Abstract:
A method for determining a velocity and density of a fluid without requiring the transmission of ultrasound through the fluid, and a system for performing such a method. The method involves the steps of delivering, receiving and analyzing ultrasound pulses sent from a longitudinal and a shear wave transducers to a member that is in contact with a fluid. The ultrasound pulses reflecting between surfaces provide a first ultrasound pulse echo series, that is transmitted, received and processed. The shear wave ultrasound pulses are also delivered through a shear wave transducer at a predesignated angle relative to the interface of the member and the fluid and the results of this are received to obtain a second ultrasound pulse echo series. Reflection coefficients for the first and second ultrasound pulse echo series are then calculated and the density of the fluid and the velocity of sound in the fluids are extracted.

Description:
BACKGROUND 
     1. Field of the Invention 
     The present invention relates to fluid analysis and more particularly, but not exclusively, to the determination of fluid properties at a solid-liquid interface without the necessity of timing the passage of ultrasound through the liquid. 
     2. Background of the Invention 
     Fluids are encountered in a wide variety of industrial applications and there is a continual need to determine properties of those fluids. A variety of methods exist, including those set forth by the present inventor in U.S. Pat. No. 6,763,698 and U.S. Pat. No. 6,877,375, the contents of which are herein incorporated by reference. The present invention provides an improved method for determining characteristics of a liquid or slurry without requiring the passage of ultrasound through this media. The present invention also allows for increased accuracy in making determinations related to the materials being tested, as well as avoids problems associated with other methods such as the impact of bubbles, attenuative fluids, or large sample volumes upon proper determinations. 
     Additional advantages and novel features of the present invention will be set forth as follows and will be readily apparent from the descriptions and demonstrations set forth herein. Accordingly, the following descriptions of the present invention should be seen as illustrative of the invention and not as limiting in any way. 
    
    
     
       BRIEF DESCRIPTION OF THE VIEWS OF THE DRAWING 
         FIG. 1  is a diagrammatic view of system for determining fluid properties. 
         FIG. 2   a  is a detailed view of the portion of the system shown in  FIG. 1 . 
         FIG. 2   b  is a detailed view of an alternate embodiment of the system shown in  FIG. 2   a.    
         FIG. 3  is a view of an incident wave against a surface. 
         FIG. 4  is a view of a portion of the block of the present invention. 
         FIG. 5  is a view of multiple echoes. 
         FIG. 6  is a graph of a single echo. 
         FIG. 7  is a graph of the FFT values for the signal in  FIG. 6 . 
         FIG. 8  is a graph relating the natural logarithm of FFT amplitude of each echo divided by that for water to the echo number. 
         FIG. 9  is a chart showing the correlative results of the measured values for the reflection coefficient compared to the theoretical values. 
     
    
    
