Abstract:
Systems and apparatus for suppressing/controlling pressure spikes in a fluid pipe system are described. In one aspect, an apparatus for controlling pressure spikes in a fluid pipe system includes, for example, a fluid pressure spike suppression pipe (“damper pipe”) portion with multiple openings for connecting to at least two network pipes in a fluid system pipe network. The damper pipe has a diameter that is larger than respective diameters of the network pipes within which fluid pressure spikes are to be suppressed. First and second openings for connecting to the network pipes are respectively positioned at proximal and distal ends of the damper pipe. The first opening in the damper pipe is for fluid ingress into the damper pipe via a first pipe network pipe. The second opening in the damper pipe is for fluid egress out of the damper pipe and into a second network pipe.

Description:
BACKGROUND 
       [0001]    Sudden opening or closure of a control valve, or tap, can cause a pressure surge or spike in plumbing as a result of forcing a fluid in motion (or, in some conditions, a gas) to stop or change direction suddenly. This phenomenon is called water or fluid hammer, and it can cause ruptures and leaks in pipes and fittings. Water hammer creates pressure waves that travel upstream and downstream of the closed/opened taps at nearly the speed of sound. There are a number of standard techniques that attempt to minimize the pressure spikes resulting from water hammer. In pipe networks, for example, common techniques to address water hammer include use of surge vessels, equilibrium tanks, pressure relief valves, and suction lines around the booster pump. In residential and light commercial/industrial applications, an air chamber and water hammer arrestor may be used for water hammer control. 
         [0002]      FIG. 1  shows a prior art pipe network that employs an air chamber to address undesirable pressure surges associated with water hammer. As shown in  FIG. 1 , this is a conventional technique wherein a short vertical section of pipe is filled with trapped air. In this scenario, when a valve is suddenly closed, the air chamber acts as a shock absorber. Air in this chamber compresses and cushions the resulting shock. The disadvantage of this conventional technique/device is that after time, the air pocket is eventually absorbed into/by the water, which renders the device ineffective. To remedy this limitation, one must drain water out of the system to recreate the air pocket. Referring to  FIG. 2 , a prior art arrestor device designed to address water hammer in a pipe network is shown. As shown in  FIG. 2 , this solution to water hammer is similar to that of the air chamber of  FIG. 1 , with the exception that the air pocket in the arrestor is separated and sealed from the water by a piston with an “O” ring or diaphragm so that the air cannot be absorbed by water. The air pocket for this type of water hammer control device is pressurized to a certain limit. One disadvantage of this “arrestor” technique/device is that the pressure level of the air pocket is typically too high for the device to work properly for low pressure applications. Another disadvantage of this device is that the moving piston generally makes it noisy. Furthermore, both the air chamber and water hammer arrestor devices have the disadvantage of being metallic (usually copper); thus, they are susceptible to corrosion and erosion. 
       SUMMARY 
       [0003]    Systems and apparatus for suppressing/controlling pressure spikes in a fluid pipe system are described. In one aspect, an apparatus for controlling pressure spikes in a fluid pipe system includes, for example, a fluid pressure spike suppression pipe (“damper pipe”) portion with multiple openings for connecting to at least two network pipes in a fluid system pipe network. The damper pipe has a diameter that is larger than respective diameters of the network pipes within which fluid pressure spikes are to be suppressed. First and second openings for connecting to the network pipes are respectively positioned at proximal and distal ends of the damper pipe. The first opening in the damper pipe is for fluid ingress into the damper pipe via a first pipe network pipe. The second opening in the damper pipe is for fluid egress out of the damper pipe and into a second network pipe. 
         [0004]    This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used as an aid in determining the scope of the claimed subject matter. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0005]      FIG. 1  shows a prior art pipe network that employs an air chamber to address undesirable pressure surges associated with water hammer. 
           [0006]      FIG. 2  shows a prior art water pipe network that employs an arrestor device to compensate for sudden water pressure surges associated with water hammer phenomena. 
           [0007]      FIGS. 3(   a ) and  3 ( b ) show exemplary embodiments of novel water/fluid pressure spike suppression pipe portions (“damper pipes”) in respective pipe networks. 
           [0008]      FIG. 4  shows a pipe network that includes a novel fluid hammer damper pipe (e.g., a “fluid pressure spike damper pipe”) with balloons installed in a typical residential or commercial plumbing network comprising a main pipe and a control valve, according to one embodiment. 
           [0009]      FIGS. 5(   a ) through  5 ( d ) show a set of exemplary data showing how a plastic embodiment of the fluid pressure spike suppression (“FPSS”)/damper/control pipe of  FIG. 3  performs as compared to a large commercial water hammer arrestor. Specifically: 
           [0010]      FIG. 5(   a ) shows water hammer results following valve closure in the test environment without using FPSS pipe device  302 ; 
           [0011]      FIG. 5(   b ) shows water hammer results following valve closure in the test environment using a standard prior art large water hammer arrestor; 
           [0012]      FIG. 5(   c ) shows exemplary water hammer results following valve closure in the test environment using a plastic embodiment of the FPSS pipe  302  of this disclosure without compressible inserts (e.g., balloons filled with air/gas), according to one embodiment; and 
           [0013]      FIG. 5(   d ) shows exemplary water hammer results following valve closure in the test environment using a FPSS pipe  302  with three balloon inserts  306  encapsulating air at a pressure equal to the normal pressure in the fluid pipe network, according to one embodiment. 
       
