particularly, but not exclusively, to a method and system for damping flow pressure pulsation. 
     Many pumps, particularly pumps of the positive displacement type, generate pressure pulsations. The pressure pulsation occurs when the pump produces a non-constant flow of fluid so that there are periods of times during which the flow is lower and other periods of time during which the flow is higher. For instance, in a piston pump operating by a crank shaft the speed profile of the piston is sinusoidal. Since the flow of the fluid correlates with the piston&#39;s speed, the flow varies periodically. This results in pressure variations both in the pump and in the fluid discharge line. 
     The fluctuations in the fluid pressure can propagate upstream the flow and can therefore induce undesirable effects on the pump, and the fluid line, which undesirable effects include, for example, hammering, high frequency harmonics, resonance, fatigue and damage. 
     Consequently, attempts have been made to attenuate pressure pulsations, using a bladder separating between the discharged fluid and a pressurized gas (e.g., nitrogen or air). When the pressure of the discharged fluid is high, the pressurized gas absorbs the pressure as elastic energy, and when the pressure of the discharged fluid is low, the elastic energy is transferred back to the discharged fluid, thus reducing the peak-to-peak variations of the pressure of the discharged fluid. 
     U.S. Pat. No. 7,353,845 discloses an accumulator for downhole operations. A housing connects inline to a hydraulic system, and an elastomeric bladder is disposed internally of the housing and separates a gas compartment from a fluid compartment. The accumulator includes an anti-extrusion device that assumes one of two positions to either prevent extrusion of the bladder into the hydraulic system, or to open fluid communication between the fluid compartment and the hydraulic system. U.S. Pat. No. 7,665,484 discloses a fluid coupling pulsation damper for fuel pumps in fuel engines. The pulsation damper consists of closed cell filled with pressurized gas that can deform according to the fluid pressure around it. U.S. Pat. No. 9,777,879 discloses a closed cell with flexible walls that is filled with a gas and may contract and expand to absorb the fluid pulsation around it. U.S. Pat. No. 10,125,583 discloses a borehole pump assembly operable in association with a windmill. The assembly includes a pump and an air chamber which provides hydraulic shock absorption between the pump and a delivery pipeline. The air chamber is provided with a partially conical diaphragm. The air chamber housing and the pump housing are larger in diameter than a riser pipe receiving liquid from the pump. 
     Additional background art includes www(dot)plastomatic(dot)com/technical-article/introduction-to-pulsation-dampeners-surge-suppressors/, and www(dot)ramuni-versal(dot)co(dot)uk/uploads/files/plckff1d3ofk51u992v8no1cocf.pdf. 
     SUMMARY OF THE INVENTION 
     According to an aspect of some embodiments of the present invention there is provided a method of attenuating pressure pulsations. The method comprises: pumping liquid by a pump into a vessel in fluid communication with a flow line by a conduit sealingly passing through a top surface of the vessel, so as to discharge the liquid into the flow line while creating an air-liquid interface in the vessel, by trapping in an upper part of the vessel air that attenuates pressure pulsations caused by the pumping; and generating condition for the liquid to drain out of the vessel to allow air to fill at least the upper portion of the vessel. 
     According to some embodiments of the invention the vessel is above the pump. 
     According to some embodiments of the invention the pumping is directly into the conduit, and wherein the conduit has an opening at a lower part of the vessel for releasing the liquid to the lower part. 
     According to some embodiments of the invention the conduit has a drain opening also outside the vessel, and the liquid is drained through the drain opening. 
     According to some embodiments of the invention the pumping is directly into the vessel, and wherein the conduit has an inlet at a lower part of the vessel for receiving the liquid from the lower part and directing the liquid to the flow line. 
     According to some embodiments of the invention the vessel comprises a drain opening at the lower part, and the liquid is drained through the drain opening at the lower part. 
     According to some embodiments of the invention the drain opening at the lower part is open at all times. 
     According to some embodiments of the invention the condition for draining are generated by temporarily ceasing the pumping. 
     According to some embodiments of the invention the condition for draining are generated by operating a valve to open the drain opening at the lower part. 
     According to some embodiments of the invention the pump comprises a drain opening formed on an encapsulation of the pump, and the liquid is drained through the drain opening on the encapsulation. 
     According to some embodiments of the invention the drain opening on the on the encapsulation of the pump is open at all times. 
     According to some embodiments of the invention the condition for draining are generated by operating a valve to open the drain opening on the encapsulation of the pump. 
     According to an aspect of some embodiments of the present invention there is provided a system for attenuating pressure pulsations. The system comprises: a vessel having a top surface, an upper part and a lower part; a conduit in fluid communication with the lower part, the conduit sealingly passing through the top surface to feed a flow line outside the vessel with liquid; a liquid inlet formed in the vessel for receiving the liquid from a pump in a manner that the liquid enters both the vessel and the conduit, and creates an air-liquid interface in the vessel, by trapping in the upper part air that attenuates pressure pulsations generated by the pump; and at least one drain opening constituted to drain the liquid out of the vessel and to allow air to fill at least the upper portion of the vessel. 
     According to some embodiments of the invention the conduit sealingly passes through the liquid inlet to connect directly to an outlet of the pump, wherein the conduit has an opening at a lower part of the vessel for releasing the liquid to the lower part. 
     According to some embodiments of the invention at least one of the drain opening(s) is formed on the conduit outside the vessel. 
     According to some embodiments of the invention the conduit is disconnected from the liquid inlet of the vessel, and comprises a conduit inlet at the lower part for receiving the liquid from the lower part and directing the liquid to the flow line. 
     According to some embodiments of the invention at least one of the drain opening(s) is formed in the vessel at the lower part. 
     According to some embodiments of the invention the vessel is devoid of any partition at the air-liquid interface. 
     According to an aspect of some embodiments of the present invention there is provided a pump system. The pump system comprises the system as delineated above and optionally and preferably as further detailed below, and a pump having an outlet connected to the liquid inlet. 
     According to some embodiments of the invention the pump system comprises a controller for temporarily ceasing operation of the pump. 
     According to some embodiments of the invention the controller is configured for opening the valve when the pump is not in operation, and closing the valve when the pump is in operation. 
     According to some embodiments of the invention the system comprises a passive valve at the drain opening, constituted to assume an opened state when the pump is not in operation, and a closed state when the pump is in operation. 