     DETAILED DESCRIPTION 
     For the purpose of promoting an understanding of the principles of the invention, reference will now be made to the embodiments illustrated in the drawings and specific language will be used to describe the same. It will nevertheless be understood that no limitation of the scope of the invention is thereby intended. Any alterations and further modifications in the described embodiments, and any further applications of the principles of the invention as described herein, are contemplated as would normally occur to one skilled in the art to which the invention relates. 
     Turning now to  FIG. 1 , a system  20  for analyzing a property of fluid  25  is depicted. Fluid  25  can be a gas, liquid, slurry, suspension, paste, emulsion and the like. In preferred forms, fluid  25  is substantially non gaseous and/or includes at least one liquid. In this form, fluid  25  might be, for example, a liquid, slurry, or suspension. Ultrasonic transducer  30  is acoustically coupled to a first surface  42  of a member  40  comprised of a solid material. In one example, transducer  30  is in direct contact with member  40 . In other examples, one or more couplants might be used between transducer  30  and member  40 , or they may be coupled as would otherwise occur to those skilled in the art. An opposed second surface  44  of member  40  is in contact with the fluid  25 . A pulser  50  is electrically coupled to transducer  30  and is operable to deliver input stimulus signal to transducer  30  to cause transducer  30  to emit acoustic energy through solid member  40  and towards fluid  25 . Transducer  30  is also operable to produce output signals in response to acoustic energy transmitted from member  40 . 
     A shear wave inducing transducer  31  is also mounted to the member  40  in a manner so that transmissions propogated by the shear wave inducing transducer  31  are reflected off of the interface  23  of the member  40  and the surface of the fluid  25  being analyzed. In the preferred embodiment this shear wave inducing transducer emits ultrasound at a generally 45 degree angle to the surface/fluid interface  23  through an angle block  33  which may be attached as a portion of the member  40  itself. The shear wave transducer  31  produces transverse waves that are perpendicular to the direction of motion of the wave. In addition, shear wave transducer  31  is oriented on member  40  so that shear-vertical waves SV are produced. For purposes of understanding the directions of these waves in relation to the other portions of the device, in a shear wave transducer, the vibrations are in the plane of the paper and shear horizontal waves SH producing vibrations that are perpendicular to the plane of the paper. The reflection of SV and SH waves at a solid-liquid interface  23  are extremely different. 
     In the embodiment shown in  FIG. 2   a , this angle block  33  which is made of a material such as quartz and is positioned within a window whereby the angled transmission from the angled transducer  31  to the interface  23  does not pass through any other materials that are not a part of the angle block  33 . In an alternative embodiment shown in  FIG. 2(   b ) the shear wave transducer  31  and the angle block  33  are connected to the outer portion of the conduit member  40 . In such an embodiment the angle block  33  is made from a material such as stainless steel or other similar types of material. This angle block is generally configured so that the shear wave transducer  31  is positioned at a general angle of 45°. This angle is generally preferred because a reflected longitudinal wave cannot generally occur at this angle. In addition to transmitting at a 45° angle this angle block  33  also serves to reflect transmitted shear waves back towards the interface  23 , and in turn back towards the shear wave emitting transducer  31 . These reflected waves are also received by the shear wave inducing transducer  31  which then transmits a quantity of information related to this wave back to the processing apparatus  22 . 
     In one embodiment, the processing apparatus  22  including receiver  60 , digitizer  70 , and computer  80 , is coupled to pulser  50  and to transducers  30 ,  31 . Processing apparatus  22  controls delivery of output signals to each of the two transducers  30 ,  31  and receives the input signals from the transducers  30 ,  31  and, as described more fully below, performs calculations to determine properties of fluid  25  based upon the receipt of transducer output signals. 
     In operation, pulser  50  generates and delivers a short duration stimulus to transducers  30 ,  31 . Transducer  30  responds to the stimulus by emitting a longitudinal. wave pulse of ultrasound into member  40 . This ultrasonic pulse reflects between surfaces  44  and  42  producing a series of pulse echoes at t ansducer  30 . This resulting echo series will be of successively diminishing echo amplitude because each successive echo will have reflected from the solid fluid interface at surface  44  one time more than the previous echo. in a similar fashion shear wave transducer  31  responds to the stimulus by emitting a shear wave pulse of ultrasound to the interface  23  between member  40  and the fluid  25 . This ultrasonic pulse reflects off of the interface  23  and in the preferred embodiment into the angle block  31 . The air on the opposing side of the angle block  31  then reflects preferably 100 percent of this ultrasonic pulse back toward the interface surface  23  and then back to the shear wave transducer  31  producing a series of pulse echoes at shear wave transducer  31 . 
