Patent Publication Number: US-7721714-B2

Title: Fuel delivery pipe

Description:
REFERENCE TO RELATED APPLICATION 
     This is a divisional application of Ser. No. 10/523,651, filed Mar. 29, 2005 which is currently allowed. The subject matter of the aforementioned prior application is hereby incorporated herein by reference. 
     TECHNICAL FIELD 
     This invention relates to a fuel delivery pipe for supplying fuel supplied from a fuel pressure pump of an engine for automobile of an electronic fuel injection type via a fuel injector, or an injection nozzle, for directly injecting each inside of intake passages and cylinders of the engine, which having an object to reduce pressure pulsations and radiant sound caused by the fuel injection. Furthermore, this invention relates to a cross-sectional structure of the fuel delivery pipe having a fuel passage, to an external structure of the fuel pipe, and to a structure, or a mechanism, for reducing the pressure pulsation and the radiant sound of the fuel delivery pipe. 
     BACKGROUND ART 
     Conventionally, a fuel delivery pipe having a plurality of injection nozzles to supply fuel, e.g., gasoline to a plurality of cylinders of an engine has been known. This fuel delivery pipe injects sequentially the fuel introduced from a fuel tank into a plurality of intake pipes or the cylinders of the engine via a plurality of the injection nozzles to mix the fuel with air, thereby burning the air-fuel mixture to generate an engine output power. 
     Though this fuel delivery pipe is, as described above, for injecting the fuel supplied through an underfloor pipe arrangement from the fuel tank into the intake pipes or the cylinders via the injection nozzles, a fuel delivery pipe as a return type have existed, which belongs to a type having a circuit for returning the surplus fuel to the fuel tank by a pressure regulator in a case of where the fuel is overly supplied into an interior of the fuel delivery pipe. To the contrary to the fuel delivery pipe as the return type, there has been known a fuel delivery pipe as a returnless type having no circuit for returning the supplied fuel to the fuel tank. 
     Those of the type to return the fuel extra supplied into the fuel delivery pipe to the fuel tank, can always keep the amount of the fuel in the fuel delivery pipe constant, thereby having an advantage such that the pressure pulsation in association with the fuel injection hardly occurs. The fuel supplied to the fuel delivery pipe arranged near the engine cylinder heated at high temperature, however, may be rendered at a high temperature, and the heated surplus fuel is returned to the fuel tank thereby increasing the temperature of gasoline inside the fuel tank. Because it is undesirable that the gasoline vaporizes due to the temperature increase and has negative effects on environment, the fuel delivery pipe as the returnless type has been proposed, which does not return the surplus fuel to the fuel tank. 
     With this fuel delivery pipe of the returnless type, where the fuel is injected from the injection nozzle into the intake pipes or the cylinders, since there is no pipe for returning the surplus fuel to the fuel tank, pressure fluctuation of the fuel inside the fuel delivery pipe becomes large and causes large pressure waves, so that the pressure pulsation occurs greatly in comparison with the fuel delivery pipe of the return type. 
     This invention uses the fuel delivery pipe of the returnless pipe having a tendency to easily cause the pressure pulsation. With the conventional arts, if the internal pressure of the fuel delivery pipe is decreased due to the fuel injection from the injection nozzle into the intake pipe or the cylinder of the engine, the pressure wave generated by this rapidly decreased pressure and by the halt of the fuel injection causes the pressure pulsation inside the fuel delivery pipe. After propagated from the fuel delivery pipe and connecting pipes connected to the fuel delivery pipe to the proximity of the fuel tank, the pressure pulsation is returned as reversed from a pressure-regulating valve assembled inside the fuel tank and is further propagated up to the fuel delivery pipe via the connecting pipe. Plural injection nozzles are formed at the fuel delivery pipe and perform injections sequentially to cause the pressure pulsation. 
     Consequently, the pressure pulsation is propagated as noises in the passenger compartment via clips fastening the under floor pipe arrangement, thereby giving uncomfortable feeing to the driver or passengers. 
     Conventionally, as a means for suppressing such an adverse effect caused by such a pressure pulsation, a pulsation damper containing a rubber diaphragm is arranged at the fuel delivery pipe of the returnless type for absorbing generated pressure pulsation energy, or the underfloor pipe arrangement arranged under the floor as extending from the fuel delivery pipe to the proximity of the fuel tank is secured under the floor by means of the clips for absorbing vibration, thereby absorbing vibration generated at the underfloor pipe arrangement connecting to the fuel delivery pipe or extending to the tank. These means are comparatively effective enough to suppress the adverse effects caused by occurrences of the pressure pulsation. 
     However, the pulsation dampers and the vibration absorbing clips are expensive and increase the number of components to result in higher costs while raising a new problem on ensuring an installation space. Therefore, for the purpose of reducing the pressure pulsation without using the pulsation dampers or the clips for absorbing vibration, a fuel delivery pipe having a pulsation absorptive function capable of absorbing the pressure pulsation, have been proposed. 
     As such a fuel delivery pipes having the pulsation absorptive function, inventions as described in Japanese Patent Application Publication Nos. JA-2000-329030, JA-2000-320422, JA-2000-329031, JA-11-37380, and JA-11-2164 have been known. With these fuel delivery pipes having the absorptive function for the pressure pulsation, a flexible absorbing surface is formed on the outer wall of the fuel delivery pipe, deforming by receiving the occurring pressure in association with the fuel injection, to absorb and reduce the pressure pulsation, thereby to prevent abnormal noise caused by the vibration of the fuel delivery pipe or other components from occurring. 
     The above described conventional arts, however, have the absorption effects for the pressure pulsation but raise problems such that noises in a high frequency area of more than several kHz are generated outside upon a speaker effect exerted by the absorbing surface. 
     With the fuel delivery pipe as described in the Japanese Patent Application Publication No. 2000-329030, the inventors of the present invention, and others have proposed making the fuel delivery pipe absorb the pulsation by making an outer wall of the fuel delivery body the flexible absorbing surface.  FIG. 46  shows an example where the fuel delivery pipe is made to absorb the pulsation by making a whole of a box shaped cross section of the fuel delivery body  81  of the fuel delivery pipe the flexible absorbing surface. Plural sockets  82  are secured to a bottom surface of the fuel delivery body  81 , so the fuel is supplied from a fuel passage  83  into the interior of the injection nozzle, not shown, via a fuel inlet opening  84  of the socket  82 . As vertical and horizontal dimensions of the fuel delivery body  81  having the thickness of 1.2 mm made of a carbon steel member, height H and width W can be set to around 32 mm and 20 mm respectively. 
     The inventors of the present invention, and others assume a situation in which the pressure of ten atmospheres exerts on the interior of the fuel delivery body  81 , and make an FEM (Finite Element Matrix) analysis under the condition that a bracket (in reference to  FIG. 1 ) for securing the fuel delivery body  81  and the socket  82  are secured to a bottom surface, thereby calculating an increasing rate of an internal volume while displaying in  FIG. 47  the changing situation of the cross section shape with enlarging a variation thereof. 
     As shown in  FIG. 47 , a left side wall  85  and a right side wall  86  of an inner wall surface of the fuel delivery body  81  are curved as expanded in a horizontal direction, e.g., from a dashed line to a solid line by receiving an internal pressure, but in terms of an upper wall  87  and a lower wall  88 , each of the walls ends up curved as shrunk inwardly, and it was turned out that the increasing rate of the internal volume remains at around 0.55%. 
     Subsequently, as a result of making the same analysis with transforming the cross section shape in a perpendicular direction to an axis of the fuel delivery body  81 , from the box shape into, e.g., a double side concaved shape, a hand drum shape, a flask shape, a reverted flask shape, a trapezoid shape, and a reverted trapezoid shape (in reference to  FIG. 1 ,  FIG. 2 ,  FIG. 4  to  FIG. 30 , and  FIG. 37  to  FIG. 42 ), it was found that the increasing rate of the internal volume greatly increases to between 1.1% and 1.8%. It is thought that because lefts and rights of these shapes are originally curved surfaces, curved surfaces are deformed, by receiving the pressure, in a direction to decrease a curvature, and therefore, bending is absorbed in the left and right directions while the upper and the lower surfaces hardly deforms, so that an amount of the internal volume becomes inceased. 
     Though the FEM analysis is a numerical analysis with use of a computer, a reliability thereof is considerably high because modifications are always made thereto with feedbacks based on a result of reproduced experiments with use of real things. 
     “A fuel feeding pipe of a fuel injector device for internal combustion engine” according to Japanese Patent Application Publication No. JA-60-240867 discloses that at least one of wall surfaces of a fuel delivery body is elastically structured to attenuate the pulsation of the fuel whereas the cross section of the fuel delivery body is in a triangular shape. The above conventional invention, however, can obtain the attenuation effect of the pressure pulsation but cannot obtain a reduction effect of the noise in the high frequency area. 
     DISCLOSURE OF THE INVENTION 
     To solve aforementioned problems, it is an object of the invention to obtain a fuel delivery pipe capable of reducing a pressure pulsation at the time of a fuel injection due to injection nozzles, preventing vibrations and noises at an underfloor pipe arrangement, and turning down a radiate sound from the fuel delivery pipe. It is another object of this invention to reduce costs by producing products having a great reduction effect of the pressure pulsations as well as the radiate noises without use of any expensive parts, e.g., pulsation dampers or clips for absorbing the vibration. It is yet another object of this invention to form the fuel delivery body without enlarging any dimension of outer diameters thereof as to be installed in a limited space, e.g., an interior of an engine room. It is further another object to provide a structure of the fuel delivery pipe exerting the attenuation effect of the pressure pulsation, capable of reducing the radiate sound, in which the outer diameter thereof does not need to be enlarged. 
     To solve aforementioned problems, the first invention is a fuel delivery pipe, in which a fuel inlet pipe connected to a fuel delivery body of a returnless type having an injection nozzle or nozzles but not having any return circuit connecting to a fuel tank is coupled to the fuel tank through an underfloor pipe arrangement, characterized in that: a cross section shape in a perpendicular direction to an axis of the fuel delivery pipe, is formed in a substantially rectangular shape; two wall surfaces at long sides of the substantially rectangular shape are respectively bent inwardly as formed in a double side concave shape; a socket for connecting each injection nozzle is secured to either of two wall surfaces in a flat shape at short sides or either of two wall surfaces at long sides; and a flexible absorbing wall surface is furnished by said two long side wall surfaces to absorb pulsation by deformation upon receiving pressure in association with fuel injection. 
     Flat portions may be respectively formed around centers of the above two long side wall surfaces. 
     The second invention is a fuel delivery pipe, in which a fuel inlet pipe connected to a fuel delivery body of a returnless type having an injection nozzle but not having return circuit connecting to a fuel tank is coupled to the fuel tank through an underfloor pipe arrangement, characterized in that: a cross section shape in a perpendicular direction to an axis of the fuel delivery pipe, is formed in a substantially flask shape, wherein a substantially rectangular shape is mounted on a top side of a trapezoid; a socket for connecting each injection nozzle, is secured to either a bottom surface or an upper surface, or either of two side surfaces of the substantially flask shaped cross section; and a flexible absorbing wall surface is furnished by two side surfaces of the substantially flask shaped cross section to absorb pulsation by deformation upon receiving pressure in association with fuel injection. 