    
    
     DETAILED DESCRIPTION 
     An Exemplary Plastic Water Hammer Damper 
       [0014]      FIGS. 3(   a ) and ( b ), which are collectively referred to hereinafter as  FIG. 3 , show exemplary embodiments of a fluid pressure spike suppression (“FPSS”)/damper (“FPSD”)/control pipe  302 . In this particular implementation, the novel FPSS device  302  is for suppressing fluid (e.g., water) hammer in residential and commercial fluid systems comprising plastic and/or metallic pipes—although, in another implementation, the concepts disclosed in this specification can also be used in gas systems, as compared to fluid systems, to dissipate sudden gas pressure spikes. In this implementation, the device comprises the FPSS pipe/vessel portion  302  (e.g., made from Polychloroethene or “uPVC” or “PVC”). FPSS  302 , which is hereinafter often referred to as a “damper pipe,” has a larger pipe diameter than the connecting pipes  304  ( 304 - 1  and  304 - 2 ) for which pressure spikes in fluids that typically result in water hammer are to be controlled/suppressed. To this end, and referring to either of  FIG. 3(   a ) or  3 ( b ), first and second network pipe portions  304 - 1  and  304 - 2  are operatively coupled to the damping pipe  302  in a substantially perpendicular orientation to the length of the damping pipe  302 . Network pipe  304 - 1  serves for fluid ingress (an “inlet”) to provide fluid flow into the damper pipe  302 . Please note that as the fluid enters the damper pipe  302  from inlet pipe  304 - 1 , the fluid is substantially perpendicularly redirected along the length of the damper pipe  302  for egress out the opposite end of the damper pipe  302  via network pipe  304 - 2  (“outlet”). Please note that in this exemplary implementation, the second portion is also perpendicular to the orientation of the damping pipe  302 . This network pipe  304  orientation to the damping pipe, which results in fluid flow through the length of the damping pipe (ingress at a proximal end  306  and egress at a distal end  308 ) in normal fluid flow operation, as well as during operation to suppress a fluid pressure spike, serves to dampen any fluid pressure spike in a substantially optimal manner. In this particular implementation, fluid ingress or egress at location(s) other than a proximal or distal end (e.g., a centralized location with respect to the length of the damper pipe) of the damper pipe  302  will not as effectively mitigate fluid pressure surges in system  300 . 
         [0015]    Although the diameter of pipe  304 - 1  may be the same as the diameter of pipe  304 - 2 , the diameter of a pipe  304  need not be the same and the diameter of a different pipe  304 . Additionally, although pipe  304 - 1  is labeled as an “outlet” and pipe  304 - 2  is labeled as an “inlet,” these labels illustrate but one exemplary embodiment of fluid flow direction. Different complementary inlet/outlet (fluid flow) configurations can be used for pipes  304  without departing from the scope of the described FPSS  302 . Damper pipe  302  does not rely on use of any bladder or water permeable screen. Moreover, damper pipe  302  is always filled with fluid, meaning that it has different characteristics and does not operate as a conventional air or vacuum chamber to alleviate pressure spikes resulting from fluid hammer. As such, the mechanism (e.g., gas) used in mitigating fluid pressure spikes will not be absorbed over time by the fluid, as in the case of an air chamber. 
         [0016]    Referring to  FIG. 3(   a ) and TABLE 1, the following exemplary design parameters of TABLE 1 pertain to but one embodiment of many possible embodiments of the damper pipe  302 . As such, these design parameters offer preliminary guidelines, but damper pipe  302  can work properly to dissipate pressure spikes resulting from water hammer conditions outside the parameters of TABLE 1. 
         [0000]    
       
