124 INSTRUMENTATION IN SCIENTIFIC RESEARCH [Chap. 1 



two capacitor plates C 1 and C 2 . The rf power — and thus the rate of 

 heat generated in the blood — is kept constant. The longer the blood 

 remains in the electric field between the capacitor plates, i.e., the 

 lower its flow velocity, the more it will heat up. The increase in blood 

 temperature, i.e., the temperature difference At between a point 

 upstream and one downstream from the heating device, is measured 

 by two thermoelements T x and T 2 in thermal contact with the outside 



of the vessel. If P is the electric 

 power converted into heat, the 

 flow velocity F of the blood can 

 be found from 



E n 





L 



T, 



A y 



K-:-:-:-:-:-:-:-:-'-:-:-:-:-:-:-:-i-;j 



Co 



F = k 



At 



rf 



Fig. (1-6)5. Flow-velocity transducer 

 for liquids, thermal method. 



where k is an apparatus constant. 

 The system measures the average 

 mass rate of flow. The transfer 

 function (thermoelement output 

 E versus flow rate F) is approxi- 

 mately hyperbolic. 



The heat produced in the walls 

 of the vessel is practically negligible. The heat losses to the outside are 

 small, and the heat exchange with the volume of the blood is suffi- 

 ciently high so as not to cause serious errors. Experiments have 

 shown that the flow pattern is of no influence upon the output if the 

 spacing of the thermoelements from the heating device is more than 

 1.2 times the diameter of the vessel. 



The system has been used for the study of flow rates in a range 

 from about 1 to 300 cm 3 /min. The output from the thermoelements 

 is in the microvolt range. The rf power requirement at the electrodes 

 is a fraction of 1 watt. 



The error varies with the construction and with the flow rate; an 

 average value of the error is ^5 per cent. Also the dynamic response 

 depends upon the apparatus construction and the flow rate. A 

 sudden variation of the flow rate becomes noticeable within less than 

 0.2 sec, but the output reaches an equilibrium in about 1 to 5 sec (up 

 to 25 sec). With special systems (improved thermal contact between 

 thermoelement wires and the walls of the vessel), pulsations of the 

 blood stream of about one pulse per second can be observed. 



The method has found wide publicity and was, for some time, the 

 only method available for the measurement of blood flow in the 

 unopened vessel. The later-developed induction method (1-62) 



