Patent Publication Number: US-7711134-B2

Title: Speaker port system for reducing boundary layer separation

Description:
RELATED APPLICATIONS 
     This application is based on U.S. Provisional Patent Application No. 60/300,640 entitled “Flare Design for Minimizing Boundary Layer Separation” and filed on Jun. 25, 2001. The benefit of the filing date of the Provisional Application is claimed for this application. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Technical Field 
     This invention relates generally to loud speakers used in audio systems. More particularly, this invention relates to a speaker port with a contour that reduces boundary layer separation. 
     2. Related Art 
     There are many types of speaker enclosures. Each enclosure type can affect how sound is produced by the speaker. Typically, a driver is mounted flushed within the speaker enclosure. The driver usually has a vibrating diaphragm for emitting sound waves in front of a cone. As the diaphragm moves back and forth, rear waves are created behind the cone as well. Different enclosures types have different ways of handling these “rear” waves. 
     Many speakers take advantage of these rear waves to supplement forward sound waves produced by the cone.  FIGS. 1 and 2  show a bass reflex enclosure that takes advantage of the rear waves. The enclosure has a small port. The backward motion of the diaphragm excites the resonance created by the spring of air inside the speaker enclosure and the mass contained within the port. The length and area of the port are generally sized to tune this resonant frequency. The port and speaker resonance is very efficient so the cone motion is reduced to near zero thereby greatly enhancing the bandwidth and the maximum output of the system that would otherwise be limited by the excursion of the cone. 
     In many speaker enclosures, sound waves passing through the port generate noise due to boundary layer separation. A sudden expansion or discontinuity in the cross-sectional area of the port can cause boundary layer separation of the sound waves from the port. Boundary layer separation occurs when there is excessive expansion along the longitudinal axis of the port. The fluid expansion causes excessive momentum loss near the wall or contour of the port such that the flow breaks off or separates from the wall of the port. 
     To minimize boundary layer separation, many port designs use flares in the shape of a nozzle at opposing ends of the port to provide smooth transitions. Often, different flares are tried until the “best” one is found. In many flare designs, the performance of the port may be poor because boundary layer separation will occur at the point along the longitudinal axis of the port where the adverse pressure gradient is largest. The pressure gradient or change in pressure may become great enough that the momentum of the sound wave or fluid is greater than the pressure holding the sound wave to the wall or contour. In this case, the sound wave separates from the wall, thus generating noise and losses. The point where the maximum pressure gradient occurs along the port limits the flow velocity from the port before separation occurs. Once the sound wave or flow separates from the port contour or wall at the point of maximum pressure gradient, flow losses increase dramatically and result in poor performance of the port. 
     SUMMARY 
     This invention provides a speaker port having a substantially constant pressure gradient that reduces or minimizes boundary layer separation. With a substantially constant pressure gradient, there essentially is no point in the speaker port where a higher pressure gradient occurs to limit the velocity of the sound waves. 
     The speaker port comprises a flare having a substantially constant pressure gradient. In a method to reduce boundary layer separation in a speaker port, the inner wall of a flare is configured to have a substantially constant pressure gradient. 
     Other systems, methods, features and advantages of the invention will be, or will become, apparent to one with skill in the art upon examination of the following figures and detailed description. It is intended that all such additional systems, methods, features and advantages be included within this description, be within the scope of the invention, and be protected by the following claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention can be better understood with reference to the following figures. The components in the figures are not necessarily to scale, emphasis instead being placed upon illustrating the principals of the invention. Moreover, in the figures, like reference numerals designate corresponding parts throughout the different views. 
         FIG. 1  is a prior art cross-sectional view of a speaker enclosure with a transducer diaphragm in a rear position relative to its freestanding position. 
         FIG. 2  is a prior art cross-sectional view of the speaker with the diaphragm in a forward position relative to its freestanding position. 
         FIG. 3  is a side view of a port. 
         FIG. 4  is a cross-sectional view along Section A-A of the port shown in  FIG. 3 . 
         FIG. 5  is an enlarged cross-sectional view along Section B of the port shown in  FIG. 4 . 
         FIG. 6  is a cross-sectional view of a flare for a port in a speaker enclosure. 
