Sec. 1-6] MECHANICAL INPUT TRANSDUCERS 127 



The ratio of counting rates at A for circular pipes, according to the 

 authors, is 



9l 



Go 



y hf\ 2 ' 



d ' \dj 



(2) 



where C t is the counting rate at the time t and C that at the beginning 

 of the experiments when the lower part of the tube is completely 

 filled with a radioactive-tracer solution. 



With an aqueous solution of radioactive sodium 24 and a concen- 

 tration of 0.05 to 0.16 mc/ml, the authors were able to follow the 

 replacement of the tracer solution by the tracer-free liquid until the 

 thickness y of the layer adjacent to the wall had diminished to 

 0.002 in. 



The application of the method is limited to special cases and single 

 runs. 



1-66. Transducers Responding to Gas Flow Velocity: 

 Thermal Systems 



a. Thomas Method. The following method originally devised by 

 Thomas 1 has been described primarily for the flow-rate or flow- 

 velocity determination in gases but is, in principle, also applicable to 

 the measurement of liquid flow (see 1-63). The method is illustrated 

 in Fig. (1-6)9. The gas, or liquid, enters a conduit with the tempera- 

 ture /j, which is measured by the thermal transducer T 1 (e.g., a resis- 

 tance thermometer) ; it then passes a heater H energized by a source 

 S, and it emerges with the (higher) temperature 1 2 , which is measured 

 by the resistance thermometer T 2 . If the specific heat is constant, 

 the flow rate F can be determined from 



PC 



where P is the electric power required to maintain the temperature 

 difference t 2 — tj_, C is the mechanic-caloric equivalent, and c p the 

 specific heat of the gas at constant pressure or the specific heat of the 

 liquid. 



The method can be used in connection with a servo system. For 

 this purpose the thermal transducers T x and T 2 are arranged in a 

 bridge circuit, Fig. (1-6)1 0, which is adjusted so that no current passes 

 through the meter relay M as long as the temperature difference 

 t 2 — ti is of a given value. A feedback loop controls the current 

 through the heater, and the arrangement acts so as to maintain the 



1 C. C. Thomas, ./. Franklin Inst., 172, 411 (1911). 