         
               
             
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                 EXEMPLARY FPSS/FPSD PIPE DESIGN PARAMETERS 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 D O  &gt; 4D n   
               
               
                   
                 L T  ≧ 4D O   
               
               
                   
                 wherein, 
               
               
                   
                 D O  = damper pipe inside diameter; 
               
               
                   
                 D n  = diameter of the network pipe for which water hammer is to be 
               
               
                   
                 controlled; and 
               
               
                   
                 L T  = total length for the damper pipe. 
               
               
                   
                   
               
             
          
         
       
     
         [0017]    In this implementation, the damper pipe (pipe  302 ) diameter is large enough so as to expand easily under water pressure. This allows damper pipe  302  to swell in the radial direction; thus it would be able to store additional fluid resulting from fluid pressure spikes for a time period long enough to allow the pressure spike to travel to the boundary and to be reflected back with negative pressure spike, resulting in a reduction of pressure and relief to the main pipe(s)  304 . Thus, the system  302  absorbs a fluid pressure spike to quickly restore normal pressure to network pipes  304 . 
       Alternate Embodiments 
     Configurable Balance between Pressure Spike Suppression Materials and Various Operating Pressure Environments 
       [0018]    In one implementation, for example, and to enhance the performance of the device  302 , a number of air-filled balloon(s)  310  (e.g., balloons  310 - 1  through  310 -N) of spherical shape are inserted into the damper pipe  302 . Each balloon  310  is comprised of a non-porous plastic or rubber material (not a cellular foam or foam-like material) that is inflated with gas (e.g., air or other gas). Since the gas inside each of the one or more balloons  310  is highly elastic, the balloon(s) will shrink when subjected to fluid pressure surge(s) during water hammer occurrence and expand when fluid pressure is reduced. Because the non-porous balloons  310  are not foam, the gas in the balloons will not be absorbed by the substantially continuous presence of liquid in the chamber  302 , wherein the presence is independent of fluid pressure spike(s). 
         [0019]    In this embodiment, a balloon  310  is inflated with gas (e.g., air) to a select target and configurable pressure that is based on characteristics of the selected balloon material and the operating pressure of the pipe network  300 . In one implementation, for example, the gas pressure inside these balloon(s) is greater than local atmospheric pressure (absolute) but less than the normal water pressure just upstream of a control valve (e.g., control valve  404  of  FIG. 4 ) plus the additional expected pressure spike (if no water hammer control is used). Low gas pressure inside the balloons may be suited to low pressure applications. High gas pressure inside the balloons may be suited for high pressure applications and applications where there may be high fluid pressure spikes, including systems that typically operate at low pressures. At the limit, when the gas pressure inside the balloon is equal to the pipe network normal pressure plus the expected pressure spike, the balloon itself will not shrink. For this reason, the gas pressure inside the balloons is selected so that it is not low enough to be reduced significantly during normal operational conditions and not high enough to reach levels beyond the maximum pressure levels recommended for the pipe(s). 
         [0020]    The following exemplary design parameters shown in TABLE 2 pertain to but one embodiment of the possible alternate embodiments of the FPSS/FPSD device  302  (please see  FIG. 3(   a )) comprising one or more balloons  310  or balloon-like devices, which are referred to collectively as “balloon(s).” As such, these design parameters offer preliminary guidelines, but this alternative embodiment of the damper pipe  302  can work properly to dissipate pressure spikes resulting from water hammer conditions outside these parameters. 
         [0000]    
       
