Abstract:
The subject matter of the present invention is a pump arrangement, in particular for use in the body&#39;s own vessels, having a pump and a sheath receiving the pump, bounding a flow passage and having a distal intake opening and a proximal outflow opening for producing a driving flow by means of the pump, wherein the pump is arranged in a first fluid-tight section having the distal intake opening and a second fluid-tight section includes the proximal outflow opening. In accordance with the invention, a further inlet opening is present between the first section, and the second section and is arranged between the intake opening and the outflow opening, with the first section and the second section being arranged with respect to one another such that the inlet opening opens into the flow proximal to the pump.

Description:
BACKGROUND OF THE INVENTION 
     The invention is in the field of mechanical engineering and fine mechanics and can in particular advantageously be used in the medical area. 
     In this respect, the subject matter is a pump arrangement in accordance with the preamble of claim  1 . 
     Pump arrangements are increasingly known from prior art in particular for use in the body&#39;s own vessels. Said pumps can be used, for example, for short-term cardiac support to relieve the cardiac muscle of a patient after a cardiogenic shock (myocardial infaction). In this process, use is sometimes made of transfemorally implanted micro-axial pumps. 
     Such a pump arrangement is known, for example, from EP 2 047 872 A1. The pump arrangement disclosed there includes a pump, a sheath receiving the pump and having a distal intake opening and a proximal outflow opening, with the pump generating a driving flow in operation from the distal intake opening toward the proximal outflow opening. A flow passage thus extends between the intake opening and the outflow opening. The pump is in this respect arranged in a first fluid-tight section of the sheath which has the distal intake opening and which is formed as a PU covering of a housing. Furthermore, a second fluid-tight section of the sheath is present which includes the proximal outflow opening and is formed as an outflow hose. The outflow hose is connected with material continuity to the PU covering. The pump arrangement is arranged such that the pump formed as a rotor can, for example, be arranged in a ventricle, with the outflow hose extending from the ventricle into the aorta. 
     All the blood entering into the aorta via outflow openings of the outflow hose moves through the intake opening into the flow passage formed by the sheath and in so doing passes through the rotor. In other words: The conveyed flow conveyed by the pump is identical to the total flow exiting at the outflow opening. 
     The subject matters of documents DE 41 24 299 A1, DE 10 2004 054 714 A1, WO 2007/112033 A2 and US 2008/132748 A1 also work in accordance with the aforesaid principle. 
     Since all blood comes into direct contact with the pump, a particularly high effort is required in the manufacture of the pump to reduce the blood-damaging effect of the moving pump parts. This blood-damaging effect is manifested in direct mechanical shear at moving and stationary pump parts and in shear by shear stress fields occurring in the fluid while passing through the flow passage (see above). Pump geometries therefore also arise which cannot be used by means of a minimally invasive procedure. 
     BRIEF SUMMARY OF THE INVENTION 
     It is the underlying object of the present invention to reduce the danger of damage to the blood or to the fluid transported through the pump. Special attention must be paid to the choice of the materials in the medical use of the following pump arrangement(s). Said materials should meaningfully satisfy the demands of biocompatibility. Interactions with foreign-body surfaces form the third big aspect, in addition to the above implementation, in blood damage and have been sufficiently examined for some time. 
     In accordance with the invention, a further inlet opening is introduced between the first section and the second section with the first section and the second section being arranged with respect to one another such that the inlet opening opens into the flow passage proximal the compressible pump. In this respect, the further inlet opening can also be formed as an inlet passage which has its inlet opening distal of or proximal to the pump or also at the level of the pump, but which only opens into the flow passage proximal to the pump. 
     It is possible with the aid of the feature in accordance with the invention that a driving flow running through the pump flows through the flow passage past the opening of the inlet opening in the direction of the outlet opening and thus effects a pressure drop with respect to the fluid pressure present in the inlet opening which results in a pulling of fluid through the inlet opening and into the flow passage. The total flow outflowing at the outflow opening is hereby larger than the driving flow directly passing through the pump and conveyed thereby since an additional intake flow is added through the inlet flow. 
     The intake flow arises in that a suction effect arises due to the driving flow such as also occurs in some kinds of turbine or water jet pumps. On the suction effect, an impulse is transmitted from the driving flow to the intake flow by friction or viscosity or turbulent mixing of the fluid. In this manner, viscous, turbulent shear stresses arise. The impulse direction of the propellant flow is transmitted to particles from the medium of the intake flow to be conveyed which are transported into a zone downstream within the sheath. 