     The third invention is a fuel delivery pipe, in which a fuel inlet pipe connected to a fuel delivery body of a returnless type having an injection nozzle but not having return circuit connecting to a fuel tank is coupled to the fuel tank through an underfloor pipe arrangement, characterized in that: a cross section shape in a perpendicular direction to an axis of the fuel delivery pipe, is formed in a shape of a substantial flask with a doom roof, in which a substantially rectangular shape is mounted on a top side of a trapezoid while a top portion of the substantially rectangular shape is bent in an arc shape; a socket for connecting each injection nozzle, is secured to a bottom surface or either of two side surfaces of the substantially flask shaped cross section; and a flexible absorbing wall surface is furnished by two side surfaces of the substantially flask shaped cross section to absorb pulsation by deformation upon receiving pressure in association with fuel injection. 
     The fourth invention is a fuel delivery pipe, in which a fuel inlet pipe connected to a fuel delivery body of a returnless type having an injection nozzle but not having return circuit connecting to a fuel tank is coupled to the fuel tank through an underfloor pipe arrangement, characterized in that: a cross section shape in a perpendicular direction to an axis of the fuel delivery pipe, is formed in a reverted flask shape, in which a reverted trapezoid is mounted on a top side of a substantially rectangular shape; a socket for connecting each injection nozzle, is secured to a bottom surface of the reverted flask shaped cross section; and a flexible absorbing wall surface is furnished by two side surfaces of the reverted flask shaped cross section to absorb pulsation by deformation upon receiving pressure in association with fuel injection. 
     The fifth invention is a fuel delivery pipe, in which a fuel inlet pipe connected to a fuel delivery body of a returnless type having an injection nozzle but not having return circuit connecting to a fuel tank is coupled to the fuel tank through an underfloor pipe arrangement, characterized in that: a cross section shape in a perpendicular direction to an axis of the fuel delivery pipe, is formed in a substantially trapezoid shape, in which two hypotenuses of the substantially trapezoid shaped cross section are respectively bent inwardly; a socket for connecting each injection nozzle, is secured to either a bottom surface or an upper surface, or either of two hypotenuses of the substantially trapezoid shaped cross section; and a flexible absorbing wall surface is furnished by two hypotenuses of the substantially trapezoid shaped cross section to absorb pulsation by deformation upon receiving pressure in association with fuel injection. 
     The sixth invention is a fuel delivery pipe, in which a fuel inlet pipe connected to a fuel delivery body of a returnless type having an injection nozzle but not having return circuit connecting to a fuel tank is coupled to the fuel tank through an underfloor pipe arrangement, characterized in that: a cross section shape in a perpendicular direction to an axis of the fuel delivery pipe, is formed in a shape of a substantial trapezoid with a doom roof, in which a substantially trapezoid shape is formed and a top portion thereof is bent in an arc shape while two hypotenuses of the substantially trapezoid shape are respectively bent inwardly; a socket for connecting each injection nozzle, is secured to a bottom surface or either of two hypotenuses of the substantially trapezoid shaped cross section; and a flexible absorbing wall surface furnished by two hypotenuses of the substantially trapezoid shaped cross section to absorb pulsation by deformation upon receiving pressure in association with fuel injection. 
     The seventh invention is a fuel delivery pipe, in which a fuel inlet pipe connected to a fuel delivery body of a returnless type having an injection nozzle but not having return circuit connecting to a fuel tank is coupled to the fuel tank through an underfloor pipe arrangement, characterized in that: a cross section shape in a perpendicular direction to an axis of the fuel delivery pipe, is formed in a reverted trapezoid shape, in which two hypotenuses of the reverted trapezoid shape are respectively bent inwardly; a socket for connecting each injection nozzle, is secured to a bottom surface of the reverted trapezoid shaped cross section; and a flexible absorbing wall surface is furnished by two hypotenuses of the reverted trapezoid shaped cross section to absorb pulsation by deformation upon receiving pressure in association with fuel injection. 
     The eighth invention is a fuel delivery pipe, in which a fuel inlet pipe connected to a fuel delivery body of a returnless type having an injection nozzle but not having return circuit connecting to a fuel tank is coupled to the fuel tank through an underfloor pipe arrangement, characterized in that: a cross section shape in a perpendicular direction to an axis of the fuel delivery pipe, is formed in a substantially key shape, in which a substantially rectangular shape having a narrower width is mounded on a top side of another substantially rectangular shape; a socket for connecting each injection nozzle, is secured to either a bottom surface or an upper surface, or either of two side surfaces of the substantially key shaped cross section; and a flexible absorbing wall surface is furnished by two side surfaces of the substantially key shaped cross section to absorb pulsation by deformation upon receiving pressure in association with fuel injection. 
     The ninth invention is a fuel delivery pipe, in which a fuel inlet pipe connected to a fuel delivery body of a returnless type having an injection nozzle but not having return circuit connecting to a fuel tank is coupled to the fuel tank through an underfloor pipe arrangement, characterized in that: a cross section shape in a perpendicular direction to an axis of the fuel delivery pipe, is formed in a shape of a substantially key with a dome roof, in which a substantially rectangular shape having a narrower width is mounded on a top side of another substantially rectangular shape while the top portion of the substantially rectangular shape having the narrower width is bent in an arc shape; a socket for connecting each injection nozzle, is secured to a bottom surface or either of two side surfaces of the substantially key shaped cross section; and a flexible absorbing wall surface is furnished by two side surfaces of the substantially key shaped cross section to absorb pulsation by deformation upon receiving pressure in association with fuel injection. 
     The tenth invention is a fuel delivery pipe, in which a fuel inlet pipe connected to a fuel delivery body of a returnless type having an injection nozzle but not having return circuit connecting to a fuel tank is coupled to the fuel tank through an underfloor pipe arrangement, characterized in that: a cross section shape in a perpendicular direction to an axis of the fuel delivery pipe, is formed in a substantially goggles shape, in which a substantially center portion of either of two long side wall surfaces of a substantially rectangular shape is inwardly bent as a concaved shape; a socket for connecting each injection nozzle, is secured to the other substantially flat shaped long side wall surface or either of two flat shaped short side wall surfaces; and a flexible absorbing wall surface is furnished by at least one long side wall surface having the substantially center portion bent as a concaved shape to absorb pulsation by deformation upon receiving pressure in association with fuel injection. 
     Two long side wall surfaces may be parallel. 
     Either of two long side wall surfaces may be formed as outwardly protruded. 
     At least one of four corners of the cross section shape of the fuel delivery body may be formed in the arc shape. 
     The eleventh invention is a fuel delivery pipe, in which a fuel inlet pipe is connected to a fuel delivery body of a returnless type having an injection nozzle and no return circuit to a fuel tank, and the fuel inlet pipe is coupled to the fuel tank through an underfloor pipe arrangement, characterized in that: a flexible absorbing wall surface is formed on a wall surface of the fuel delivery body, in which the absorbing wall is loosened due to internal pressure changes to render internal volume of the fuel delivery body increasable while α L /√{square root over ( )}V determined by sonic speed α L  of fuel flowing through the fuel delivery body and the internal volume V of the fuel delivery body is set as 20×10 3 (m −0.5 ·sec −1 )≦α L /√{square root over ( )}V≦85×10 3 (m −0.5 ·sec −1 ); and a ratio α L /α H  of equivalent sonic speed α H  in a high frequency area of the fuel flowing through an interior of the fuel delivery body to the sonic speed α L  of the fuel is set as α L /α H ≦0.7. 
     α L /√{square root over ( )}V may be equal to 35×10 3 (m −0.5 ·sec −1 )≦α L /√{square root over ( )}V≦85×10 3 (m −0.5 ·sec −1 ) while α L /α H  may be equal to α L /α H ≦0.7. 
     α L /√{square root over ( )}V may be equal to 20×10 3 (m −0.5 ·sec −1 )≦α L /√{square root over ( )}V≦35×10 3 (m −0.5 ·sec −1 ) while α L /α H  may be equal to 0.35≦α L /α H ≦0.7. 
     The absorbing wall surface can be formed to increase the internal volume of the fuel delivery body by forming at least one portion of the fuel delivery body surfaces as inwardly bent to render the bent portion relaxing outwardly to the change of the internal pressure. 
     Since this invention is thus structured, with the fuel delivery pipe as described in the first invention to the tenth invention, a volume changing rate in a case of a reception of the same pressure as before increases sharply, and the absorption effect for the pulsation by the flexible absorbing wall surface is enhanced, so that transmission, propagation, and radiation of the abnormal noises, e.g., the radiant sound are adequately suppressed. Since it is almost unnecessary to enlarge the outside dimension of the fuel delivery body, the fuel delivery body can be installed in the limited space inside the engine room even where made to replace existing fuel delivery pipes, so the fuel delivery pipe can maintain interchangeability as a component. 
     As a theoretical basis for a pulsation absorption by the absorbing wall surface, it is understood that when a shock wave occurring at the time of opening and closing of the injection nozzle flows into or, because of a momentary backward flow, flows out of a fuel inlet opening of the socket, shocks or pulsations are absorbed by a flexion of the flexible absorbing wall surface, and that a thin member having a comparatively low spring constant loosens and deforms to change the internal volume, thereby absorbing fluctuations in the pressure of the fuel. 
     Each of the first invention to tenth invention demonstrates the same advantageous effects by adopting various types of cross section shapes as described below:
     (1) the cross section shape in a perpendicular direction to an axis of the fuel delivery body is a substantially rectangular shape, in which two wall surfaces at long sides of the rectangular shape are respectively bent inwardly as formed in a double side concave shape;   (2) the substantially hand dram shape, in which flat portions are respectively formed around centers of two long side wall surfaces of the cross section in the double side concaved shape;   (3) the cross section shape in the perpendicular direction to the axis of the fuel delivery body is a substantially flask shape, in which the substantially rectangular shape is mounted on a top side of a trapezoid;   (4) the cross section shape in the perpendicular direction to the axis of the fuel delivery body is a substantially flask shape, in which a substantially rectangular shape is mounted on the top side of the trapezoid while a top portion of the substantially rectangular shape is bent in the arc shape as formed in a shape of the substantial flask with a doom roof;   (5) the cross section shape in the perpendicular direction to the axis of the fuel delivery body is a reverted flask shape, in which the reverted trapezoid is mounted on a top side of the substantially rectangular shape;   (6) the cross section shape in the perpendicular direction to the axis of the fuel delivery body is a substantially trapezoid shape;   (7) the cross section shape in the perpendicular direction to the axis of the fuel delivery body is a substantially trapezoid shape, in which a top portion of a shape of the trapezoid is bent in the arc shape as formed in a substantial trapezoid with the doom roof;   (8) the cross section shape in the perpendicular direction to the axis of the fuel delivery body is the reverted trapezoid shape, in which two hypotenuses of the reverted trapezoid shape are respectively bent inwardly;   (9) the cross section shape in the perpendicular direction to the axis of the fuel delivery body is the substantially key shape, in which the substantially rectangular shape having the narrower width is mounded on a top side of another substantially rectangular shape;   (10) the cross section shape in the perpendicular direction to the axis of the fuel delivery body is the substantially key shape, in which the top portion of the substantially rectangular shape having the narrower width is bent in the arc shape as formed in the substantially key with the dome roof; and   (11) the cross section shape in the perpendicular direction to the axis of the fuel delivery body is the substantially rectangular shape, in which a substantially center portion of either of two long side wall surfaces is inwardly bent in a concaved shape as formed in a substantially goggles shape.   