         
               
             
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                 EXEMPLARY FPSS/FPSD PIPE 
               
               
                 BALLOON DESIGN PARAMETERS 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 L b  &lt; 0.8L T   
               
               
                 D b  ≦ 0.9D O   
               
               
                 P atm  ≦ P b  ≦ P n  + N 
               
               
                 wherein, 
               
               
                 D b  = Balloon diameter, 
               
               
                 L b  = Summation of balloon diameters, 
               
               
                 P atm  = Local atmospheric pressure (absolute), 
               
               
                 P b  = Air pressure inside balloon (absolute), 
               
               
                 P n  = Normal network pressure just upstream of control (absolute), and 
               
               
                 N = Pressure increase at the location of the damper due to the spike 
               
               
                 from water hammer if no pressure spike suppression device is used. The 
               
               
                 magnitude of this variable is obtained by subtracting the normal pressure 
               
               
                 before spike from the maximum pressure level after pressure spike due 
               
               
                 to fluid transient. 
               
               
                   
               
             
          
         
       
     
         [0021]    In one implementation, and because different materials have corresponding elastic or tensile strength properties, respective ones of the balloon(s)  310  are comprised of material that is particularly selected to correspond to target in-balloon gas pressure level(s) to respectively allow or to constrain volume contraction or expansion of the respective balloons. This provides for the balloon material(s) to be selectively matched with target internal gas pressures when configuring the design of the damper device  302  for a particular fluid network application (e.g., high, low, and/or medium pressure application(s)). 
       Retaining Mesh to Encapsulate Balloon in High Pressure Operations 
       [0022]    In one embodiment, and as shown in  FIGS. 3(   a ) and  3 ( b ), one or more balloons  310  is/are encapsulated in a retaining mesh  312 . Such a retaining mesh  312  is shown as a matrix of intersecting lines on a balloon  310 . A balloon  310  without the retaining mesh  312  is shown as balloon  310 -N in  FIG. 3(   b )). The retaining mesh  312  maintains a fixed balloon volume even when the gas pressure that has been configured inside the balloon would otherwise expand the balloon&#39;s diameter (i.e., if the mesh were not there to constrain such expansion). This is in contrast to conventional water hammer suppression systems, wherein pressure in such conventional systems may be limited to a maximum, which is when the balloon diameter is equal to the inner diameter of the water hammer suppression chamber. 
         [0023]    In one embodiment, the retaining mesh  312  comprises wire and/or other non-elastic material. A balloon  310  encapsulated in a retaining mesh is hereinafter often referred to as a “caged balloon.” The mesh  312  is constructed such that it has holes between respective portions of the mesh, wherein each hole allows a configurable portion of fluid pressure in the FPSS chamber  302  to influence a configurable portion of the surface of the balloon for corresponding contraction of the balloon in desired circumstances (e.g., fluid pressure spikes of configurable magnitude). In one implementation, the size of the holes in the encapsulating mesh is configured based on one or more of: (a) elastic and/or tensile characteristics of the balloon material; (b) normal operating pressure of the pipe network that includes the FPSS device  302 ; and (c) internal pressure of the gas inside the balloon. One exemplary use of one or more caged balloons is in a fluid pipe network that operates normally at high pressure and wherein corresponding fluid pressure spikes will be high pressure. In this scenario, and to suppress fluid hammer in such a system, the gas pressure inside the balloon(s)  310  is increased to accommodate for corresponding fluid pressure spikes in the system. 
         [0024]    In one implementation, low gas pressure in the balloons  310  is used to suppress fluid hammer in a low pressure system. In this scenario, one or more caged balloons  310  may or may not be used, as desired, in the same suppression chamber  302  to address a range of system conditions. For example, in one implementation, a combination of non-caged balloons  310  and caged balloons  310  are used in a damper pipe  302  that is targeted/installed for/in a low pressure system to address any occurrence of a high pressure fluid pressure spike in the system. In another example, caged balloons and balloons without cages could be used in the same chamber  302  so that the caged balloons take care of positive pressure spikes (pressure increases) and balloons without cages take care of low pressure spikes (negative pressures) by expanding according to Boyle&#39;s law. 