     According to some embodiments of the invention a volume of the vessel is at least (ps+Δp)×V r ×p s /(Δp×p atm ), wherein p s  is an expected static pressure at an outlet of the pump, p atm  is an expected atmospheric pressure outside the vessel, and V r  and the Δp are predetermined volume and pressure tolerance parameters. 
     According to some embodiments of the invention the draining is over a draining period of from about 1 hour to about 10 hours. 
     According to some embodiments of the invention the pump is a positive displacement pump. According to some embodiments of the invention the positive displacement pump is a reciprocating pump. According to some embodiments of the invention the positive displacement pump is a double action pump. According to some embodiments of the invention the positive displacement pump is a rotary pump. According to some embodiments of the invention the pump is a centrifugal pump. According to some embodiments of the invention the pump is a borehole pump. 
     According to an aspect of some embodiments of the present invention there is provided a valve device. The valve device comprises: a valve body formed with an opening; a peripheral sealing member positioned within the valve body and being movable towards and away from the opening; and two liquid ports formed at opposite sides of the valve body, and being sealingly connectable to liquid conduits; wherein the peripheral sealing member is positioned and configured such that inflow of liquid through the first port biases the sealing member against the opening, and inflow of liquid through the first port releases the sealing member from the opening. 
     According to some embodiments of the invention the peripheral sealing member comprises a sealing ring. According to some embodiments of the invention the peripheral sealing member comprises a thermoplastic. According to some embodiments of the invention the thermoplastic is a polyoxymethylene. 
     According to an aspect of some embodiments of the present invention there is provided a pump system. The pump system comprises: an encapsulation formed with an inlet port for suctioning liquid, an outlet port for delivering the liquid to a flow line, and a drain opening for draining liquid out of the encapsulation when the pump system is not operating; and a pump mechanism for generating the suction at the inlet port and pressurize the liquid through the outlet port. 
     According to some embodiments of the invention the outlet port and the drain opening are at the same side of the encapsulation. 
     According to some embodiments of the invention the system comprises a valve at the drain opening of the encapsulation. According to some embodiments of the invention the valve is a controllable valve. According to some embodiments of the invention the valve is a passive valve. 
     According to some embodiments of the invention the drain opening of the encapsulation is open at all times. 
     According to some embodiments of the invention the system is other than a centrifugal pump system. 
     According to an aspect of some embodiments of the present invention there is provided a pump system. The pump system comprises: a pump having an inlet port for generating an inflow of liquid, and an outlet port for generating an outflow of the liquid, wherein the inlet is configured to also allow a backflow of the liquid out of the pump when the pump is not operating; an air vessel, being devoid of any partition and having an interior in fluid communication with the outlet of the pump; and a conduit, sealingly passing through a top surface of the vessel to establish fluid communication between the interior of the vessel and the atmosphere. According to some embodiments of the invention the system is a centrifugal pump system. 
     Unless otherwise defined, all technical and/or scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the invention pertains. Although methods and materials similar or equivalent to those described herein can be used in the practice or testing of embodiments of the invention, exemplary methods and/or materials are described below. In case of conflict, the patent specification, including definitions, will control. In addition, the materials, methods, and examples are illustrative only and are not intended to be necessarily limiting. 
     Implementation of the method and/or system of embodiments of the invention can involve performing or completing selected tasks manually, automatically, or a combination thereof. Moreover, according to actual instrumentation and equipment of embodiments of the method and/or system of the invention, several selected tasks could be implemented by hardware, by software or by firmware or by a combination thereof using an operating system. 
     For example, hardware for performing selected tasks according to embodiments of the invention could be implemented as a chip or a circuit. As software, selected tasks according to embodiments of the invention could be implemented as a plurality of software instructions being executed by a computer using any suitable operating system. In an exemplary embodiment of the invention, one or more tasks according to exemplary embodiments of method and/or system as described herein are performed by a data processor, such as a computing platform for executing a plurality of instructions. Optionally, the data processor includes a volatile memory for storing instructions and/or data and/or a non-volatile storage, for example, a magnetic hard-disk and/or removable media, for storing instructions and/or data. Optionally, a network connection is provided as well. A display and/or a user input device such as a keyboard or mouse are optionally provided as well. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
       Some embodiments of the invention are herein described, by way of example only, with reference to the accompanying drawings. With specific reference now to the drawings in detail, it is stressed that the particulars shown are by way of example and for purposes of illustrative discussion of embodiments of the invention. In this regard, the description taken with the drawings makes apparent to those skilled in the art how embodiments of the invention may be practiced. 
       In the drawings: 
         FIGS. 1A-B  are schematic illustrations of a system for attenuating pressure pulsations, according to some embodiments of the present invention; 
         FIGS. 2A-C  are schematic illustrations showing various optional locations for a drain opening, according to some embodiments of the present invention; 
         FIGS. 3A-B  are schematic illustrations of a passive valve according to some embodiments of the present invention; 
         FIG. 4  is a schematic illustration of a deployment of a system in embodiments in which a borehole pump is employed; 
         FIG. 5  is a graph which exemplifies a velocity of a piston of a piston pump, in experiments performed obtained according to some embodiments of the present invention; 
         FIG. 6  shows air volume as a function of a static pressure at an outlet of a pump, as calculated according to some embodiments of the present invention; 
         FIGS. 7A-B  show results of experiments performed according to some embodiments of the present invention, where  FIG. 7A  shows results obtained without attenuation of pressure pulsation, and  FIG. 7B  shows results obtained with attenuation of pressure pulsation; 
         FIGS. 8A-C  are schematic illustrations of configurations in which a drain opening is formed on an encapsulation of a pump  40 ; and 
         FIGS. 9A-B  are schematic illustrations describing flow of liquid during a stage in which the pump is in operation ( FIG. 9A ), and during a stage in which the pump is not in operation ( FIG. 9B ). 
     