     Substantially, the principle of a jet pump is realized with the aid of the feature in accordance with the invention, with the driving flow directly passing through the pump and conveyed thereby carrying along an intake flow entering through the further inlet opening. 
     The inlet opening in this respect extends between the first section and the second section, with the entry to the inlet opening being able to be proximal to or distal of the pump, with it being advantageous if the entry is distal of the outflow opening. Only the opening of the inlet opening into the flow passage should be proximal the pump so that the suction effect which is caused by the driving flow is utilized well. 
     A compressible pump is understood as a preferably radially compressible pump or pump arrangement. In this respect, the pump or the first section and/or the second section and/or the housing and/or the rotor are formed such that the pump can be conducted to the target site in a catheter, with the catheter having an inner diameter which is smaller than the first section and second section or the housing in the unfolded condition. Such pumps or pump arrangements are known, for example, in EP 2 047 872 A1, in WO 2010/063494 A1, in U.S. 61/120,095 or in WO 2010/127871 and in U.S. 61/175,519 A1. 
     An inlet opening formed between the intake opening and the outflow opening is particularly advantageous. 
     The first section and the second section of the sheath can be formed in one piece or as components separate from one another. 
     In a first embodiment, the cross-section of the proximal end of the first section is smaller than the cross-section of the distal end of the second section. The conveyed flow is hereby concentrated onto an area of the cross-section of the proximal end of the first section and can take along further medium on entry into the second section, said medium being able to flow in at least through accesses in the region of the remaining area of the cross-section of the distal end of the second section. 
     In a further embodiment, the cross-section of the first section converges toward its proximal end. Due to this convergence, the first section is of nozzle form at its proximal end. This results in an improvement in the efficiency and thus in an increase in the sucked-in intake flow. In addition, the feature helps effect a reduction in the total pump arrangement. 
     In a further embodiment, the distal end of the second section and the proximal end of the first section overlap, i.e. the distal end of the second section is further distal than the proximal end of the first section. In this respect, it is advantageous if the inlet opening between the first section and the second section is in each case formed as an intake passage or in the manner of a passage from the distal end of the second section toward the proximal end of the first section. The intake flow hereby preferably flows almost coaxially to the conveyed direction of the driving flow through the intake passage into the flow passage in the direction of the outflow opening. In this respect, an impulse of the driving flow in the direction of the outflow opening is already transmitted to the intake flow due to the main axis of the intake passage which is preferably directed in the direction of the conveyed flow. This results in an improvement in efficiency. 
     In a further embodiment, the distal end of the second section is further proximal than or at the same level as the proximal end of the first section. Due to the spacing, the concentrated driving flow exiting the proximal end of the first section is incident onto a fluid of different pressure and different directions so that the concentrated conveyed flow, like a fluid of higher density, flows on into the start of the second section defined by the distal end of the second section and takes along fluid which is located between the first section and the second section. The total flow hereby becomes larger with respect to the driving flow passing through the pump. In this respect, care must, however, be taken that the spacing between the distal end of the second section and the proximal end of the first section is kept small in order not to effect any dispersion of the conveyed flow with respect to the flow present outside the sheath. The spacing should be approximately from 0 to ¼ of the diameter of the proximal outlet opening of the first section. 
     In a further embodiment, the second section includes at least one partial region made from a flexible material. It is hereby possible that a second section which is disposed between, for example, a ventricle and a blood vessel, with the ventricle and the blood vessel being connected by means of a valve closing and opening rhythmically, can be pressed through the valve and the fluid is thus conveyed in turn with the rhythmic movement of the valve. PU, PE, PP, silicone or Parylene are, for example suited as suitable materials provided that they satisfy the mechanical and geometrical demands and the demands on biocompatibility. 
     In a further embodiment, the pump arrangement has a housing receiving the pump. This is in particular suitable when the pump is a compressible pump which is conveyed to its working site by means of a catheter together with the housing. In addition, the housing gives the pump arrangement additional stability. The housing can, for example, be manufactured from Nitinol. 