     Transducers  30 ,  31  respond to the echoes by producing an output signal proportional to the echo amplitude that is amplified by receiver  60 , digitized by digitizer  70  and passed to computer  80 . Computer  80  includes programming instructions encoded on fixed and/or removable memory devices  84 ,  86 , respectively, to gather the select a peak echo amplitude for the series echoes and to determine the average decay rate of the peak echo amplitudes with increasing echo number in the echo series. Alternatively, computer  80  can be at least partially hard wired with dedicated memory devices and configured to execute logic according to the present invention. Computer  80  is operatively coupled to display  82  to output selected information about fluid  25  integrated with transducers  30 ,  31 . 
     A shear wave transducer is used for transducer  31  rather than a longitudinal one because when a longitudinal wave strikes a solid-liquid interface at an angle (no matter the size of the angle), the following will always be produced: (1) a reflected longitudinal wave at the same angle as the incident one, (2) a mode-converted shear wave at about half the angle of the incident longitudinal (depending upon Snell&#39;s Law) and (3) a transmitted longitudinal wave in the liquid. Thus, if the reflected longitudinal waves are observed, there would be only a few reflections (particularly for stainless steel) because energy has been used to create the mode-converted shear waves. 
     When a shear wave transducer (SV mode of operation) is used at small incident angles with the vertical, a mode-converted reflected longitudinal wave is produced. That is, all three types of waves are produced as has just been discussed in the preceding paragraph. However, when the incident angle is 45°, a reflected shear wave is produced, but a reflected mode-converted longitudinal wave simply cannot be produced. The reason is that the reflected longitudinal wave always has a greater angle than the reflected shear wave, but at some incident angle (slightly less than 45°) the mode-converted longitudinal wave becomes 90°. Since 90° is the limit for the mode-converted reflected longitudinal wave, this wave is simply not produced at 45°. For a shear wave incident upon a solid-liquid interface at a 45°, two types of waves are produced: (1) reflected shear wave and (2) a transmitted longitudinal wave in the liquid. Therefore, when the reflected shear wave is observed, energy is available for many reflections. In summary, more reflections are observed using a SV shear wave transducer at an incident angle of 45° than would be obtained using a longitudinal transducer. 
     The transducers  30 ,  31  can be applied to any solid unit, but there are two materials that have special significance for process control: (1) stainless steel and (2) fused quartz. Fused quartz is often used as windows in a pipeline and the pipeline is often constructed of stainless steel. Fused quartz has a very low attenuation of ultrasound and so is a very good choice for the material. Stainless steel may be preferred in some cases, but it can be quite attenuative. For this reason, the experiments were carried out to show that this method can be applicable even for stainless steel. 
     Preferably a number of echo amplitudes, for example [5] five or more, spanning a range of echo numbers are used in computing the decay rate both the longitudinal wave reflections emanating and being reflected through transducer  30 , as well as the shear wave reflections being sent from sent from shear wave transducer  31 . This feature referred to at times as “self-calibration” preferably occurs with the information received from each of the two transducers. Information from the longitudinal transducer  30  yields the reflection coefficient for ultrasound perpendicular to the solid-liquid interface, while that from the shear wave transducer  31  yields the reflection coefficient for ultrasound incident at 45°. In one preferred form, each reflection coefficient depends upon the density of the liquid or slurry that is being measured and the velocity of the sound in the liquid. By then solving these two equations for each of these two unknowns, the density and velocity of the sound in the liquid can be determined. 
     In one embodiment the computer  80  is programmed to first compute the fast Fourier transform (FFT) of the digitized signals, converting them from the time domain to the frequency domain and then determine the peak amplitude at a selected frequency, where the frequency is selected to be, for example, the center frequency of transducer  30  and transducer  31 . 
     The objective is to compare the experimental measurement of each reflection coefficient with a theoretical calculation and to extract the density of the material and the velocity of sound. The experimental measurement of the perpendicular coefficient and the coefficient at a 45° are both measured by looking at the multiple echo pattern. However, each set of multiple reflections has a different decay rate and hence, a different value for the reflection coefficient. The following description applies to both types of reflections. 
     The FFT amplitude at a given frequency is proportional to RC N , where RC is the reflection coefficient and N is the echo number.
 
