THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

486 17. Commercial and Medical Ultrasound Applicationsdifference φ is given byφ = Lωc 0[ (cc 0)n( ]c−c 0)pwhere ω denotes the angular frequency, L is the acoustic path length, c 0 is the shearwave velocity in the unstressed medium, and (c/c 0 ) n and (c/c 0 ) p representthe fractional shear velocity for polarizations in directions normal to and parallelwith the direction of stress, respectively. The value of L is found simply fromlongitudinal wave measurements while φ is obtained by the means of a suitablephase-shift network. This methodology is also applied to determine third-orderelastic constants.The Ultrasonic FlowmeterThe Doppler principle constitutes the operating basis of the ultrasonic flowmeter.Two reversible transducers are submerged in the liquid along the line of flow. Onetransducer acts as a signal source of ultrasonic pulses and the other acts as a receiver.At short regular intervals the roles of the transducers are reversed, so that the sourcebecomes the receiver and the receiver becomes the source. The wave velocities arec + u along the direction of the flow and c − u in the opposite direction, where crepresents the propagation velocity of sound in the fluid and u the velocity of thestreamline flow of the liquid. A number of techniques have been used to comparethe upstream and downstream propagation rates. A “sing-around” method uses apulse generator to produce a short train of ultrasonic waves. The received signal isamplified and used to retrigger the pulse generator. If we neglect delay times dueto the electronic system and the distance the pulse travels beyond the fluid stream,the difference between the downstream and upstream pulse repetition rates isf 1 − f 2 = 2udwhere d represents the distance between the two transducers.Another type of ultrasonic flowmeter is based upon the deflection of an ultrasonicbeam by the fluid flow (Dalke and Welkowitz, 1960). In Figure 17.6, a transmittingtransducer located on one side of the fluid conduit emits a continuous signal into thefluid stream. A split transducer on the other side of the pipe determines the amountof beam deflection. A differential amplifier is used to determine the difference inthe outputs of the two receiving transducers. If there is no flow, the beam fallsmidway between the two receiving sections, and the two sections generate equalvoltages, and the output from the differential amplifier will be zero. When fluid flowoccurs, the beam shifts in the direction to the flow by an amount corresponding tothe flow speed, and the outputs from the two sections differ. The difference voltagethen corresponds to the rate of flow. Assuming a constant flow rate across the pipe,the deflection φ of the beam is computed from(φ = tan −1 u)c