     It is to be noted that each of the cross section shapes does not need to be exactly in a horizontally symmetric shape. The socket to be connected to the fuel delivery body may be arranged at any position of an upper surface, a bottom surface, and two side surfaces of the wall surface while the fuel delivery body is used in a state where the wall surface connected to the socket is exposed a lower side. 
     Furthermore, the fuel delivery bodies having the predetermined cross section shapes as described the above can be formed in use of well-known fabrication methods as described below with following materials for forming each cross section shape,
     (A) a seamless pipe (except for seams at the time of manufacturing a annular pipe) fabricated from the annular pipe;   (B) a pipe formed by combining two channel members with welding a seam between the two channel members; and   (C) a pipe in which a member partly overlapped on one another by pressing work.   

     With the first to tenth inventions, a plate thickness, an aspect ratio, or material or strength of constructing members of an outer wall portion and the absorbing wall surface of the fuel delivery body can be determined through experiments or analyses so that the vibration or pulsation is to be at the lowest level particularly during the period of an engine idling. 
     The fuel delivery pipe according to the first to tenth inventions can maintain the interchangeability with conventional fuel delivery pipes by maintaining an installation dimension of brackets. 
     The eleventh invention relates to a structure (mechanism) for reducing the pressure pulsation and the radiant sound, and where the pressure pulsation occurs in association with the fuel injection via the injection nozzles, value of a pressure fluctuation relates closely to sonic speed α L  of fuel flowing through the interior of the fuel delivery pipe and to internal volume of the fuel delivery body, and the relation thereof is set as a proportional expression described as following Numerical Expression 1. 
                   P   ∝       α   ⁢           ⁢   L       V               [     Numerical   ⁢           ⁢   Expression   ⁢           ⁢   1     ]               
P: the value of pressure fluctuation, α L : the sonic speed of fuel inside the fuel delivery pipe, V: the internal volume of the fuel delivery body
 
     Therefore, by reducing the sonic speed α L  of fuel flowing through the interior of the fuel delivery pipe, the pulsation fluctuation P can be reduced With respect to the sonic speed α L , the following numerical expression is satisfied based on the law of momentum and an equation of continuity. Furthermore, the following numerical expression is satisfied based on the definition of the volume elasticity. 
                     α   L     =         1   ρ         1     K   ⁢           ⁢   f       +     1     K   ⁢           ⁢   r                     [     Numerical   ⁢           ⁢   Expression   ⁢           ⁢   2     ]               
ρ: density of the fuel, K f : the volume elasticity of the fuel, K r : the volume elasticity inside the duel delivery pipe.
 
                   Kr   =       Δ   ⁢           ⁢   p         Δ   ⁢           ⁢   V     V               [     Numerical   ⁢           ⁢   Expression   ⁢           ⁢   3     ]               
Δp: a variation of the internal pressure inside the fuel delivery body, ΔV: a volume variation for an elasticity of the fuel delivery body at the time of adding the internal pressure
 
     Based on the numerical analysis, e.g., FEM, with use of the above numeral Expressions, the sonic speed α L  of the fuel flowing through the fuel delivery body can be sought. The sonic speed α L  of the fuel can be reduced just by reducing K r , i.e., the volume elasticity inside the fuel delivery body, and Kr can be reduced just by increasing the internal volume of the fuel delivery body at the time of adding the internal pressure. Herein, with the fuel delivery pipe according to this invention, having the flexible absorbing wall surface, the flexible absorbing wall surface loosens outwardly due to the change of the internal pressure thereby to increase the internal volume, so that the fuel delivery pipe according to this invention has the great absorption effect for the pressure pulsation and can suppress the transmission and the propagation of the pulsations and the noises to the underfloor pipe arrangement. 
     On the other hand, it is possible to calculate equivalent sonic speed α H  in a high frequency area of several kHz or more considered as a problem on clicking noises occurring when a spool of the injection nozzle is seated on a valve seat and other radiant sounds, by seeking a mode and frequency of an air column vibration inside the fuel delivery body. That is, the mode of the air column vibration applies to a condition of the air column with both ends thereof being blocked, so the relation as the following Numerical Expression is satisfied. 
                   f   =       n   ⁢           ⁢   α   ⁢           ⁢   H       2   ⁢           ⁢   l               [     Numerical   ⁢           ⁢   Expression   ⁢           ⁢   4     ]               
f: the frequency, n: mode order of the air column vibration, l: air column length of the fuel delivery pipe
 
     Based on the above Numerical Expression 4, the following Numerical Expression 5 can determine the equivalent sonic speed α H  in the high frequency area. 
     