     On the presence of a housing, the first section can be made as a jacket of the housing or as a coating of the housing, with only a partial region of the housing, preferably an axial partial region, having to have a fluid-tight jacketing or coating. Materials are suitable as coatings or jacketings here such as were already named in the description of the second section made from a flexible material. 
     In a further embodiment, the housing has a constriction and/or a bulge proximal to the pump. In this respect, a constriction is to be understood as a convergence of the cross-section of the housing with respect to the region of housing receiving the pump. A bulge has a cross-section of the housing enlarged with respect to a constriction or with respect to the region receiving the pump. Converging portions of the first section or lager cross-sections of the second section can be implemented in a particularly easy and advantageous manner with the aid of such a shape. The second section can also be connected to the housing. 
     In a further embodiment, the first section and the second section are connected to one another with material continuity or are preferably formed in one piece. 
     In a further embodiment, the second section is formed as an outflow hose. 
     In a further embodiment, the first section, the second section or any housing includes support elements such as a support ring, plastic threads, wires, connecting struts or a preferably compressible sleeve for spacing apart the first section and the second section so that an intake flow flowing through the inlet opening does not have the result that a surface of the second section is sucked onto the surface of the first section and thus interrupts the intake flow or to ensure that the further inlet opening is permanently open in pump operation. The support elements are in this respect connected to the first section or to the second section such that they are compressible together with the pump. This can be achieved, for example, via flexible support elements or support elements made from hyper elastic materials or support elements made from memory materials such as Nitinol. 
     The second section can furthermore have a support ring in the region of the inlet opening, said support ring ensuring a spacing of the first section from the second section in the region of the inlet opening so that an intake flow flowing through the inlet opening does not have the result that a surface of the second section is sucked onto the surface of the first section and thus interrupts the intake flow. This is in particular advantageous when the second section is a section made from flexible material such as an outflow hose. 
     In a further embodiment, the second section has a sleeve which includes the further inlet apparatus or partly includes the further inlet opening. Said sleeve can be connected as an additional special part, for example, to a flexible region of the second section. In this respect, it is advantageous if the sleeve is of stable shape and thus forms a suitable resistance with respect to the fluid in the working state which is defined, for example, by an unfolding of the pump arrangement at its work site in the body so that the intake flow is channeled by the sleeve and flows into the flow passage. 
     Instead of a sleeve, a further hose section or a tube can also be used. 
     In a further embodiment, the pump is a compressible pump, which results in a lighter introduction of the pump into the bloodstream or into a vessel. 
     It is furthermore advantageous if the pump is an axial flow pump which is fastened on a rotatable shaft which drives the pump. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention will be described in the following in more detail with reference to some embodiments. There are shown: 
         FIG. 1  the use of a pump arrangement in a heart; 
         FIG. 2  a schematic representation of an embodiment of the pump arrangement; 
         FIG. 3  a schematic representation of an inlet opening of an embodiment of the pump arrangement; 
         FIG. 4  an embodiment of a pump arrangement; 
         FIG. 5 a    a further embodiment of a pump arrangement; 
         FIG. 5 b    a schematic representation of the pump arrangement of  FIG. 5   a;    
         FIG. 6  a further embodiment of a pump arrangement; 
         FIG. 7  a further embodiment of a pump arrangement; and 
         FIGS. 8 a -8 c    cross-sections through different pump arrangements. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     A possible use for the pump arrangement  1  is shown in  FIG. 1 . The pump arrangement  1  includes an elongate catheter which extends through the blood vessel  2  and in which a shaft extends which drives the pump present in the pump arrangement  1  and formed as a rotor. The proximal end of the pump arrangement (viewed without the catheter) is located in the blood vessel  2 , whereas the distal end of the pump arrangement  1  including the pump is located in the ventricle  3 . The blood vessel  2  is bounded by the vessel wall  4 . The valve  5  which opens and closes rhythmically furthermore bounds the ventricle  3  and enables the blood flow from the ventricle  3  into the blood vessel  2 . 
     Further uses are possible in addition to the shown use of a pump arrangement in accordance with the information. The pump can thus, for example, be used in a different vessel of the body to increase the conveying performance. 