         [0025]    The described implementations of system  300 , wherein a retaining mesh  312  is used to constrain expansion of a balloon  310 , are in contrast to conventional water hammer suppression devices that may not be useful; for example, to address water hammer in high and/or low pressure systems. This is because, in such standard systems, pressurizing a balloon may cause corresponding balloon volume expansion, and de-pressurizing a balloon may cause corresponding balloon volume collapse. For instance, a conventional system for water hammer suppression may prescribe use of crushable plastic foam (or cellular plastic) in a pressure vessel to address negative effects of water hammer. Cellular foam is generally considered to be a substance formed by trapping many gas bubbles in a liquid or solid. In such a standard system: (a) the inside pressure of bubbles in cellular foam or other container is generally limited; (b) elasticity of the foam and its response to loading and unloading conditions is generally too poor/limited to handle surge pressures in pipelines; (c) air bubbles in the foam will likely dissipate over time responsive to water hammer shock (or otherwise be absorbed into the fluid in the system); and (d) a prohibitively large volume of foam may be required to provide a desired air (bubble) volume. 
         [0026]      FIG. 4  shows an exemplary FPSS/FPSD device  302  with balloons  310  installed in a typical residential or commercial plumbing network comprising a main pipe  402  and a control valve  404 , according to one embodiment. 
       Plastic Water Hammer Damper 
       [0027]    In one implementation, damper pipe  302  is made of plastic. In this implementation, there are no corrosion/erosion problems that occur for metallic dampers/arrestors. Since there are no moving parts in this particular implementation of damper pipe  302 , the device will not result in noise or bangs, as compared to the noise generally associated with a conventional water hammer arrestor. 
       Exemplary Performance 
       [0028]    An exemplary set of parameters that effect the following are described: (a) pressure spike suppression when using a plastic chamber without balloons; and (b) pressure spike suppression when using air-filled balloons inserted in a steel chamber. As described, steel chamber response to pressure spike is negligible. Isolating the effect of chamber enables quantifying the effect of the balloons only. 
       Plastic Pressure Spike Damper (Plastic Chamber Without Balloons) 
       [0029]    The parameters that affect the performance of this device are pipe diameter (D), pipe length (L), fluid velocity or discharge (Q), Young&#39;s modulus of elasticity for the damper material (E D ), damper length (L D ), damper diameter (D D ), damper wall thickness (e D ), pressure spike in pipe network due to water hammer (when no pressure surge control device is used) (N), fluid modulus of elasticity (K), Young&#39;s modulus of elasticity for the pipe (E), and pipe wall thickness (e). The following equations relate the reduction of pressure spike by the spike suppression device as a function of these parameters: 
         [0000]    
       
         
           
             
               
                 
                   R 
                   = 
                   
                     
                       
                         Δ 
                          
                         
                             
                         
                          
                         
                           V 
                           D 
                         
                       
                       
                         Δ 
                          
                         
                             
                         
                          
                         
                           V 
                           
                             D 
                             - 
                             max 
                           
                         
                       
                     
                     = 
                     
                       
                         
                           ( 
                           
                             N 
                              
                             
                                 
                             
                              
                             π 
                              
                             
                                 
                             
                              
                             
                               D 
                               D 
                               3 
                             
                              
                             