       
         
           
             
               
                 
                   
                     α 
                     H 
                   
                   = 
                   
                     
                       2 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       fl 
                     
                     n 
                   
                 
               
               
                 
                   [ 
                   
                     Numerical 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Expression 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                   ] 
                 
               
             
           
         
       
     
     When calculated with use of the above Numerical Expressions, the equivalent sonic speed α H  in the high frequency of the conventional fuel delivery pipe is approximately same as the sonic speed α L  of said fuel, and where α L  is reduced to reduce the pressure pulsation, α H  also reduces, thereby raising a problem such that the radiant sound becomes larger. With the fuel delivery pipe according to this invention, however, the absorbing wall surface forms, because of the pulsation in the high frequency considered as the problem with respect to the radiant sound, into a mode shape having a number of loops and nodes, or an not-readily bent shape, so that the absorbing wall surface in the high frequency is less loosened. The equivalent sonic speed α H  in the high frequency, therefore, does not reduce even where the sonic speed α L  is reduced, so that occurrences of the loud radiant sound are suppressed effectively. 
     As the result of the numeral analyses and the experiments made by the inventor of the present invention, and others, the fuel delivery pipe having great effects, both the absorption effect for the pressure pulsation and the prevention effect for the radiant sound is obtainable with the structure such that α L /√{square root over ( )}V determined by sonic speed α L  of fuel and the internal volume V of the fuel delivery body is set as 20×10 3 (m −0.5 ·sec −1 )≦α L /√{square root over ( )}V≦85×10 3 (m −0.5 ·sec −1 )as well as such that a ratio α L /α H  of equivalent sonic speed α H  in the high frequency area to the sonic speed α L  of the fuel is set as α L /α H ≦0.7. 
     To keep within the above range, i.e., to render α L /√{square root over ( )}V&lt;20×10 3 (m 0.5 ·sec −1 ) satisfied, it is necessary to reduce α L  or to increase V. The internal volume V needs to be increased in order to increase α L , and furthermore, a thickness of the wall surface needs to be thinly formed to increase the internal volume V, so that the fuel delivery pipe for the pulsation at the time of the fuel injection is made less durable. Furthermore, it is necessary to increase a width, a height, and a length of the formation of the fuel delivery body in order to increase the internal volume V, so the internal volume V becomes bulky, the pipe looses compactness on vehicle layout. Conversely, where α L /√{square root over ( )}V≦85×10 3 (m −0.5 ·sec −1 ) is satisfied, the increasing rate of the internal volume V due to the internal pressure decreases to result in rendering the products poorly absorptive for the pulsation, so that the underfloor pipe arrangement may be vibrated. 
     Furthermore, on condition that α L /α H &gt;0.7 is satisfied, where the sonic speed α L  of the fuel is reduced to enhance a pulsation absorptiveness, the equivalent sonic speed α H  in the high frequency area is also reduced in proportion to the sonic speed α L , resulting in the radiant sound louder, so the product has a poor suppression effect for the radiant sound, thereby causing clicking noised. 
     With the fuel delivery pipe according to this invention, like the above, it becomes possible not only to have the great absorption effect for the pressure pulsation due to the fuel injection via the injection nozzles to prevent effectively the vibration or the noise from occurring at the underfloor pipe arrangement, but also to suppress sound radiation in the high frequency area, e.g., clicking noises occurring when the spool of the injection nozzle is seated on the valve seat or the like. It is therefore unnecessary to use the expensive components, e.g., the pulsation dampers or the clips for absorbing the vibration, thereby being able to reduce of the production costs, and it is also possible to obtain the not-bulky product suppressing enlargement of the outside dimension thereof and having great layout property allowing installation in the limited space, e.g., the engine room, and the product can be replaced with the existing fuel delivery pipes, thereby being able to maintain the interchangeability as the component. 
     Where α L /√{square root over ( )}V is set as 35×10 3 (m −0.5 ·sec −1 )≦α L /√{square root over ( )}V≦85×10 3 (m −0.5 ·sec −1 ) while α L /α H  is set as α L /α H &gt;0.7, the fuel delivery pipe is suitable for use in, e.g., compact automobiles mounted with a comparatively small engine (660-1000 cc class) with four cylinders or the like, though the reduction effect for the pressure pulsation may be comparatively low. 
     Where α L /√{square root over ( )}V is set as 20×10 3 (m −0.5 ·sec −1 )≦α L /√{square root over ( )}V≦35×10 3 (m −0.5 ·sec −1 ) while α L /α H  is set as 0.35≦α L /α H ≦0.7, the prevention effect for the radiant sound or the pressure pulsation absorptiveness of the fuel delivery pipe is particularly superior, so the fuel delivery pipe is suitable for use in, e.g., automobiles mounted with a large size engine (1300-2500 cc class) with four to six or more cylinders, requiring the great reduction effect for the pressure pulsation. 
     It is physically impossible that the value of the equivalent sonic speed α H  in the high frequency area becomes faster than the original sonic speed of the fuel inside the fuel delivery pipe, so the sonic speed α L  of the fuel needs to be reduced in order to reduce the sonic speed α L /α H , which, as described above, means that wall thickness is made thin in order to enlarge the amount of deformation to lead to deterioration of the durability. It is therefore desirable to set α L /α H  to 0.35 or higher since the value of α L  is limited to avoid breakdown of the fuel delivery body due to the internal pressure in use. 
     The absorbing wall surface may be formed in any shape capable of enlarging the internal volume of the fuel delivery body by loosening upon receiving the internal pressure, but where at least one portion of the wall surface of the fuel delivery body is made to be bent inwardly, i.e., more desirably, made to curved gently with a comparatively large radius of curvature to form the absorbing wall surface, it becomes possible to make the internal volume of the fuel delivery body increase since the curved portion loosened outwardly to a change of the internal pressure. As an effect of the absorbing wall surface like the above, in a case of the absorbing wall surface not having the wall surface curved inwardly, where the absorbing wall surface is outwardly loosened, a portion of non-absorbing wall surface, conversely, may shrink inwardly, so it is difficult to increase greatly the internal volume. However, where the wall surface is made to be curved inwardly to form the absorbing wall surface, the curved portion loosens outwardly to be in a liner shape, thereby lengthening a distance between end points of the absorbing wall surfaces, so that the non-absorbing wall surface continuous to the above absorbing wall surface does not shrink inwardly but, conversely, expands outwardly, and so that the increasing rate of the internal volume of the fuel delivery body can be greatly improved. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a perspective view showing a fuel delivery pipe according to the first embodiment of this invention; 
         FIG. 2  is a cross-sectional view along a line A-A of  FIG. 1 ; 
         FIG. 3  is a conceptual diagram showing a state where an absorbing wall surface of the fuel delivery body according to the first embodiment yields to a internal pressure to change the internal volume of the fuel delivery body; 
         FIG. 4  is an essential cross-sectional view of a fuel delivery body according to the second embodiment, and a cross section shape is in a double side concaved shape; 
         FIG. 5  is an essential cross-sectional view of a fuel delivery body in a flask shape according to the third embodiment; 
         FIG. 6  is an essential cross-sectional view of a fuel delivery body in a key shape according to the fourth embodiment; 
         FIG. 7  to  FIG. 13  are essential cross-sectional views of a fuel delivery body in the double side concaved shape according to the fifth embodiment to the eleventh embodiment; 
         FIG. 14  to  FIG. 19  are essential cross-sectional views of a fuel delivery body in a goggles shape according to the twelfth embodiment to the seventeenth embodiment; 
         FIG. 20  to  FIG. 23  are essential cross-sectional views of a fuel delivery body in the key shape according to the eighteenth embodiment to the twenty-first embodiment; 
         FIG. 24  is an essential cross-sectional view of a fuel delivery body in the double side concaved shape according to the twenty-second embodiment; 
         FIG. 25  to  FIG. 27  are essential cross-sectional views of a fuel delivery pipe in the flask shape according to the twenty-third embodiment to the twenty-fifth embodiment; 
         FIG. 28  is an essential cross-sectional view of a fuel delivery pipe in a trapezoid shape according to the twenty-sixth embodiment; 
         FIG. 29  is an essential cross-sectional view of a fuel delivery body in the flask shape formed by combining a plurality of shaped plate materials according to the twenty-seventh embodiment; 
         FIG. 30  is an essential cross-sectional view of a fuel delivery body in the flask shape formed by superimposing parts of plate materials one another by means of a press working according to the twenty-eighth embodiment; 
         FIG. 31  is a conceptual diagram showing a state of nodes and loops at a mode of an air column vibration, based on an FEM analysis, in a frequency of around four kHz of the fuel delivery body in a double side concaved shape according to the first embodiment and the second embodiment; 
         FIG. 32  is a conceptual diagram showing nodes and loops at the mode of the air column vibration, based on a FEM analysis, in the frequency of around four kHz of the fuel delivery body in the flask shape according to the third embodiment; 
         FIG. 33  is a conceptual diagram showing nodes and loops at the mode of the air column vibration in the frequency of around four kHz of the fuel delivery body in a flat shape according to the second conventional example to the sixth conventional example, wherein A to I in the  FIG. 31  to  FIG. 33  shows a change of an internal pressure in a certain phase of the fuel delivery body; 
         FIG. 34  is a correlation graph of the number of modes of an air column vibration in a high frequency area and the frequency thereof at fuel delivery pipes according to the first conventional example to the fourth conventional example and the fist embodiment to the fourth embodiment; 
         FIG. 35  is a linear approximation graph of the mode two or later at the fuel delivery pipes according to the first conventional example to the fourth conventional example and the first embodiment to the fourth embodiment; 
         FIG. 36  is a graph showing a comparison of radiant sounds between the fuel delivery pipes according to the fist embodiment and the sixth conventional example respectively having equal pulsation absorbencies each other; 
         FIG. 37  is a cross-sectional perspective view of the twenty-ninth embodiment, wherein an evaginated portion is formed at a middle of a fuel delivery body in a trapezoid shape; 
         FIG. 38  is an essential cross-sectional view of a fuel delivery body having a cross section in a shape of a substantially flask with a doom roof according to the thirtieth embodiment; 
         FIG. 39  is an essential cross-sectional view of a fuel delivery body having the cross section in a shape of a substantially trapezoid with the doom roof according to the thirty-first embodiment; 
         FIG. 40  is an essential cross-sectional view of a fuel delivery body having the cross section in a shape of a substantially key with the doom roof according to the thirty-second embodiment; 
         FIG. 41  is an essential cross-sectional view of a fuel delivery body in a reverted flask shape according to the thirty-third embodiment and  FIG. 42  is an essential cross-sectional view of a fuel delivery body in a reverted trapezoid shape according to the thirty-fourth embodiment, wherein both fuel delivery bodies in  FIG. 41  and  FIG. 42  are formed by combining a plurality of shaped plate materials; 
         FIG. 43  is a conceptual diagram showing a state where internal volume of a fuel delivery body in a double side concaved shape with center portions of long side wall surfaces thereof in a smooth arc shape, not having flat portions, changes upon receiving internal pressure; 
         FIG. 44  is a conceptual diagram showing a state where the internal volume of a fuel delivery body in the substantially flask shape changes upon receiving the internal pressure; 
         FIG. 45  is a conceptual diagram showing a state where the internal volume of a fuel delivery body in the reverted flask shape changes upon receiving the internal pressure; 
         FIG. 46  is a sectional view of a fuel delivery body and a socket of a conventional fuel delivery pipe; 
         FIG. 47  is a conceptual diagram showing a deformation state of a conventional fuel delivery body; and 
         FIG. 48  is a cross-sectional view of a fuel delivery pipe in the flat shape according to the second conventional example to the sixth conventional example used in an experiment. 
     