         FIG. 7  is a graph illustrating a configuration for a flare. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       FIGS. 3-5  illustrate side and cross-sectional views of a loud speaker port  200 . Port  200  has a cylinder  202  between two flares  204  and  206  that form a hollow core  208 . Port  200  has an essentially circular cross-sectional area across the hollow core  208 . Port  200  may have other cross-sectional areas across the hollow core  208  including an essentially elliptical cross-section. The port  200  may be non-circular and may be straight, bent, or have one or more curves. The port  200  may be symmetrical or non-symmetrical along a center axis. The port  200  may have other or a combination of configurations. The cylinder  202  and flare  204  and  206  may have the same or different configurations. The flares  204  and  206  are configured or shaped to provide a substantially constant pressure gradient for the sound wave or air flow through the port  200 . The substantially constant pressure gradient reduces or minimizes boundary layer separation thus increasing or maximizing the air flow velocity through port  200 . Each of the flares  204  and  206  has an inner wall or contour  210  between an inlet duct  212  and an outlet duct  214 . The inner wall  210  is shaped or configured to provide substantially a constant pressure gradient over the entire length between the inlet and outlet ducts  212  and  214 . While particular configurations are shown and discussed, port  200  may have other configurations including these with fewer or additional components. 
     The flares  204  and  206  each have an inner wall  210  that reduces or minimizes boundary layer separation so that fluids, such as air or sound waves, may flow through the flare at a higher velocity without boundary layer separation. The inner wall  210  is contoured so that the pressure gradient or change in pressure along the longitudinal axis of the flare from its inlet duct  212  to outlet duct  214  is substantially constant. The pressure gradient is substantially similar along the longitudinal axis of the flare. If the momentum or velocity of the fluid overcomes the pressure forces holding the flow to the wall, boundary layer separation can occur along the entire length of the flare. The performance of the flare improves because there is essentially no point along the longitudinal axis of the flare in which a higher pressure gradient occurs to limit velocity of the fluid. The point where a maximum or highest pressure gradient occurs has been changed so that performance is improved or optimized. With an essentially constant pressure gradient over the entire length of the flare, there is no peak or maximum pressure gradient at any point along the flare that limits the flow velocity of the fluid or sound wave. 
     In one aspect, the cylinder  202  is the interior portion of port  200  that has an essentially constant diameter. In this aspect, the flares  204  and  206  are the exterior portions of port  200  that have variable diameters. Generally, the cylinder  202  may be a separate or integral component of the flares  204  and  206 . There may be no cylinder  202 , when flare  204  transitions directly into flare  206 . There may be only one flare or other multiples of flares. Flare  204  is essentially the same as flare  206 . However, flare  204  may have different dimensions and/or a different configuration from flare  206 . 
       FIG. 6  represents a cross-sectional view of a flare  304  for a port in a speaker enclosure (not shown). The flare  304  provides substantially a constant pressure gradient over the entire length of the inner wall  310 . The inner wall  310  is shaped or configured to achieve substantially a constant pressure gradient between inlet and outlet ducts  312  and  314 . With a substantially constant pressure gradient, the flow velocity U(x) of fluid or sound waves passing through the flare at any given point along the x axis of the port is increased or maximized without boundary layer separation occurring. The pressure gradient is generally defined as dp/dx or simply, the change in pressure p over the change in distance x. 
     A substantially constant pressure gradient along the length of the flare  304  minimizes or reduces the adverse affect of the pressure gradient on any point and allows for a higher or maximum velocity of air flow to occur without boundary layer separation. A flare without a constant pressure gradient has one or more points from the inlet duct  312  to the outlet duct  314  with higher pressure gradients. Boundary layer separation can occur at high pressure gradient points along the flare with air velocities that are comparatively lower than if there was a constant pressure gradient. 
     The pressure at points along the length of the flare  304 , P 0 (x) through P 6 (x), changes with respect the widening of the flare. If the change in pressure with respect to the change in distance is too high, an excessive adverse pressure gradient occurs. The pressure along the boundary of the walls  310  will not be enough to overcome the momentum of the sound wave or air flow U(x). An essentially constant pressure gradient allows a higher or maximum air flow velocity without flow separation because the constant pressure gradient causes the flow to expand uniformly along the points of the flare length as the sound wave or flow progresses through the flare  304 . 
     The shape or contour of the inner wall  310  provides a substantially constant pressure gradient along the length of a circular flare and is defined or determined as follows: 
     