                               
                                 L 
                                 D 
                               
                               
                                 4 
                                  
                                 
                                   e 
                                   D 
                                 
                                  
                                 
                                   E 
                                   D 
                                 
                               
                             
                           
                           ) 
                         
                          
                         
                           
                             1 
                             + 
                             
                               
                                 K 
                                  
                                 
                                     
                                 
                                  
                                 D 
                               
                               
                                 E 
                                  
                                 
                                     
                                 
                                  
                                 e 
                               
                             
                           
                         
                       
                       
                         2840 
                          
                         
                             
                         
                          
                         Q 
                          
                         
                             
                         
                          
                         L 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         Δ 
                          
                         
                             
                         
                          
                         
                           p 
                           
                             w 
                              
                             
                                 
                             
                              
                             o 
                           
                         
                       
                       - 
                       
                         Δ 
                          
                         
                             
                         
                          
                         
                           p 
                           w 
                         
                       
                     
                     
                       Δ 
                        
                       
                           
                       
                        
                       
                         p 
                         w 
                       
                     
                   
                   = 
                   
                     f 
                      
                     
                       ( 
                       R 
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0000]    wherein ΔV D  is the extra volume available due to damper pipe expansion from pressure spike, ΔV D-max  is the fluid volume admitted for complete water hammer elimination and is equal to the volume of fluid that enters the pipe in a time equal to 2Q/a, Δp wo  is the pressure spike in the pipe when no damping device is used, and Δp w  is the pressure spike in the pipe when the spike suppression device is used. 
         [0030]    Using different values for all the above parameters, more than 80 points were investigated. The left hand side of Eq. 2 is multiplied by 100 and plotted against the right hand side of Eq. 2 as shown in TABLE 3. If one knows the different parameters on the right-hand side of Eq. 2, that means the R value is known and it is possible to estimate the expected reduction; or, if there is a target reduction of pressure spike, one could enter the graph and obtain R from which it is possible to decide about which parameters values could be used to result in the desired R value: 
         [0000]    
       
         
               
             
           
               
                 TABLE 3 
               
               
                   
               
             
             
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
               
               
                   
               
             
          
         
       
     
       Air-Filled Balloons Inserted in a Steel Chamber 
       [0031]    The parameters that affect the performance of the pressure spike suppression device are: local atmospheric pressure (p atm ), gas pressure inside the balloon (p b ), pipe pressure during normal system operation (p p1 ), maximum pressure spike in the pipe if no spike control device is used (p p2 ), pipe length (L), fluid modulus of elasticity (K), pipe diameter (D), Young&#39;s modulus of elasticity for the pipe (E), pipe wall thickness (e), discharge in the pipe (Q), caged balloon volume (V 0 ), and balloon initial pressure (the pressure necessary to inflate the balloon until it just starts pressing the cage) (p 0 ). The equations analogous to Eqs. (1) and (2) above are: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         R 
                         = 
                         
                           
                             Δ 
                              
                             
                                 
                             
                              
                             
                               V 
                               D 
                             
                           
                           
                             Δ 
                              
                             
                                 
                             
                              
                             
                               V 
                               
                                 D 
                                 - 
                                 max 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           ( 
                           
                             
                               
                                 ( 
                                 
                                   
                                     p 
                                     atm 
                                   
                                   + 
                                   
                                     p 
                                     b 
                                   
                                   - 
                                   
                                     p 
                                     0 
                                   
                                 
                                 ) 
                               
                                
                               
                                 
                                   V 
                                   0 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       1 
                                       
                                         
                                           p 
                                           
                                             p 
                                              
                                             
                                                 
                                             
                                              
                                             2 
                                           
                                         
                                         + 
                                         
                                           p 
                                           atm 
                                         
                                       
                                     
                                     - 
                                     
                                       1 
                                       
                                         
                                           p 
                                           
                                             p 
                                              
                                             
                                                 
                                             
                                              
                                             1 
                                           
                                         
                                         + 
                                         
                                           p 
                                           atm 
                                         
                                       
                                     