    
    
     DESCRIPTION OF SPECIFIC EMBODIMENTS OF THE INVENTION 
     The present invention, in some embodiments thereof, relates to flow control and, more particularly, but not exclusively, to a method and system for damping flow pressure pulsation. 
     Before explaining at least one embodiment of the invention in detail, it is to be understood that the invention is not necessarily limited in its application to the details of construction and the arrangement of the components and/or methods set forth in the following description and/or illustrated in the drawings and/or the Examples. The invention is capable of other embodiments or of being practiced or carried out in various ways. 
     The Inventors found that existing designs for attenuation of pressure pulsation in water lines are disadvantageous since they require service, whereby due to gas leaks, there is a need to fill pressurized gas from time to time. This is particularly difficult when the pulsation damper is not easily accessible, for example, in situation in which the damper is near a pump that is submerged in a borehole well under the ground. The Inventors found that existing designs for attenuation of pulsation in water lines are disadvantageous also because these designs require adjustment of the gas pressure according to the liquid pressure. This is particularly disadvantageous in situation in which the damper is used to attenuate pulsation caused by a pump that is submerged in a borehole well under the ground, because due to seasonal or other changes in the water level in the borehole the pressure varies with time, and so adjustment of the gas pressure is required repeatedly. 
     While conceiving the present invention it has been hypothesized and while reducing the present invention to practice it has been realized that attenuation of pulsation can be improved by creating an air-liquid interface in a vessel. This allows refilling the vessel with air by draining the liquid out of the vessel, without accessing the vessel. 
     Referring now to the drawings,  FIGS. 1A and 1B  illustrate a system  10  for attenuating pressure pulsations, according to some embodiments of the present invention. System  10  comprises a vessel  12  having a top surface  14 , a bottom surface  34 , an upper part  16  and a lower part  18 . Vessel  12  is preferably rigid and can be made of any material that is non-permeable to liquid and gas, e.g., to water and air. For example, vessel  12  can be made of polyvinyl chloride, stainless steel, or the like. The bottom part of vessel is formed with an inlet opening  36  for receiving liquid  50  (e.g., water) from a pump  40 . Vessel  12  is preferably above pump  40 . System  10  is preferably positioned in close proximity to as possible to pump  40 . 
     System  10  also comprises a conduit  20  in fluid communication with the lower part  18  of vessel  12 . Conduit  20  sealingly passes through conduit-receiving opening  24  in top surface  14  of vessel  12 . For example, conduit  20  can be fitted into opening  24  by means of a gasket  26  or bonding or the like, which resiliently supports conduit  20  in opening  24  and provides a leak-proof seal between the surface of opening  24  and the outer surface of conduit  20 . Conduit  20  serves for feeding a flow line  22  outside vessel  12  with liquid  50 . A pipe connector  28  provides a fluid connection between conduit  20  and flow line  22 . 
     The fluid communication between conduit  20  and lower part  18  can be achieved in more than one way. 
     In some embodiments, illustrated in  FIG. 1A , conduit  20  has one or more openings  30  at the section of conduit  20  which occupies the lower part  18  of vessel  12 . In these embodiments, inlet opening  36  serves as a conduit-receiving opening and conduit  20  sealingly extends through opening  36 , for receiving the liquid pumped out of pump  40  through its outlet  42 . A leak-proof seal between the surface of opening  36  and the outer surface of conduit  20 , can be provided, for example, by bonding or by means of an additional gasket  32  which can be of the same type and function as gasket  26  described above. 
     In some embodiments, illustrated in  FIG. 1B , conduit  20  is mounted in proximity, but does not sealingly connect, to inlet opening  36  of vessel  12 , such that there is a non-sealed fluid communication between inlet opening  36  of vessel  12  and a conduit inlet  38  of conduit  20 . Typically, conduit  20  is open at its bottom end, whereby the conduit inlet  38  is the open end of conduit  20 . Preferably, as illustrated in  FIG. 1B , the open end  38  of conduit  20  has an outwardly-flared shape so as to reduce flow losses at the interface between inlet  36  of vessel  12  and open end  38  of conduit  20 . 
     In any of the configurations, the liquid  50  fills the lower part  18  of vessel  12 . In the configuration illustrated in  FIG. 1A , liquid  50  enters vessel  12  via the opening(s)  30  at the section of conduit  20  which occupies the lower part  18  of vessel  12 . Thus, in this configuration, the liquid  50  enters conduit  20  before filling the lower part  18  of vessel  12 . In the configuration illustrated in  FIG. 1B , the non-sealed fluid communication between inlet opening  36  of vessel  12  and conduit inlet  38  of conduit  20  is utilized for filling the lower part  18  of vessel  12 , whereby liquid  50  enters the lower part  18  of vessel  12  through the gap between the inlet  36  of vessel  12  and the conduit inlet  38  of conduit  20 . Thus, in this configuration, liquid  50  from pump  40  enters the lower part  18  of vessel  12  before entering conduit  20 . 
     The top surface  14  and the side walls of the upper part  16  are sealed, so that the sealed engagement between conduit  20  and conduit-receiving opening  24  ensures that air  52  is trapped in the upper part  16  of vessel  12  when liquid  50  fills the lower part  18 . This creates an air-liquid interface  54  in vessel  12 . During parts of the pumping cycle at which the pressure generated by pump  40  is increased, the pressure in vessel  12  is increased, causing the air to compress, and interface  54  is shifted upwards. During parts of the pumping cycle at which the pressure generated by pump  40  is decreased, the opposite occurs. The pressure above interface  54  is higher than the pressure below interface  54 , interface  54  is shifted downwards and air  52  is decompressed. Thus, air  52  absorbs mechanical energy from the liquid when the pressure is increased, and releases mechanical energy to the liquid when the pressure is decreased. This reduces the peak-to-peak amplitude of the pressure, and therefore effectively attenuates the pressure pulsations at the lower part  18  of vessel  12 . Since conduit  20  is in fluid communication with the lower part  18 , the trapped air  52  also attenuates the pressure pulsations in conduit  20  and flow line  22 . 
     Based on a desired, and predetermined, volume parameter V r  that represents the maximal volume change of air  52  during compression, and based on a desired, and predetermined, pressure tolerance parameter Δp that represents the peak-to-peak pressure difference after the attenuation, the volume of vessel  12  can be selected for a given expected static pressure p s  at outlet  42  of pump  40 . In these embodiments, the volume of vessel  12  can be at least (p s +Δp)×V r ×p s /(Δp×p atm ), where p atm  is the expected atmospheric pressure outside vessel  12  (e.g., 1 atmosphere). 
     In various exemplary embodiments of the invention system  10  is devoid of any partition at air-liquid interface  54 . This is advantageous over traditional pulsation dampers, since it eliminates the need to perform maintenance operations on such partition. Another advantage is that it ensures that the pressure at lower part  18  is the same as the pressure at upper part  16 , and does not require maintaining a different pressure of the air at upper part  16 . 