       
         
           
             
               
                 
                   
                     
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                   convenience 
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                     ∫ 
                     
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                   Rearrange 
                   . 
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
             
               
                 
                   
                     y 
                     ⁡ 
                     
                       ( 
                       x 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
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                           ⁢ 
                           
                               
                           
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                           ⁢ 
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                           ⁢ 
                           
                               
                           
                           ⁢ 
                           x 
                         
                       
                     
                     4 
                   
                 
               
               
                 
                   Final 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     Equation 
                     . 
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     The contour of a flare is calculated using Equation (14) with an initial velocity U in , an initial flare area A in  that specifies the initial radius r in  such as A in =πr in   2 , a desired pressure gradient Δ=dp/dx, the fluid density ρ, and the integration constant c. Equation 14 may vary depending upon the initial cross-section area and other cross-sectional areas of the flare, especially when the flare is non-circular. 
       FIG. 7  is a graph illustrating the plot of a contour specifying the radius y in inches for a given position x in inches along the length of a flare. The pressure gradient remains constant at 240. The integration constant c initial  is 1.375. The initial radius is 1.375 in. The fluid density is 0.0000466 lb/in 3 . These particular values and the related graph in  FIG. 4  are for illustration purposes. Other values, graphs, and contours may be used. Any mathematical plot may be used to determine the contour of a port so long as the pressure gradient dp/dx remains substantially constant. 
     In another aspect, the shape or contour of the inner wall  310  provides a substantially constant pressure gradient along the length of a circular flare and is defined or determined as follows: 
     
       
         
           
             
               
                 
                   
                     
                       ⅆ 
                       p 
                     
                     
                       ⅆ 
                       x 
                     
                   
                   = 
                   
                     constant 
                     = 
                     Δ 
                   
                 
               
               
                 
                   The 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   pressure 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   gradient 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     
                       ⅆ 
                       p 
                     
                     / 
                     
                       ⅆ 
                       x 
                     
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   is 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   a 
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
             
               
                 
                     
                 
               
               
                 
                   constant 
                   ⁢ 
                   
                       
                   
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                     Δ 
                     . 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       ⅆ 
                       p 
                     
                     
                       ⅆ 
                       x 
                     
                   
                   = 
                   
                     
                       - 
                       ρ 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       U 
                       ⁡ 
                       
                         ( 
                         x 
                         ) 
                       
                     
                     ⁢ 
                     
                       ⅆ 
                       
                         ( 
                         
                           U 
                           ⁡ 
                           
                             ( 
                             x 
                             ) 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   The 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   Prantdl 
                   ⁢ 
                   
                     / 
                   
                   ⁢ 
                   Bernoulli 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   Momentum 
                   ⁢ 
                   
                     - 
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
             
               
                 
                     
                 
               
               
                 
                   Integral 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   relationship 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   relates 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                     
                 
               
               
                 
                   the 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   pressure 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   gradient 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   is 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   to 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   the 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                     
                 
               
               
                 
                   velocity 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   U 
                   ⁢ 
                   
                     ( 
                     x 
                     ) 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     
                       in 
                       sec 
                     
                     ) 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   and 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   fluid 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                     
                 
               
               
                 
                   density 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   ρ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     
                       ( 
                       
                         lb 
                         
                           in 
                           3 
                         
                       
                       ) 
                     
                     . 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     Δ 
                     ⁢ 
                     
                       ∫ 
                       
                         ⅆ 
                         x 
                       
                     
                   
                   = 
                   
                     
                       - 
                       ρ 
                     
                     ⁢ 
                     
                       ∫ 
                       
                         
                           U 
                           ⁡ 
                           
                             ( 
                             x 
                             ) 
                           
                         
                         ⁢ 
                         
                           ⅆ 
                           
                             ( 
                             
                               U 
                               ⁡ 
                               
                                 ( 
                                 x 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Integrate 
                   . 
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
             
               
                 
                   
                     → 
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       x 
                     
                   
                   = 
                   
                     
                       
                         - 
                         ρ 
                       
                       ⁢ 
                       
                         
                           
                             U 
                             2 
                           
                           ⁡ 
                           
                             ( 
                             x 
                             ) 
                           
                         
                         2 
                       
                     
                     + 
                     c 
                   
                 
               
               
                 
                   Integration 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     result 
                     . 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     x 
                   
                   = 
                   
                     
                       
                         - 
                         ρ 
                       
                       ⁢ 
                       
                         
                           
                             A 
                             in 
                             2 
                           
                           ⁢ 
                           
                             U 
                             in 
                             2 
                           
                         
                         
                           2 
                           ⁢ 
                           
                             
                               A 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               x 
                               ) 
                             
                           
                         
                       
                     
                     + 
                     c 
                   
                 
               
               
                 
                   
                     
                       Substitute 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         U 
                         ⁡ 
                         
                           ( 
                           x 
                           ) 
                         
                       
                     
                     = 
                     
                       
                         
