Fig. 3- Complete probe equivalent circuit. 



AA/V 



and the time constant of the insulation equals 



;2 



(230) (0-175) ) (i n°' 00175 ) 

 (1) (2) ' ^ 0.00092^ 



- 0.00092' 



= 2.87 x 10" 5 hrs 

 = 0.10^ sec. 



The volume of the 0.0017- inch diameter platinum 

 wire is small and is neglected. 



Solving for the series circuit shown in 

 Fig. 3 yields 



T . 1+S ( C 1 B 1 +C 2 R2 +C 2 R 1 ) +s2 ( C2 R 2 C 1 R 1 ) 



(7) 



Letting T Q = 1, as a convention, and S as the 

 transfer function equal to the negative recipro- 

 cal of RC or the reciprocal of the time constant, 

 T, gives 



-O E O- 



Fig. h. Bridge circuit 

 P = 80,000 x 



-" - 

 D \3 



) 2 ] 



(9) 



where t is tube wall thickness in inches, D is 

 tube diameter in inches and P is crushing pres- 

 sure in psi. The constant in the foregoing gives 

 a result reasonably valid for material with a 

 yield strength of approximately 1+0,000 psi. The 

 configuration described withstands about 8,000 psi. 

 It should be noted that some care is necessary in 

 manufacture to avoid making the element suscep- 

 tible to changing pressure as in a strain gauge. 

 In units tested, strain effect was not measurable 

 (less than 0.001 C) at an external pressure of 

 1,000 psi. 



T 2 +(C 1 R 1 +C 2 R 2 +C 2 R 1 )T+(C 1 R 1 )(C 2 R 2 ) =0. (8) 



Substituting C 1 R 1 = 0.012, C2R2 = 0.1CA and 

 CgRi = 0.005 gives a characteristic time con- 

 stant polynomial 



T 2 + 0.121T + 0.0012U8 = 



which yields T = 0.1118 second. This varies 

 from the experimentally determined value by a 

 factor of 3 which is presumably due to boundary 

 layer effects . No effort has been made to solve 

 with the complex physical shapes involved. 



PRESSURE EFFECT 



The pressure resistance of the probe may be 

 calculated using Lane's empirical approximation 

 for the crushing strength of long tubes-3 



THE BRIDGE 



To avoid unpredictable sources of error due 

 to resistance in conductors and from resistance 

 changes in similar but not entirely equal lead 

 conductors, the measuring bridge (Fig. k) is 

 installed in the bulb head where it is protected 

 by the relatively uniform water environment from 

 the effect of gross thermal change. Since the 

 bridge is unbalanced a zener voltage regulator is 

 also mounted at the probe. The unbalanced bridge 

 has an output computed as follows from Thevenin ' s 

 principle: 



E(AS-BX) 



^o R E ( A+B+S+X ) 4 ( A+B ) (X+S ) 



(10) 



where E Q is open circuit voltage across detector, 

 E is source voltage, A, B and S are fixed bridge 

 resistors, X is the platinum resistor and R E is 

 the source impedance. The current, I d , passing 



^5 