     System  10  optionally and preferably also comprises one or more drain openings  44  to drain liquid  50  out of vessel  12 . Preferably, drain openings  44  are positioned to facilitate draining solely by the gravitational force. The drain openings  44  can be formed on the vessel, for example, at the bottom surface  34 , on conduit  20  itself, below the conduit-receiving opening  36  of vessel  12 , on a dedicated valve  46  connected between vessel  12  and pump  40 , or it can be formed on the encapsulation of pump  40  itself. Combinations of these embodiments, whereby openings  44  are formed on more than one of these components are also contemplated.  FIGS. 1A and 1B  schematically illustrate configurations in which a drain opening  44  is formed on a dedicated valve  46 . Configurations in which a drain opening  44  is formed on the vessel  12  are schematically illustrated in  FIGS. 2A and 2C , a configuration in which a drain opening  44  is formed on the conduit  20  is schematically illustrated in  FIG. 2B , and a configuration in which a drain opening  44  is formed on the encapsulation of pump  40  is schematically illustrated in  FIGS. 8A-C  and  9 A-B. 
     In some embodiments of the present invention, pump  40  allows backflow of the liquid through its inlet port when pump  40  is not operative. In these embodiments, there is no need for system  10  to include drain opening  44 , because the draining can be via the inlet port of pump  40 , which can serves as a draining opening when pump  40  is not operating. 
     The size of drain openings  44  is preferably selected so as to ensure that vessel  12  is completely drained over a draining period of from about 1 hour to about 10 hours. 
     In use of system  10 , the draining of liquid  50  out of vessel  12  typically empties vessel  12  from 50 during periods of time at which pump  40  is not operating (e.g., at times at which flow line is not required to deliver liquid). This allows more air to fill at least the upper portion  16  of vessel  12 . This is advantageous over traditional pulsation dampers because it does not require pressurizing the air into the damper. Rather, it only requires generating conditions for vessel  12  to be drained out of liquid  50 . An additional advantage of the present embodiments is that emptying vessel  12  allows an easier start of the pump, since it does not have to start under full load of hydrostatic pressure on flow line  22 . 
     The air preferably enters vessel  12  from above through flow line  22 . In the latter embodiments, at least during the draining stage, the flow line  22  is open to the atmosphere, or is connected to a fluidic system that is open to the atmosphere. For example, when pump  40  is used to fill a liquid tank (not shown, see  FIGS. 4, 9A and 9B , tank  116 ), flow line  22  can be an open ended at an end that is distal from system  10 . In this case, when vessel  12  is drained, air enters into flow line  22  through its open end, and than flows into vessel  12 . Flow line  22  can be an open ended at all times, or it can be provided with a valve or a tap (not shown, see  FIGS. 4, 9A and 9B , tap  118 ). When flow line  22  is provided with a valve or a tap, the valve or tap is opened automatically or manually during the draining stage. 
     When drain opening  44  is formed on a dedicated valve  46  connected between vessel  12  and pump  40  ( FIGS. 1A and 1B ), the draining through drain opening  44  is controlled by valve  46 . When drain opening  44  is formed on vessel  12  or conduit  20  it can remain open at all times, or alternatively be controlled by a valve  48  mounted at opening  44 . Any of valves  44  and  46  can be controllable valves, such as, but not limited to, a solenoid valve or a servo valve. In these embodiments, the respective valves and pump  40  are optionally and preferably controlled by the circuit of the same controller  60  (not shown in  FIGS. 2A-C , see  FIGS. 1A and 1B ), which can be mounted on pump  40  or, more preferably, remote from pump  40 . The circuit of controller  60  can be configured to open the respective valve when the operation of pump  40  is temporarily ceased, thereby synchronizing between the draining of vessel  12  and the operation of pump  40 . 
     In some embodiments of the present invention the valve that controls the drain opening  44  is a passive valve. A representative example of a passive valve suitable for the present embodiments is illustrated in  FIGS. 3A and 3B . The illustration and description below are for the case in which valve  46  is connected between the vessel and the pump (both not shown in  FIGS. 3A and 3B , see  FIGS. 1A and 1B ), but similar principles can be employed, mutatis mutandis, for making valve  48  also passive. Valve  46  comprises a valve body  64 , a first port  66 , a second port  68 , opposite to the first port  66 , and a movable peripheral sealing member  70 , such as, but not limited to, a sealing ring. Sealing member can be made, for example, of a thermoplastic, such as, but not limited to, polyoxymethylene. Drain opening(s) are formed on body  64 , facing away from the inlet  66 . 
       FIG. 3A  illustrates a closed state of valve  46 . When pump  40  is in operation, liquid from pump  40  fills port  66 , and flows into body  64 . This inflow is represented by block arrow  72 . The liquid flow biases (pushes member  70  upward) member  70  against drain opening  44  thereby at least partially preventing the liquid from leaking out of opening  44 . As the pump  40  continues pumping more liquid into body  64 , the flow of liquid continues through the central portion of member  70 , and exits through second port  68 , which serves as an outlet for feeding vessel  12  ( FIG. 1B ) or conduit  20  ( FIG. 1A ) with the liquid. This continued flow is represented by block arrow  74 .  FIG. 3B  illustrates an opened state of valve  46 . When the operation of the pump is temporarily ceased, there is no inflow into port  66  and there is no bias on member  70  against drain opening  44 . Member  70  thus falls back by the gravitational force. Design considerations for on member  70  are provided in the Examples section that follows. The liquid thus begins to flow backwards into second port  68 , which now functions as the inlet of valve  46 . This backward flow is represented by block arrow  76 . Since the pump is still connected to valve  46 , first port  66  is still filled with liquid, the liquid flows out of drain opening(s)  44 . This flow is represented by block arrows  78 . The flow out of drain opening(s)  44  continues as long as pump  40  is not in operation, or until vessel  12  is drained. Thus, valves  46  of the present embodiments toggles between a closed state when the pump is not in operation and an opened state when the pump is in operation, without being energized by any mechanism except the liquid flow itself. 
     It is appreciated that the closed state of valve  46  need not provide hermetic seal, because even in the case of a partial seal the pump can still generate flow into vessel  12  and conduit  20 , except that a portion of the liquid pumped by the pump, which is typically a small portion, for example, less than 10% or less than 5% of the flow rate generated by the pump, exits through opening  44 . 
     The present embodiments, as stated, also contemplate configurations in which drain opening  44  remains open at all times. In these embodiments the size of drain opening  44  is selected to ensure that the flow rate entering system  10  from pump  40  is substantially higher (e.g., at least 10 times or at least 10 times or at least 50 times or at least 100 times higher) than the flow rate of liquid exiting from system  10  through drain opening  44 . A representative example of a procedure for determining the size of opening  44  is provided in the Examples section that follows. 
