479 
ment corresponding to peak pressure i } a, is the radial Lagrange coordi- 
nate of the generating surface, and dA is the Euler area element into 
we 
which the Lagrange area element errdz, 1,is transformed by the passage 
ba 
of the shock nie Now NR, Zz, ¢o) 
(RZ) u sot Adt= (R, Z) dr. dH , (9.5) 
tle) 4 
where fe is the Euler position vector of the area element, r(r. lS “oy t) 
is the Euler radial coordinate at time f » and where the variable of inte- 
gration is restricted by the path and the definition of aA to the radial 
coordinate, The integrand of equation 9.5 can be shown to be anexact dif- 
ferential of [¥, and t along any path of constant 2 ar Accordingly, the 
path of integration can be changed to 
% r(a,, Z,00) n(R, Z, “) 
[ete Z[] + a) + 2) 
: r(a, 7) Z, 00) 
Si Q : ne 
[4,21] ar 49 Tao ee 2h dz oats ; 
RE) 5 
since Euler and Lagrange coordinates are identical at or ahead of the shock 
ee rl 20) R 
(6£Z){ dr- dA = 1V,i ler, dzdis 
nla ,L,00) an 
With the equation of continulty, , = [Yue | i? Eq. 9.5 becomes 
ie 
(Ir, Z) gtaes Ain dA At + (2. emr,dz,4r, , (9.6) 
é(R) a, 