                           A 
                           in 
                         
                         ⁢ 
                         
                           U 
                           in 
                         
                       
                       
                         A 
                         ⁡ 
                         
                           ( 
                           x 
                           ) 
                         
                       
                     
                   
                   , 
                   where 
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
             
               
                 
                     
                 
               
               
                 
                   
                     A 
                     in 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   is 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   the 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   initial 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   area 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     
                       π 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         r 
                         2 
                       
                     
                     ) 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   at 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   the 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                     
                 
               
               
                 
                   
                       
                   
                   ⁢ 
                   
                     port 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     opening 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     or 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     inlet 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     duct 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     312 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                     
                 
               
               
                 
                   and 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     U 
                     in 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   is 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   the 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   initial 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   velocity 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   at 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   the 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                     
                 
               
               
                 
                   
                       
                   
                   ⁢ 
                   
                     flare 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     beginning 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     or 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     inlet 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     duct 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     312. 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   p 
                   = 
                   
                     Δ 
                     - 
                     
                       
                         ρ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           A 
                           in 
                           2 
                         
                         ⁢ 
                         
                           U 
                           in 
                           2 
                         
                       
                       
                         2 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           π 
                           2 
                         
                         ⁢ 
                         
                           y 
                           4 
                         
                       
                     
                     + 
                     c 
                   
                 
               
               
                 
                   
                     Substitute 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       A 
                       ⁡ 
                       
                         ( 
                         x 
                         ) 
                       
                     
                   
                   = 
                   
                     π 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       y 
                       2 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     and 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     solve 
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
             
               
                 
                     
                 
               
               
                 
                   for 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     y 
                     . 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     y 
                     ⁡ 
                     
                       ( 
                       x 
                       ) 
                     
                   
                   ⁢ 
                   
                     : 
                   
                   ⁢ 
                   
                     
                       
                         
                           - 
                           ρ 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           A 
                           in 
                           2 
                         
                         ⁢ 
                         
                           U 
                           in 
                           2 
                         
                       
                       
                         
                           2 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             π 
                             2 
                           
                           ⁢ 
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           x 
                         
                         + 
                         c 
                       
                     
                     4 
                   
                 
               
               
                 
                   Final 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     Equation 
                     . 
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
             
               
                 
                   
                     where 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     c 
                   
                   = 
                   
                     - 
                     
                       
                         ρ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           A 
                           in 
                           2 
                         
                         ⁢ 
                         
                           U 
                           in 
                           2 
                         
                       
                       
                         2 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         
                           r 
                           in 
                           4 
                         
                       
                     
                   
                 
               
               
                 
                     
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     Y 
                     ⁡ 
                     
                       ( 
                       0 
                       ) 
                     
                   
                   = 
                   
                     
                       r 
                       in 
                     
                     . 
                   
                 
               
               
                 
                     
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     The contour of a flare is calculated using Equation (20) with an initial velocity U in , an initial flare area A in  (which specifies the initial radius r in  such as A in =πr in   2 ), a desired pressure gradient Δ=dp/dx, and the fluid density ρ. Equation 20 may vary depending upon the initial cross-section area and other cross-section areas of the flare, especially when the flare is non-circular. 
     With either Equations (14) or (20), the inner wall  310  of the flare  304  may be shaped or configured to provide a substantially similar pressure gradient over the length of the flare  304  between the inlet and outlet ducts  312  and  314 . With either Equation, the length of flare  304  between the inlet and outlet ducts  312  and  314  may be used to increase the velocity of the fluid or sound wave through the flare  304  while avoiding boundary layer separation. The inner wall of the flare  304  is thus shaped so that the pressure gradient along the flare  304  is substantially similar or constant, thus minimizing or reducing boundary layer separation. 
     The same port performance can be achieved using non-circular sections, non-symmetrical sections, or a combination. Equations 14 and 20 are adjusted by substituting the appropriate area relationship for the configuration of the port. In addition, the port may not be rotationally symmetrical. One side could be flat while the other side is varied to maintain the desired area expansion. 
     Other pressure and/or fluid equations may be used to shape or configure the inner wall to provide a substantially constant pressure gradient. Various computer programs may be used to perform the calculations of this invention including Matlab™ and Mathematica.™ These programs may be used to plot the contour of a flare while keeping the pressure gradient constant. 
     While various embodiments of the application have been described, it will be apparent to those of ordinary skill in the art that many more embodiments and implementations are possible within the scope of this invention. Accordingly, the invention is not to be restricted except in light of the attached claims and their equivalents.