     As stated, when pump  40  allows backflow of liquid through its inlet port during the time period at which pump  40  is not operative, the inlet port of pump  40  can serve as a draining opening. This is a typical situation when pump  40  is, for example, a centrifugal pump. In embodiments of the invention in which pump  40  does not allow the liquid to leak out of its inlet port, and in which it is desired the draining to be executed through pump  40 , pump  40  is provided with drain opening  44 . Representative examples of such configurations are shown in  FIGS. 8A-C  which are schematic illustrations of embodiments in which drain opening  44  is formed on the encapsulation  120  of pump  40 . Shown in  FIGS. 8A-C  are pump  40  connected to a liquid line, which can be for example, conduit  20 , by means of a connector  146 . Drain opening  44  is preferably formed on the upper surface of the encapsulation  120 . When pump  40  is not operating, the gravitational force generated in conduit  20  flow of liquid from vessel  12  (not shown) downwards into encapsulation  120 . This results in an overflow through drain opening  44 , allowing more liquid to flow downwards into encapsulation  120 , and ensuring drainage of vessel  12 . In embodiments in which the fluid line  22  is open ended during the darning stage, the air enters into vessel  12  during the overflow in encapsulation  120 . When drain opening  44  is formed on the encapsulation  120  of pump  40 , it can remain open at all times, as illustrated in  FIG. 8A , it can be controlled by a controllable valve  82  as illustrated in  FIG. 8B , or it can be controlled by a passive valve  84  as illustrated in  FIG. 8C . The principles and operations of valve  82  can be the same as those described above with respect to valve  48 , and the principles and operations of valve  84  can be the same as those described above with respect to valve  46 . 
     System  10  of the present embodiments can be employed to attenuate pressure pulsations generated by many types of pumps, including. In some embodiments of the present invention pump  40  is a positive displacement pump. Representative examples of positive displacement pump suitable for the present embodiments include, without limitation, reciprocating pumps (e.g., plunger pumps, piston pumps, diaphragm pumps, circumferential piston pumps), double action pumps, rotary pumps (e.g., gear pumps, screw pumps, rotary vanes, peristaltic pumps.). Also contemplated for use with system  10  are centrifugal pumps. In various exemplary embodiments of the invention pump  40  is a borehole pump. 
     It is expected that during the life of a patent maturing from this application many relevant pumps will be developed and the scope of the term pump is intended to include all such new technologies a priori. 
     Reference is now made to  FIG. 4  which is a schematic illustration of a deployment of system  10  with pump  40  in embodiments in which pump  40  is a borehole pump. System  10  and pump  40  can be deployed, for example, within a well  114  (e.g., an aquifer well), the shape of well  114  can include a wider section at its lower part, as illustrated in  FIG. 4 , or it can have a non-tapered, typically cylindrical, shape. Pump  40  serves for pumping liquid  50  (e.g., water) from well  114  into flow line  22 . From flow line pipe  22  the pumped liquid is delivered to a consumer or a consumer system (a liquid tank  116 , in the present example). Pump  40  preferably comprises a tubular encapsulation  120  having a proximal end  128  and a distal end  130 . When pump  40  is deployed within well  114 , proximal end  128  is connected to system  10  (e.g., via a connector  146 ) and distal end  130  is at a depth level that is below the depth level of proximal end  128 . In use, at least distal end  130 , but more preferably both ends  128  and  130 , are submerged under the level  150  of liquid  50 . Tubular encapsulation  120  can be made of any material that may be used under water without affecting both the water quality, and the encapsulation itself, such as, but not limited to, PVC, stainless steel and the like. Pump  40  can connect to system  10  according to any of the aforementioned configurations, which, for clarity of presentation, are not shown in  FIG. 4 . Specifically, pump  40  can connect directly, or via valve  46 , to conduit  20  (see, e.g.,  FIG. 1A ) or to the inlet  36  of vessel  12  (see, e.g.,  FIG. 1B ). System  10  is preferably positioned above the level  150  of liquid  50 . 
     In configurations in which drain opening  44  is formed on vessel  12 , on conduit  20 , or on dedicated valve  46 , system  10  is preferably deployed such that drain opening  44  is above liquid level  150 . In configurations in which drain opening  44  is formed on encapsulation  120  of pump  120 , drain opening  44  can be below liquid level  150 , as will now be explained with reference to  FIGS. 9A and 9B . 
       FIG. 9A  illustrates a stage at which pump  40  is in operation. Liquid flows upwards from pump  40  into vessel  12  and conduit  20 , the air-liquid interface  54  is formed in vessel  12 , and the pressure pulsation is attenuated by the air  52 . The liquid continues to flow through conduit  20  into the liquid line  22 . From liquid line  22  the liquid is delivered, at attenuated pressure pulsations, to the consumer or a consumer system (e.g., liquid tank  116 ). When drain opening  44  is open at all times, some liquid may also flow out of pump  40  through drain opening  44  due to the pressure generated by pump  40 . Thus, in these embodiments, the diameter of drain opening  44  is smaller (e.g., at least 2 times smaller or at least 4 times smaller or at least 8 times smaller) than the internal diameter of connector  146 . When the flow out of drain opening  44  is controlled by controllable valve  82  (see  FIG. 8B ) this valve is controlled to its closed state during this stage. When the flow out of drain opening  44  is controlled by passive valve  84  (see  FIG. 8C ), the valves assumes its closed state since its sealing member is biased onto the drain opening by the pump-generated flow. 
       FIG. 9B  illustrates a stage at which pump  40  is not in operation. The liquid flows downwards from vessel  12  back into pump  40 , exits through drain opening  44 , and vessel  12  is emptied. During the backflow of the liquid, more air enters through the open end of liquid line  22  and flow through liquid line  22  and conduit  20  into vessel  12 . When flow line  22  is provided with a valve or a tap, the valve or tap is opened automatically or manually during this stage. When the flow out of drain opening  44  is controlled by controllable valve  82  (see  FIG. 8B ) this valve is controlled to its opened state during this stage. When the flow out of drain opening  44  is controlled by passive valve  84  (see  FIG. 8C ), the valves assumes its opened state since its sealing member is no longer biased by the pump-generated flow. 
     Pump  40  is particularly useful for pumping liquid  50  from wells having a borehole diameter of from about 9 cm to about 25 cm, or from about 10 cm to about 20 cm (approximately equivalent to a borehole diameter of from about 4 inches to about 8 inches). In these preferred embodiments, tubular encapsulation  120  has a diameter from about 8 cm to about 24 cm, or from about 8 cm to about 19 cm, so as to fit into wells having such borehole diameters. 
     Preferably, pump system is a double action reciprocating pump system. In experiments performed by the present inventors, a double action reciprocating pump system constructed according to the teachings described herein was able to provide more than 3 cubic meters per hour, at pump head of about 30 meters. 
     A representative example of a borehole pump suitable according to some embodiments of the present invention is described in U.S. Pat. No. 10,753,355, the contents of which are hereby incorporated by reference. 