     The mode of operation of a pump arrangement in accordance with the invention should be explained with reference to  FIG. 2 . The pump arrangement  10  includes a pump  11  which is formed as a rotor. The pump  11  is set into rotation by means of a shaft which is shown, but not numbered and can thus transport a driving flow Q T . The pump arrangement  10  has a sheath  12  which includes a first section  12   a  and a second section  12   b . An intake opening  13  is located in the first section  12   a  through which intake opening a fluid can enter into the lumen of the first section  12   a , is sucked in by the pump  11  and is transported as a driving flow Q T  in the direction of the outflow opening  14 . The sheath  11  defines the flow passage S between the intake opening  13  and the outflow opening  14 , said flow passage completely including the lumen of the first section  12   a  and partially including a lumen of the second section  12   b.    
     The first section and the second section overlap between the proximal end of the first section  12   a  and the distal end of the second section  12   b . An inlet opening  15  is defined by the overlap through which the fluid can enter into the flow passage S from a region outside the lumen of the first section  12   a . A pressure drop occurs in the region  17  in the region of the proximal end of the first section  16  due to the driving flow Q T  conveyed by the pump. This is shown in  FIG. 3 . 
     Further fluid is sucked through the inlet opening  15  in the direction of the outflow opening  14  due to the pressure drop in the region  17  and enters into the flow passage as the intake flow Q S  proximal to the proximal end of the first section  16 . 
     The first section  12   a  and the second section  12   b  both include a lumen. In this respect, the lumen of the first section  12   a  has a cross-sectional area A 1 ; the lumen of the second section  12   b  has a cross-sectional area A 2 . In the present embodiment, the cross-sections A 1  and A 2  remain the same over the total length of the respective section; however, this is not a compulsory feature. The intake flow already receives an impulse direction in the direction of the outflow opening  14  due to the passage extending parallel to the driving flow between the distal end of the second section  12   b  and the proximal end of the first section  12   a  and formed as an inlet opening  15 . The volume per time Q A  which has flowed out at the outflow opening  14  is larger due to the additional intake flow Q S  than the driving flow Q T  passing through the pump. 
     A further embodiment of a pump arrangement is described in  FIG. 4 . The pump arrangement  20  is located in a blood vessel which is bounded by the vessel walls  4 . The distal end of the pump arrangement  20  is located distal of the valve  5 ; the proximal end is located proximal to the valve  5 . 
     The pump arrangement  20  includes a compressible rotor  21  which is fastened to the shaft  22  at one side. The bearing is located at the proximal end of the rotor. The rotor  21  is surrounded by a housing  23  which can be manufactured from Nitinol. The housing comprises individual threads, wires or struts of Nitinol which mutually cross and produce a diamond pattern. The fluid can pass through the diamonds and so reach the rotor  21 . 
     The housing  23  is partly covered by a jacketing  24  in a fluid-tight manner. In this respect, the jacketing  24  extends over a length L 24  so that a driving flow Q T  driven by the rotor is bundled and exits the housing  23  at the proximal end of the jacketing  24  and flows in the direction of the outflow openings  29  which are arranged in an outflow hose  25 . 
     The jacketing  24  in the embodiment of the pump arrangement  20  forms the first section of the sheath; the outflow hose  25  forms the second section of the sheath. The distal end of the outflow hose is fastened to the housing  23  and is further distal than the proximal end of the sheath  24 . 
     The sheath  34  converges from the region of the rotor  21  in the proximal direction. The lumen formed by the sheath  24  thus has a cross-sectional area A 1D  in the region of the rotor  21  which is larger than the cross-sectional area A 1P  of the proximal end of the sheath  24 . A nozzle effect is hereby produced which accelerates the driving flow Q T  in accordance with the principle of the Venturi tube so that it flows in the direction of the outflow openings  29  at a higher flow speed at the proximal end of the sheath  24 . The intake passage  26  which is accessible through the inlets  27  is located between the sheath  24  and the outflow hose  25 . It can be recognized from  FIG. 4  that a plurality of inlets  27  are present, with the inlets being designed as circular sections of the outflow hose in the region of its distal end. Due to the reduced pressure in the region of the exiting driving flow Q T  an intake flow Q S  is sucked through the inlet  27  and the intake passage  26  and flows into the flow passage S, which transports the total conveyed flow to the outflow openings  29 . 
     A support ring  28  which is stable in shape in the working state of the pump is located radially peripherally proximal to the inlets  27  and the outflow hose  25 . A suction of the surface of the outflow hose  25  to the sheath  24  due to the occurring intake flow is thus prevented. The intake passage  26  thus remains open and further fluid is sucked through the intake passage  26 , caused by the driving flow Q T , into the flow passage S. 
