234 SHOCK WAVE MEASUREMENTS 



gible compared with the first at increasing distance R from the source. 

 Its magnitude increases with the time t to which the integration is ex- 

 tended as a result of the slow decrease of P in the tail of the shock wave. 

 The effect of the afterfiow is not ordinarily considered at distances 

 exceeding ten-twenty charge radii, and energy flux density is estimated 

 by the first term only in Eq. (7.4). This term in itself is not exact, be- 

 cause it is obtained in the acoustic approximation. An estimate of the 

 correction necessary at the shock front can be made by expressing the 

 exact result of Eq. (7.3) in terms of pressure by employing the Rankine- 

 Hugoniot conditions of section 2.5, which are valid at the shock front. 

 These give: 



-f 



Ef = -\ dt 



Expressing the shock front velocity U in terms of pressure by the rela- 

 tion U = Co{l + aP) and expanding in powers of P then gives correc- 

 tion terms to the integral (l/poCo)J^P^dt. For an exponential shock 

 wave of peak pressure Pm (lb. /in. 2) in sea water, these reduce to the 

 result (4) that 



(7.5) Ef=(l- 1.67 X lO-'Pm - 4.9 X lO-^'^PJ) (l/poc) fp'dt 



For a pressure Pm = 20,000 Ib./in.^, the correction amounts to 3.5 per 

 cent and hence is insignificant at lower pressures. 



D. Units. Of the many units which have been, and are, employed 

 to express explosion pressures, the most common in English speaking 

 countries is pounds per square inch (Ib./in.^). In some of the theoretical 

 developments in Chapters 3 and 4, the more convenient metric unit of 

 kilobars (1 kilobar = 10^ dyne/cm.- = 14,513 Ib./in.^) is employed, but 

 the use of (Ib./in.^) is so general in experimental and engineering work 

 that the experimental results discussed in this and later chapters are 

 expressed in this unit. Lengths such as distance from the charge and 

 depth of water are expressed in feet, also in conformance with the most 

 usual practice, and times are given in seconds or decimal fractions of 

 seconds (milliseconds, microseconds). 



The derived quantity impulse is conveniently expressed in units of 

 (lb. sec. /in. 2). The energy flux density, as defined in part (C), has 

 really the nature of intensity, or energy per unit area, and the total 

 energy flux through a surface is given by the integral of this quantity 

 over the surface. The engineering unit of work or energy which is 

 readily obtained from the experimental used pressure unit is inch- 