     Controller  60 , which may be part of system  10  or pump  40  or a system combining system  10  and pump  40 , is shown external to encapsulation  120 , but need not necessarily be the case, since in some embodiments of the present invention controller is encapsulated within encapsulation  120 . Control electrical lines can be connected to one or more components of pump  40  (e.g., to an electrical motor thereof). In embodiments in which controllable valves are employed by system  10 , control electrical lines can be connected to the controllable valves for synchronizing the opening and closing of these valves with the operation of pump  40 . Control electrical lines are all collectively represented in  FIG. 4  by line  104 . 
     The circuit of controller  60  is configured to control the operations of one or more pumps  40 . In particular, the circuit of controller  60  is preferably configured for temporarily ceasing the operation of pump  40 . The temporary cessation of the operation can be automatically, e.g., according to a predetermined timing protocol (for example, temporary cessation during night hours), or in response to user input. When system  10  does not include controllable valves, the temporary cessation of the pump&#39;s operation by itself generates the condition for vessel  12  to drain out the liquid  50  either via a passive valve (e.g., valve  46 , see  FIGS. 3A and 3B ), or, when drain opening  44  is opened at all time, by the continuous leak of liquid through drain opening  44  and the absence of liquid inflow into vessel  12 . 
     As used herein the term “about” refers to ±10% 
     The terms “comprises”, “comprising”, “includes”, “including”, “having” and their conjugates mean “including but not limited to”. 
     The term “consisting of” means “including and limited to”. 
     The term “consisting essentially of” means that the composition, method or structure may include additional ingredients, steps and/or parts, but only if the additional ingredients, steps and/or parts do not materially alter the basic and novel characteristics of the claimed composition, method or structure. 
     As used herein, the singular form “a”, “an” and “the” include plural references unless the context clearly dictates otherwise. For example, the term “a compound” or “at least one compound” may include a plurality of compounds, including mixtures thereof. 
     Throughout this application, various embodiments of this invention may be presented in a range format. It should be understood that the description in range format is merely for convenience and brevity and should not be construed as an inflexible limitation on the scope of the invention. Accordingly, the description of a range should be considered to have specifically disclosed all the possible subranges as well as individual numerical values within that range. For example, description of a range such as from 1 to 6 should be considered to have specifically disclosed subranges such as from 1 to 3, from 1 to 4, from 1 to 5, from 2 to 4, from 2 to 6, from 3 to 6 etc., as well as individual numbers within that range, for example, 1, 2, 3, 4, 5, and 6. This applies regardless of the breadth of the range. 
     Whenever a numerical range is indicated herein, it is meant to include any cited numeral (fractional or integral) within the indicated range. The phrases “ranging/ranges between” a first indicate number and a second indicate number and “ranging/ranges from” a first indicate number “to” a second indicate number are used herein interchangeably and are meant to include the first and second indicated numbers and all the fractional and integral numerals therebetween. 
     It is appreciated that certain features of the invention, which are, for clarity, described in the context of separate embodiments, may also be provided in combination in a single embodiment. Conversely, various features of the invention, which are, for brevity, described in the context of a single embodiment, may also be provided separately or in any suitable subcombination or as suitable in any other described embodiment of the invention. Certain features described in the context of various embodiments are not to be considered essential features of those embodiments, unless the embodiment is inoperative without those elements. 
     Various embodiments and aspects of the present invention as delineated hereinabove and as claimed in the claims section below find experimental support in the following examples. 
     EXAMPLES 
     Reference is now made to the following examples, which together with the above descriptions illustrate some embodiments of the invention in a non-limiting fashion. 
     Example 1 
     Design Considerations 
     Pressure Variations and Air Volume 
     In positive displacement pumps, the pressure variations in the flow line depends on the pump&#39;s duty cycle. The duty cycle is defined as the ratio between the time periods during which the pump delivers water to the flow line at lower rate and at maximum rate. For instance, in a simple plunger or piston pump, the duty cycle is defined as 1−(acceleration time)/(de-acceleration time) or 1−(dead time)/(full stroke time), where the dead time is the time the piston halts at the end of the stroke before it changes the stroke direction. A representative Example of a graph describing the velocity of a piston of a piston pump is shown in  FIG. 5 . The pump&#39;s duty cycle in this case can be expressed as t 1 /t 2 . Typical values for the duty cycle in plunger and piston pumps are from about 0.7 to about 0.9. Higher values for the duty cycle correspond to less expected pressure pulsation. 
     The volume change of the trapped air in vessel  12  depends inter alia on the duty cycle. Specifically, the rate at which the volume of air in vessel  12  varies can be estimated as V S ·(1−T), where V S  is the stroke volume of the pump and T is its duty cycle. For example, when the full stroke volume of a pump  40  is about 100 ml, and its duty cycle is about 0.7, a rough estimate for the variation rate of the volume of trapped air in vessel  12  is about 30 ml per stroke. 
     The volume change of the trapped air in vessel  12  also depends on the expected static pressure at the output of pump  40 . Higher static pressure corresponds to higher compression of the air. In various exemplary embodiments of the invention the volume of vessel  12  is designed and constructed to reduce all shocks of pressure in the liquid for an expected range of static pressure at the pump&#39;s outlet. This is advantageous over traditional systems that require an adjustment of the gas pressure in response to the pump&#39;s static pressure. According to some embodiments of the present invention the desired volume of captivated air is calculated for atmospheric pressure. The air is pressurized only when the pump applies the static head. 
     Ideally, the trapped air would reduce the pressure variations to almost zero. However, such ideal situation is rare, if at all attainable. Therefore, the volume change of the trapped air is calculated for a given tolerance Δp of pressure fluctuations in the flow line. 
     This example considers a pump in operation with an average static pressure of p s . The volume of air in vessel  12  at this pressure is denoted V s . The system pressure increases by the defined tolerance Δp. The air volume at a pressure of p s +Δp is denoted V c . The difference between V s  and V c  is denoted V r , and is used as an input volume parameter representing the amplitude of volumetric compression of the air while the pressure varies within the tolerance Δp. V r  is given by a percentage of the stroke volume of the piston or plunger as derived from the duty cycle or velocity profile (see  FIG. 5 ). 
     Using an ideal gas approximation for the air, and neglecting temperature variations during a single stroke of the pump, the following relations can thus be defined: 
         p*V =constant  (EQ. 1)
 