VαRC N   (1)
 
For example, if the RC is 0.8, then the amplitude of the 5 th  echo is equal to 0.32768 C and that of the first echo, equal to 0.8 C, where C is a constant of proportionality. Thus, the amplitude of the 5 th  echo is about 41% of that for the first echo.
 
     This proportionality can be written for a liquid and for water. For the same experimental setup, the (unknown) constant of proportionality is the same for both. Thus, the constant of proportionality drops out when the two equations are divided.
 
 V liq( N )/ V wtr( N )= RC liq N   /RC wtr N   (2)
 
Taking the natural logarithm of both sides yields the following:
 
Ln( V liq( N )/ V wtr( N ))= N  ln( RC liq/ RC wtr)  (3)
 
     Vliq is identified as the EFT amplitude for a liquid and similarly defined for Vwtr, When the left-hand quantity is plotted on the vertical axis (y) of a graph and the echo number N, on the horizontal axis (x), then the result is a straight line, y=mx+b in the standard form. The quantity m is the slope and b is the intercept on the y-axis. The slope of the straight line is given by
 
Slope=ln( RCliq/RCwtr )  (4)
 
     Eq. (4) can be rewritten as follows:
 
RCliq=RCwtr e Slope   (5)
 
     In summary, the reflection coefficient for ultrasound striking a solid-liquid interface can be obtained by plotting the natural logarithm of the quantity (Vliq/Vwtr) versus the echo number and finding the slope of the line. The reflection coefficient RCliq is then determined from Eq. (5). The reflection coefficient RCwtr is determined from well-known formulations for the reflection coefficient, such as Krautkramer and Krautkramer (1990), 
     The above method uses the FFT amplitude at one frequency—one point on the amplitude-versus-frequency curve—but greater accuracy can be achieved by using several points as the following demonstrates. In this preferred application of the present invention the reflection coefficient does not depend upon frequency. While the peak of the FFT amplitude curve at a frequency fl has usually been chosen, it is by no means unique. The quantity V(f 2 , N) is defined as the FFT amplitude at frequency f 2  for echo N. Thus, it is another point of the EFT amplitude curve. Writing Eq. (3) for three frequencies f 1 , f 2 , and f 3  yields the following:
 
Ln( Vliq ( f 1, N )/ Vwtr ( f 1, N ))= N  ln( RCliq/RCwtr )  (6)
 
Ln( Vliq ( f 2, N )/ Vwtr ( f 2, N ))= N  ln( RCliq/RCwtr )  (7)
 
Ln( Vliq ( f 3, N )/ Vwtr ( f 3, N )= N  ln( RCliq/RCwtr )  (8)
 
Adding the three equations together and realizing that the summation of logarithms is the same as products yields:
 
Ln [Vliq( f 1, N ) Vliq ( f 2, N ) Vliq ( f 3, N )/ Vwtr ( f 1, N ) Vwtr ( f 2, N ) Vwtr ( f 3, N )]=3  N  ln( RCliq/RCwtr )  (9) This can be rewritten as:
 
Ln [ Vliq ( f 1, N ) Vliq ( f 2, N ) Vliq ( f 3, N )/ Vwtr ( f 1, N ) Vwtr ( f 2, N ) Vwtr ( f 3, N )] 1/3 = N  ln( Rliq/Rwtr )  (10)
 
In this case, the quantity on the left side of Eq. (10) is plotted versus the echo number N, where the slope on this plot is determined. As before, the reflection coefficient is obtained using Eq. (4) and Eq. (5).
 
     Eq.(5) shows that in order to determine the reflection coefficient for the liquid the theoretical formulation is required in order to determine the reflection coefficient for water for the perpendicular incidence and for incidence at 45° 
     A, Perpendicular Incidence 
     The formulation for the reflection coefficient for ultrasound traveling in a solid and striking the solid-liquid interface perpendicularly is given by:
 
 RC =( Z liquid− Z solid)/( Z liquid+ Z solid)  (11)
 
Z is the acoustic impedance defined as the density multiplied by the velocity of sound. For a calibration liquid, such as water and the known solid, the acoustic impedance of both the liquid and solid are known and so the RCwater can be determined.
 
     From Eq. (5), the RCliquid can be determined from the reflection coefficient for water and the slope of the line on a plot, as has been discussed. 
     From the fluid specific reflection coefficient (RCfluid), computer  80  calculates the acoustic impedance of the fluid (Zfluid) according to Eq. (12).
 
 Z liquid= Z solid(1 −RC liquid)/(1 +RC liquid)  (12)
 
where Zsolid is the acoustic impedance of the solid member  40 . Eq. (12) was obtained by solving Eq. (11) for Zliquid.
 
     The acoustic impedance of the fluid (Zliquidlis defined as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
                         Zliquid 
                         = 
                           
                         ⁢ 
                         
                           ( 
                           
                             density 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             of 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             the 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             liquid 
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       
                           
                         ⁢ 
                         
                           
                             ( 
                             
                               velocity 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               of 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               sound 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               in 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               the 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               liquid 
                             
                             ) 
                           
