SHOCK WAVE MEASUREMENTS 265 



in the acoustic approximation and the duration continues to increase 

 slowly. It is to be remembered in this connection that propagation 

 theories of shock waves are based on the assumptions that dissipative 

 processes can be neglected except at the shock front, where they are 

 implicitly included in the Rankine-Hugoniot conditions, and that the 

 undisturbed water has everywhere the same density and sound velocity. 

 At short distances, where the path traversed is small and the pressure 

 discontinuity large, both assumptions are good ones. 



For longer paths and lower pressures, appreciable effects of viscosity 

 and inhomogeneity of the fluid may well occur. The observed phe- 

 nomena, although of considerable scientific and practical interest, in- 

 volve to an increasing extent departures from the concept of an ideal 

 fluid and effects of the surface and bottom. Their understanding then 

 becomes as much a problem in oceanography and submarine geology as 

 one in hydrodynamics, and a complete analysis is out of place here. 



A. Observed pressures. For shock wave pressures of the order 

 1,000-40,000 lb. /in. 2, the extensive investigations outlined in sections 

 7.3 and 7.4 show that the initial peak pressure at the shock front de- 

 creases approximately as i^~«, where a has values of the order 1.15, and 

 at the same time the initial rate of decay decreases gradually. This 

 broadening of the profile is difficult to measure with high accuracy, but 

 its existence is unmistakable. This is shown, for example, in Fig, 7.5. 

 Less direct proof is contained in the more gradual decrease of impulse, 

 which includes the effect of peak pressure and duration, as i^-[o-9-io5]^ 

 compared with the decrease of peak pressure as R-^-^^. For these high 

 pressures, the increase in time constant is very roughly as R^-'^~^-^. 



A natural question is that of the distances and pressures to which 

 empirical laws of this kind remain approximately valid. Less extensive 

 investigations have been made for pressures of the order of hydrostatic. 

 However, a number of measurements of peak pressures of the order 

 50-150 lb. /in. 2 for 60 to 300 pound charges at distances of 500 feet are 

 in good quantitative agreement with the empirical formulas of section 

 7.4. The pressure-time curve also shows the expected broadening, as 

 shown in Plate V for example. Although the shock front appears vir- 

 tually discontinuous for the time scale of Plate V, measurements of the 

 records give an indicated time of rise of the order of 50 ^sec. at these 

 pressure levels. This value is far in excess of that to be expected from 

 gauge and amplifier transient response characteristics. It also seems 

 unreasonable that such values can indicate a real loss in high frequency 

 components of the shock wave, because the change in slope of the curve 

 at the peak is virtually discontinuous. Measurements with smaller 

 charges (3^ to 10 pounds) at pressure levels down to pressures of the 

 order 15 Ib./in.^ reveal rise times of the same order but the records show 

 a rounded peak rather than a discontinuity in slope. 