                                   
                                   ) 
                                 
                               
                                
                               
                                 
                                   1 
                                   + 
                                   
                                     
                                       K 
                                        
                                       
                                           
                                       
                                        
                                       D 
                                     
                                     
                                       E 
                                        
                                       
                                           
                                       
                                        
                                       e 
                                     
                                   
                                 
                               
                             
                             
                               2840 
                                
                               
                                   
                               
                                
                               Q 
                                
                               
                                   
                               
                                
                               L 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         Δ 
                          
                         
                             
                         
                          
                         
                           p 
                           wo 
                         
                       
                       - 
                       
                         Δ 
                          
                         
                             
                         
                          
                         
                           p 
                           w 
                         
                       
                     
                     
                       Δ 
                        
                       
                           
                       
                        
                       
                         p 
                         w 
                       
                     
                   
                   = 
                   
                     f 
                      
                     
                       ( 
                       R 
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
         [0032]    Ten tests were carried out with a range of values for all the parameters mentioned above. The left-hand side of Eq. 4 is multiplied by 100 and plotted against the right-hand side of Eq. 3 to obtain  FIG. 4 . With all the values of the pipe and balloon parameters known, one could estimate the reduction in pressure spike from TABLE 4; or if it is desired to have a given target reduction, one could enter the curve from the reduction % axis and read the value of the volume ratio. When this value is used in Eq. 3, one could decide which parameters take which values to reach this value of volume ratio, as shown in TABLE 4: 
         [0000]    
       
         
               
             
           
               
                 TABLE 4 
               
               
                   
               
             
             
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
               
               
                   
               
             
          
         
       
     
       An Exemplary Plastic Water Hammer Damper with Balloons 
       [0033]    One could use balloons inside a plastic chamber to obtain the performance of the device as indicated; for example, in TABLES 3 and 4. For instance, if the desired spike reduction is 80%, one could use 70% of this value for the balloons and the remaining 30% would be for the plastic chamber to absorb. These are target reductions. 
         [0034]      FIGS. 5(   a ) through  5 ( d ) show a set of exemplary data to compare exemplary performance of the disclosed plastic water hammer damper  302  with performance of a large commercial water hammer arrestor in a substantially similar plumbing network. For purposes of exemplary comparison, a test, the information and results of which are shown in respective ones of  FIGS. 5(   a ) through  5 ( d ), was carried out in the ground floor of a residential building with an elevated storage tank that supplies water to the building by gravity. In this example, the elevation difference between the control valve and the water level in the elevated storage tank was about 10-12 m. The water hammer damper  302  for this test was having a damper pipe diameter of 101.6 mm and damper pipe length of 750 mm.  FIG. 5(   a ) shows water hammer results following valve closure in the test environment without using damper pipe device  302 .  FIG. 5(   b ) shows water hammer results following valve closure in the test environment using a commercially available large water hammer arrestor.  FIG. 5(   c ) shows exemplary water hammer results following valve closure in the test environment using the plastic water hammer damper  302  of this configuration without balloons  310 , according to one embodiment.  FIG. 5(   d ) shows exemplary water hammer results following valve closure in the test environment using a FPSS  302  with three balloons  310  with pressure equal to the normal pressure in the network, according to one embodiment. As shown, in  FIGS. 5(   a ) through  5 ( d ), the FPSS  302  provides substantially better reduction of water hammer pressure than the commercial water hammer arrestor (please see  FIG. 5(   b )). Additionally, use of the FPSS  302  with a set of balloons  310  substantially enhances performance of the device  302  to address fluid pressure surges responsive to the water hammer. Please note that fluid pressures responsive to the water hammer were further reduced as the number of balloons  310  used in the device  302  is increased. 
         [0035]    Although the above sections describe systems and methods for a FPSS  302  in language specific to structural features and/or methodological operations or actions, the implementations defined in the appended claims are not necessarily limited to the specific features or actions described. Rather, the specific features and operations for the FPSS  302  are disclosed as exemplary forms of implementing the claimed subject matter.