                           = 
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           ρ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           c 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     Where ρ is the density of the liquid and c is the speed of the sound in the liquid. A value has been obtained for the acoustic impedance of the liquid, but there are two unknowns: ρ and c. A second equation is obtained from the incidence at an angle of 45°, which is discussed next. 
     B. Incidence at 45° angle at solid-liquid interface 
     Eq. 5). shows that in order to determine the reflection coefficient for ultrasound striking the solid-liquid interface at 45°, a theoretical calculation of the reflection coefficient for water (or the calibration liquid) is needed and the “Slope” obtained from experimental measurements of multiple reflections, as discussed above. This procedure yields the experimental value of the reflection coefficient at 45°. 
     The objective of the measurements is to obtain values for the reflection coefficient at 90° (RC 90 ) and at 45° (RC 45 ). Since the theoretical equations include the density of the liquid and the velocity of sound in the liquid (which are unknown), as well as known properties of the solid and calibration liquid, the two unknown quantities can be determined. The following is a formulation for the reflection coefficient for SV shear waves striking a solid-liquid interface at an angle. 
     Referring now to  FIG. 3 ,  FIG. 3  shows a shear wave striking a surface at an angle α T  and a reflected shear wave at angle α T . For some incident angles α T , a longitudinal wave is also produced in the solid at angle α L  and the restrictions will be discussed shortly. A longitudinal transmitted wave is also produced in the liquid at angle α. The longitudinal velocity in the solid is denoted by c L  and the shear wave velocity, by c T . The velocity of sound in the liquid is given by c. The density of the solid is given by ρ f  and the density of the liquid by ρ. 
     As the angle α T  increases, the angle α L  also increases. The angle α L  cannot increase, obviously, beyond 90°. Thus, for some angle α T , a longitudinal wave is simply not possible and does not exist. For a steel-water interface, this critical angle is about 33°. Beyond 33° the reflected longitudinal waves are not present. This is very advantageous because all of the reflected energy will be concentrated in the reflected shear wave. Calculations of the reflection coefficients for an incident angle α T  less than 33°, can be calculated according to the known formulas such as the one described by Krautkramer and Krautkramer (1990). However, for larger angles, the formulae are not provided but a method of derivation for obtaining such a value is described. Because the incident angle in these experiments is 45°, a derivation was carried out and the resulting reflection coefficient Rtt (using the notation of Krautkramer and Krautkramer) is given by:
 
 Rtt ={[( N 1 −N 3) 2   +N 2 2 ]/[( N 1 +N 3) 2   +N 2 2 ]} 0.5   (14)
 
The parameter Con is defined as follows:
 
 Con =( c   L   /c   T )sin α T   (15)
 
     N 1 , N 2 , and N 3  are defined as follows:
 
 N 1=( c   T   /c   L ) 2 [2 Con ( Con   2 −1) 0.5 ] sin 2α T   (16)
 
N2=cos 2  2α T   (17)
 
 N 3=(ρ c/ρ   f   c   L )( Con   2 −1) 0.5 /cos α  (18)
 
     For an incident angle of 45°, the term for N 2  is equal to 0 and the reflection coefficient reduces to
 
 Rtt =( N 1 −N 3)/( N 1 +N 3)  (19)
 
     One objective is to show that the density and velocity of sound can be obtained from RC 90  and RC 45 . The above equations show that this is possible. In Eq. (16) for N 1 , all of the quantities are known and so N 1  can be evaluated numerically. in Eq (18) for N 3 , there are two unknown terms: ρ c and cos α, where α is the angle of the transmitted beam in the liquid. Solving Eq (19) for N 3  and using the syn bol RC 45  for Rtt, we find the following:
 
 N 3 =N 1(1 −RC 45)/(1 +RC 45)  (20)
 
     Therefore, N 3  can be evaluated since values have been obtained for both N 1  and RC 45 . 
     In Eq ( 18 ) for N 3 , there are two unknown terms: ρ c and cos α, where α is the angle of the transmitted beam in the liquid. However, the acoustic impedance of the liquid ρ c is known from Eq (13) Thus, Eq. (18) can be solved for cos α and, of course, the angle α can also be determined. 
     The velocity of sound can be determined from Snell&#39;s law of refraction, as follows:
 
Sin α T /sin α= c   T   /c   (21)
 
     Since the angle a has been determined, the only unknown in Eq. (21) is the velocity of sound in the liquid, c. Thus, the velocity of sound can be determined. The density can be determined from the value of the acoustic impedance of the liquid, Zliq.
 