         p   s   *V   s =( p   s   +Δp )* V   c   (EQ. 2)
 
         V   c   =V   s   −V   r ,  (EQ. 3)
 
     leading to the following expression for V s : 
     
       
         
           
             
               
                 
                   
                     
                       V 
                       s 
                     
                     = 
                     
                       
                         
                           ( 
                           
                             
                               p 
                               s 
                             
                             + 
                             
                               Δ 
                               ⁢ 
                               p 
                             
                           
                           ) 
                         
                         * 
                         
                           V 
                           r 
                         
                       
                       
                         Δ 
                         ⁢ 
                         p 
                       
                     
                   
                   . 
                 
               
               
                 
                   ( 
                   
                     EQ 
                     . 
                     
                         
                     
                     ⁢ 
                     4 
                   
                   ) 
                 
               
             
           
         
       
     
     EQ. 4 provides the air volume at static pressure that can attenuate any pressure pulsation provided by a pump having a static pressure of p s  to be within the predetermined tolerance Δp. 
     Using the aforementioned ideal gas approximation, EQ. 1, the pressure p s  and volume V s  satisfy: 
         p   s   ·V   s   =p   atm   ·V   atm .  (EQ. 5)
 
     EQ. 5 can then be used together with EQ. 4 to estimate the volume of the air at atmospheric pressure V atm  for a given predetermined values of Δp and V r : 
     
       
         
           
             
               
                 
                   
                     V 
                     
                       at 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       m 
                     
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             p 
                             s 
                           
                           + 
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             p 
                           
                         
                         ) 
                       
                       · 
                       
                         V 
                         r 
                       
                       · 
                       
                         p 
                         s 
                       
                     
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         p 
                         · 
                         
                           p 
                           
                             at 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             m 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     EQ 
                     . 
                     
                         
                     
                     ⁢ 
                     6 
                   
                   ) 
                 
               
             
           
         
       
     
     As a representative example, consider a piston pump characterized by a stroke volume of 100 ml, and a predetermined volume parameter V r  which is 20% of the pump&#39;s stoke volume, namely 14=20 ml.  FIG. 6  shows the calculated value of V atm  as a function of p s , for three different values of the pressure tolerance parameter Δp: 0.1 bar, 0.15 bar, and 0.2 bar. 
     Size of Drain Opening 
     When drain opening  44  is opened at all time, its size is optionally and preferably selected to reduce losses during the times at which the pump is operative (e.g., during day times) while allowing the vessel to be emptied through drain opening  44  during the times at which the pump is not operative (e.g., during night times). For example, when the pump is powered by solar energy pump, the size of drain opening  44  can be selected such that the maximal time period for draining the vessel is about ten hours (e.g., from about 1 hour to about 10 hours). 
     The flow losses in m 3 /s through drain opening  44  for at a constant or average static pressure, can be estimated as: 
         Q   l   =C   DC   ·A   o ·√{square root over (2· g·h )},  (EQ. 7)
 
     where C DC  is the characteristic discharge coefficient through drain opening  44 , A o  is the cross-sectional area of drain opening  44 , g the gravitational constant, and h the head of liquid that is in fluid communication with drain opening  44 . For a circular shape of drain opening  44  with diameter d 0 , A o  is given by 
     
       
         
           
             
               
                 
                   
                     A 
                     o 
                   
                   = 
                   
                     
                       π 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         d 
                         o 
                         2 
                       
                     
                     4 
                   
                 
               
               
                 
                   ( 
                   
                     EQ 
                     . 
                     
                         
                     
                     ⁢ 
                     8 
                   
                   ) 
                 
               
             
           
         
       
     
     To calculate the draining time period t d  a dynamic approach is employed, since the head and pressure change over time. Integrating and reorganizing EQ. 7, the following expression is obtained for the draining time period t d  in seconds: 
     
       
         
           
             
               
                 
                   
                     t 
                     d 
                   
                   = 
                   
                     
                       
                         A 
                         c 
                       
                       
                         
                           C 
                           
                             D 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             C 
                           
                         
                         * 
                         
                           A 
                           o 
                         
                       
                     
                     * 
                     
                       ( 
                       
                         
                           
                             h 
                             i 
                           
                         
                         - 
                         
                           
                             h 
                             f 
                           
                         
                       
                       ) 
                     
                     * 
                     
                       ( 
                       
                         
                           2 
                           g 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   
                     EQ 
                     . 
                     
                         
                     
                     ⁢ 
                     9 
                   
                   ) 
                 
               
             
           
         
       
     
     where, A c  is the cross-sectional area of the container being emptied (conduit  20 , vessel  12 , flow line  22 ), and h i  and h f  are upper and lower bounds for the head. Since draining is typically of the vessel  12 , the conduit  20 , and the flow line  22  which is connected to the conduit  20 , the draining time period is the sum of the draining times of each container. 
     For example, assuming the same diameter for both conduit  20  and flow line  22 , the combined draining time t dc  is given by: 
     
       
         
           
             
               
                 
                   
                     t 
                     
                       d 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       c 
                     
                   
                   = 
                   
                     
                       
                         
                           2 
                           g 
                         
                       
                       
                         
                           C 
                           
                             D 
                             ⁢ 
                             C 
                           
                         
                         * 
                         
                           A 
                           o 
                         
                       
                     
                     * 
                     
                       ( 
                       
                         
                           
                             A 
                             cp 
                           
                           * 
                           
                             ( 
                             
                               
                                 
                                   h 
                                   
                                     i 
                                     ⁢ 
                                     p 
                                   
                                 
                               
                               - 
                               
                                 
                                   h 
                                   
                                     f 
                                     ⁢ 
                                     p 
                                   
                                 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           
                             A 
                             
                               c 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               d 
                             
                           
                           * 
                           
                             ( 
                             
                               
                                 
                                   h 
                                   id 
                                 
                               
                               ⁢ 
                               
                                   
                               
                               - 
                               
                                 
                                   h 
                                   fd 
                                 
                               
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   
                     EQ 
                     . 
                     
