MEASUREMENT OF PRESSURES 177 



the indicated pressure-time curve as a result of the finite gauge size. 

 For peak pressure from a twenty-five gram charge, for example, the 

 error predicted from the overall dimension of the gauge is seventeen per 

 cent. If, however, the record is extrapolated back to the time at which 

 the shock front has reached the gauge center, as shown in Fig. 5.13, a 

 corrected peak pressure can be obtained. In the gauge tests men- 

 tioned, the correction found for twenty-five gram charges amounted to 

 about fifteen per cent, in excellent agreement with the value predicted 

 by consideration of gauge size. Other tests with larger charges gave 

 similarly good results and hence it appears practicable to use the cor- 

 rection technique with confidence in its essential validity, provided the 

 limitations of accuracy are realized. 



5.7. Piezoelectric Gauge Calibration 



The ideal pressure calibration of gauges, piezoelectric or otherwise, 

 would be one in which a known transient pressure wave could be ap- 

 plied to the gauge under conditions similar to those in measurements 

 made with the gauge. For this purpose, a suitable source should estab- 

 lish a pressure wave of simple form, accurately known by direct experi- 

 mental proof or calculation, and amplitude comparable with pressures 

 to be measured. This pressure wave should then be applied to the 

 gauge and recording equipment as they would be used in measurement. 

 Up to the present, no single method has been developed which satisfies 

 all of these requirements, but the various techniques employed have led 

 to fairly satisfactory determination of gauge characteristics. 



A. Static methods. The simplest method of calibration is of course 

 a static one in which a known hydrostatic pressure, read by a calibrated 

 Bourdon or other pressure gauge, is applied to the gauge under test 

 mounted in a liquid-filled pressure cylinder. This method in its sim- 

 plest form is not applicable to piezoelectric gauges, the reason being 

 that such gauges have no static response. For slowly changing pres- 

 sures, a piezoelectric gauge is equivalent to an EMF Vo of value KAP/Co 

 in series with a capacitance Co, the quantity KA being the gauge con- 

 stant for applied hydrostatic pressure P, and Co its electrostatic capaci- 

 tance. Any external circuit to which the gauge is connected must have 

 associated with it leakage resistance R and shunt capacitance C. (The 

 leakage in general includes surface and volume leakage of the gauge 

 crystal which, though never infinite, are very high for quartz and tour- 

 maline.) With these parameters included, the schematic circuit to be 

 considered is as drawn in Fig. 5.14(a). It is evident that the terminal 

 voltage V developed by an EMF Vo resulting from an applied hydro- 

 static pressure decays exponentially with time to zero as indicated in 

 Fig. 5.14(b). The time required for V to fall to l/e = 0.368 of its origi- 

 nal maximum is given by the value oi R(C + Co), the tune constant of 