    
    
     BEST MODE FOR CARRYING OUT THE INVENTION 
     Hereinafter, embodiments according to this invention will be described in detail with reference to the drawings. The following table 1 shows sonic speed α L (m/s), cross-sectional area A (mm 2 ), internal volume V (mm 3 ), α L /√{square root over ( )}V (m −0.5 ·sec −1 ), equivalent sonic speed α H  (m/s) in a high frequency area, α L /α H , and thickness (mm) of a fuel delivery body according to the first embodiment to the twenty-fifth embodiment of this invention. For the sake of comparison, Table 1 shows data of a rectangular shaped fuel delivery body (the first conventional example) not having an absorbing wall surface and flat shaped fuel delivery bodies (the second conventional example to the sixth conventional example) having an absorbing wall surface, respectively. 
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                   
                   
                   
                   
                 α L /√V 
                   
                   
                   
               
               
                 type 
                 α L  (m/s) 
                 A (mm 2 ) 
                 V (mm 3 ) 
                 (10 m −0.5  · s −1 ), 
                 α H  (m/s) 
                 α L /α H   
                 thickness 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 1st conventional example 
                 916 
                 184 
                 59426 
                 119 
                 902 
                 1.02 
                 1.2 
               
               
                 W16 × H16 × L325 
               
               
                 2nd conventional example 
                 415 
                 191 
                 61540 
                 53 
                 407 
                 1.02 
                 1.2 
               
               
                 W28 × H10.2 × L325 
               
               
                 3rd conventional example 
                 302 
                 236 
                 76251 
                 35 
                 306 
                 0.99 
                 1.2 
               
               
                 W34 × H10.2 × L325 
               
               
                 4th conventional example 
                 362 
                 236 
                 40796 
                 57 
                 357 
                 1.01 
                 1.2 
               
               
                 W34 × H10.2 × L175 
               
               
                 5th conventional example 
                 491 
                 200 
                 34476 
                 84 
                 357 
                 1.01 
                 1.2 
               
               
                 W28 × H10.2 × L175 
               
               
                 6th conventional example 
                 261 
                 247 
                 79682 
                 29 
                 267 
                 1.01 
                 1 
               
               
                 W32.7 × H10.2 × L325 
               
               
                 1st embodiment 
                 287 
                 468 
                 150879 
                 23 
                 663 
                 0.43 
                 1.2 
               
               
                 double side concaved shape 
               
               
                 placed vertically L325 
               
               
                 2nd embodiment 
                 298 
                 468 
                 150879 
                 24 
                 587 
                 0.51 
                 1.2 
               
               
                 double side concaved shape 
               
               
                 placed horizontally L325 
               
               
                 3rd embodiment 
                 276 
                 289 
                 93097 
                 29 
                 620 
                 0.45 
                 1.2 
               
               
                 large flask shape placed 
               
               
                 horizontally L325 
               
               
                 4th embodiment 
                 252 
                 205 
                 66155 
                 31 
                 446 
                 0.57 
                 1.2 
               
               
                 small key shape placed 
               
               
                 horizontally L325 
               
               
                 5th embodiment 
                 320 
                 221 
                 74647 
                 37 
                 610 
                 0.52 
                 1.2 
               
               
                 double side concaved shape 
               
               
                 L340 
               
               
                 6th embodiment 
                 308 
                 136 
                 46041 
                 45 
                 568 
                 0.54 
                 1 
               
               
                 double side concaved shape 
               
               
                 L340 
               
               
                 7th embodiment 
                 362 
                 229 
                 77408 
                 41 
                 650 
                 0.56 
                 1.2 
               
               
                 double side concaved shape 
               
               
                 L340 
               
               
                 8th embodiment 
                 486 
                 228 
                 76938 
                 55 
                 699 
                 0.7 
                 1.2 
               
               
                 double side concaved shape 
               
               
                 L340 
               
               
                 9th embodiment 
                 277 
                 177 
                 59701 
                 36 
                 586 
                 0.47 
                 1 
               
               
                 double side concaved shape 
               
               
                 L340 
               
               
                 10th embodiment 
                 284 
                 238 
                 80201 
                 32 
                 757 
                 0.37 
                 1 
               
               
                 double side concaved shape 
               
               
                 L340 
               
               
                 11th embodiment 
                 209 
                 159 
                 53515 
                 29 
                 486 
                 0.43 
                 1 
               
               
                 double side concaved shape 
               
               
                 L340 
               
               
                 12th embodiment 
                 280 
                 194 
                 65419 
                 35 
                 555 
                 0.5 
                 1 
               
               
                 goggles shape L340 
               
               
                 13th embodiment 
                 263 
                 234 
                 78993 
                 30 
                 513 
                 0.51 
                 1.2 
               
               
                 goggles shape L340 
               
               
                 14th embodiment 
                 262 
                 221 
                 74642 
                 30 
                 519 
                 0.5 
                 1.2 
               
               
                 goggles shape L340 
               
               
                 15th embodiment 
                 249 
                 218 
                 73523 
                 29 
                 483 
                 0.52 
                 1 
               
               
                 goggles shape L340 
               
               
                 16th embodiment 
                 267 
                 218 
                 73463 
                 31 
                 464 
                 0.58 
                 1.2 
               
               
                 goggles shape L340 
               
               
                 17th embodiment 
                 211 
                 250 
                 84567 
                 23 
                 469 
                 0.45 
                 1 
               
               
                 goggles shape L340 
               
               
                 18th embodiment 
                 274 
                 199 
                 67099 
                 33 
                 517 
                 0.53 
                 1.2 
               
               
                 key shape L340 
               
               
                 19th embodiment 
                 269 
                 205 
                 69067 
                 32 
                 514 
                 0.52 
                 1.2 
               
               
                 key shape L340 
               
               
                 20th embodiment 
                 243 
                 188 
                 63631 
                 30 
                 452 
                 0.54 
                 1.2 
               
               
                 key shape L340 
               
               
                 21st embodiment 
                 284 
                 198 
                 66826 
                 35 
                 488 
                 0.58 
                 1 
               
               
                 key shape L340 
               
               
                 22nd embodiment 
                 276 
                 188 
                 63562 
                 35 
                 566 
                 0.49 
                 1.2 
               
               
                 double side concaved shape 
               
               
                 L340 
               
               
                 23rd embodiment 
                 316 
                 237 
                 80015 
                 35 
                 527 
                 0.6 
                 1.2 
               
               
                 flask shape L340 
               
               
                 24th embodiment 
                 336 
                 201 
                 67734 
                 41 
                 573 
                 0.59 
                 1.2 
               
               
                 flask shape L340 
               
               
                 25th embodiment 
                 284 
                 293 
                 99024 
                 29 
                 633 
                 0.45 
                 1.2 
               
               
                 flask shape L340 
               
               
                   
               
               
                 W = width, H = height, L = length 
               
            
           
         
       