                         
                     
                     ⁢ 
                     10 
                   
                   ) 
                 
               
             
           
         
       
     
     where the subscript p relates to the combined head of the conduit  20  and the flow line  22  and the subscript d relates to the head of vessel  12 . 
     As a numerical example, the values of the parameters in Table 1, below, are assumed. 
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
             
            
               
                   
                 d 0   
                 0.6 
                 mm 
               
               
                   
                 A 0   
                 2.826 × 10 −7   
                 m 2   
               
            
           
           
               
               
               
            
               
                   
                 C DC   
                 0.8 
               
            
           
           
               
               
               
               
            
               
                   
                 g 
                 9.81 
                 m/s 2   
               
               
                   
                 A cp   
                 0.00055 
                 m2 
               
               
                   
                 A cd   
                 0.005869 
                 m2 
               
               
                   
                 h fp   
                 0.72 
                 m 
               
               
                   
                 h ip   
                 50 
                 m 
               
               
                   
                 h fd   
                 0.001 
                 m 
               
               
                   
                 H id   
                 0.71 
                 m 
               
               
                   
                   
               
            
           
         
       
     
     Substituting the values of the parameters listed in Table 1 into EQ. 10, the obtained draining time is t dc ≈4.5 hours. Subsisting the values of the parameters listed in Table 1 into EQ. 7, the obtained flow losses are Q l ≈7.083×10 −6  m 3 /s. 
     Passive Valve 
     Use of a passive valve, such as the valve illustrated in  FIGS. 3A and 3B  is advantageous since it allows using larger drain opening, since it is not necessary to apply considerations regarding flow losses. A larger drain opening saves on the draining time and also reduces the risk of clogging due to sediments, biological material, or other impurities in the water. 
     This Example assumes an operating range of the pump from about 10 to about 50 liters per minute, and a one-and-a-half-inch diameter at the valve&#39;s ports  66  and  68 , so that the water velocities are from about 0.146 to about 0.73 m/s. 
     To assess if this velocity is sufficient to bias the member  70  against the opening  44 , the forces acting upon member  70  are considered. The weight F W  of member  70  is given by: 
         W=mg=ρ   d   ·A·h·g   (EQ. 11)
 
     where m is the mass of member  70 , ρ d  is the density of member  70 , and A and h are the area and thickness of member  70 , respectively. Taking buoyancy into account the following expression for the effective weight is obtained: 
         F   w =(ρ d −ρ w )· A·h·g   (EQ. 12)
 
     The drag force during the operation of the pump is given by: 
     
       
         
           
             
               
                 
                   
                     F 
                     D 
                   
                   = 
                   
                     
                       C 
                       D 
                     
                     · 
                     
                       ρ 
                       w 
                     
                     · 
                     A 
                     · 
                     
                       
                         v 
                         2 
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   
                     EQ 
                     . 
                     
                         
                     
                     ⁢ 
                     13 
                   
                   ) 
                 
               
             
           
         
       
     
     where C D  is the coefficient of the drag, and ρ w  and v are the density and velocity of the water, respectively. 
     The equilibrium velocity at which the drag force F D  balances the effective weight F W  is, therefore: 
     
       
         
           
             
               
                 
                   
                     
                       v 
                       eq 
                     
                     = 
                     
                       
                         
                           2 
                           · 
                           
                             ( 
                             
                               
                                 ρ 
                                 d 
                               
                               - 
                               
                                 ρ 
                                 w 
                               
                             
                             ) 
                           
                           · 
                           h 
                           · 
                           g 
                         
                         
                           
                             C 
                             D 
                           
                           · 
                           
                             ρ 
                             w 
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   
                     EQ 
                     . 
                     
                         
                     
                     ⁢ 
                     14 
                   
                   ) 
                 
               
             
           
         
       
     
     wherein any velocity above ν eq  is sufficient to bias member  70  against opening  44 . 
     As a numerical example, the values of the parameters in Table 2, below, are assumed. Substituting those values into EQ. 14, an equilibrium velocity of about 0.15 m/s is obtained. It is appreciated that the value of v eq  can be reduced using a lower density material. 
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 2 
               
               
                   
                   
               
             
            
               
                   
                 ρ w   
                 997 
                 kg/m 3   
               
               
                   
                 ρ d   
                 1410 
                 kg/m 3   
               
               
                   
                 g 
                 9.81 
                 m/s 2   
               
               
                   
                 h 
                 0.003 
                 m 
               
            
           
           
               
               
               
            
               
                   
                 C D   
                 1.1 
               
               
                   
                   
               
            
           
         
       
     
     Example 2 
     Experimental Results 
     Experiments were conducted using a prototype system as illustrated in  FIG. 1B . The volume of the vessel  12  was 3 liters, and the pump was a piston pump. The pressure generated by the pump was adjusted by a pressure regulator at the end of the flow line  22 . The speed of the piston was measured by the controller of the pump. In this experiment no drain opening was employed. 
     The results are shown in  FIGS. 7A and 7B , where  FIG. 7A  shows the pressure (upper line) and the velocity (lower line) at the outlet of the pump, without pulsation attenuation, and  FIG. 7B  shows the pressure and the velocity at the outlet of the pump, with pulsation attenuation using the prototype system. 
     As shown, the pressure at the outlet of the pump is oscillatory, and the system of the present embodiments successfully stabilizes the pressure, hence attenuates the pressure pulsation. 
     Although the invention has been described in conjunction with specific embodiments thereof, it is evident that many alternatives, modifications and variations will be apparent to those skilled in the art. Accordingly, it is intended to embrace all such alternatives, modifications and variations that fall within the spirit and broad scope of the appended claims. 
     It is the intent of the applicant(s) that all publications, patents and patent applications referred to in this specification are to be incorporated in their entirety by reference into the specification, as if each individual publication, patent or patent application was specifically and individually noted when referenced that it is to be incorporated herein by reference. In addition, citation or identification of any reference in this application shall not be construed as an admission that such reference is available as prior art to the present invention. To the extent that section headings are used, they should not be construed as necessarily limiting. In addition, any priority document(s) of this application is/are hereby incorporated herein by reference in its/their entirety.