     A further embodiment of the pump arrangement in accordance with the invention is shown in  FIG. 5 a   . The pump arrangement  30  includes a rotor  31  which is supported at both sides, i.e. distal and proximal, at an axle  32 . The rotor  31  is arranged in a housing  33  which is sectionally jacketed by a PU coating  34 . The PU coating  34  in this respect extends over a length L 34  up to a region disposed proximal to the proximal end of the rotor  31 . The housing  33  has a constriction  33   a  and expands proximal of the constriction  33   a  to form a bulge  33   b . In the region of the bulge  33   b , the outflow hose  35  is connected to the housing  33  with material continuity. The bulge  33   b  and the constriction  33   a  are spaced apart from one another, measured along the axis  32 , by a spacing d which amounts to around 0 to ¼ of the diameter of the constriction  33   a . In this respect, the spacing d is selected so that due to the driving flow Q T  exiting the proximal end of the PU coating  34  and driven by the rotor  31 , an intake flow Q S  is sucked in through the inlet opening  36  resulting between the PU coating  34  and the outflow hose  35 . The driving flow Q T  exiting the jacketing is flowed out at a pressure P 1 . A pressure P 2  applies outside the jacketing  34  which is lower than the pressure P 1 . An intake flow Q S  is sucked into the inlet opening  36  due to this pressure difference and is transported through the outflow hose toward the outflow opening  39  where it is expelled as a total current Q A  at a pressure P 3  which is greater than the pressure P 2 . The total flow Q A  is in this respect lower than the driving flow Q T . 
     Even if the flow passage S, which extends between the intake opening distal of the rotor  31  and the outflow opening  39 , is permeable for fluid between the proximal end of the PU coating  34  and the distal end of the outflow hose  35 , the inflow opening  36  nevertheless opens into the flow passage which is defined by the flow course of the driving flow. If the driving flow is correspondingly high, it enters practically directly into the outflow hose. 
     It is possible due to the inlet opening present in addition to the intake opening disposed distal of the rotor  31  that a partial flow of the total flow Q A  exiting at the outflow opening  39  does not pass the rotor  31  and there is thus no risk of blood damage by the rotor  31 . 
     The embodiment of the pump arrangement  30  of  FIG. 5 a    is shown again schematically in  FIG. 5 b   . It can be recognized here that the distal end of the PU coating  34  has a cross-sectional area A 1D  which is larger with respect to the cross-sectional area A 1P  which is present at the proximal end of the PU coating  34 . The lumen surrounded by the PU coating  34  thus converges, which has the consequence of an efficiency improvement. The cross-sectional area A 2D  of the lumen of the outflow hose  35  is in turn larger than the cross-sectional area A 1P . An inlet opening  36  is thus defined at least by the region of the cross-sectional area A 2D  which remains after the subtraction of the cross-sectional area A 1P . Said inlet opening in turn opens into the flow passage S. 
     A further embodiment of a pump arrangement is shown in  FIG. 6 . In this respect, a detailed description of the axle and of the pump drive is dispensed with. The pump arrangement  40  includes a rotor  41  as well as a first section  42   a  and a second section  42   b  of a sheath. The intake opening  43  which supplies fluid to the pump  41  is located at the distal end of the first section  42   a . The fluid supplied to the pump  41  is accelerated and is expelled as a driving flow Q T  at the proximal end of the first section  42   a . The second section  42   b  is composed of a flexible region  420   b  which is connected to a compressible sleeve  421   b  which is of stable shape and is rigid in the working state of the rotor. The compressible sleeve  421   b  is connected to the first section  42   a  by means of plastic threads or wires  422   b . The cross-section extending in converging manner from the distal end of the sleeve  421   b  to the proximal end of the sleeve  421   b  has the effect in conjunction with the driving flow Q T  of sucking in an intake flow Q S  through the inlet opening  45  which is formed between the sleeve  421   b  and the first section  42   a , with the intake flow Q S  being combined with the driving flow Q T  and, in the flow passage S, flowing out of the outflow opening  44  as the total flow Q A . It is in turn obvious from  FIG. 6  that the inlet opening  45  opens into the flow passage S. 
