Sec. 1-6] 



MECHANICAL INPUT TRANSDUCERS 



125 



furnishes more accurate results but requires more space. Both 

 methods require surgical procedures. 



1-64. Sonic Method 



The basic setup of a sonic flow- velocity transducer system is shown 

 in Fig. (1-6)6; it consists of a sonic transmitter T and a receiver R 

 separated by a distance d. The transmitter sends an acoustic signal 

 (pulse or wave train) into the flowing medium. The signal is received 

 at R at a time At later. The transit time in the flow direction is A^ = 

 d/(c + v), where c is the sound propagation velocity and v the linear 

 flow velocity of the medium. A signal traveling against the flow 

 direction requires a transit time At 2 = d/(c — v). A sinusoidal signal 

 of the frequency / traveling in the flow direction will arrive with a 

 phase shift A^ = 2irfdj(c + v); 

 a signal traveling in the oppo- 

 site direction will have a phase 



T 



.R 



< d 



Fig. (1-6)6. Flow-velocity trans- 

 ducer for liquids, sonic method. 



Fig. (1-6)7. Modification of the 

 sonic flow-velocity transducer shown 

 in Fig. (1-6)6. 



shift Acp 2 = 27rfdl(c — v). The velocity can be determined from 

 measurements of the transit time or of the phase difference between 

 the emitted and the received signal. 



Hess, Swengel, and Waldorf 1 and Kalmus 2 have described sonic 

 systems for the measurement of flow velocities as schematically 

 shown in Fig. (1-6)7. Two piezoelectric crystals X 1 and X 2 are 

 arranged in the medium or pressed against a plastic tube in which 

 liquid travels, so that sound is transmitted between the crystals and 

 the liquid. An oscillator furnishes an alternating voltage (order of 

 magnitude 100 kc) to the crystal^. Crystal X 2 acts as a microphone. 

 The functions of X x and X 2 are periodically interchanged by a 



1 W. B. Hess, R. C. Swengel, and S. K. Waldorf, AIEE Misc. Papers 50-214, 

 August, 1950; Elec. Eng., 69, 983 (1950); ASME Annual Meeting, Paper 54-A- 

 54, 1954; Elec. Eng., 73, 1082 (1954). 



2 H. P. Kalmus, Natl. Bur. Standards Tech. News Bull., 37, .'50 (1!).").'}), and 

 Rev. Sci. Instr., 25, 201 (1954). 