Density of liquid ρ= Z liq/ c   (22)
 
     The use of the perpendicular measurement of multiple reflections and the self-calibrating feature of these measurements has been documented in U.S. Pat. No. 6,763,698, in which an accurate value of the acoustic impedance of the liquid is obtained. in this technique, the velocity of sound is obtained by measuring the passage of ultrasound through the liquid or slurry. The present invention omits the measurement through the liquid or slurry and instead utilizes the measurement of the SV shear reflection coefficient for incidence at an angle to a solid-liquid interface. The experimental data focuses on the data obtained for incidence at a 45° angle at a solid-liquid interface. The material for the 45° triangular wedge was chosen to be stainless steel, which leads to a more difficult measurement than using fused quartz. Fused quartz results in many echoes. 
     The measurements were performed using a stainless steel (SS 304 ) triangular wedge as shown in  FIG. 4 . The base of the triangular wedge was immersed in various concentrations of sugar water, for which the density and velocity of sound were measured directly utilizing traditional methods, and then again utilizing the presently described methods. The objective was to show that the experimental measurement of the reflection coefficient is in agreement with the calculations of the reflection coefficient for an incidence of 45°, using known values for the density and velocity of sound in sugar water solutions. 
       FIG. 4  the base of the triangle is 1.5inches and the angles at the base are 45°. A commercial shear wave transducer having a diameter of 0.5 inches and a frequency of 1 MHz was coupled to the unit using shear-wave coupling gel. The shear wave transducer was mounted so as to produce vibrations that create shear vertical waves (ST). A pulse of ultrasound is reflected twice at the solid-liquid interface during each roundtrip. As many as five echoes can e observed by the transducer, as shown in  FIG. 5 . The advantage of using a 45° angle is that no reflected longitudinal wave in steel can be produced (as discussed previously), while at a smaller angle—say, 20°—a reflected longitudinal wave is produced. Thus, when the incident shear wave strikes the steel-liquid interface only two waves result: 1) the reflected shear wave and 2) the longitudinal wave transmitted into the liquid. As a result, the reflected shear wave has sufficient energy to produce echoes. 
     An expanded view of one echo is shown in  FIG. 6  and the fast Fourier transform of that signal is shown in  FIG. 7 . The usual treatment is to take the maximum FFT amplitude for a liquid (or slurry) and compare it with the maximum FFT amplitude for water. The original derivation has been extended to include the amplitude at several frequencies, as this has been discussed and the derivation carried out in Eq.(6) through Eq. (10). 
       FIG. 8  shows the data obtained for the five echoes for 50% sugar water, using the extended method to obtain the FFT amplitude, as described in Eq. (10). For the sake of simplicity, this is referred to as the PFT amplitude, A similar calculation was obtained for the FFT amplitude for water for five echoes. For each echo, the HT amplitude for a liquid was divided by that for water and the natural logarithm of that quantity was obtained. In  FIG. 8  the ordinate is the following: Log (FFT amplitude for liquid for echo N/FFT amplitude for water for echo N), while the abscissa is the echo number N. As described earlier, the reflection coefficient is related to the slope of the line. Similar calculations and graphs were obtained for each liquid. 
     Because two reflections occur in each round trip, Eq. (5). is modified by including, a factor of 2.
 
 RC liq/ RC wtr= e   slope/2   (23))
 