     
     With the aforementioned fuel delivery body of the first conventional example, as shown in Table 1, a cross section thereof is defined as being in a substantially square shape with a width of 16 mm and a height of 16 mm while a thickness and a pipe length thereof are respectively set as 1.2 mm and 325 mm. Furthermore, as shown in  FIG. 48 , in the second conventional example to the sixth conventional example, the cross section of the fuel delivery body  81  is defined as in a flatly rectangular shape. In the second conventional example, the cross section the fuel delivery body is defined as being in the flatly rectangular shape with a width of 28 mm and a height of 10.2 mm while a thickness and a pipe length thereof are respectively defined as 1.2 mm and 325 mm. In the third conventional example, the cross section of the fuel delivery body is defined as being in the flatly rectangular shape with a width of 34 mm and a height of 10.2 mm while a thickness and a pipe length thereof are respectively defined as 1.2 mm and 325 mm. In the fourth conventional example, the cross section of the fuel delivery body is defined as being in the flatly rectangular shape with a width of 34 mm and a height of 10.2 mm while a thickness and a pipe length thereof are respectively defined as 1.2 mm and 175 mm. In the fifth conventional example, the cross section of the fuel delivery body is defined as being in the flatly rectangular shape with a width of 28 mm and a height of 10.2 mm while a thickness and a pipe length thereof are respectively defined as 1.2 mm and 175 mm. In the sixth conventional example, the cross section of the fuel delivery body is defined as being in the flatly rectangular shape with a width of 32.7 mm and a height of 10.2 mm while a thickness and a pipe length thereof are respectively defined as 1.0 mm and 325 mm. 
     Furthermore, with the fuel delivery body in each of the embodiments, a cross section thereof is formed in a particular shape by means of a roll forming process using pipes made of carbon steel, stainless steel, or the like having a circle shaped cross section. 
     Subsequently, where the first embodiment shown in  FIG. 1 ,  FIG. 2 , and  FIG. 3  is described in detail, numeral  1  is a fuel delivery body, where sockets  2  capable of connecting injection nozzles, not shown, are formed on one surface of the fuel delivery body. For example, four sockets  2  are formed with predetermined intervals and angles in a case of a four-cylinder engine. Furthermore, the fuel delivery body  1  has each of ends sealed with an end cap  12 , and one end is connected as secured, by means of brazing or welding, to a fuel inlet pipe  3  connected to a fuel tank, not shown, through an underfloor pipe arrangement, not shown. A return pipe for a return to the fuel tank can be formed to the other end or side surfaces of the fuel delivery body  1  but is not formed to the fuel delivery pipe of a returnless type. 
     Furthermore, fuel in the fuel tank is transferred through the underfloor pipe arrangement to the fuel inlet pipe  3  and then, as an arrow indicates in  FIG. 1 , flows from the fuel inlet pipe  3  to the fuel delivery body  1 , thereby being injected directly into air intake duct or cylinders through the injection nozzle connected to the socket  2 . With the fuel delivery pipe  1 , a thick and firm bracket  4  for connecting the fuel delivery body  1  securely to an engine body is formed on a side at which the sockets  2  are formed. 
     The fuel delivery body  1  according to the first embodiment, as shown in  FIG. 2 , has the cross section in a substantially double side concaved shape, having two flat wall surfaces at short sides and two inwardly bent wall surfaces at long sides. A bottom surface as one side of the flat wall surfaces at the short sides is defined as a lower wall  5  and equipped with the socket  2 . The upper surface as the other side of the flat wall surfaces at the short sides, facing the lower wall  5  is defined as an upper wall  6 . With a left side wall  7  and a right side wall  8  as wall surfaces at the long sides, coupling the upper wall  6  to the lower wall  5 , as shown in  FIG. 2 , coupling portions of the upper wall  6  and lower wall  5  are formed in an arc shape while the cross section is formed in a substantially double side concaved shape like a hand drum shape, in which a pair of flexible absorbing wall surfaces  10  are formed as bent inwardly to form a trapezoid shape comprising a flat straight side and a pair of hypotenuses. The inwardly bent absorbing wall surface  10  yields outwardly to deform because of a change of internal pressure at the time of a fuel injection via the injection nozzles, thereby being able to increase internal volume of the fuel delivery body  1 . 
     The above described fuel delivery body  1  in a double concaved shape according to the first embodiment is composed of the upper wall  6 , the lower wall  5 , the left side wall  7 , and the right side wall  8 , in which the left side wall  7  and the right side wall  8  are couple to the upper wall  6  and the lower wall  5  through an arc shaped curve portions  11 . Furthermore, as shown in  FIG. 2 , the left side wall  7  and the right side wall  8  are inwardly bent to shape a trapezoid shape, thereby being set as the absorbing wall surfaces  10  with a height of 33.6 mm made to face each other with a maximum outer diameter of 22 mm, wherein a length of substantially straight sides of the absorbing wall surface  10  is set to 10.2 mm and an outer diameter between the straight portions of the left side wall  7  and the right side wall  8  is set to 15.2 mm. Furthermore, as shown in Table 1, a thickness is set to 1.2 mm and cross sectional area A inside the fuel delivery body  1  is set to 468 mm 2  while the fuel delivery body  1  is formed with a pipe length of 325 mm, whereas the internal volume V is set to 150879 mm 3 , and the sockets  2  for the injection nozzles are formed, as shown in  FIG. 2 , to the lower wall  5 . 
     In the second embodiment shown in  FIG. 4 , the fuel delivery body  1  is defined as a horizontally long shape, wherein the formation width between the upper wall  6  and the lower wall  5  is set to 33.6 mm, and the height of the left side wall  7  and the right side wall  8  coupled to the upper wall  6  and the lower wall  5  through the arc shape curve portions  11  is set to 22 mm. The upper wall  6  and the lower wall  5 , furthermore, are respectively bent inwardly to shape the trapezoid shape, thereby forming a pair of the absorbing wall surfaces  10 . A length of the substantially straight sides of a pair of the absorbing wall surfaces  10  is set to 10.2 mm, and the outer diameter between the straight portions of the upper wall  6  and the lower wall  5  is set to 15.2 mm. As shown in the table 1, a thickness is set to 1.2 mm and a cross sectional area A inside the fuel delivery body  1  is set to 468 mm 2  while the fuel delivery body  1  is formed with a pipe length of 325 mm, whereas the internal volume V is set to 150879 mm 3 , and the socket  2  for the injection nozzle is formed to the lower wall  5  as a chain double-dashed line indicates in  FIG. 4 . 
     The fuel delivery body  1  according to another embodiment, the third embodiment, as shown in  FIG. 5 , is in the flask shape, wherein a substantially rectangular shape is mounted on a top side of the trapezoid, and the upper wall  6  and the lower wall  5  are formed as bent inwardly to form the absorbing wall surfaces  10  while the left side wall  7  and the right side wall  8  are the substantially straight sides, whereas the cross section shape of the fuel delivery body  1  is formed in a horizontally long flask shape. Furthermore, the heights of the left side wall  7  and the right side wall  8  are respectively set to 9.4 mm and 22 mm, and the outer diameter between the left side wall  7  and the right side wall  8  is set to 32 mm. The left side wall  7  and the right side wall  8  are formed as coupled through the arc shape curve portions  11  to the upper wall  6  and the lower wall  5  respectively composed of the substantially straight side and the hypotenuse. With the upper wall  6  and the lower wall  5 , a length of the substantially straight sides at a side of the left side wall  7  is set to 16.24 mm. Furthermore, as shown in the table 1, a thickness is set to 1.2 mm to set a cross sectional area A inside the fuel delivery body  1  to 289 mm 2  while the fuel delivery body  1  is formed with a pipe length of 325 mm, whereas the internal volume V is set to 93097 mm 3 , and the sockets  2  for the injection nozzles are formed at the side of the substantially straight side of the lower wall  5  as a chain-dashed line indicates in  FIG. 5 . 
     The fuel delivery body  1  according to another embodiment, the fourth embodiment, as shown in  FIG. 6 , is in a key shape, wherein two rectangular shapes of large and small sizes are combined, and the upper wall  6  and the lower wall  5  are formed as bent inwardly to be form absorbing wall surfaces  10  while the left side wall  7  and the right side wall  8  are substantially straight sides, whereas the cross section shape of the fuel delivery body  1  is formed as arranged in a horizontally long key shape. Furthermore, the heights of the left side wall  7  and the right side wall  8  are respectively set to 6.4 mm and 13.6 mm, and the formation width between the upper wall  6  and the lower wall  5  is set to 32 mm. The upper wall  6  and the lower wall  5  are formed by coupling, through hypotenuses, the substantially straight sides with a length of 12.73 formed at the side of the left side wall  7  to the substantially straight sides with a length of 9 mm formed at the side of the right side wall  8 , and both end portions of each of the left side wall  7  and the right side wall  8  are couple to the upper wall  6  and the lower wall  5  through the arc shape curve portions  11 . As shown in the table 1, a thickness is set to 1.2 mm to set a cross sectional area A inside the fuel delivery body  1  to 205 mm 2  while the fuel delivery body  1  is formed with a pipe length of 325 mm, whereas the internal volume V is set to 66155 mm 3 , and the sockets  2  for the injection nozzles are formed at the upper wall  5 , i.e., at the substantially straight side with a length of 9 mm at the side of the right side wall  8 . Though the table 1 shows data in a case of the fuel delivery bodies  1  arranged as shaped in a horizontally long flask shape as the third embodiment and in a horizontal long key shape as the fourth embodiment, it is also possible to use the fuel delivery body  1  arranged as shaped in a vertically long flask shape or key shape, in which, as the chain double-dashed lines in  FIG. 4  and  FIG. 5  indicate, the sockets  2  are formed to either the left side wall  7  or to the right side wall  8  and the wall having the sockets  2  is exposed to an lower side. With the third embodiment as shown in  FIG. 5 , it is to be noted that where the socket  2  are formed to the left side wall  7 ,the fuel delivery body  1  becomes to be in a reverted flask shape. 
