62 HYDRODYNAMICAL RELATIONS 



is 112,500 lb. /in. 2 (^' = 2.0) or three times the incident pressure. The 

 larger values of P' indicated by the dashed curves, which correspond to 

 the larger value of a, are not realized; and the locus of pressures corre- 

 sponding to the maximum value oiextr is represented by the dashed curve 

 marked aextr- It is evident that the maximum angle for regular reflec- 

 tion is determined by the condition d^'/da = oo, as the curves of ^' 



ur 





CO 

 CO 

 UJ 



or 



0** 



15' 



sd- 



45' 



60 



75 



90-- 



ANGLE OF INCIDENCE Of 



Fig. 2.12 Pressure behind a reflected shock front, expressed by the variable 

 i' = {P' + B)/{Po -|- B), as a function of incident pressure. 



vs. a are vertical for a = aextr- This condition is more formally estab- 

 lished from Eqs. (2.39), (2.40) as representing the boundary of solutions. 

 With this condition it is readily shown from these equations that 



(2.41) 



OJextr = 



± i^'{^"" - 1) + (r - 1) 



It is of interest to compare the pressure behind the reflected wave 

 for aextr with the value for normal incidence. Several such values are 

 given in Table 2.5, together with the values of aextr, oi'extr. It is seen 

 that the pressure is greater for oblique incidence in all cases, and for 