     The experimental value of RClig/RCwater was determined using Eq. 23 by finding the slope of the line, similar to that in  FIG. 8  for 50% sugar water. The experimental values of the ratio RCliq/RCwtr for six sugar water solutions are plotted versus the sugar water concentration in FIG.  FIG. 9  using a diamond shape and the theoretical values of the ratio RCliq/RCwir by squares. 
     The theoretical calc lation was carried out using Eq. (19). for water and the six sugar water solutions. in each case, the density of the solution and the velocity of sound in the solution were measured independently by standard techniques. The velocity of sound was obtained by measuring the time-of-flight through the liquid and the density was obtained by weighing a known volume of a sugar water solution. These values were then used in the theoretical formulae in Eq.(14). through Eq. (21). to obtain the reflection coefficient for water and the reflection coefficient for each sugar water solution. For each sugar water solution, the ratio RCliq/RCwtr were obtained and plotted in  FIG. 9 . The comparison between the experimental and theoretical values in  FIG. 9  shows very good agreement. 
     In a preferred form, the speed of sound in the fluid (c) is determined by performance of multiple reflections of a shear wave at a non-perpendicular, preferably a 45 degree angle of incidence at the solid-liquid interface. Preferably this is performed utilizing a fused quartz window in a pipeline and a 45-degree quartz triangular wedge in contact with the slurry. Because fused quartz has a smaller acoustic impedance (density×velocity of sound) than stainless steel, this design permits very high accuracy in the density measurement because the reflection coefficient for fused quartz is smaller than that for stainless steel, leading to a more sensitive measurement. In addition, more echoes are obtained with quartz because its ultrasonic attenuation is quite small. Calculations indicate that an uncertainty in the density measurement of 0.05% may be possible with the quartz design. In another design the shear wave transducer  31  is directly mounted on the stainless steel pipeline or spool piece and the 45-degree triangular wedge (preferably in a single stainless steel unit) is in contact with the liquid or slurry. In yet another design, the 45-degree wedge consists of two pieces, in which a part of the stainless steel pipeline wall is connected to a 45-degree trapezoid fastened to the wall, such as shown in  FIG. 2 . 
     Comparison of the reflection for perpendicular longitudinal waves and the reflection for 45° shear waves show that the sensitivity for the 450 shear waves is 1.5 times that for the perpendicular longitudinal waves. The calculations also show that the 45° angle of incidence is optimum and about 90% of the ultrasound is reflected at the SS-liquid interface. Therefore, even though stainless steel is more attenuative than quartz, a sufficient number of echoes can be observed using a frequency of 2.25 MHz or 1 MHz. 
     Multiple reflections can be observed for both transducers  30  and  31  and so the self-calibrating feature applies to both transducers. In an alternative embodiment the shear wave inducing transmitter  31  is connected to an angle block  33  that is fastened directly to the wall member  40 . While in this embodiment the material for the wedge is the same as the wall, there will undoubtedly be reflections at the interface between the two pieces, but those reflections will not travel to transducer  31 . However, due to the multiple reflections and self-calibrating feature, these undesirable reflections will not affect the reflection coefficient measurement at 45°, but the number of echoes may well be reduced and that can affect the accuracy of the density measurement. 
     However, in either design, the velocity of sound can be determined without passage of ultrasound through a very attenuative medium or through a large vessel. 
     Preferably, the transducers that are useful for forming and receiving the ultrasound pulse echo series in practicing the present invention can operate in the range of about 0.5 to 20 MHz, more preferably between about 1 and 10 MHz, and most preferably about 5 MHz. However, due to the longer path for incidence at 45°, a smaller frequency such as 1 MHz may be advantageous. In certain applications of the invention, the thickness T of member  40  will be predetermined, and depending on the wavelength of ultrasound in the member  40 , the ratio of thickness T to wavelength could be significant, for example greater than about 0.05. As one example, it is contemplated that member  40  would be the existing wall of a stainless steel pipe or container about 0.15 inches thick. For at least some selected ultrasonic frequencies, the wavelength of ultrasound will be significant relative to the wall thickness. 
     In another form of the invention, because of materials desired for solid member  40  and fluid  25 , the acoustic impedance ratio Zsolid/Zliquid will be significant, for example, greater than about [5] five or [10] ten. The multiple reflections serve to amplify the effect of small changes in properties of fluid  25 . This amplification occurs because the amplitude of the pulse is diminished in accordance with the reflection coefficient (RCliquid) with each successive reflection with surface  44 . Also, because the higher echoes undergo more reflections with surface  44  and because the reflection coefficient (R.Cliquid) is a function of fluid properties, the effect of Thanges in these fluid properties are more pronounced in the higher echo numbers. Consequently, in one form of the invention, it is preferred that at least some of the higher number echoes are used in computing the decay rate. 
     In further forms of the invention, where reduction of the adverse effects of divergence and/or attenuation is of concern, selection of transducers  30 ,  31 , member  40  dimensions, angle block  33  materials and their associated properties can be of particular interest. For example, the near field can be considered the region immediately in front of an ultrasonic transducer where the sound beam does not diverge and signal loss is at a minimum. The near field length (NO for an ultrasonic transducer can be approximated by Eq. (24)
 
 Nf= 0.25 D   2 /lambda  (24)
 
where lambda is the wavelength of the ultrasound in the medium (equal to local speed of sound divided by the frequency) and D is the largest dimension of the transducer face  32  associated with the member  40 . For circular transducers, D will be the diameter of the face  32  whereas for rectangular transducers D will be the larger length dimension of the rectangle. In one form of the invention, the near field of the transducer  30  is selected to encompass one or more of the reflections used to calculate the decay rate. In a preferred form a plurality of the echoes used to calculate the decay rate are within the near field length estimated by Eq. (24). in a further preferred form, the majority of the echoes used to calculate the decay rate are within this length.
 