     Hereinafter,  FIG. 7  to  FIG. 13  show the fifth embodiment to the eleventh embodiment, all of which are the fuel delivery bodies  1  in the double side concaved shape. It is to be noted that the ninth embodiment shown in  FIG. 11  is in the double side concaved shape, wherein center portions of the wall surfaces at the long sides are in an arc shape while the fifth embodiment to the eighth embodiment, the tenth embodiment, and the eleventh embodiment shown in  FIG. 7  to  FIG. 10 ,  FIG. 12 , and  FIG. 13  are in the same double side concaved shape like the substantially-hand drum shape as the first embodiment, wherein the flat straight sides are formed at the centers of the wall surfaces at the long sides. Each of the drawings shows the cross section shape and the dimension of the outer diameter, while a thickness, a cross sectional area A, the internal volume V, and a pipe length thereof are as shown in the table 1. As shown in each of the drawings, the fifth embodiment to the eleventh embodiment are arranged to be in the horizontally long shape, wherein the absorbing wall surfaces  10  are arranged to the upper wall  6  and the lower wall  5  while, as the chain-dashed line shows, the upper wall  6  is formed as equipped with the socket  2  for the injection nozzle, and measurement of the sonic speed or the like shown in table 1 is done. However, it is also possible to use the fuel delivery body  1  arranged as shaped in the vertically long shape in both upward and downward directions, in which, as the chain double-dashed lines indicate, the sockets  2  are formed to either the right side wall  8  or the left side wall  7  and the wall having the sockets  2  is exposed to the lower side. 
     The twelfth embodiment to the seventeenth embodiment shown in  FIG. 14  to  FIG. 19  are in the rectangular shape comprising two wall surfaces at the long sides and two wall surfaces at the short sides, in which the center portion of the upper wall  6  as the one side of two wall surfaces at the long sides is formed as curved inwardly to form the concaved shape, thereby forming the absorbing wall surface  10 , whereas the cross section of the fuel delivery body  1  is set to be in a goggles shape. Each of the drawings shows the cross section shape and the dimension of the outer diameter, while a thickness, a cross sectional area A, the internal volume V, and a pipe length thereof are as shown in the table 1. Herein, the dimension of the outer diameter of seventeenth embodiment shown in  FIG. 19  is same as that of the thirteenth embodiment but, as shown in the table 1, a thickness, a cross sectional area A, and the internal volume V of the thirteenth embodiment are respectively set to 1.2 mm, 234 mm 2 , and 78993 mm 3  while a thickness of the seventeenth embodiment is set to 1.0 mm to set a cross sectional area V and the internal volume V thereof to 250 mm 2  and 84567 mm 3 . With each of the embodiments, as shown in the drawings, the socket  2  for the injection nozzle is formed, as the chain dashed line indicates, to the lower wall  5  on the side opposite to the upper wall  6  having the curved side in a concaved shape. In a case of the fuel delivery body  1  in the goggles shape, in like manner, the fuel delivery body  1  may also be used in a state of being arranged in the vertically long shape in both upward and downward directions, in which the sockets  2  for the injection nozzles may also be formed, as the chain double-dashed lines indicate, to either the right side wall  8  or to the left side wall  7  and the wall having the sockets is exposed to the lower side. 
     With the fuel delivery body  1  as the sixteenth embodiment shown in  FIG. 18 , the lower wall  5  as the one side of the wall surfaces at the long sides is formed as outwardly extending though with the fuel delivery bodies  1  in the goggles shape shown in  FIG. 14  to  FIG. 17  and  FIG. 19 , the upper wall  6  and the lower wall  5  as the wall surfaces at the long sides are formed in parallel with each other. 
     Furthermore, the eighteenth embodiment to the twenty-first embodiment shown is  FIG. 20  to  FIG. 23  are the fuel delivery bodies  1  in the key shape; the twenty-second embodiment shown in  FIG. 24  is the fuel delivery body  1  in the double side concaved shape; and the twenty-third to the twenty-five embodiment shown in  FIG. 25  to  FIG. 27  are the fuel delivery bodies  1  in the flask shape, and each of the drawings shows the cross section shape the dimension of the outer diameter while the table 1 shows a thickness, a cross sectional area A, the internal volume V, and a pipe length. Regarding to the eighteenth embodiment to the twenty-fifth embodiment, in like manner, the table shows the data in a case where the fuel delivery body  1  is arranged as horizontally long shaped, in which the socket  2  is formed to the position indicated by the chain-dashed line. However, the above fuel delivery body  1  may be arranged as vertically long shaped in both upward and downward directions, and in that case, the fuel delivery body  1  is used in a state where the sockets  2  are formed, as the chain double-dashed line indicates, to the right side wall  8  exposed to the lower side. Furthermore, where the fuel delivery body  1  has comparatively long left side wall  7  , e.g., the eighteenth embodiment, the twenty-second embodiment, the twenty-third embodiment, the twenty-fourth embodiment, and the twenty-fifth embodiment, the fuel delivery body  1  can be used in state where the sockets  2  are formed to the left side wall  7  which is arranged as exposed to the lower side. 
     It is possible to determine, based on the FEM analysis with use of the above described expressions, the sonic speed α L , shown in the table 1, of the fuel flowing through the interior of the fuel delivery body  1  as the first embodiment to the twenty-fifth embodiment and the first conventional example to the sixth conventional example. 
     Furthermore, a modal analysis is made, in which the fuel in the fuel delivery body  1  and the fuel delivery body  1  are coupled to each other, and the mode of the air column vibration inside the fuel delivery body  1 , of more than several kHz as the problem with respect to the radiant sound, is extracted, thereby determining the equivalent sonic speed α H  in a high frequency area.  FIG. 34  shows a correlation graph of a cumulative coefficient of the number of the modes of air column vibration and the frequency regarding to the first embodiment to the fourth embodiment and the first conventional example to the fourth conventional example. Based on the graph of  FIG. 34 ,  FIG. 35  shows a liner graph of a degree of a mode two or higher regarding to the first embodiment to the fourth embodiment and the first conventional example to the fourth conventional example. Tilt (f/n) is determined based on the above graph, and multiplied, with use of the aforementioned expression 5, by double rail length of each of the fuel delivery bodies  1 , so that the equivalent sonic speed α H  in the high frequency area can be determined. 
     In  FIG. 34  and  FIG. 35 , the cumulative coefficient of the number of modes of the conventional example is approximately equal to one, and where the number of modes of a degree of a mode two or higher and the frequency are linearized, a line nearly passes through an origin. More specifically, the sonic speed α L  of the fuel and equivalent sonic speed α H  in the high frequency area are approximately the same. 
     In contrast, the cumulative coefficient of the number of modes of the embodiments is approximately greater than one, and where the number of modes on and after a degree of a mode two and the frequency are linearized, an intersection point with a X-axis shifts greatly toward a plus side, so the line does not pass through the origin. More specifically, the sonic speed α L  of the fuel and equivalent sonic speed α H  in the high frequency area becomes greater than the sonic speed α L  of the fuel, so that α L /α H ≦0.7 is satisfied. 
     Hereinafter, actions of the pulsation absorption and reduction of the radiant sound of the fuel delivery pipe according to this invention will be described with reference to the first embodiment. When the pressure pulsation occurs in association with the fuel injection via the injection nozzles, the internal volume of the fuel delivery body  1  increases as the flexible absorbing wall surface  10  of the fuel delivery body  1  yields outwardly and deforms.  FIG. 3  shows a schematic view of an increased state of this internal volume analyzed with the FEM analysis, wherein the dashed line indicates an inner wall surface of the fuel delivery body  1  before the increase of the internal volume, while a full line indicates the inner wall surface thereof at the time of the increase of the internal volume. As shown in  FIG. 3 , each flexible absorbing wall surface  10  flexes outwardly for a distance A and deforms as a straight line because of a rise of the internal pressure, and thus, as indicated by B in  FIG. 3 , the distance between the end points of each of the flexible absorbing wall surfaces  10 , i.e., the distance between an upper wall  6  and a lower wall  5  becomes longer. 
     Therefore, the great increase of the internal volume (about 1.1%) of the fuel delivery body  1  becomes possible, and as shown in the table 1, so the sonic speed α L  of fuel can reduce by several hundreds Hz, and inevitably, α L /√{square root over ( )}V can reduce to be equal to ≦45×10 3 (m −0.5 ·sec −1 ), so the superior absorption effect for the pressure pulsation can be obtained. As a result, it is possible to suppress effectively the transmission or the propagation of the pressure pulsation or noises to the underfloor pipe arrangement or the like. 
     On the other hand, with the fuel delivery pipes according to the conventional arts in the case of the equivalent sonic speed α H  in the high frequency area of more than several kHz considered as the problem with respect to the radiant sound, e.g., a clicking noise occurring when a spool of the injection nozzle is seated on a valve seat or the like, where the fuel delivery pip is made to flex easily so the sonic speed α L  of the fuel reduces, the flexure in the high frequency area also greatens inevitably while the number of modes increases as shown in  FIG. 3 . Therefore, as shown in the table 1, the equivalent sonic speed α H  in the high frequency area reduces, and it became difficult to suppress the radiant sound. 
