问题描述：
英语翻译
It is assumed in the theory of ultrasonic flowmeters that a planar wave is radiated [i] ;
then the forward propagation (in the flow direction) and the backward propagation (against
the flow) are symmetrical,and therefore there is complete balancing of the diffraction
effects taken over the differential time,which is equal to the difference between the times
of propagation from the source to detector and back again (when the source acts as a detector
and vice versa).
In fact,the wave in the near zone (the Fresnel zone) is not exactly planar,and it goes
gradually over to spherical form as the distance from the source plate increases [2].However,
the symmetry of the forward and backward waves is then violated,and one therefore expects
that a diffraction effect will be present.We show below that this idealization of the
wave pattern can result in considerable error.
We omit the detailed formulation of the equations and the solution and merely note that
the vibrations of the source plate are represented,as usual,as those of a piston; we also
neglect the effects of any pockets in the walls,reflections from the boundaries of the moving
and immobile media,acoustic-wind effects,and the like.The following are the expressions
for the mean pressure set up at the detection plate and for the time of the signal to
progagate from the radiator to the detector:(这里是1个公式,省略）
where Re is the real part of the expression appearing within the braces,0 is the density of
the medium,vo is the amplitude of the vibrational velocity,c is the speed of sound in the
medium,d2 = I + (r/z)cos 8,z is the distance between the emitting and receiving plates
(these are coaxial and parallel),B is the angle between the axis of the acoustic channel and
the axis of the tube,r = vro/c,v is the flow speed of the fluid,（公式） d is the
diameter of the pipe,m is the circular frequency,k is the wave number,（公式*n）
where a is the radius of the plate (this is taken as the same for the emitting and receiving
plates for simplicity,but there is no difficulty in discussing plates differ~mg in radii),
（公式）,is the vibrational frequency of the emitting plate,and（公式）
The triple sums in the expressions for and N2 may be neglected if the flow speed is
low,since the contributions for these become negligible.
It is assumed in the theory of ultrasonic flowmeters that a planar wave is radiated [i] ;
then the forward propagation (in the flow direction) and the backward propagation (against
the flow) are symmetrical,and therefore there is complete balancing of the diffraction
effects taken over the differential time,which is equal to the difference between the times
of propagation from the source to detector and back again (when the source acts as a detector
and vice versa).
In fact,the wave in the near zone (the Fresnel zone) is not exactly planar,and it goes
gradually over to spherical form as the distance from the source plate increases [2].However,
the symmetry of the forward and backward waves is then violated,and one therefore expects
that a diffraction effect will be present.We show below that this idealization of the
wave pattern can result in considerable error.
We omit the detailed formulation of the equations and the solution and merely note that
the vibrations of the source plate are represented,as usual,as those of a piston; we also
neglect the effects of any pockets in the walls,reflections from the boundaries of the moving
and immobile media,acoustic-wind effects,and the like.The following are the expressions
for the mean pressure set up at the detection plate and for the time of the signal to
progagate from the radiator to the detector:(这里是1个公式,省略）
where Re is the real part of the expression appearing within the braces,0 is the density of
the medium,vo is the amplitude of the vibrational velocity,c is the speed of sound in the
medium,d2 = I + (r/z)cos 8,z is the distance between the emitting and receiving plates
(these are coaxial and parallel),B is the angle between the axis of the acoustic channel and
the axis of the tube,r = vro/c,v is the flow speed of the fluid,（公式） d is the
diameter of the pipe,m is the circular frequency,k is the wave number,（公式*n）
where a is the radius of the plate (this is taken as the same for the emitting and receiving
plates for simplicity,but there is no difficulty in discussing plates differ~mg in radii),
（公式）,is the vibrational frequency of the emitting plate,and（公式）
The triple sums in the expressions for and N2 may be neglected if the flow speed is
low,since the contributions for these become negligible.
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