     From an examination of equation (24) one possibility for increasing the near field length is to increase the frequency of the ultrasound. However, there is a practical limit to the effectiveness of this approach, at least because losses due to attenuation of the ultrasound generally increase with increasing frequency. The near field length is therefore preferably maintained at a desired relative length by adjusting the ratio of the size of transducer size D to thickness T. Increasing the transducer size D increases the near field length whereas decreasing T decreases the pathlength of the echoes, allowing more echoes to be detected inside a given near field length, it is to be understood that the pathlength for each echo is the distance the pulse travels for each reflection (2T) times the echo number (the first echo has a pathlength of 2T, the second 4T, the third 6T, etc.). While any ratio can be utilized as would occur to those of skill in the art, in one form of the invention the ratio of D/T is preferably greater than about one. In other forms, the ratio Dif is about two [2] or above. 
     An advantage is realized by using the decay rate of the echo amplitudes in determining fluid properties. It has been found that, unlike the absolute magnitude of individual echo amplitudes, the slope of echo amplitude versus echo number is substantially independent of characteristics of the ultrasound pulse used to create the echoes. Thus, the self-calibrating feature of the multiple echoes is realized. For example, if the pulser voltage changes by, say, 1%, then each echo changes by the same amount and the Slope of the line, previously described, remains unchanged. 
     Exemplary materials for solid member  40  and angle block  33  include aluminum, stainless steel, fused quartz, and plastics. Preferably member  40  is non-porous is does not absorb fluid  25 . In particular applications, such as food processing and the transport of toxic material, stainless steel or other non-corrosive materials are preferred materials for these pieces. 
     In a further variation, data transmission between computer  80  and transducers  30 ,  31  can be achieved wirelessly by provision of appropriate wireless communication devices. 
     Another application is the design of the unit for placement inside a tank for measurement of the density and velocity of sound. In such a design, the side of the 45° angular wedge could be made watertight so that ultrasound could still reflect from air on one side of the triangle. In another design, a material of known properties could be fastened to the side 45° angular wedge now found in air so that the reflection at this surface can be easily calculated. The reflection at this surface would be less than air, and the reflection at this surface for each echo can be taken into account. 
     It is also to be understood that another embodiment of the present invention is a unique technique to determine fluid properties wherein an ultrasonic transducer  30  is provided on a surface  42  of a solid member  40  having an opposed second surface  44  in contact with the fluid  25 . A second ultrasonic transducer  31  configured to transmit a shear wave to the interface  23  between the fluid  25  and the material is also provided. This technique can include delivering an ultrasonic pulse through these two transducers  30 ,  31  detecting a multiplicity of pulse echoes caused by reflections of the ultrasonic pulse between the solid-fluid interface and the transducer-solid interface, and determining the decay rate of the detected echo amplitude as a function of echo number. The determined decay rate is compared to a calibrated decay rate, such as obtained using water or another calibration fluid, to determine an acoustic property of the fluid. In some applications this includes a reflection coefficient which can be further calculated to obtain a value such as the density of the material or the velocity of sound through the fluid. 
     While the invention has been illustrated and described in detail in the drawings and foregoing description, the same is to be considered illustrative and not restrictive in character, it being understood that only the preferred embodiment has been shown and described and that all changes, equivalents, and modifications that come within the scope of the inventions described herein or defined by the following claims are desired to be protected. Any experiments, experimental examples, or experimental results provided herein are intended to be illustrative of the present invention and should not be construed to limit or restrict the invention scope. Further, any theory, mechanism of operation, proof, or finding stated herein is meant to further enhance understanding of the present invention and is not intended to limit the present invention in any way to such theory, mechanism of operation, proof, or finding. In reading the claims, words such as “a”, “an”, “at least one”, and “at least a portion” are not intended to limit the claims to only one item unless specifically stated to the contrary. Further, when the language “at least a portion” and/or “a portion” is used, the claims may include a portion and/or the entire item unless specifically stated to the contrary.