     However, the fuel delivery pipe according to the first embodiment, as shown in  FIG. 31 , the absorbing wall surface  10  forms into a mode shape having a number of loops and nodes, which is a not readily bent shape, so that the flexure of the absorbing wall surface  10  in the high frequency is reduced. Therefore, while the sonic speed α L  of the fuel is 287 m/s, the equivalent sonic speed α H  in the high frequency area is 663 m/s, thereby not being reduced, so that it is possible to keep the radiant sound small in comparison with the conventional arts. 
     In the  FIG. 36  shows a graph showing a comparison of the fuel delivery pipes between the first embodiment and the sixth conventional example both having close α L /√{square root over ( )}V and the equal absorptiveness for the pulsation. As can be seen from this graph, the fuel delivery pipe in the first embodiment according to the present invention has a higher suppression effect for the radiant sound in comparison with the sixth conventional example. 
     The fuel delivery body  1 , furthermore, may be formed in different shapes from the first embodiment to the different twenty-fifth embodiment, wherein the side of the upper wall  6  with a narrower width, the side of the lower wall  5  with a wider width, and the left side wall  7  and the right side wall  8  inwardly curved in a gently arc shape may be arranged to form the fuel delivery body  1  which cross section shape may be in the substantially trapezoid shape, like the twenty-sixth embodiment as shown in  FIG. 28 , which is different from others. Furthermore, as the chain-dashed line indicates, the fuel delivery pipe  1  in the substantially trapezoid shape may be used in a state that the socket  2  is formed to the lower wall  5 , or to the upper wall  6 , wherein the upper wall  6  having the socket  2  is exposed to the lower side to shape the fuel delivery pipe  1  in a reverted trapezoid shape. 
     Furthermore, the above described fuel delivery body  1  according to the first embodiment to the twenty-sixth embodiment can be formed easily by means of the above described roll forming process. Furthermore, the fuel delivery body  1  may be formed, e.g., the twenty-seventh embodiment as shown in  FIG. 29 , by combining and brazing or welding two shaped plate materials after forming respectively and separately an upper half portion and a lower half portion. The fuel delivery body  1 , furthermore, may be formed, e.g., the twenty-eight embodiment as shown in  FIG. 29 , by fixing to bond both ends by brazing or welding after superimposing both ends of the press formed board materials. In these cases, the fuel delivery pipe  1  is arranged to shape in the vertically long flask shape or in the reverted flask shape, and the fuel delivery pipe  1  may be used in a state that the socket  2  is, as the chain-dashed line indicates, formed to the lower wall  5  or to the upper wall  6  with exposing the wall surface having the socket  2  to the lower side, or the fuel delivery pipe  1  may be used in a state that the socket  2  is, as the chain double-dashed line indicates, formed to the right side wall  8  with arranging the fuel delivery pipe  1  in a horizontally long flask shape. 
     The cross sectional views shown in  FIG. 2  and  FIG. 4  to  FIG. 30  show the main cross sections of the fuel delivery body  1  according to the embodiments respectively, and the cross section shape does not have to necessarily be identical from one end to the other end in a direction of a length of the fuel delivery body  1 , so the cross section of the fuel delivery body  1  may be partially in a different shape from the main cross section shape according to installation space or the like. For example, like the twenty-ninth embodiment as shown in  FIG. 37 , an extending portion  13  may be formed, according to need, to a middle of the fuel delivery body  1  to regulate a flow volume of the fuel, or the middle may be narrowed to prevent an interference with other components, which is not shown in drawings though. Furthermore, with each of the above described embodiment, four corners have the arc shape curve portions  11  but do not have to necessarily be curved in the arc shape, so, like; e.g., the twenty-ninth embodiment shown in  FIG. 27 , some corners may be formed in a rectangular shape to facilitate the formation thereof. However, when the corner is curved in the arc shape, adaptability thereof to the deformation of the absorbing wall surface  10  for the change of the internal pressure at the time of the fuel injection via the injection nozzles, is improved. 
       FIG. 38  shows the fuel delivery body  1  according to the thirtieth embodiment, which cross section is the shape of the substantially flask shape with the doom roof as the deformation of the substantially flask shape, in which the upper wall  6  is formed in the arc shape. Furthermore,  FIG. 39  shows the fuel delivery body  1  according to the thirty-first embodiment, which cross section is the shape of the substantially trapezoid shape with the doom roof as the deformation of the substantially trapezoid shape, in which the upper wall  6  is formed in the arc shape.  FIG. 40  shows the fuel delivery body  1  according to the thirty-second embodiment, which cross section is the shape of the substantially key shape with the doom roof as the deformation of the substantially key shape, in which the upper wall  6  is formed in the arc shape. 
     With these cases of the thirty embodiments, the thirty-first embodiment, and the thirty-second embodiment, the fuel delivery body  1  may be arranged in the vertically long shape in both upward and downward directions, wherein the socket  2  may be formed, as the chain-dashed lines indicate, to the flat upper wall  5  while the fuel delivery body  1  may be arranged in the horizontally long shape, wherein the socket  2  may be formed to, as the chain double-dashed lines indicate, either of the left wall  7  or the right wall  8  as the bottom surface. 
     With the thirty-third embodiment as shown in  FIG. 41 , where the fuel delivery body  1  in the reverted flask shape is formed, after forming separately the upper wall  6  in a flat plate shape and a bent material in a cup shape including the lower wall  5 , the left side wall  7  ,and the right side wall  8 , by bonding both the upper wall  6  and the bent material by means of the brazing or the welding in a state that the ends of the both thereof are superimposed mutually. 
     With the thirty-fourth embodiment as shown in  FIG. 42 , the fuel delivery body  1  in the substantially trapezoid shape is formed, after forming separately the flat lower wall  5  in the plate shape and the bent material comprising the upper wall  5 , the left side wall  7 , and the right side wall  8 , by bonding both the lower wall  5  and the bent material by means of the brazing or the welding in a state that the ends of the both thereof are overlapped mutually. 
       FIG. 43  shows the result of the FEM analysis of the transformation in a case where the internal pressure is applied to the fuel delivery body  1  in the double side concaved shape, wherein the centers of the wall surfaces at the long sides do not have the flat portions, thereby being formed as the smooth arc shaped. As shown in  FIG. 43 , the inner wall surface of the fuel delivery body  1  expands from the dashed line to the full line in a horizontal direction, but the large amount of movement e in the horizontal direction results in the amount of deformation remaining very slight with the view to the top and the bottom, and thus it is understood that the increasing rate of the internal volume is about 1.1%. Therefore, in the case of the fuel delivery pipe  1  in the substantially double side concaved shape as shown in  FIG. 43 , the same operational effect as the first embodiment in  FIG. 3  can be also exercised. 
       FIG. 44  shows the result of the FEM analysis of the transformation in a case where the internal pressure is applied to the fuel delivery pipe  1  in the substantially flask shape while  FIG. 45  shows the result of the FEM analysis of the transformation in a case where the internal pressure is applied to the fuel delivery pipe  1  in the reverted flask shape. In these cases, the same operational effect as the first embodiment in  FIG. 3  can be also exercised. 
     INDUSTRIAL APPLICABILITY 
     A fuel delivery body according to the present invention is structured like the above, wherein by forming a cross section shape in a perpendicular direction to an axis in a double side concaved shape, a flask shape, a trapezoid shape, a key shape a goggle shape or the like, an internal volume changing rate in a case of a receipt of the same pressure as before increases sharply, and an absorption effect for a pulsation by a flexible absorbing wall surface is enhanced, so that transmission, propagation, and radiation of an abnormal noise, e.g., a radiant sound is prevented. Since it is almost unnecessary to enlarge an outside dimension of the fuel delivery body, the fuel delivery body can be installed in a limited space inside engine room even where made to replace existing fuel delivery pipes, so a technical effect thereof is significantly prominent in which, e.g., the fuel delivery pipe can maintain interchangeability as a component. 
     Furthermore, by setting α L /√{square root over ( )}V determined by sonic speed α L  of fuel flowing through an interior of the fuel delivery body and the internal volume V of the fuel delivery body as 20×10 3  to 85×10 3 (m −0.5 ·sec −1 ) while by forming the fuel delivery pipe so a ratio of the sonic speed α L  of the fuel and equivalent sonic speed α H  in a high frequency area is set as α L /α H ≦0.7, it is possible, because of a deformation for flexure, to greatly increase the internal volume of the fuel delivery body according to a change of an internal pressure, so that the absorption effect for a pressure pulsation at the time of a fuel injection is to be high. Therefore, mechanical vibration in a low frequency area is hardly propagated to an underfloor pipe arrangement or the like, so that an occurrence of noises can be prevented. The fuel delivery pipe hardly flexes because of the pulsation in a high frequency area, so the equivalent sonic speed α H  does not reduce, and therefore, it becomes possible to prevent effectively the noise in the high frequency area, e.g., a clicking noise occurring when a spool of the injection nozzle is seated on a valve seat or the like, from radiating outwardly. As described above, it becomes possible to prevent the occurrence of the noises from the low frequently area to the high frequently area, so that production cost can be reduced since it is unnecessary to use pulsation dumpers or clips for absorbing the vibration.