     A further embodiment of a pump arrangement is shown in  FIG. 7 . The pump arrangement  50  includes a pump  51  which is formed as an axial-flow pump having a rotor. Furthermore, a sheath  52  is present which can be divided into a first section  52   a  and into a second section  52   b . In this respect, the first section and the second section are connected to one another with material continuity or are manufactured in one piece. An intake opening  53 , which supplies fluid to the rotor, is located at the distal end of the sheath  52  so that a driving flow Q T  is conveyed in the working state of the rotor. The driving flow Q T  is conveyed in the direction of the outflow opening  54 . An inlet opening  55  through which an intake flow Q S  effected by the driving flow Q T  can enter into the flow passage S defined by the sheath  52  is located between the first section  52   a  and the second section  52   b . The special feature of this embodiment is that the sheath  52  is made in one piece, in contrast to the previously shown embodiments in which the first section represents a separate component with respect to the second section. 
     Some different geometries of entries of the inlet openings should be shown with respect to  FIGS. 8 a   - c.    
     A cross-section of the embodiment of  FIG. 6  is shown in  FIG. 8 a   . What can be seen is the intake opening  543  with a cross-sectional area A 1P . Disposed proximal thereto, i.e. further into the plane of the drawing, the sleeve  421   b  is located with the cross section A 2D  measured at its widest periphery. The plastic threads  422   b  connect the sleeve  421   b  to the first section  42   a.    
     The embodiment of  FIG. 5 a    is shown in  FIG. 8 b   . The intake opening  33  can be recognized which is defined by the PU coating  34 . The PU coating  34  simultaneously defines a lumen which has a cross-sectional area A 1P  in the region of the rotor. In addition, the axle  32  can be recognized at the center of the intake opening  33 . Proximal to the rotor (cf.  FIG. 5 a   ), the housing  33  which is formed by threads, wires or struts of Nitinol converges to a cross-sectional area A 1P  which is defined by the constriction  33   a . At proximal, the housing  33  widens to form a bulge  33   b , with the outflow hose  35  being connected to the housing in the region of the bulge. It can clearly be recognized with reference to the representation shown in  FIG. 8 b    that the region  36  disposed between the outflow whose  35  and the PU coating  34  serves as an inlet opening for an intake flow. 
     In  FIG. 8 c   , the embodiment of  FIG. 4  is shown. In this respect, the cross-section is shown at the level of the support ring  28 . The lumen defined by the jacketing  24  of the first section and having the cross-sectional area A 1D  can be recognized. The intake passage  26  through which additional fluid is sucked in, driven by the driving flow running through the lumen of the jacketing  24  in the proximal direction, is located between the jacketing  24  and the outflow hose  25 . The outflow hose  25  has a cross-sectional area of A 2D  in this region. The support ring  28  can clearly be recognized, as can the connection struts  28   a  which connect the support ring to the jacketing  24 . The support ring is composed of a plurality of segments  28   b  which can be brought into a folded state for introduction of the pump arrangement with the aid of a catheter. 
     REFERENCE NUMERAL LIST 
     
         
           1 ,  10 ,  20 ,  30 ,  40 ,  50  pump arrangement 
           2  blood vessel 
           3  ventricle 
           4  vessel wall 
           5  heart valve 
           6  vessel valve 
           11 ,  41 ,  51  pump 
           12 ,  42 ,  52  sheath 
           12   a ,  42   a ,  52   a  1st section of the sheath 
           12   b ,  42   b ,  52   b  2nd section of the sheath 
           13 ,  43 ,  53  intake opening 
           14 ,  44 ,  54  outflow opening 
           15  inlet opening 
           16  proximal end of the 1st section 
           17  region of pressure drop 
           21 ,  31  rotor 
           22 ,  32  axle 
           23 ,  33  housing 
           24 ,  34  jacketing 
         L 24 , −L 34  length of the jacketing 
           25 ,  35 ,  420   b  outflow hose 
           26 ,  36  intake passage 
           27  inlets 
           28  support ring/spacer 
           33   a  constriction 
           33   b  bulge 
           421   b  sleeve 
           422   b  spacer 
         Q T  conveyed flow 
         Q S  intake flow 
         Q A  total flow 
         A 1 , A 2 , A 1D , A 1P , A 2D , cross-section